6400lecturespreadsheets.xlsx 6ft6l

The worksheets presented here are arranged by topics covered in lectures. Lecture topics are identified in the tabs at the bottoms of the worksheets. It may be useful to use these worksheets in conjunction with your lecture notes to follow the computations. Also, these worksheets may be useful to students who were unable to attend certain lectures. Perhaps, most students will find this collection of worksheets useful in understanding many of the more quantitative topics discussed in the course and provide opportunities to practice many of the computations. In many instances, students can use these worksheets to create additional problems which can be worked through by hand and then checked with solutions given on the worksheets.

covered in lectures. of the worksheets. with your orksheets may n lectures. heets useful in scussed in the he computations. o create and and then

Computing Geometric Mean Return on Investment: Real Price Data

On this worksheet, we make use of use historical stock price quotes provided by Yahoo (See http://webpage.pace.edu/jteall/sp Two years of monthly price quote for GM and PCS are ed in spreadsheet format from Yahoo. Then monthly returns a is added to each of the returns in column H. Geometric mean returns are computed in Column J.

GM Stock: October, 2000 to September 2002, Monthly Returns Date Open High Low Close Volume 3-Sep-02 47.5 47.51 38.11 38.9 5414895 1-Aug-02 46.4 50.05 41.08 47.86 4259440 1-Jul-02 53.3 54.08 40.5 46.55 6527578 3-Jun-02 62.5 63.1 50 53.45 5193919 1-May-02 64 67.8 62.15 62.15 3616043 1-Apr-02 59.56 65.94 58.32 63.68 3917782 1-Mar-02 52.81 61.55 52.81 60.01 5743195 1-Feb-02 50.35 55.39 47.24 52.59 5055470 2-Jan-02 47.9 50.27 47.09 50.25 3096881 3-Dec-01 47.66 52.3 46.01 47.76 2938333 1-Nov-01 40.13 49.3 39.52 48.84 2470372 1-Oct-01 41.28 44.51 39.35 40.13 2847620 4-Sep-01 52.47 54.32 38.04 41.66 3648700 1-Aug-01 61.62 62.63 51.96 53.17 2548600 2-Jul-01 61.67 65.33 59.14 61.28 2346600 1-Jun-01 54.83 62.52 54.63 62 2721754 1-May-01 52.48 56.17 51.66 54.83 2021760 2-Apr-01 49.58 55.25 47.94 52.34 2472395 1-Mar-01 50.93 57.01 47.99 49.51 3011243 1-Feb-01 50.91 55.13 48.51 50.92 2980480 2-Jan-01 48.21 54.06 48.09 50.82 3771677 1-Dec-00 46.85 51.7 46.08 48.21 2857576 1-Nov-00 58.27 59.8 45.84 46.85 2963281 2-Oct-00 61.32 64.02 51.12 58.27 2658817

r(t) -0.18721 0.028142 -0.12909 -0.13998 -0.02403 0.061156 0.141091 0.046567 0.052136 -0.02211 0.217045 -0.03673 -0.21648 -0.13234 -0.01161 0.130768 0.047574 0.05716 -0.02769 0.001968 0.054138 0.029029 -0.19598 N/A

1+r(t) 0.812787 1.028142 0.870907 0.860016 0.975974 1.061156 1.141091 1.046567 1.052136 0.977887 1.217045 0.963274 0.783525 0.867657 0.988387 1.130768 1.047574 1.05716 0.97231 1.001968 1.054138 1.029029 0.804016 #VALUE!

PI(1+r(t)) ROG(g) ROI(g)/Yr ROG(g) ROI(g)/Yr

PCS Stock: October, 2000 to September 2002, Monthly Returns Date Open High Low Close Volume r(t) 1+r(t) 3-Sep-02 3.82 3.93 1.75 1.96 11035885 -0.50505 0.494949 1-Aug-02 3.8 5.14 3.15 3.96 7020356 -0.03415 0.965854 1-Jul-02 4.52 6.93 2.36 4.1 11209278 -0.08277 0.917226 3-Jun-02 10.13 10.44 3.5 4.47 15463276 -0.57184 0.428161 1-May-02 11.25 12 9.34 10.44 7701569 -0.06869 0.931311 1-Apr-02 10.25 13.45 9 11.21 10386886 0.089407 1.089407 1-Mar-02 10 12.2 8.12 10.29 12611519 0.112432 1.112432 1-Feb-02 16.09 16.7 7.22 9.25 21943820 -0.43529 0.564713 2-Jan-02 24.45 25.2 15.01 16.38 15091195 -0.32896 0.671036 3-Dec-01 25 26.37 22.3 24.41 6145352 -0.02164 0.978357 1-Nov-01 22.5 27.5 22.25 24.95 5252709 0.118834 1.118834 1-Oct-01 26.4 29.05 21.5 22.3 10553704 -0.15177 0.848231 4-Sep-01 25.05 27.1 22.25 26.29 10464787 0.052442 1.052442 1-Aug-01 25.98 26.5 22.43 24.98 11239554 -0.03627 0.963735 2-Jul-01 24.15 27 22.7 25.92 6663486 0.073292 1.073292 1-Jun-01 22.03 24.16 19.21 24.15 4679895 0.097727 1.097727 1-May-01 25.63 27.5 20.25 22 5211639 -0.14163 0.858369

PI(1+r(t)) ROG(g) ROI(g)/Yr ROG(g) ROI(g)/Yr

2-Apr-01 1-Mar-01 1-Feb-01 2-Jan-01 1-Dec-00 1-Nov-00 2-Oct-00

19.25 24 30.75 20.75 23.12 38.25 37

26.9 24.35 32.4 33.25 29.38 38.44 39.19

16.43 15.72 20 17.62 19.38 21.88 29

25.63 19 25.18 30.5 20.44 22.69 38.12

7444519 0.348947 1.348947 6083813 -0.24543 0.754567 5503705 -0.17443 0.825574 8484931 0.492172 1.492172 5440242 -0.09916 0.900837 7432204 -0.40477 0.595226 5709582 N/A #VALUE!

ee http://webpage.pace.edu/jteall/spreadsheets.htm for information). from Yahoo. Then monthly returns are computed in Column G. One

0.667582 -0.0167 -0.18294 -0.0167 -0.18294

The product of (1+r(t)) for 24 months The geometric mean return over the 24 month period The annualized geometric mean rate of return The geometric mean return over the 24 month period The annualized geometric mean rate of return

0.051417 -0.11632 -0.77325 -0.11632 -0.77325

The product of (1+r(t)) for 24 months The geometric mean return over the 24 month period The annualized geometric mean rate of return The geometric mean return over the 24 month period The annualized geometric mean rate of return

Expected Return, Variance and Standard Deviation Stock A i 1 2 3

R(i) -0.2 0.1 0.4 E[R] =

P(i) R(i)P(i) R(i)-E[R(i)] (R(i)-E[R(i)])^2 (R(i)-E[R(i)])^2*P(i) 0.2 -0.04 -0.33 0.1089 0.02178 0.5 0.05 -0.03 0.0009 0.00045 0.3 0.12 0.27 0.0729 0.02187 0.13 Variance = 0.0441 Standard Deviation = 0.21

Historical Variances for Stocks A and B t 1 2 3 4 5 6 7 8

R(A,t) R(B,t) 0.4 0.2 0.9 0.1 -0.8 0.12 0.9 0.05 0.9 0.02 0.9 0.09 -0.2 0.11 -0.1 0.12 0.3625 0.1013 Average Returns

0.00017578 0.03611328 0.16892578 0.03611328 0.03611328 0.03611328 0.03955078 0.02673828 0.37984375 0.61631465

0.001218945 1.95313E-07 4.39453E-05 0.00032832 0.000825195 1.58203E-05 9.57031E-06 4.39453E-05 0.002485938 0.049859177

Squared Differences for A and B divided by eight

Variances of A and B Standard Deviations of A and B

Computing Variances and Standard Deviations of Returns: Real Price Data Returns are computed in the "Geometric Returns" Worksheet for GM and PCS from which to compute variances and standard

GM Stock: October, 2000 to September 2002, Monthly Returns Date Close r(t) 1+r(t) (Ri-E[Ri])^2 / 23 3-Sep-02 38.9 -0.18721 0.812787 0.001347717 1-Aug-02 47.86 0.028142 1.028142 6.71292E-05 1-Jul-02 46.55 -0.12909 0.870907 0.000604786 3-Jun-02 53.45 -0.13998 0.860016 0.000721642 1-May-02 62.15 -0.02403 0.975974 7.20692E-06 1-Apr-02 63.68 0.061156 1.061156 0.000227324 1-Mar-02 60.01 0.141091 1.141091 0.001007737 1-Feb-02 52.59 0.046567 1.046567 0.000144846 2-Jan-02 50.25 0.052136 1.052136 0.000174143 3-Dec-01 47.76 -0.02211 0.977887 5.224E-06 1-Nov-01 48.84 0.217045 1.217045 0.002264066 1-Oct-01 40.13 -0.03673 0.963274 2.84366E-05 4-Sep-01 41.66 -0.21648 0.783525 0.001832951 1-Aug-01 53.17 -0.13234 0.867657 0.000638584 2-Jul-01 61.28 -0.01161 0.988387 9.25098E-09 1-Jun-01 62 0.130768 1.130768 0.000875701 1-May-01 54.83 0.047574 1.047574 0.000149941 2-Apr-01 52.34 0.05716 1.05716 0.000202891 1-Mar-01 49.51 -0.02769 0.97231 1.18928E-05 1-Feb-01 50.92 0.001968 1.001968 7.48337E-06 2-Jan-01 50.82 0.054138 1.054138 0.000185337 1-Dec-00 48.21 0.029029 1.029029 7.01943E-05 1-Nov-00 46.85 -0.19598 0.804016 0.001485351 2-Oct-00 58.27 N/A #VALUE! E[R] = -0.01115 VAR = 0.012060596

PI(1+r(t)) ROG(g) ROI(g)/Yr ROG(g) ROI(g)/Yr VAR(GM) StD(GM) StD(GM)

0.667582 -0.0167 -0.18294 -0.0167 -0.18294 0.012061 0.109821 0.38043

The product of (1+r(t)) for 24 months The geometric mean return over the 24 The annualized geometric mean rate of The geometric mean return over the 24 The annualized geometric mean rate of The monthly return variance The monthly return standard deviation The annual return standard deviation

PCS Stock: October, 2000 to September 2002, Monthly Returns Date Close r(t) 1+r(t) (Ri-E[Ri])^2 / 23 3-Sep-02 1.96 -0.50505 0.494949 0.007732515 1-Aug-02 3.96 -0.03415 0.965854 0.000105177 1-Jul-02 4.1 -0.08277 0.917226 1.34576E-08 3-Jun-02 4.47 -0.57184 0.428161 0.010375684 1-May-02 10.44 -0.06869 0.931311 9.32088E-06 1-Apr-02 11.21 0.089407 1.089407 0.001297316 1-Mar-02 10.29 0.112432 1.112432 0.001666221 1-Feb-02 9.25 -0.43529 0.564713 0.0053858 2-Jan-02 16.38 -0.32896 0.671036 0.002623289 3-Dec-01 24.41 -0.02164 0.978357 0.000165448 1-Nov-01 24.95 0.118834 1.118834 0.001776977 1-Oct-01 22.3 -0.15177 0.848231 0.000203644 4-Sep-01 26.29 0.052442 1.052442 0.000801484 1-Aug-01 24.98 -0.03627 0.963735 9.63092E-05 2-Jul-01 25.92 0.073292 1.073292 0.001066546 1-Jun-01 24.15 0.097727 1.097727 0.001425299 1-May-01 22 -0.14163 0.858369 0.00014778 2-Apr-01 25.63 0.348947 1.348947 0.008124525 1-Mar-01 19 -0.24543 0.754567 0.001142488

PI(1+r(t)) 0.051417 The product of (1+r(t)) for 24 months ROG(g) -0.11632 The geometric mean return over the 24 ROI(g)/Yr -0.77325 The annualized geometric mean rate of ROG(g) -0.11632 The geometric mean return over the 24 ROI(g)/Yr -0.77325 The annualized geometric mean rate of VAR(PCS) 0.06341 The monthly return variance StD(PCS) 0.251814 The monthly return standard deviation StD(PCS) 0.872308 The annual return standard deviation

1-Feb-01 2-Jan-01 1-Dec-00 1-Nov-00 2-Oct-00

25.18 -0.17443 0.825574 30.5 0.492172 1.492172 20.44 -0.09916 0.900837 22.69 -0.40477 0.595226 38.12 N/A #VALUE! E[R] = -0.08333 VAR =

0.000360802 0.014400141 1.08982E-05 0.004492445 0.063410124

Price Data

mpute variances and standard deviations in Column G.

uct of (1+r(t)) for 24 months metric mean return over the 24 month period alized geometric mean rate of return metric mean return over the 24 month period alized geometric mean rate of return hly return variance hly return standard deviation al return standard deviation


Returns Covariance Stocks A and B i 1 2 3

R(A,i) -0.2 0.1 0.4

R(B,i) 0.5 0.4 -0.2

E[R(A)] = 0.13 E[R(B)] = 0.24 s(A) = 0.21 s(B) = 0.29052 r (A,B) = -0.90479 r2(A,B) = 0.81865

P(i) (R(A,i)-E[R(A)]) (R(B,i)-E[R(B)]) Product of Deviations and Probability 0.2 -0.33 0.26 -0.01716 0.5 -0.03 0.16 -0.0024 0.3 0.27 -0.44 -0.03564 Covariance = -0.0552

ns and Probability

Computing Variances and Standard Deviations of Returns Returns are computed in the "Geometric Returns" Worksheet for GM and PCS from which to compute variances and standard

GM Stock: October, 2000 to September 2002, Monthly Returns Date Close r(t) 1+r(t) (Ri-E[Ri])^2 / 23 3-Sep-02 38.9 -0.18721 0.812787 0.001347717 1-Aug-02 47.86 0.028142 1.028142 6.71292E-05 1-Jul-02 46.55 -0.12909 0.870907 0.000604786 3-Jun-02 53.45 -0.13998 0.860016 0.000721642 1-May-02 62.15 -0.02403 0.975974 7.20692E-06 1-Apr-02 63.68 0.061156 1.061156 0.000227324 1-Mar-02 60.01 0.141091 1.141091 0.001007737 1-Feb-02 52.59 0.046567 1.046567 0.000144846 2-Jan-02 50.25 0.052136 1.052136 0.000174143 3-Dec-01 47.76 -0.02211 0.977887 5.224E-06 1-Nov-01 48.84 0.217045 1.217045 0.002264066 1-Oct-01 40.13 -0.03673 0.963274 2.84366E-05 4-Sep-01 41.66 -0.21648 0.783525 0.001832951 1-Aug-01 53.17 -0.13234 0.867657 0.000638584 2-Jul-01 61.28 -0.01161 0.988387 9.25098E-09 1-Jun-01 62 0.130768 1.130768 0.000875701 1-May-01 54.83 0.047574 1.047574 0.000149941 2-Apr-01 52.34 0.05716 1.05716 0.000202891 1-Mar-01 49.51 -0.02769 0.97231 1.18928E-05 1-Feb-01 50.92 0.001968 1.001968 7.48337E-06 2-Jan-01 50.82 0.054138 1.054138 0.000185337 1-Dec-00 48.21 0.029029 1.029029 7.01943E-05 1-Nov-00 46.85 -0.19598 0.804016 0.001485351 2-Oct-00 58.27 N/A #VALUE! E[R] = -0.01115 VAR = 0.012060596

PI(1+r(t)) ROG(g) ROI(g)/Yr ROG(g) ROI(g)/Yr VAR(GM) StD(GM) StD(GM)

0.667582 -0.0167 -0.18294 -0.0167 -0.18294 0.012061 0.109821 0.38043

The product of (1+r(t)) for 24 months The geometric mean return over the 24 The annualized geometric mean rate of The geometric mean return over the 24 The annualized geometric mean rate of The monthly return variance The monthly return standard deviation The annual return standard deviation

PCS Stock: October, 2000 to September 2002, Monthly Returns Date Close r(t) 1+r(t) (Ri-E[Ri])^2 / 23 3-Sep-02 1.96 -0.50505 0.494949 0.007732515 1-Aug-02 3.96 -0.03415 0.965854 0.000105177 1-Jul-02 4.1 -0.08277 0.917226 1.34576E-08 3-Jun-02 4.47 -0.57184 0.428161 0.010375684 1-May-02 10.44 -0.06869 0.931311 9.32088E-06 1-Apr-02 11.21 0.089407 1.089407 0.001297316 1-Mar-02 10.29 0.112432 1.112432 0.001666221 1-Feb-02 9.25 -0.43529 0.564713 0.0053858 2-Jan-02 16.38 -0.32896 0.671036 0.002623289 3-Dec-01 24.41 -0.02164 0.978357 0.000165448 1-Nov-01 24.95 0.118834 1.118834 0.001776977 1-Oct-01 22.3 -0.15177 0.848231 0.000203644 4-Sep-01 26.29 0.052442 1.052442 0.000801484 1-Aug-01 24.98 -0.03627 0.963735 9.63092E-05 2-Jul-01 25.92 0.073292 1.073292 0.001066546 1-Jun-01 24.15 0.097727 1.097727 0.001425299 1-May-01 22 -0.14163 0.858369 0.00014778 2-Apr-01 25.63 0.348947 1.348947 0.008124525 1-Mar-01 19 -0.24543 0.754567 0.001142488

PI(1+r(t)) 0.051417 The product of (1+r(t)) for 24 months ROG(g) -0.11632 The geometric mean return over the 24 ROI(g)/Yr -0.77325 The annualized geometric mean rate of ROG(g) -0.11632 The geometric mean return over the 24 ROI(g)/Yr -0.77325 The annualized geometric mean rate of VAR(PCS) 0.06341 The monthly return variance StD(PCS) 0.251814 The monthly return standard deviation StD(PCS) 0.872308 The annual return standard deviation

1-Feb-01 2-Jan-01 1-Dec-00 1-Nov-00 2-Oct-00

25.18 -0.17443 0.825574 30.5 0.492172 1.492172 20.44 -0.09916 0.900837 22.69 -0.40477 0.595226 38.12 N/A #VALUE! E[R] = -0.08333 VAR =

0.000360802 0.014400141 1.08982E-05 0.004492445 0.063410124

mpute variances and standard deviations in Column G.



Computing Return Covariances: Real Price Data

Returns are computed in the "Geometric Returns" Worksheet for GM and PCS from which to compute covariances and Corela

GM And PCS Stock: October 2000 to September 2002, Monthly Returns Date Close P(GM) 3-Sep-02 38.9 1-Aug-02 47.86 1-Jul-02 46.55 3-Jun-02 53.45 1-May-02 62.15 1-Apr-02 63.68 1-Mar-02 60.01 1-Feb-02 52.59 2-Jan-02 50.25 3-Dec-01 47.76 1-Nov-01 48.84 1-Oct-01 40.13 4-Sep-01 41.66 1-Aug-01 53.17 2-Jul-01 61.28 1-Jun-01 62 1-May-01 54.83 2-Apr-01 52.34 1-Mar-01 49.51 1-Feb-01 50.92 2-Jan-01 50.82 1-Dec-00 48.21 1-Nov-00 46.85 2-Oct-00 58.27 E[R] =

r(t)GM (RiGM-E[RiGM]) Close P(PCS) -0.18721 -0.176061073 1.96 0.028142 0.039293413 3.96 -0.12909 -0.11794098 4.1 -0.13998 -0.128832279 4.47 -0.02403 -0.012874752 10.44 0.061156 0.072308104 11.21 0.141091 0.152243093 10.29 0.046567 0.057718795 9.25 0.052136 0.063287309 16.38 -0.02211 -0.010961392 24.41 0.217045 0.228196235 24.95 -0.03673 -0.025574246 22.3 -0.21648 -0.205323826 26.29 -0.13234 -0.121191712 24.98 -0.01161 -0.000461273 25.92 0.130768 0.141919458 24.15 0.047574 0.058725188 22 0.05716 0.0683118 25.63 -0.02769 -0.016538864 19 0.001968 0.01311936 25.18 0.054138 0.065289776 30.5 0.029029 0.040180446 20.44 -0.19598 -0.184832581 22.69 N/A 38.12 -0.01115 E[R] =

r(t)PCS (RiPCS-E[RiPCS]) -0.50505 -0.421720106 -0.03415 0.049184057 -0.08277 0.00055635 -0.57184 -0.488508682 -0.06869 0.014641728 0.089407 0.17273759 0.112432 0.195762831 -0.43529 -0.351956536 -0.32896 -0.245633141 -0.02164 0.061687112 0.118834 0.20216448 -0.15177 -0.068438334 0.052442 0.135772352 -0.03627 0.047064967 0.073292 0.156622324 0.097727 0.181057672 -0.14163 -0.058300502 0.348947 0.432277767 -0.24543 -0.162102484 -0.17443 -0.091095831 0.492172 0.57550261 -0.09916 -0.015832228 -0.40477 -0.321443998 N/A -0.08333 COV[GM,PCS] = VAR[GM] = VAR[PCS] = StD[GM] = StD[PCS] = Corr.Coef[GM,PCS]=

compute covariances and Corelation Coefficients in Column G.

0.074248495 0.00193261 -6.56164E-05 0.062935687 -0.000188509 0.012490328 0.029803539 -0.020314507 -0.01554546 -0.000676177 0.046133173 0.001750259 -0.027877299 -0.005703884 -7.22456E-05 0.025695607 -0.003423708 0.029529672 0.002680991 -0.001195119 0.037574437 -0.000636146 0.059413324 0.013412585 Covariance 0.012060596 0.063410124 0.109820743 0.251813668 0.485007886 Correlation Coefficient 0.23523265 r-square

Yield to Maturity Example

Enter Bond data into Column B of the Yellow Region. Revise your y estimate until you are sufficiently close to the bond's correc Bond Details F 1000 c 0.1 Guess for y 0.15 n 30 Initial Bond Price 1000 PV Bond 671.701 DECREASE YOUR y ESTIMATE

Note: This calculator assumes that coupon payments are made annually beginning in one year.

ufficiently close to the bond's correct yield.

2X2 Matrix Inversion: Gauss-Jordan Elimination This worksheet provides a step-by-step example on how to invert a 2X2 matrix by hand. Suppose that we wish to invert the following matrix one step at a time using a Gauss-Jordan elimination procedure: 1 2 3 4 First, we augment the matrix with the identity matrix (a matrix with 1's in the Principal Diagonal and zeros elsewhere): 1 2 1 0 3 4 0 1 We start in the first column and the first row. Simply perform row operations to obtain a 1 in the first row of the first column: 1 2 1 0 Row 1 * 1/A7 3 4 0 1 Now, perform row operations to obtain a zero in the second row of the first column: 1 2 1 0 0 -2 -3 1 Row 2 - A11 * Row 1 Now, perform a row operation to obtain a 1 in the second row of the second column: 1 2 1 0 0 1 1.5 -0.5 Row 2 * 1/B14 Now, perform row operations to obtain a zero in the first row of the second column: 1 0 -2 1 Row 1 - B16 * Row 2 0 1 1.5 -0.5 The last two columns represent the inverse of our original matrix. We can check our work below: -2 1 1.5 -0.5 You may use this worksheet for any 2X2 matrix. Simply enter elements into the yellow input area A4:B5 and output will appear in the red areas just above here. The matrix will be solved step-by-step.

n elimination procedure:

onal and zeros elsewhere):

n the first row of the first column:

ut area A4:B5

Matrix Inversion: Gauss-Jordan Elimination This worksheet provides a step-by-step example on how to invert a 3X3 matrix by hand. Suppose that we wish to invert the following matrix one step at a time using a Gauss-Jordan elimination procedure: 5 0 8 2 4 0 4 8 4 First, we augment the matrix with the identity matrix (a matrix with 1's in the Principal Diagonal and zeros elsewhere): 5 0 8 1 0 0 2 4 0 0 1 0 4 8 4 0 0 1 We start in the first column and the first row. Simply perform row operations to obtain a 1 in the first row of the first column: 1 0 1.6 0.2 0 0 Row 1 * 1/A8 2 4 0 0 1 0 4 8 4 0 0 1 Now, perform row operations to obtain a zero in the second row of the first column: 1 0 1.6 0.2 0 0 0 -4 3.2 0.4 -1 0 Row 1 * A13 - Row 2 4 8 4 0 0 1 Now, perform row operations to obtain a zero in the third row of the first column: 1 0 1.6 0.2 0 0 0 -4 3.2 0.4 -1 0 0 -8 2.4 0.8 0 -1 Row 1*A18 - Row 3 Now, perform a row operation to obtain a 1 in the second row of the second column: 1 0 1.6 0.2 0 0 0 1 -0.8 -0.1 0.25 0 Row 2 * 1/B21 0 -8 2.4 0.8 0 -1 Now, perform row operations to obtain a zero in the first row of the second column: 1 0 1.6 0.2 0 0 Row 1 - Row 2 * B24 0 1 -0.8 -0.1 0.25 0 0 -8 2.4 0.8 0 -1 Now, perform row operations to obtain a zero in the third row of the second column: 1 0 1.6 0.2 0 0 0 1 -0.8 -0.1 0.25 0 0 0 -4 0 2 -1 Row 3 - B30 * Row 2 Now, perform a row operation to obtain a 1 in the third row of the third column: 1 0 1.6 0.2 0 0 0 1 -0.8 -0.1 0.25 0 0 0 1 0 -0.5 0.25 Row 3 * 1/C34 Now, perform row operations to obtain a zero in the first row of the third column: 1 0 0 0.2 0.8 -0.4 Row 1 - C36 * Row 3 0 1 -0.8 -0.1 0.25 0 0 0 1 0 -0.5 0.25 Now, perform row operations to obtain a zero in the second row of the third column: 1 0 0 0.2 0.8 -0.4 0 1 0 -0.1 -0.15 0.2 Row 2 - $C41 * Row 3 0 0 1 0 -0.5 0.25 The last three columns represent the inverse of our original matrix. We can check our work below: 0.2 0.8 -0.4 -0.1 -0.15 0.2 0 -0.5 0.25 You may use this worksheet for any 3X3 matrix. Simply enter elements into the yellow input area A4:C6

and output will appear in the red areas just above here. The matrix will be solved step-by-step.

n elimination procedure:

onal and zeros elsewhere):

n the first row of the first column:

ut area A4:C6

Inverting Matrices and Solving Systems of Linear Equations 0.01 0 0.02

0 0.04 0.03 V

0.02 0.03 0.09

245.5 54.55 -72.73 54.55 45.45 -27.27 -72.73 -27.27 36.36 V-1

Let V represent a 3X3 matrix that we wish to invert

V-1 is the inverse of Matrix V

1 1E-16 0 1 0 0 I

Steps: 1. Enter elements of matrix to be inverted into cells A3:C5. 2. Highlight A8:C10 for location of inverse matrix. 3. Left click the "Paste Function" (fx) button on the menu bar. 4. Select "MATH & TRIG" in the Dialogue Box. 5. Select "MINVERSE" in the Dialogue Box and left click OK. 6. Enter A3:C5 as the array to invert. Do not click OK. 7. Simultaneously enter "Ctrl" "Shift" and "Enter." 8. The inverted matrix should now appear in the highlighted region.

0 0 1

We check to see if V X V-1 = I

We check to see if

Portfolio Variance Matrices: w'Vw = s2p Assume three securities with w(1) =.2, w(2) = .3 and w(3) = .5. Security variances are .01, .04 and .09. Covariances are COV(1,2) = 0, COV(1,3) = .02 and COV(2,3) = .03. Find portfolio standard deviation. Weights Vector Variance/Covariance Matrix

0.2 0.3 0.5 w

0.01 0 0.02

0 0.04 0.03 V

0.02 0.03 0.09

These are the weights and variance/covariance matrices to be multiplied First, multiply w'V

0.2

0.012

0.3 w'

0.027 w'V

0.5

0.058

0.01 0 0.02

0.2 0.3 0.5 w

0 0.04 0.03 V

0.02 0.03 0.09

=

0.012

0.027 w'V

Next, multiply w'V by w

=

0.04 Portfolio Variance

Standard deviation is the square root of variance

0.199 Portfolio Standard Deviation

0.058

root of variance

dard Deviation

Holmes and Market Risk s: Calculating Beta

0.14 0.12

Year Holmes Co. Market T-Bill 2006 12% 10% 6% 2007 18% 14% 6% 2008 7% 6% 6% 2009 3% 2% 6% 2010 10% 8% 6%

0.1 0.08 0.06 0.04 0.02

rH-rf 0.06 0.12 0.01 -0.03 0.04

rM-rf 0.04 0.08 0 -0.04 0.02

0

-0.04

0.006

X Variable 1 Residual Plot 0.004 Residuals

0.0032 0.00252

σH,M = b1 = ρH,M =

.04

-0.02

Summary Output: Excel Functions

σH2 = σM2 =

.02

-.04

0.002 0.0025 1.25 0.996

-0.06

0.0016

1

0.002

0.5 -0.04 0 0

0 -0.02 -0.002 0

0.02

0.01 -0.004

0.02

0.002

0.04

0.03

X Variable 1

-0.006

1.25

0.996

ρ2H,M = 0.99206 0.99206 b0 = 0.015 0.015 Summary Output with Matrix Mathematics

1

1

0.04

0.08

1

T

X

1

1

0 -0.04

0.02

*

1

0.04

1

0.08

1 1 1

0 -0.04 0.02 X

0.06

=

0.25 -2.5

-2.5 125

*

1 0.04

1 0.08

(XTX)-1

1 0

1 -0.04

1 0.02

=

XT

0.15

0.05

0.25

0.35

2.5

7.5

-2.5

-7.5 4E-16

(XTX)-1XT

0.2

*

0.06

0.015

0.12 0.01 -0.03 0.04 y

1.25 =

b

SUMMARY OUTPU

Regression Stat Multiple R R Square Standard Error Observations ANOVA Regression Residual Total

-0.03

0.01 0.04 0.06

0.12

SUMMARY OUTPUT: Excel Spreadsheet Regression Regression Statistics Multiple R

0.996023841

R Square

0.992063492

Adjusted R Square

0.989417989

Standard Error

0.005773503

Observations

5

ANOVA .08

df

0.0125

0.0125

Residual

3

1E-04

3.33E-05

Total

4

0.0126

Coefficients

0.03

X Variable 1

0.1

0.04

F

1

Intercept 0.08

MS

Regression

Residual Plot 0.06

SS

Standard Error

t Stat

375

P-value

0.015

0.002886751 5.196152 0.013847

1.25

0.064549722 19.36492 0.000301

RESIDUAL OUTPUT

0.05

Observation

5

0.1

0.1

0.01 XTX

=

Predicted Y

Residuals Standard Residuals

1

0.065

-0.005

-1

2

0.115

0.005

1

3

0.015

-0.005

-1

4 5

-0.035 0.04

0.005 -6.939E-18

1 -1E-15

n

Σxi

Σxi

Σxi2

0.15 2.5

0.05 7.5

0.25 -2.5

0.35 -7.5

0.2 4.44E-16

(XTX)-1XT

= b0 = b1

SUMMARY OUTPUT Regression Statistics Multiple R 0.996024 R Square 0.992063 Adjusted R Square 0.989418 Standard Error 0.005774 Observations 5 ANOVA df 1 3 4

MS 0.0125 0.0125 1E-04 3.33333E-05 0.0126

Coefficients 0.015 1.25

Standard Error t Stat 0.002886751 5.196152423 0.064549722 19.36491673

Regression Residual Total

Intercept X Variable 1

SS

RESIDUAL OUTPUT Observation Predicted Y 1 0.065 2 0.115 3 0.015 4 -0.035 5 0.04

Residuals -0.005 0.005 -0.005 0.005 -6.93889E-18

F

Significance F 375 0.000301

P-value Lower 95%Upper 95% 0.013846833 0.005813 0.024187 0.000300795 1.044574 1.455426

Significance F 0.000300795

Lower 95%

Upper 95%Lower 95.0% Upper 95.0%

0.005813069 0.024187 0.005813 0.024187 1.044573974 1.455426 1.044574 1.455426

Lower 95.0% Upper 95.0% 0.005813069 0.024187 1.044573974 1.455426

Jensen's Alpha Illustration: Simple OLS Rp-rf Rm-rf 0.11 0.09 0.02 0.13 0.01 0.11 0.22 0.21 0.08 -0.12 0.06 0.16 0.15 -0.07 -0.01 0.22 0.15 0.13 -0.11 0.13

0.02 0.01 0.03 0.08 -0.14 0.06 0.09 0.13 -0.01 -0.15 0.02 0.11 0.09 -0.11 -0.13 0.15 0.04 0.03 -0.18 0.07

SUMMARY OUTPUT

Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations

0.930122286 0.865127468 0.857634549 0.038425474 20

ANOVA

df Regression Residual Total

SS 1 18 19

Coefficients Intercept X Variable 1

0.073509121 0.951512255

MS

F

0.170477693 0.170477693 115.4593 0.026577307 0.001476517 0.197055

Standard Error

t Stat

0.00864236 8.505677269 0.088552299 10.74520108

P-value 1.01E-07 2.92E-09

Significance F 2.92226E-09

Lower 95%

Upper 95%Lower 95.0% Upper 95.0%

0.055352198 0.091666 0.055352 0.091666 0.765470779 1.137554 0.765471 1.137554

Back Test for Mean Reversion or Momentum Evidence Date t Pricet 2/1/2007 1 49 2/2/2007 2 50 2/3/2007 3 51 2/4/2007 4 52 2/5/2007 5 55 2/6/2007 6 57 2/7/2007 7 58 2/8/2007 8 59 2/9/2007 9 58 2/10/2007 10 55 2/11/2007 11 53 2/12/2007 12 52

Returnt

Returnt-1

0.020408163 0.02 0.019607843 0.057692308 0.036363636 0.01754386 0.017241379 -0.016949153 -0.051724138 -0.036363636 -0.018867925

0.020408163 0.02 0.019607843 0.057692308 0.036363636 0.01754386 0.017241379 -0.016949153 -0.051724138 -0.036363636

Test for Significance of Momentum Coefficient t Returnt Returnt-1 3 4 5 se(b)= 6 0.23679 7 8 t= 9 3.2593291 10 11 12

0.02 0.01961 0.05769 0.03636 0.01754 0.01724 -0.0169 -0.0517 -0.0364 -0.0189

0.020408163 0.02 0.019607843 0.057692308 0.036363636 0.01754386 0.017241379 -0.016949153 -0.051724138 -0.036363636

rˆ = .002

E[Rt]

,i

0.013735899 0.013420889 0.013118232 0.042510901 0.026049948 0.011525299 0.011291852 -0.015095574 -0.041934067 -0.030079203

0.00626 0.00619 0.04457 -0.0061 -0.0085 0.00572 -0.0282 -0.0366 0.00557 0.01121 SSR=

0.000775 = COV(rt, rt-1) 0.001004 = VAR( rt-1) 0.771776 = b

Evidence for Momentum

-0.00201 = a

rˆ = .0020142  .7717758  rˆt 1

, i2 3.92E-05 3.83E-05 0.001987 3.78E-05 SSE 7.24E-05 n2 3.27E-05 se(b) = = 2 ( r  r ) 0.000798 t t 0.001342 3.1E-05 0.000126 Significant at .025 level 0.004503



.000562888 = .056069 = .23679 .01003

69 = .23679

Stock Y against the Market and Industry On this sheet, we use matrices to compute regression coefficients b0, b1 and b2 for our stock return illustration.

Original Data Year

Stock Y

Market

2000

0.15

2001 2002

Industry 0.1

0.4

0.25

0.1

-0.02

0.5

0.25

0.5

2003

0.35

0.25

0.5

2004

-0.18

-0.03

-0.4

2005

-0.3

0.08

-0.5

2006

0.4

0.3

0.6

2007

-0.17

-0.05

-0.23

2008

-0.35

-0.25

-0.4

2009

0.35

0.15

0.65

1 -0.03 -0.4

1 0.08 -0.5

1 0.3 0.6

1 -0.05 -0.23

1 -0.25 -0.4

1 0.15 0.65

1 0.08 -0.5

1 0.3 0.6

1 -0.05 -0.23

1 -0.25 -0.4

1 0.15 0.65

0.1 X 1 0.1 0.4

1 0.1 -0.02

1 0.25 0.5

1 0.25 0.5

XT

0.143411 -0.6315 0.122029 -0.6315 10.72305 -3.03254 0.122029 -3.03254 1.37181 (XTX)-1 1 0.1 0.4

1 0.1 -0.02

1 0.25 0.5

1 0.25 0.5

1 -0.03 -0.4 XT

1 1 1 1 1 1 1 1 1 1

0.1

0.4

0.1

-0.02

0.25

0.5

0.25

0.5

-0.03

-0.4

0.08

-0.5

0.3

0.6

-0.05

-0.23

-0.25

-0.4

0.15

0.65

10 0.9 1.1

0.9 0.3298 0.649

1.1 0.649 2.0658

XTX

-0.00928 = b0

X

0.666086 = b1 0.15 0.25 0.5 0.35 -0.18 -0.3 0.4 -0.17 -0.35 0.35 y

1 0.5024 1.3486 Xty

0.448505 = b2 b

Stock Y against the Market and Industry

On this sheet, we use the Excel Add-in regression function to compute regression coefficients b0, b1 and b2 for our stock return

Original Data Year

Stock Y

Market

Industry

2000

0.15

0.1

0.4

2001

0.25

0.1

-0.02

2002

0.5

0.25

0.5

2003

0.35

0.25

0.5

2004

-0.18

-0.03

-0.4

2005

-0.3

0.08

-0.5

2006

0.4

0.3

0.6

2007

-0.17

-0.05

-0.23

2008

-0.35

-0.25

-0.4

2009

0.35

0.15

0.65

SS 0.830212274 0.083587726 0.9138

MS 0.415106137 0.011941104

SUMMARY OUTPUT Regression Statistics Multiple R 0.953167 R Square 0.90852733 Adjusted R Square 0.882392281 Standard Error 0.109275357 Observations 10 ANOVA df Regression Residual Total

2 7 9

F Significance F 34.7627946 0.000231483

Coefficients Standard Error t Stat P-value -0.009283302 0.041382246 -0.224330555 0.828907356 0.666086037 0.357833902 1.861439158 0.104989409 0.44850508 0.127987984 3.504274896 0.009935665

Intercept X Variable 1 X Variable 2

RESIDUAL OUTPUT Observation 1 2 3

Predicted Y 0.236727334 0.0483552 0.381490747

Residuals -0.086727334 0.2016448 0.118509253

Lower 95% -0.107136764 -0.180056685 0.145861589

4 5 6 7 8 9 10

0.381490747 -0.208667915 -0.180248959 0.459645557 -0.145743772 -0.355206843 0.382157905

-0.031490747 0.028667915 -0.119751041 -0.059645557 -0.024256228 0.005206843 -0.032157905

s b0, b1 and b2 for our stock return illustration.

Upper 95% Lower 95.0% 0.088570159 -0.107136764 1.512228759 -0.180056685 0.751148571 0.145861589

Upper 95.0% 0.088570159 1.512228759 0.751148571

Stock Y against the Market and Industry

On this sheet, we conduct simple calculations to regression coefficients b0, b1 and b2 and other outputs for our stock retu

Original Data Year

Stock Y

Market

2000

0.15

2001 2002

Industry 0.1

0.4

0.25

0.1

-0.02

0.5

0.25

0.5

2003

0.35

0.25

0.5

2004

-0.18

-0.03

-0.4

2005

-0.3

0.08

-0.5

2006

0.4

0.3

0.6

2007

-0.17

-0.05

-0.23

2008

-0.35

-0.25

-0.4

2009

0.35

0.15

0.65

y̅=

0.1 0.3298 SUM (Rm)2

SUMMARY OUTPUT Regression Statistics Multiple R 0.953167 R Square 0.90852733 Adjusted R Square 0.88239228 Standard Error 0.10927536 Observations 10

0.953167 0.90852733 0.882392281 0.109275357

= Multiple r = r-square = adjusted r-square = Standard Error

ANOVA df Regression Residual Total

2 7 9

SS MS F Significance F 0.830212274 0.415106 34.7627946 0.0002315 0.083587726 0.011941 34.7627946 = F 0.9138 0.9138 = SS

Coefficients Standard Error t Stat P-value Lower 95% -0.0092833 0.041382246 -0.22433 0.828907356 -0.1071368 0.66608604 0.357833902 1.861439 0.104989409 -0.1800567 0.44850508 0.127987984 3.504275 0.009935665 0.1458616 T-Dist = 0.828907356 0.5887499 T-Dist = 0.104989409 0.0313411 T-Dist = 0.009935665 0.0002289


Upper 95% 0.0885702 1.5122288 0.7511486 p-Value (Normal Distribution) p-Value (Normal Distribution) p-Value (Normal Distribution)

RESIDUAL OUTPUT Observation 1 2

Predicted Y Residuals 0.23672733 -0.086727334 0.0483552 0.2016448

Squared Residuals 0.00752163 0.040660625

-0.086727

3 4 5 6 7 8 9 10

0.38149075 0.38149075 -0.20866792 -0.18024896 0.45964556 -0.14574377 -0.35520684 0.38215791

0.118509253 -0.031490747 0.028667915 -0.119751041 -0.059645557 -0.024256228 0.005206843 -0.032157905 0.009287525 0.083587726

=

0.014044443 0.000991667 0.000821849 0.014340312 0.003557592 0.000588365 2.71112E-05 0.001034131 0.083587726

0.0119411 34.762795 130.09091 119.25 110.07692 102.21429 95.4 89.4375 84.176471

and other outputs for our stock return illustration.

yi - y ̅ 0.05 0.15 0.4 0.25 -0.28 -0.4 0.3 -0.27 -0.45 0.25 0

(yi - y )̅ 2 0.0025 0.0225 0.16 0.0625 0.0784 0.16 0.09 0.0729 0.2025 0.0625 0.9138 = SS 0.4569 = SS/m

r(y,m) = r(y,I) = r(m,I) =

0.864904 0.929112 0.790679

R-square = 0.908527 0.15 0.1 0.4

0.25 0.1 -0.02

0.34756 0.654304

0.0119411

Lower 95.0% Upper 95.0% -0.10713676 0.0885702 -0.18005669 1.5122288 0.145861589 0.7511486 p-Value (Normal Distribution) p-Value (Normal Distribution) p-Value (Normal Distribution)

0.3108

0.5 0.25 0.5

0.35 0.25 0.5

=F

96.36363636

112.72727 41.73913

42.12

-0.18 -0.03 -0.4

-0.3 0.08 -0.5

0.4 0.3 0.6

-0.17 -0.05 -0.23

-0.35 -0.25 -0.4

0.35 0.15 0.65

Stock Y against the Market and Industry On this sheet, we use matrices to compute regression coefficients b0, b1 and b2 for our stock return illustration.

Original Data Year

Stock Y

Market

2000

0.15

2001 2002

Industry 0.1

0.4

0.25

0.1

-0.02

0.5

0.25

0.5

2003

0.35

0.25

0.5

2004

-0.18

-0.03

-0.4

2005

-0.3

0.08

-0.5

2006

0.4

0.3

0.6

2007

-0.17

-0.05

-0.23

2008

-0.35

-0.25

-0.4

2009

0.35

0.15

0.65

1 -0.03 -0.4

1 0.08 -0.5

1 0.3 0.6

1 -0.05 -0.23

1 -0.25 -0.4

1 0.15 0.65

1 0.08 -0.5

1 0.3 0.6

1 -0.05 -0.23

1 -0.25 -0.4

1 0.15 0.65

0.1 X 1 0.1 0.4

1 0.1 -0.02

1 0.25 0.5

1 0.25 0.5

XT

0.143411 -0.6315 0.122029 -0.6315 10.72305 -3.03254 0.122029 -3.03254 1.37181 (XTX)-1 1 0.1 0.4

1 0.1 -0.02

1 0.25 0.5

1 0.25 0.5

1 -0.03 -0.4 XT

0.129074 -0.77221 0.367499

0.236727

Residuals -0.08673

-0.08673 0.201645

0.077821

0.50146 -0.20866

0.048355

0.201645

0.0498 0.0498

0.381491 0.381491

0.118509 -0.03149

0.113545 0.259828 -0.33572 0.031877 1.742618 -0.80648 0.02718 0.765898 0.035354

-0.20867 -0.18025 0.459646

0.028668 -0.11975 -0.05965

0.146919 -0.47016 -0.04186

-0.14574

-0.02426

-0.00754 0.128045

0.252474 -2.09924

0.33144

-0.35521

0.005207

0.001457 -0.03621

0.128006 -0.99419 0.558825

0.382158

-0.03216

0.046552 0.532999 0.046552 0.532999

X(XTX)-1

X(XTX)-1XTy Predicted Values

e = y - X(XTX)-1XTy Residuals

0.083588 eTe

= Sum of Squared Resid

0.001712 -0.00754

T

T

Est. Var.[b|X] = (1/(n-m-1))*e e(X X

1 1 1 1 1 1 1 1 1 1

0.1

0.4

0.1

-0.02

0.25

0.5

0.25

0.5

-0.03

-0.4

0.08

-0.5

0.3

0.6

-0.05

-0.23

-0.25

-0.4

0.15

0.65

10 0.9 1.1

0.9 0.3298 0.649

1.1 0.649 2.0658

XTX

-0.00928 = b0

X

0.666086 = b1 0.15 0.25 0.5 0.35 -0.18 -0.3 0.4 -0.17 -0.35 0.35

1 0.5024 1.3486

0.448505 = b2 b

XTy

y

0.118509 -0.03149 0.028668 -0.11975 -0.05965 -0.02426 0.005207 -0.03216

eT = Sum of Squared Residuals 0.001457

0.041382 = SE(b0)

-0.22433 = t(b0)

-0.03621

0.357834 = SE(b1)

1.861439 = t(b1)

0.127988 = SE(b2)

3.504275 = t(b2)

0.016381 T

T

|X] = (1/(n-m-1))*e e(X X)

-1

Bond Yields: Dt Against t and t2

1 1 1

D(2.5) =

0.7999402

y(0,2.5)=

0.09339477

1 2 4

1 3 9 X

3.323076923 -2.1961538 -2.196153846 1.7173077 0.326923077 -0.2788462 (XTX)-1 1 1 1 2 1 4

1

1 4 14

1 5 25

1 4 14

1 5 25

T

0.326923077 -0.278846154 0.048076923 1 3 9 XT

SUMMARY OUTPUT Regression Statistics Multiple R 0.999731062 R Square 0.999462196 Adjusted R Square 0.998924391 Standard Error 0.005092511 Observations 5 ANOVA df Regression Residual

SS 2 0.0963909 2 5.1867E-05

MS F Significance F 0.048195451 1858.41211 0.0005378 2.59337E-05

Total

4 0.09644277 Coefficients Standard Error 1.044110521 0.0092833 -0.097281394 0.00667354 -0.000154693 0.00111661


t Stat P-value Lower 95% 112.4719606 7.9042E-05 1.0041677 -14.57718677 0.00467305 -0.1259953 -0.138538637 0.90250508 -0.0049591

RESIDUAL OUTPUT Observation

Upper 95% 1.08405332 -0.0685675 0.00464968

Residual Maker:

1 2 3

Predicted Y Residuals Residuals-Squared 0.946674434 -0.0032782 1.07466E-05 0.848928961 0.00524333 2.74925E-05 0.750874101 0.0004407 1.94217E-07

1 1 1 1

1 2 3 4

4 5

0.652819241 -0.0034986 0.553836221 0.00109274

1

5

1.22399E-05 1.19407E-06

X

5 15 53

15 55 217

53 217 919

3.3230769 -2.1961538 0.3269231

T

XX

1.453846154 -0.7576923 0.238461538 0.1230769 -0.323076923 0.4461538 -0.884615385 0.7692308 0.515384615 -0.5807692

0.096153846 -0.038461538 -0.076923077 -0.115384615 0.134615385

0.7923077 0.3230769 0.3230769 0.3307692 0.0461538 0.2615385 -0.2307692 0.1923077 0.0692308 -0.1076923

X(XTX)-1 1 0 0 0 0

0 1 0 0 0

0 0 1 0 0 I

0 0 0 1 0

0 0 0 0 1

Original Data 2

t

y0,t

Dt

t

t

1 2 3 4 5

0.06 0.082 0.1 0.114 0.125

0.943396226 0.85417229 0.751314801 0.649320683 0.554928957

1 2 3 4 5

1 4 9 14 25

1 1 1 1

1 2 3 4

1 4 9 14

1

5

25

5 15 53

15 55 217 T

XX

X

0.94339623 0.85417229 0.7513148 0.64932068 0.55492896 y

3.753132957 10.27761273 34.08563209

1.044110521 -0.09728139 -0.00015469 b

t

Xy

53 217 919

Lower 95.0% Upper 95.0% 1.00416772 1.08405332 -0.12599531 -0.06856748 -0.00495907 0.00464968

Residual Maker:

1 1 1

1 4 9 14

1 2 4

1 3 9

1 4 14 X

25

1 5 25

T

-2.1961538 0.32692308 1.71730769 -0.27884615 -0.2788462 0.04807692 T

(X X)

-1

0.04615385 0.26153846 0.32307692 0.38461538 -0.0153846

-0.23076923 0.19230769 0.38461538 0.57692308 0.07692308

0.069230769 -0.10769231 -0.01538462 0.076923077 0.976923077

X(XTX)-1XT 0.20769231 -0.3230769 -0.0461538 0.23076923 -0.0692308

-0.32307692 0.66923077 -0.26153846 -0.19230769 0.10769231

-0.04615385 -0.26153846 0.676923077 -0.38461538 0.015384615

0.230769 -0.19231 -0.38462 0.423077 -0.07692

I - X(XTX)-1XT M = The Residual Maker M is idempotent and symetric

-0.06923 0.107692 0.015385 -0.07692 0.023077

0.943396 0.854172 0.751315 0.649321 0.554929 y

Residuals -0.00328 0.005243 0.000441 -0.0035 0.001093 e

Multi-Index Model: Index 1 and Index 2 On this sheet, we use matrices to compute regression coefficients b0, b1 and b2 for our 2-index model.

Original Data Year

Return

Index 1

2001

0.15

2002 2003

Index 2 0.1

-0.2

0.25

0.1

-0.02

0.5

0.25

0.5

2004

0.35

0.25

-0.5

2005

-0.27

-0.03

-0.4

2006

-0.3

0.08

-0.5

2007

0.4

0.3

-0.2

2008

-0.28

-0.05

-0.23

2009

-0.1

-0.25

-0.34

2010

0.5

0.15

0.1

1 -0.03 -0.4

1 0.08 -0.5

1 0.3 -0.2

1 -0.05 -0.23

1 -0.25 -0.34

1 0.15 0.1

1 0.08 -0.5

1 0.3 -0.2

1 -0.05 -0.23

1 -0.25 -0.34

1 0.15 0.1

0.12 X 1 0.1 -0.2

1 0.1 -0.02

1 0.25 0.5

1 0.25 -0.5

X

T

0.208756 -0.57114 0.320413 -0.57114 4.594739 -0.88051 0.320413 -0.88051 1.347301 T

(X X) 1 0.1 -0.2

-1

1 0.1 -0.02

1 0.25 0.5

1 0.25 -0.5

1 -0.03 -0.4 XT

0.1

0.1

0.25

0.25

0.1

-0.2

-0.03

0.08

0.3

-0.05

10 0.9 -1.79

0.9 0.3298 0.0015

-1.79 0.0015 1.1689

-0.25

0.15

0.13355 =E[R(i)] 0.690847



σ(i)2

1 1 1 1 1 1 1 1 1 1

0.1

-0.02

0.25

0.5

0.25

-0.5

-0.03

-0.4

0.08

-0.5

0.3

-0.2

-0.05

-0.23

-0.25

-0.34

0.15

0.1

T

XX

0.099129 = b0

X

1.154299 = b1 0.15 0.25 0.5 0.35 -0.27 -0.3 0.4 -0.28 -0.1 0.5 y

1.2 0.4706 0.3664 Xty

0.463778 = b2 b

0.3298 1.1689

-0.2 -0.02 0.5 -0.5 -0.4 = -0.5 -0.2 -0.23 -0.34 0.1

=VAR[I(1)] =VAR[I(2)]

0.0015

Annual S&P500 Returns Regressed on Changes in 10-Yr. T-Bond Rates and Presidential Party

S&P 500 returns are reflected for the year ending prior to the start of the year (e.g., the return for year 1971 was .104931009). The variable 10-T Rate is the change in the prior year 10-year Treasury bond rate from one year earlier (e.g., the rate increased The Dummy variable for the presidential party affiliation takes a value of 1 is the president as of the year start is a Republican (e

Annual S&P500 Returns Regressed on Changes in 10-Yr. T-Bo DATE 1972-01-01 1973-01-01 1974-01-01 1975-01-01 1976-01-01 1977-01-01 1978-01-01 1979-01-01 1980-01-01 1981-01-01 1982-01-01 1983-01-01 1984-01-01 1985-01-01 1986-01-01 1987-01-01 1988-01-01 1989-01-01 1990-01-01 1991-01-01

S&P Return 10-T Rate D/R 0.104931009 1 0.146176186 0.51 1 -0.188260135 0.53 1 -0.245031734 0.51 1 0.334895259 0.24 1 0.071649804 -0.53 1 -0.130539499 0.75 0 0.104819945 1.14 0 0.112225454 1.7 0 0.199278629 1.77 0 -0.118045113 2.02 1 0.230179028 -4.13 1 0.153153153 1.21 1 0.03125 -0.29 1 0.213286713 -2.19 1 0.270413064 -2.11 1 -0.052930057 1.59 1 0.139321357 0.42 1 0.191205326 -0.88 1 -0.042591993 -0.12 1

1992-01-01 1993-01-01 1994-01-01 1995-01-01 1996-01-01 1997-01-01 1998-01-01 1999-01-01 2000-01-01 2001-01-01 2002-01-01 2003-01-01 2004-01-01 2005-01-01 2006-01-01 2007-01-01 2008-01-01 2009-01-01 2010-01-01

0.278318842 0.046024803 0.086758725 -0.016363982 0.320623321 0.24706227 0.257289029 0.296265155 0.14159533 -0.063103697 -0.146312976 -0.214320169 0.264198964 0.043169216 0.082376144 0.113730029 -0.031878441 -0.372204009 0.298066037 0.131979921

-1.06 -0.43 -0.85 2.03 -2.13 0.93 -1.04 -0.82 1.94 -1.5 -0.12 -0.99 0.1 0.07 0.2 0.34 -1.02 -1.22 1.21

1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0



2 35 37

SS 0.139476326 1.016798967 1.156275293

Coefficients Standard Error 0.154900697 0.048006201 -0.031136909 0.02118257 -0.116144017 0.060079523

Annual S&P500 Returns Regressed on Changes in 10-Yr. T-Bo SUMMARY OUTPUT Regression Statistics Multiple R 0.137999705 R Square 0.019043918 Adjusted R Square -0.037010715 Standard Error 0.179889907 Observations 38 ANOVA df Regression Residual Total


2 35 37

SS 0.021988135 1.132613259 1.154601393

Coefficients Standard Error 0.114025259 0.050666466 -0.002926917 0.022356403 -0.052076156 0.063408832

and Presidential Party Affiliation; 1973 to 2010

year 1971 was .104931009). earlier (e.g., the rate increased by .51% in 1972). e year start is a Republican (e.g., on January 1, 1977, the president was a Republican).

on Changes in 10-Yr. T-Bond Rates and Presidential Party Affiliation; 1973 to 2010

MS F Significance F 0.069738163 2.400509629 0.105449 0.029051399

t Stat P-value Lower 95%Upper 95%Lower 95.0% Upper 95.0% 3.226680989 0.002717375 0.057443 0.252358 0.057443 0.252358 -1.469930621 0.150513397 -0.07414 0.011866 -0.07414 0.011866 -1.933171414 0.061337043 -0.23811 0.005824 -0.23811 0.005824

on Changes in 10-Yr. T-Bond Rates and Presidential Party Affiliation; 1974 (lagged independent variables) to 2011


t Stat P-value Lower 95%Upper 95%Lower 95.0% Upper 95.0% 2.250507454 0.030802901 0.011167 0.216884 0.011167 0.216884 -0.13092077 0.896587624 -0.04831 0.042459 -0.04831 0.042459 -0.821276069 0.41704832 -0.1808 0.076651 -0.1808 0.076651

t variables) to 2011

Management Compensation = f(merger, stock performance, interaction)

Firm 1 2 3 4 5 6 7 8 9 10

(000's) Stock Merger Interaction Compensation Return Dummy Term 1309.057596 0.15 0 0 968.3782619 0.1 0 0 1507.801144 0.22 0 0 1764.293366 0.45 0 0 861.3526143 -0.07 0 0 3265.62936 0.18 1 0.18 1845.469454 -0.02 1 -0.02 4155.041237 0.31 1 0.31 2910.433255 0.15 1 0.15 3180.97272 0.17 1 0.17


SS 3 11245146 6 71585.23 9 11316731

Coefficients Standard Error Intercept 964.5202 69.16621 X Variable 1 1868.567 288.0425 X Variable 2 996.8745 111.9759 X Variable 3 5157.474 545.909


SS 2 10180254 7 1136478 9 11316731

Coefficients Standard Error Intercept 720.4253 236.6764 X Variable 1 3304.419 902.6088 X Variable 2 1828.986 255.0665

Compensation on return, merger dummy and interaction

MS F Significance F 3748382 314.1751 5.52E-07 11930.87

t Stat 13.94496 6.487122 8.902582 9.447497

P-value Lower 95% Upper 95%Lower 95.0% Upper 95.0% 8.48E-06 795.2766 1133.764 795.2766 1133.764 0.000638 1163.752 2573.382 1163.752 2573.382 0.000112 722.8794 1270.87 722.8794 1270.87 8E-05 3821.683 6493.265 3821.683 6493.265

Compensation on return and merger dummy

MS F Significance F 5090127 31.35204 0.000321 162353.9

t Stat P-value Lower 95% Upper 95%Lower 95.0% Upper 95.0% 3.043926 0.018743 160.7747 1280.076 160.7747 1280.076 3.660965 0.00806 1170.089 5438.75 1170.089 5438.75 7.170624 0.000182 1225.849 2432.122 1225.849 2432.122

Price Data for Three Target Firms Target Firm Fleet Boston Disney AT&T Wireless

FBF Date

Symbol Announcement Date FBF 10/27/2003 DIS 2/11/2004 AWE 1/18/2004

Calendar Date Open 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

High

Low

Close Volume

10-Nov-03

40.32

40.6

40.21

40.35

7-Nov-03

41

41.02

40.5

40.5

4,188,800 6,886,200

6-Nov-03

40.55

40.94

40.1

40.93

10,945,000

5-Nov-03

40.02

40.57

40

40.55

11,056,600

4-Nov-03

40.45

40.8

40.14

40.26

13,285,900

3-Nov-03

40.3

40.57

39.91

40.52

12,562,300

31-Oct-03

40

40.48

40

40.39

11,617,100

30-Oct-03

39.95

40.23

39.46

40.1

18,065,700

29-Oct-03

38.62

39.9

38.6

39.55

27,672,400

28-Oct-03

39.05

39.5

38.39

38.8

29,173,800

27-Oct-03

39.81

40.44

39

39.2

57,491,700

24-Oct-03

32.04

32.05

31.56

31.8

2,836,800

23-Oct-03

31.99

32.23

31.84

32.06

4,354,300

22-Oct-03

32.02

32.29

31.9

31.99

3,514,300

21-Oct-03

32.76

32.76

32.4

32.41

3,773,000

20-Oct-03

32.73

32.74

32.35

32.7

2,893,400

17-Oct-03

32.97

32.98

32.51

32.61

2,856,100

16-Oct-03

32.4

32.99

32.31

32.85

4,096,100

15-Oct-03

32.8

32.95

32.35

32.52

3,479,400

14-Oct-03

32.5

32.69

32.26

32.63

3,323,900

13-Oct-03

32.16

32.77

32.16

32.4

2,393,700

DIS Adj. Close Date Calendar Date Open High Low Close Volume 39.69 26.55 26.98 26.43 26.73 11,276,200 10 26-Feb-04 39.84 26 26.39 25.91 26.3 11,904,100 9 25-Feb-04 40.26 26.39 26.43 25.8 25.96 15,608,700 8 24-Feb-04 39.89 26.55 26.75 26.02 26.75 13,472,900 7 23-Feb-04 39.6 26.99 26.99 26.39 26.55 12,971,100 6 20-Feb-04 39.86 27 27.05 26.7 27 9,837,000 5 19-Feb-04 39.73 26.8 26.86 26.56 26.71 11,572,900 4 18-Feb-04 39.45 27.4 27.51 26.49 26.9 28,275,500 3 17-Feb-04 38.9 27.6 27.75 26.85 26.92 42,695,100 2 13-Feb-04 38.17 27.95 28.41 27.61 28 57,864,600 1 12-Feb-04 38.56 27.92 28 27.27 27.6 115,014,800 0 11-Feb-04 31.28 23.85 24.3 23.75 24.08 7,287,000 -1 10-Feb-04 31.54 23.35 23.98 23.28 23.77 10,311,600 -2 9-Feb-04 31.47 23.1 23.53 22.9 23.35 10,002,400 -3 6-Feb-04 31.88 23.3 23.52 23.14 23.2 7,344,900 -4 5-Feb-04 32.17 23.06 23.72 23.05 23.19 8,963,500 -5 4-Feb-04 32.08 23.43 23.88 23.1 23.26 10,004,600 -6 3-Feb-04 32.31 23.8 24.03 23.6 23.8 9,242,300 -7 2-Feb-04 31.99 23.72 24.18 23.7 24 17,033,000 -8 30-Jan-04 32.1 23.8 24.65 22.98 24.45 15,418,200 -9 29-Jan-04 31.87 24.07 24.13 23.51 23.67 7,306,500 -10 28-Jan-04

AWE Adj. Close Date Calendar Date Open High 26.73 11.09 10 3-Feb-04 26.3 11.12 9 2-Feb-04 25.96 8 30-Jan-04 11.05 26.75 7 29-Jan-04 11.18 26.55 6 28-Jan-04 11.17 27 5 27-Jan-04 10.83 26.71 4 26-Jan-04 10.85 26.9 3 23-Jan-04 10.73 26.92 2 22-Jan-04 10.86 28 1 21-Jan-04 10.61 27.6 0 20-Jan-04 10.43 24.08 9.93 -1 16-Jan-04 23.77 9.89 -2 15-Jan-04 23.35 9.45 -3 14-Jan-04 23.2 8.23 -4 13-Jan-04 23.19 8.16 -5 12-Jan-04 23.26 8.19 -6 9-Jan-04 23.8 8.25 -7 8-Jan-04 24 8.47 -8 7-Jan-04 24.45 7.98 -9 6-Jan-04 23.67 8 -10 5-Jan-04

Low

Close

Volume

Adj. Close

11.18

11.03

11.08

14,936,800

11.08

11.22

10.94

11.16

15,673,900

11.16

11.23

11

11.05

28,907,200

11.05

11.22

10.91

11.03

25,697,400

11.03

11.42

11

11.02

31,273,600

11.02

11.3

10.83

11.17

39,559,300

11.17

10.95

10.81

10.93

24,564,500

10.93

10.73

10.38

10.61

33,173,600

10.61

10.88

10.55

10.56

48,225,200

10.56

11

10.58

10.99

47,392,700

10.99

10.75

10.25

10.39

53,621,200

10.39

10.05

9.86

9.99

36,760,400

9.99

10.17

9.53

9.81

55,545,100

9.81

10.1

9.15

9.99

73,782,600

9.99

8.63

8.15

8.55

26,165,300

8.55

8.16

7.94

8.13

16,523,200

8.13

8.21

8.08

8.15

14,415,300

8.15

8.32

8.16

8.24

14,480,700

8.24

8.5

8.1

8.21

16,616,700

8.21

8.31

7.92

8.29

16,318,100

8.29

8.08

7.76

8.03

27,337,700

8.03

Returns Data for Three Target Firms Target Firm Symbol Announcement Date Fleet Boston FBF 10/27/2003 Disney DIS 2/11/2004 AT&T Wireless AWE 1/18/2004 PRICES RETURNS Date FBF DIS AWE FBF DIS AWE 10 39.69 26.73 11.08 -0.004 0.016 -0.01 9 39.84 26.3 11.16 -0.01 0.013 0.01 8 40.26 25.96 11.05 0.009 -0.03 0.002 7 39.89 26.75 11.03 0.007 0.008 9E-04 6 39.6 26.55 11.02 -0.007 -0.02 -0.01 5 39.86 27 11.17 0.003 0.011 0.022 4 39.73 26.71 10.93 0.007 -0.01 0.03 3 39.45 26.9 10.61 0.014 -0 0.005 2 38.9 26.92 10.56 0.019 -0.04 -0.04 1 38.17 28 10.99 -0.01 0.014 0.058 0 38.56 27.6 10.39 0.233 0.146 0.04 -1 31.28 24.08 9.99 -0.008 0.013 0.018 -2 31.54 23.77 9.81 0.002 0.018 -0.02 -3 31.47 23.35 9.99 -0.013 0.006 0.168 -4 31.88 23.2 8.55 -0.009 4E-04 0.052 -5 32.17 23.19 8.13 0.003 -0 -0 -6 32.08 23.26 8.15 -0.007 -0.02 -0.01 -7 32.31 23.8 8.24 0.01 -0.01 0.004 -8 31.99 24 8.21 -0.003 -0.02 -0.01 -9 32.1 24.45 8.29 0.007 0.033 0.032 -10 31.87 23.67 8.03 N/A N/A N/A

DATA FOR THE S&P 500 (^GSPC) Calendar Date Open

High

Low

Close

Volume

26-Feb-04

1,140.94

1,147.22

1,138.67

1,144.91

1,620,109,952

25-Feb-04

1,140.30

1,145.18

1,138.76

1,143.67

1,607,939,968

24-Feb-04

1,137.74

1,144.52

1,134.61

1,139.09

1,994,489,984

23-Feb-04

1,146.56

1,146.66

1,137.35

1,140.99

1,820,160,000

20-Feb-04

1,147.06

1,149.68

1,139.07

1,144.11

1,850,130,048

19-Feb-04

1,157.82

1,158.54

1,146.83

1,147.06

1,975,500,032

18-Feb-04

1,156.99

1,157.32

1,149.85

1,151.82

1,674,780,032

17-Feb-04

1,153.76

1,158.99

1,145.81

1,156.99

1,667,270,016

13-Feb-04

1,153.28

1,156.75

1,143.76

1,145.81

1,624,380,032

12-Feb-04

1,154.88

1,157.76

1,151.43

1,152.11

1,697,430,016

11-Feb-04

1,144.79

1,158.76

1,142.38

1,157.76

2,102,109,952

10-Feb-04

1,139.38

1,146.87

1,138.91

1,145.54

1,554,960,000

9-Feb-04

1,143.23

1,144.45

1,139.21

1,139.81

1,507,350,016

6-Feb-04

1,128.89

1,142.77

1,128.58

1,142.76

1,772,659,968

5-Feb-04

1,128.42

1,131.10

1,124.45

1,128.59

1,941,209,984

4-Feb-04

1,128.74

1,136.03

1,124.84

1,126.52

2,146,780,032

3-Feb-04

1,134.86

1,137.31

1,131.45

1,136.03

1,740,009,984

2-Feb-04

1,132.58

1,142.47

1,127.88

1,135.26

1,948,329,984

30-Jan-04

1,133.06

1,133.20

1,127.81

1,131.13

1,309,560,064

29-Jan-04

1,130.06

1,134.19

1,122.41

1,134.11

1,631,110,016

28-Jan-04

1,146.31

1,149.08

1,126.61

1,128.48

1,483,849,984

27-Jan-04

1,154.38

1,155.14

1,144.05

1,144.05

1,379,830,016

26-Jan-04

1,141.15

1,155.37

1,141.15

1,155.37

1,180,950,016

23-Jan-04

1,145.98

1,150.21

1,136.84

1,141.55

1,322,759,936

22-Jan-04

1,147.99

1,150.43

1,143.04

1,143.94

1,390,669,952

21-Jan-04

1,137.85

1,148.91

1,134.65

1,147.62

1,404,349,952

20-Jan-04

1,140.80

1,142.80

1,135.41

1,138.77

1,444,819,968

16-Jan-04

1,134.57

1,139.83

1,133.52

1,139.83

1,580,880,000

15-Jan-04

1,128.67

1,136.35

1,123.76

1,132.05

1,451,590,016

14-Jan-04

1,122.68

1,130.74

1,122.68

1,130.52

1,218,739,968

13-Jan-04

1,127.11

1,129.04

1,115.24

1,121.22

1,292,179,968

12-Jan-04

1,123.10

1,127.85

1,121.06

1,127.23

1,162,499,968

9-Jan-04

1,128.92

1,131.30

1,120.97

1,121.86

1,386,509,952

8-Jan-04

1,126.33

1,131.92

1,124.91

1,131.92

1,571,629,952

7-Jan-04

1,122.32

1,126.33

1,116.45

1,126.33

1,376,790,016

6-Jan-04

1,120.74

1,124.44

1,118.52

1,123.67

1,239,250,048

5-Jan-04

1,112.35

1,122.22

1,112.35

1,122.22

1,306,880,000

2-Jan-04

1,112.61

1,118.70

1,105.02

1,108.48

951,875,008

31-Dec-03

1,109.54

1,112.52

1,106.26

1,111.92

817,198,976

30-Dec-03

1,108.65

1,109.75

1,106.40

1,109.64

774,324,992

29-Dec-03

1,097.53

1,109.48

1,097.53

1,109.48

813,236,992

26-Dec-03

1,094.75

1,098.46

1,094.75

1,095.89

258,871,008

24-Dec-03

1,094.56

1,096.38

1,092.75

1,094.04

392,068,000

23-Dec-03

1,091.88

1,096.79

1,091.77

1,096.02

934,430,976

22-Dec-03

1,086.58

1,092.94

1,085.82

1,092.94

984,177,984

19-Dec-03

1,090.02

1,091.03

1,084.24

1,088.67

1,445,660,032

18-Dec-03

1,076.92

1,089.45

1,076.92

1,089.18

1,257,990,016

17-Dec-03

1,074.16

1,076.52

1,071.16

1,076.48

1,094,589,952

16-Dec-03

1,068.37

1,075.91

1,068.34

1,075.13

1,245,350,016

Adj. Close Return FBF 1,144.91 0.001084 1,143.67 0.004021 1,139.09 -0.00167 1,140.99 -0.00273 1,144.11 -0.00257 1,147.06 -0.00413 1,151.82 -0.00447 1,156.99 0.009757 1,145.81 -0.00547 1,152.11 -0.00488 1,157.76 0.010667 1,145.54 0.005027 1,139.81 -0.00258 1,142.76 0.012555 1,128.59 0.001838 1,126.52 -0.00837 1,136.03 0.000678 1,135.26 0.003651 1,131.13 -0.00263 1,134.11 0.004989 1,128.48 -0.01361 1,144.05 -0.0098 1,155.37 0.012106 1,141.55 -0.00209 1,143.94 -0.00321 1,147.62 0.007772 1,138.77 -0.00093 1,139.83 0.006872 1,132.05 0.001353 1,130.52 0.008295 1,121.22 -0.00533 1,127.23 0.004787 1,121.86 -0.00889 1,131.92 0.004963 1,126.33 0.002367 1,123.67 0.001292 1,122.22 0.012395 1,108.48 -0.00309 1,111.92 0.002055 1,109.64 0.000144 1,109.48 0.012401 1,095.89 0.001691 1,094.04 -0.00181 1,096.02 0.002818 1,092.94 0.003922 1,088.67 -0.00047 1,089.18 0.011798 1,076.48 0.001256 1,075.13 0.006638

15-Dec-03

1,080.11

1,082.82

1,068.04

1,068.04

1,248,720,000

1,068.04

12-Dec-03

1,072.14

1,074.77

1,067.83

1,074.14

948,680,000

1,074.14

11-Dec-03

1,059.55

1,073.62

1,059.55

1,071.21

1,159,949,952

1,071.21

10-Dec-03

1,061.06

1,063.01

1,053.52

1,059.05

1,187,289,984

1,059.05

9-Dec-03

1,070.74

1,071.77

1,059.26

1,060.18

1,194,749,952

1,060.18

8-Dec-03

1,061.12

1,069.53

1,061.02

1,069.30

975,227,008

1,069.30

5-Dec-03

1,066.88

1,068.26

1,060.06

1,061.50

1,041,070,016

1,061.50

4-Dec-03

1,065.28

1,070.32

1,063.15

1,069.72

1,239,149,952

1,069.72

3-Dec-03

1,067.73

1,074.21

1,064.64

1,064.73

1,266,130,048

1,064.73

2-Dec-03

1,069.01

1,071.20

1,065.31

1,066.62

1,136,499,968

1,066.62

1-Dec-03

1,061.89

1,070.43

1,061.89

1,070.12

1,143,100,032

1,070.12

28-Nov-03

1,057.92

1,060.64

1,056.79

1,058.20

396,096,992

1,058.20

26-Nov-03

1,055.76

1,058.45

1,048.52

1,058.45

912,113,024

1,058.45

25-Nov-03

1,051.73

1,058.00

1,049.29

1,053.89

1,100,470,016

1,053.89

24-Nov-03

1,038.54

1,052.08

1,038.54

1,052.08

1,089,609,984

1,052.08

21-Nov-03

1,035.77

1,037.52

1,031.24

1,035.28

1,054,049,984

1,035.28

20-Nov-03

1,040.56

1,046.46

1,033.39

1,033.65

1,103,810,048

1,033.65

19-Nov-03

1,034.74

1,043.79

1,034.19

1,042.44

1,126,210,048

1,042.44

18-Nov-03

1,045.19

1,048.73

1,034.09

1,034.15

1,190,979,968

1,034.15

17-Nov-03

1,048.68

1,048.68

1,035.23

1,043.63

1,125,090,048

1,043.63

14-Nov-03

1,057.86

1,063.65

1,048.11

1,050.35

1,162,480,000

1,050.35

13-Nov-03

1,055.98

1,059.65

1,052.97

1,058.41

1,188,499,968

1,058.41

12-Nov-03

1,046.64

1,059.14

1,046.64

1,058.56

1,076,380,032

1,058.56

11-Nov-03

1,046.93

1,048.25

1,043.46

1,046.57

931,601,984

1,046.57

10-Nov-03

1,053.16

1,053.58

1,045.58

1,047.11

1,013,539,968

1,047.11

7-Nov-03

1,059.01

1,062.39

1,052.19

1,053.21

1,244,009,984

1,053.21

6-Nov-03

1,053.14

1,058.97

1,046.89

1,058.05

1,285,590,016

1,058.05

5-Nov-03

1,052.99

1,054.58

1,044.89

1,051.81

1,180,329,984

1,051.81

4-Nov-03

1,058.01

1,058.12

1,051.64

1,053.25

1,244,120,064

1,053.25

3-Nov-03

1,051.75

1,061.44

1,051.75

1,059.02

1,185,389,952

1,059.02

31-Oct-03

1,047.79

1,053.10

1,047.79

1,050.71

1,216,169,984

1,050.71

30-Oct-03

1,050.13

1,052.89

1,043.83

1,046.94

1,384,019,968

1,046.94

29-Oct-03

1,045.91

1,049.85

1,043.34

1,048.11

1,302,809,984

1,048.11

28-Oct-03

1,032.94

1,046.79

1,032.94

1,046.79

1,468,050,048

1,046.79

27-Oct-03

1,030.50

1,037.78

1,029.17

1,031.13

1,154,749,952

1,031.13

24-Oct-03

1,030.75

1,030.75

1,018.27

1,028.91

1,312,199,936

1,028.91

23-Oct-03

1,027.98

1,035.45

1,025.83

1,033.77

1,375,010,048

1,033.77

22-Oct-03

1,043.93

1,043.93

1,028.39

1,030.36

1,287,069,952

1,030.36

21-Oct-03

1,045.20

1,049.40

1,042.53

1,046.03

1,212,889,984

1,046.03

20-Oct-03

1,039.39

1,044.69

1,036.13

1,044.68

1,007,980,032

1,044.68

17-Oct-03

1,050.02

1,051.92

1,036.56

1,039.32

1,185,810,048

1,039.32

16-Oct-03

1,045.14

1,052.98

1,043.99

1,050.07

1,212,999,936

1,050.07

15-Oct-03

1,052.95

1,053.72

1,043.10

1,046.76

1,361,500,032

1,046.76

14-Oct-03

1,044.69

1,049.49

1,040.84

1,049.48

1,043,310,016

1,049.48

13-Oct-03

1,039.60

1,048.93

1,039.60

1,045.35

908,182,976

1,045.35

-0.00568 0.002735 0.011482 -0.00107 -0.00853 0.007348 -0.00768 0.004687 -0.00177 -0.00327 0.011264 -0.00024 0.004327 0.00172 0.016227 0.001577 -0.00843 0.008016 -0.00908 -0.0064 -0.00762 -0.00014 0.011456 -0.00052 -0.00579 -0.00457 0.005933 -0.00137 -0.00545 0.007909 0.003601 -0.00112 0.001261 0.015187 0.002158 -0.0047 0.00331 -0.01498 0.001292 0.005157 -0.01024 0.003162 -0.00259 0.003951 #DIV/0!

10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

DIS

AWE 10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

10 9 8 7 6 5 4 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

Abnormal Returns Data for Three Target Firms Target Firm Symbol Announcement Date Fleet Boston FBF 10/27/2003 Disney DIS 2/11/2004 AT&T Wireless AWE 1/18/2004 Abnormal Returns Average Date FBF DIS AWE Residuals (ARs) 10 0.002027 0.015266 -0.0078467 0.00314854 9 -0.00586 0.009076 0.0063035 0.003174039 8 0.003343 -0.02787 0.0044408 -0.006694588 7 0.00869 0.01026 -0.0040816 0.004956275 6 -0.00107 -0.01409 0.0001807 -0.004996184 5 -0.00464 0.01499 0.0317556 0.014036246 4 0.003497 -0.00259 0.0180539 0.006318598 3 0.015255 -0.0105 0.0068241 0.003859667 2 0.017864 -0.0331 -0.0359198 -0.017053025 1 -0.0253 0.019373 0.0499763 0.01468261 0 0.230579 0.135512 0.04097 0.135686966 -1 -0.00354 0.008014 0.0114761 0.005316123 -2 -0.00109 0.020569 -0.0193714 3.73539E-05 -3 0.00212 -0.00609 0.1601265 0.052052089 -4 -0.01031 -0.00141 0.0569922 0.015093001 -5 -0.00235 0.005362 -0.0072407 -0.001410205 -6 0.003119 -0.02337 -0.0020348 -0.007427746 -7 0.006841 -0.01198 -0.0013089 -0.002150834 -8 -0.00084 -0.01578 -0.0120174 -0.009543251 -9 0.003266 0.027964 0.0310865 0.020772193 -10 N/A N/A N/A N/A

Residual s 0.0116 0.00794 0.01834 0.00787 0.0079 0.01821 0.01061 0.01313 0.03027 0.03786 0.0948 0.00786 0.01999 0.09369 0.03656 0.00635 0.01404 0.00944 0.00777 0.01524 N/A

Normal Deviate 0.2715 0.39957 -0.3649 0.63007 -0.6321 0.77059 0.59555 0.29393 -0.5633 0.38784 1.43123 0.67597 0.00187 0.55561 0.41285 -0.2219 -0.5289 -0.2278 -1.2279 1.36292 N/A

CAR 0.229858 0.226709 0.223535 0.23023 0.225274 0.23027 0.216234 0.209915 0.206055 0.223108 0.208426 0.072739 0.067423 0.067385 0.015333 0.00024 0.00165 0.009078 0.011229 0.020772 N/A

CAR FBF 0.241609 0.239582 0.24544 0.242097 0.233407 0.234481 0.239118 0.235621 0.220366 0.202502 0.227803 -0.00278 0.000767 0.001852 -0.00027 0.010039 0.012391 0.009272 0.002431 0.003266 N/A

CAR DIS 0.1196 0.104334 0.095258 0.123125 0.112865 0.12696 0.11197 0.114565 0.125065 0.158168 0.138796 0.003284 -0.00473 -0.0253 -0.01921 -0.0178 -0.02317 0.000202 0.012187 0.027964 N/A

CAR AWE 0.328365 0.336212 0.329908 0.325467 0.329549 0.329368 0.297613 0.279559 0.272735 0.308654 0.258678 0.217708 0.206232 0.225603 0.065477 0.008485 0.015725 0.01776 0.019069 0.031086 N/A

CAR 0.229858 0.226709 0.223535 0.23023 0.225274 0.23027 0.216234 0.209915 0.206055 0.223108 0.208426 0.072739 0.067423 0.067385 0.015333 0.00024 0.00165 0.009078 0.011229 0.020772 N/A

CAR s 0.104878 0.116474 0.118849 0.101692 0.108571 0.10127 0.094913 0.085448 0.074868 0.07733 0.062246 0.125584 0.120244 0.137692 0.044446 0.015645 0.021555 0.008781 0.00836 0.015241 N/A

Normal Deviate 2.191678 1.946444 1.880836 2.263999 2.074906 2.273827 2.278221 2.456643 2.752261 2.885135 3.348411 0.579205 0.560715 0.489392 0.34498 0.01535 0.076564 1.033889 1.343124 1.362916 N/A

Normally Distributed Random Variables with a Known Event Disturbance Mean return for stocks is zero σ= 0.02 Disturbances: Day 15 = Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Stock 1 -0.02133 0.015773 -0.01916 0.017415 0.025689 -0.01876 -0.01072 0.00216 -0.00472 0.029143 0.004585 -0.03029 -0.02533 -0.01699 -0.01917 0.106761 0.010656 0.007613 0.013551 -0.02974 -0.00667 -0.00836 -0.00221 -0.00128 -0.01382 -0.03214 -0.02543 -0.02439 0.003008 0.015923 -0.01271

Stock 2 -0.03944 -0.02728 0.024521 -0.02116 0.023127 0.001734 -0.02337 -0.00315 -0.00629 -0.02718 0.010937 -0.01757 -0.00744 0.024913 0.014273 0.066392 0.020415 -0.00832 0.014452 -0.00764 -0.01979 0.02472 0.015561 0.031332 0.004126 -0.00242 -0.02197 0.005896 -0.02399 -0.01956 -0.01835

Stock 3 -0.04063 -0.04608 0.021839 0.01447 0.010833 -0.01694 -0.03337 -0.00324 -0.02614 0.016767 0.060108 0.020814 0.027665 -0.01844 0.001384 0.114192 0.015694 -0.01971 0.00883 0.009313 -0.00178 -0.01234 -0.01557 0.041078 0.00842 0.016916 0.007834 -0.00592 0.015248 0.022825 -0.01987

0.02 Day 16 = Stock 4 0.013753 0.036016 -0.01059 0.053503 0.050723 0.036527 -0.01564 0.001318 0.018582 -0.01752 -0.00965 -0.00673 0.014545 -0.00421 0.011203 0.128066 0.032765 -0.0292 0.013437 0.000268 -0.01232 0.001888 0.011987 0.00423 0.013696 -0.03128 0.023475 0.005561 -0.00081 0.009641 0.008931

Stock 5 0.024338 -0.01579 0.015296 0.031664 -0.01718 0.022324 0.001881 0.002044 -0.00741 -0.01263 -0.0124 0.018264 0.010801 0.002734 0.03121 0.106272 0.00482 -0.00726 0.017094 -0.04274 -0.02101 0.011671 -0.00782 -0.02593 0.003421 -0.0125 -0.01929 0.010012 0.014718 0.005737 -0.01053

0.1 Day 17 = Stock 6 0.013901 0.020201 0.003858 0.0114 0.009295 0.017004 0.03148 0.018464 -0.04172 0.014528 -0.01598 0.012137 0.03043 -0.00533 0.039011 0.12978 0.016734 -0.01084 -0.01235 -0.01019 8.93E-06 -0.01718 0.004691 -0.01894 0.028837 -0.00611 -0.00766 -0.00781 0.02874 -0.01406 -0.02104

Stock 7 0.002214 -0.01644 0.008798 -0.01967 0.022964 0.004413 -0.02824 0.016201 -0.02901 -0.01582 -0.01194 0.008318 0.00987 -0.02348 0.021403 0.100843 0.031472 0.015776 -0.00264 0.004781 0.007307 -0.00104 -0.009 0.008255 -0.00805 -0.03522 -0.00279 -0.01585 -0.02566 0.005194 -0.03053

0.02 Stock 8 -0.00786 0.000586 -0.01135 0.022197 -0.0097 -0.0153 -0.00838 0.017189 0.010515 -0.0085 -0.00724 0.00511 -0.00304 -0.00064 0.03697 0.112434 0.024403 0.005767 -0.01017 -0.00481 -0.00158 0.025131 0.035956 -0.0101 -0.05296 -0.00394 0.007546 -0.0102 -0.01668 0.000836 0.003643

Stock 9 -0.0221 0.047479 0.006264 -0.04761 0.015227 -0.04079 0.024362 -0.001 -0.00245 -0.02511 -0.00955 -0.02764 0.002565 0.033674 -0.00857 0.08292 0.003825 0.006824 -0.01576 0.005346 0.028634 0.011139 -0.00646 0.013808 0.007706 -0.00854 -0.01022 -0.02482 0.020984 -0.02827 -0.02711

Stock 10 0.021087 -0.01646 -0.00213 -0.02857 -0.04834 0.019562 -0.01798 -0.00966 0.017057 -0.00598 -0.00416 0.016869 0.02285 -0.00753 -0.00816 0.093259 0.018472 0.035206 -0.01148 0.014929 -0.0017 0.001011 0.021277 0.001965 0.0156 0.017427 0.010563 -0.00132 -0.04635 0.007682 0.012813

Average Residuals ARt σt Normal Deviate -0.0056064 -0.00019872 0.003735327 0.003365117 0.008263766 0.000978712 -0.00799727 0.004031824 -0.00715971 -0.00523023 0.000469207 -7.1639E-05 0.008290974 -0.00152889 0.011955126 0.104092048 0.017925548 -0.00041351 0.001495071 -0.00604884 -0.00289113 0.003663406 0.004842045 0.004441952 0.000698365 -0.00978096 -0.00379523 -0.0068832 -0.00307908 0.000595317 -0.01147522

0.024316 0.029563 0.014593 0.031277 0.027434 0.023696 0.021496 0.009785 0.020064 0.019038 0.022503 0.019233 0.017207 0.018324 0.020359 0.019481 0.009899 0.018573 0.013184 0.017925 0.014252 0.014498 0.016159 0.020781 0.022303 0.018776 0.016019 0.012273 0.024245 0.016203 0.015107

-0.23056279 -0.00672202 0.255961867 0.107590806 0.301218451 0.041302543 -0.37204036 0.412047361 -0.35684533 -0.2747229 0.020850837 -0.00372472 0.481845111 -0.08343793 0.587229672 5.343287332 1.810760682 -0.02226351 0.113403536 -0.33745768 -0.20286412 0.252676017 0.299647653 0.213748429 0.03131315 -0.5209155 -0.23692451 -0.56081869 -0.12699609 0.036741347 -0.75958633

Averages: 0.003441412 0.018986

0.2004433

Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

Cumulative Average Residuals for Ind Stock 1 Stock 2 Stock 3 -0.02133 -0.03944 -0.04063 -0.00555 -0.06672 -0.08671 -0.02471 -0.0422 -0.06487 -0.0073 -0.06336 -0.0504 0.01839 -0.04023 -0.03956 -0.00037 -0.0385 -0.0565 -0.01108 -0.06186 -0.08987 -0.00892 -0.06501 -0.09311 -0.01364 -0.07131 -0.11925 0.015499 -0.09849 -0.10248 0.020084 -0.08755 -0.04237 -0.01021 -0.10512 -0.02156 -0.03554 -0.11256 0.006105 -0.05253 -0.08765 -0.01233 -0.0717 -0.07338 -0.01095 0.035059 -0.00698 0.103246 0.045715 0.01343 0.11894 0.053328 0.00511 0.099234 0.066879 0.019563 0.108064 0.037139 0.01192 0.117377 0.030468 -0.00788 0.115594 0.022103 0.016844 0.103249 0.019893 0.032406 0.087677 0.01861 0.063738 0.128755 0.004794 0.067864 0.137174 -0.02734 0.065447 0.154091 -0.05277 0.04348 0.161925 -0.07716 0.049376 0.156006 -0.07415 0.025385 0.171254 -0.05823 0.005825 0.194079 -0.07094 -0.01252 0.174205

verage Residuals for Individual Stocks Stock 4 Stock 5 Stock 6 0.013753 0.024338 0.013901 0.04977 0.008547 0.034101 0.039183 0.023843 0.037959 0.092686 0.055508 0.049359 0.143409 0.038329 0.058654 0.179936 0.060652 0.075658 0.164293 0.062534 0.107138 0.165611 0.064578 0.125602 0.184194 0.057169 0.08388 0.166679 0.044536 0.098408 0.157026 0.032131 0.08243 0.150296 0.050394 0.094567 0.16484 0.061195 0.124997 0.160627 0.063929 0.119671 0.17183 0.095139 0.158681 0.299896 0.201411 0.288462 0.332661 0.206231 0.305196 0.30346 0.198975 0.294357 0.316897 0.216069 0.282002 0.317165 0.173331 0.271807 0.304846 0.152318 0.271816 0.306734 0.163989 0.254637 0.318721 0.156172 0.259328 0.322951 0.130247 0.240391 0.336647 0.133668 0.269229 0.305368 0.121164 0.263114 0.328843 0.101869 0.255449 0.334404 0.111881 0.247639 0.33359 0.1266 0.276379 0.343231 0.132336 0.262323 0.352162 0.121804 0.241287

Stock 7 0.002214 -0.01422 -0.00542 -0.02509 -0.00213 0.002286 -0.02596 -0.00976 -0.03877 -0.05459 -0.06653 -0.05822 -0.04835 -0.07183 -0.05042 0.050421 0.081894 0.097669 0.09503 0.099811 0.107119 0.106083 0.097085 0.105341 0.097289 0.062065 0.059272 0.043423 0.017764 0.022958 -0.00757

Stock 8 -0.00786 -0.00727 -0.01862 0.003581 -0.00612 -0.02142 -0.02979 -0.01261 -0.00209 -0.01059 -0.01784 -0.01273 -0.01577 -0.01641 0.020562 0.132996 0.157399 0.163166 0.152995 0.148185 0.146609 0.17174 0.207696 0.197592 0.144637 0.140694 0.14824 0.138041 0.121366 0.122202 0.125845

Stock 9 -0.0221 0.025376 0.031639 -0.01597 -0.00074 -0.04153 -0.01716 -0.01816 -0.02061 -0.04572 -0.05528 -0.08291 -0.08035 -0.04667 -0.05524 0.027677 0.031503 0.038326 0.022562 0.027908 0.056543 0.067681 0.061224 0.075032 0.082738 0.074202 0.063982 0.039166 0.06015 0.031881 0.004769

Stock 10 0.021087 0.00463 0.002501 -0.02607 -0.07441 -0.05485 -0.07283 -0.0825 -0.06544 -0.07141 -0.07558 -0.05871 -0.03586 -0.04339 -0.05155 0.041709 0.06018 0.095386 0.083903 0.098832 0.097127 0.098139 0.119416 0.121381 0.136981 0.154409 0.164972 0.163651 0.117302 0.124984 0.137797

Cumulative Average Residual Stati CARt Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

-0.00561 -0.00581 -0.00207 0.001295 0.009559 0.010538 0.002541 0.006572 -0.00059 -0.00582 -0.00535 -0.00542 0.002871 0.001342 0.013297 0.117389 0.135315 0.134901 0.136396 0.130348 0.127456 0.13112 0.135962 0.140404 0.141102 0.131321 0.127526 0.120643 0.117564 0.118159 0.106684 Averages:

ulative Average Residual Statistics σt Normal Deviate 0.024316 -0.23056 0.042554 -0.13642 0.035722 -0.05794 0.04975 0.026037 0.061158 0.1563 0.074937 0.140622 0.082666 0.030732 0.086478 0.076 0.08815 -0.00666 0.088089 -0.06604 0.078581 -0.06806 0.081152 -0.06679 0.088668 0.032379 0.084508 0.015881 0.095049 0.139899 0.110848 1.059011 0.113407 1.19318 0.103166 1.307613 0.103878 1.313047 0.101313 1.286589 0.09861 1.292524 0.094449 1.388253 0.098923 1.374417 0.090312 1.55465 0.096623 1.460336 0.098023 1.339697 0.109966 1.159683 0.11648 1.03574 0.121736 0.965728 0.123696 0.955235 0.130682 0.81636 0.08948 0.628627

Normally Distributed Random Variables with a Known Event Disturbance Mean return for stocks is zero σ= 0.02 Disturbances: Day 3 = Day 1 2 3 4 5 6 7

Stock 1 0.00318 -0.00288 0.013999 0.04621 0.035914 -0.04138 -0.03061

Stock 2 -0.0026 -0.00708 -0.00835 0.092033 -0.00261 -0.0159 0.031943

Stock 3 -0.00347 0.021229 0.005475 0.051475 0.014795 -0.04062 -0.00187

0 Day 4= Stock 4 -0.00122 0.009362 0.014003 0.023577 0.03354 0.022924 -0.0097

Stock 5 -0.00875 -0.02235 0.008172 0.028341 0.033865 0.014363 0.00519

0.05 Day 5 = Stock 6 0.024333 0.018954 0.010376 0.075461 0.007626 0.008188 0.003875

Stock 7 0.028207 0.013334 -0.01584 0.014567 -0.01289 -0.00821 0.006989

Normally Distributed Random Variables with a Known Event Disturbance Mean return for stocks is zero σ= 0.01 Disturbances: Day 3 = 0 Day 4= 0.05 Day 5 = Day -3 -2 -1 0 1 2 3

Stock 1 -0.00378 0.01016 -0.0107 0.056038 0.027321 -0.0079 0.013774

Stock 2 0.018743 -0.01003 -0.00437 0.049864 0.004862 0.015381 -0.00935

Stock 3 -0.00634 -0.0116 -0.00469 0.053117 0.032417 0.015806 0.003762

Stock 4 0.019228 0.009446 -0.00562 0.038451 0.038128 -0.00549 -0.00397

Stock 5 -0.00426 -0.00836 0.001884 0.073299 0.021311 0.016388 -0.00168

Stock 6 -0.01817 -0.00897 -0.01665 0.058178 0.014303 0.009416 -0.00976

Stock 7 0.008591 0.005675 -0.00129 0.055564 0.034802 0.002636 0.005142

Normally Distributed Random Variables with a Known Event Disturbance Mean return for stocks is zero σ= 0.02 Disturbances: Day 3 = 0 Day 4= 0.05 Day 5 = Day -3 -2 -1 0 1 2 3

Stock 1 0.043863 0.03598 -0.01593 0.071611 0.00084 -0.00275 -0.02504

Stock 2 0.043183 -0.02902 0.011724 0.032228 0.038864 0.010675 -0.00957

Stock 3 0.018956 0.047024 -0.00297 0.050559 0.007568 -0.01687 -0.0027

Stock 4 -0.01272 0.009618 0.032047 0.027148 0.004719 -0.00832 -0.03424

Stock 5 0.003188 -0.00858 0.02854 0.031698 0.04624 -0.01089 -0.01744

Stock 6 0.008026 0.003285 -0.00151 0.032934 0.010986 -0.01277 -0.00145

Stock 7 -0.01812 0.004673 -0.00846 0.074865 0.002 0.038231 -0.03445

0.02 Stock 8 0.032912 -0.0391 -0.04022 0.087915 0.013571 0.019581 0.008317

Stock 9 0.022793 0.003159 -0.03256 0.061385 0.004919 0.009966 0.027909

0.02 Stock 8 -0.00556 -0.00263 -0.00795 0.053724 0.012471 -0.01348 0.009899

Stock 9 -0.00883 0.010073 0.010509 0.037404 0.015684 0.002745 0.01582

0.02 Stock 8 -0.04478 0.029908 0.012117 0.045448 0.036629 0.01076 0.001693

Stock 9 -0.02437 0.003578 -0.00533 0.054037 0.022253 -0.01551 0.01658

Average Residuals ARt σt Normal Deviate

Day 1 2 3 4 5 6 7

Cumulative Average Residuals for Ind Stock 1 Stock 2 Stock 3 0.00318 -0.0026 -0.00347 0.000295 -0.00968 0.017757 0.014294 -0.01804 0.023232 0.060504 0.073996 0.074707 0.096418 0.071385 0.089502 0.055042 0.055483 0.048887 0.024435 0.087426 0.047015

-3 -2 -1 0 1 2 3

Average Residuals ARt σt Normal Deviate 0.000140959 0.012061 0.011687539 -0.00071146 0.008908 -0.07986364 -0.00213311 0.010028 -0.21270907 0.051526657 0.01094 4.71002395 0.022382602 0.010769 2.078396361 0.001420697 0.013189 0.107718447 0.002813911 0.00895 0.314410681

Day 1 2 3 4 5 6 7

Cumulative Average Residuals for Ind Stock 1 Stock 2 Stock 3 -0.00378 0.018743 -0.00634 0.006384 0.008718 -0.01794 -0.00431 0.00435 -0.02262 0.051724 0.054215 0.030494 0.079045 0.059077 0.062911 0.071148 0.074458 0.078717 0.084922 0.065105 0.082479

-3 -2 -1 0 1 2 3

Average Residuals ARt σt Normal Deviate -0.00081726 0.029721 -0.02749757 0.010619319 0.022164 0.479130267 0.004409405 0.016103 0.273825859 0.046764675 0.016635 2.811231325 0.021620524 0.018684 1.15719514 -0.00154511 0.017046 -0.0906435 -0.01316934 0.016876 -0.78033693

Day 1 2 3 4 5 6 7

Cumulative Average Residuals for Ind Stock 1 Stock 2 Stock 3 0.043863 0.043183 0.018956 0.079842 0.014159 0.06598 0.063915 0.025884 0.063008 0.135526 0.058112 0.113566 0.136367 0.096976 0.121134 0.133619 0.107651 0.104266 0.108576 0.098082 0.101562

Stock 10 -0.0241 0.014394 0.02553 0.094826 0.024658 0.028506 -0.00039

0.007128961 0.000901084 -0.00194264 0.057579064 0.015339231 -0.0002572 0.004165119

0.018767 0.019355 0.021627 0.029546 0.016583 0.025332 0.017702

0.379865237 0.046555079 -0.08982447 1.948810723 0.924997307 -0.01015315 0.235286034

Averages: 0.011844803 0.021273 0.490790966

Stock 10 Day 0.001769 -0.00088 0.017535 0.039626 0.022527 -0.02129 0.004503

Stock 10 Day -0.02541 0.009727 -0.00614 0.047118 0.046106 -0.00802 -0.02507

verage Residuals for Individual Stocks Stock 4 Stock 5 Stock 6 -0.00122 -0.00875 0.024333 0.008141 -0.0311 0.043288 0.022145 -0.02293 0.053663 0.045722 0.005415 0.129125 0.079262 0.03928 0.136751 0.102186 0.053643 0.144939 0.092485 0.058833 0.148813

Stock 7 0.028207 0.041541 0.025699 0.040266 0.027381 0.019175 0.026164

Stock 8 0.032912 -0.00619 -0.04641 0.041501 0.055072 0.074652 0.082969

Stock 9 0.022793 0.025953 -0.00661 0.054775 0.059694 0.06966 0.097569

Stock 10 -0.0241 -0.0097 0.015828 0.110655 0.135313 0.163819 0.163427

Cumulative Average Residual Stati CARt Day 1 2 3 4 5 6 7

0.007129 0.00803 0.006087 0.063666 0.079006 0.078749 0.082914 Averages:

verage Residuals for Individual Stocks Stock 4 Stock 5 Stock 6 0.019228 -0.00426 -0.01817 0.028675 -0.01262 -0.02714 0.023054 -0.01074 -0.04379 0.061505 0.062559 0.014389 0.099633 0.08387 0.028692 0.094138 0.100258 0.038108 0.090171 0.098574 0.028352

Stock 7 0.008591 0.014266 0.012976 0.06854 0.103342 0.105978 0.11112

Stock 8 -0.00556 -0.00819 -0.01613 0.03759 0.050061 0.036576 0.046475

Stock 9 -0.00883 0.001247 0.011756 0.04916 0.064844 0.067589 0.083409

Stock 10 0.001769 0.000893 0.018428 0.058055 0.080582 0.059293 0.063797

Cumulative Average Residual Statis Day CARt 1 0.000141 2 -0.00057 3 -0.0027 4 0.048823 5 0.071206 6 0.072626 7 0.07544

verage Residuals for Individual Stocks Stock 4 Stock 5 Stock 6 -0.01272 0.003188 0.008026 -0.0031 -0.00539 0.011311 0.028948 0.023152 0.009802 0.056096 0.05485 0.042736 0.060815 0.10109 0.053722 0.052496 0.090199 0.040957 0.018261 0.072762 0.039505

Stock 7 -0.01812 -0.01345 -0.02191 0.052957 0.054957 0.093188 0.058734

Stock 8 -0.04478 -0.01487 -0.00275 0.042698 0.079327 0.090087 0.09178

Stock 9 -0.02437 -0.02079 -0.02612 0.027916 0.050169 0.034662 0.051242

Stock 10 -0.02541 -0.01568 -0.02181 0.025304 0.07141 0.063389 0.038318

Cumulative Average Residual Statis Day CARt 1 -0.00082 2 0.009802 3 0.014211 4 0.060976 5 0.082597 6 0.081052 7 0.067882

ulative Average Residual Statistics σt Normal Deviate 0.018767 0.379865 0.024044 0.333968 0.029257 0.20807 0.035846 1.776106 0.036766 2.148889 0.045266 1.739684 0.046739 1.773966 0.033812 1.194364

ulative Average Residual Statistics σt Normal Deviate 0.012061 0.011688 0.016419 -0.03475 0.020942 -0.1291 0.016696 2.924155 0.022758 3.128764 0.023747 3.058281 0.024781 3.044296

ulative Average Residual Statistics σt Normal Deviate 0.029721 -0.0275 0.035299 0.277684 0.033034 0.430207 0.03573 1.70659 0.030156 2.738962 0.031988 2.533773 0.031268 2.17096

Annual Stock Against S&P500 and Industry Returns; 1971 to 2010 Year 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Stock Return 0.10744 -0.20158 -0.52248 0.43227 -0.05039 -0.37331 0.27566 0.20091 0.23306 -0.27492 0.27318 0.43995 0.11354 0.45988 0.33915 -0.39223 0.22408 0.21501 -0.13159 0.35984 -0.05446 0.20876 -0.16123 0.67425 0.42950 0.46644 0.40817 0.35882 -0.16301 -0.20730 -0.19424 0.43350 0.21498 0.06276 0.19643 -0.29032 -0.62574 0.56938 0.40864 0.24785

S&P Return 0.146176 -0.18826 -0.24503 0.334895 0.07165 -0.13054 0.10482 0.112225 0.199279 -0.11805 0.230179 0.153153 0.03125 0.213287 0.270413 -0.05293 0.139321 0.191205 -0.04259 0.278319 0.046025 0.086759 -0.01636 0.320623 0.247062 0.257289 0.296265 0.141595 -0.0631 -0.14631 -0.21432 0.264199 0.043169 0.082376 0.11373 -0.03188 -0.3722 0.298066 0.13198 0.10493

Industry Return 0.14585 -0.17561 -0.23107 0.33108 0.08910 -0.13011 0.09815 0.11660 0.19621 -0.13030 0.23046 0.16905 0.03702 0.21460 0.26119 -0.04328 0.14231 0.21137 -0.05571 0.27623 0.05752 0.09084 -0.01437 0.32173 0.24886 0.26269 0.31905 0.12999 -0.07217 -0.16259 -0.19132 0.24827 0.04769 0.07588 0.10720 -0.02119 -0.37522 0.29622 0.11869 0.09907



SS 2 3.438999416 37 0.548033658 39 3.987033074

Coefficients Standard Error -0.021423527 0.021616345 3.006318797 1.856435223 -1.293186386 1.863567292



SS 1 3.431866985 38 0.555166089 39 3.987033074

Coefficients Standard Error -0.023684743 0.021223049 1.720471469 0.112254024

SUMMARY OUTPUT Regression Statistics Multiple R 0.923473656 R Square 0.852803593

Adjusted R Square

0.848930003

Standard Error

0.124274415

Observations

40

ANOVA df Regression

1

Residual Total


SS 3.40015613

38 0.586876945 39 3.987033074 Coefficients Standard Error -0.025774435 0.021901833 1.719083457 0.115858862



SS 1 1.146283555 38 0.004264964 39 1.150548519

Coefficients Standard Error 0.001748561 0.001860176 0.994324825 0.009838936

Regression on Full Data Set

MS F Significance F 1.7195 116.0905 1.1374E-16

t Stat P-value Lower 95% Upper 95%Lower 95.0% Upper 95.0% -0.99108 0.328084 -0.0652224 0.022375 -0.06522 0.022375 1.619404 0.113854 -0.75517623 6.767814 -0.75518 6.767814 -0.69393 0.49206 -5.06913236 2.48276 -5.06913 2.48276

Regression on the S&P500 Return Only


t Stat P-value Lower 95% Upper 95%Lower 95.0% Upper 95.0% -1.11599 0.271433 -0.06664856 0.019279 -0.06665 0.019279 15.32659 7.44E-18 1.49322508 1.947718 1.493225 1.947718

Regression on Industry Return Only

0.066121

MS

F

3.400156 220.1585


Table 5: SSE and r-Square Values t Stat P-value Lower 95% Upper 95%Lower 95.0% Upper 95.0% -1.17682 0.246588 -0.07011238 0.018564 -0.07011 0.018564 14.83774 2.15E-17 1.48453946 1.953627 1.484539 1.953627

Industry Returns Against S&P 500 Returns

MS F Significance F 1.146284 10213.16 8.3398E-48 0.000112

t Stat P-value Lower 95% Upper 95%Lower 95.0% Upper 95.0% 0.939998 0.353156 -0.00201717 0.005514 -0.00202 0.005514 101.0602 8.34E-48 0.97440694 1.014243 0.974407 1.014243

Table 2 Table 3 0.54803

Table 4

0.555166

0.58688 0.86255 0.86076 0.852804

SSE and r-Square Values =

0.012847 0.012847

=

0.066186 0.066186

Annual Stock Against S&P500 and Industry Returns; 1971 to 2010 b0 =

Year 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

0.03 b1 = Stock Return 0.10744 -0.20158 -0.52248 0.43227 -0.05039 -0.37331 0.27566 0.20091 0.23306 -0.27492 0.27318 0.43995 0.11354 0.45988 0.33915 -0.39223 0.22408 0.21501 -0.13159 0.35984 -0.05446 0.20876 -0.16123 0.67425 0.42950 0.46644 0.40817 0.35882 -0.16301 -0.20730 -0.19424 0.43350 0.21498 0.06276 0.19643 -0.29032 -0.62574 0.56938 0.40864 0.24785

S&P Return 0.146176 -0.18826 -0.24503 0.334895 0.07165 -0.13054 0.10482 0.112225 0.199279 -0.11805 0.230179 0.153153 0.03125 0.213287 0.270413 -0.05293 0.139321 0.191205 -0.04259 0.278319 0.046025 0.086759 -0.01636 0.320623 0.247062 0.257289 0.296265 0.141595 -0.0631 -0.14631 -0.21432 0.264199 0.043169 0.082376 0.11373 -0.03188 -0.3722 0.298066 0.13198 0.10493

1.1 b2 = Industry Return 0.14585 -0.17561 -0.23107 0.33108 0.08910 -0.13011 0.09815 0.11660 0.19621 -0.13030 0.23046 0.16905 0.03702 0.21460 0.26119 -0.04328 0.14231 0.21137 -0.05571 0.27623 0.05752 0.09084 -0.01437 0.32173 0.24886 0.26269 0.31905 0.12999 -0.07217 -0.16259 -0.19132 0.24827 0.04769 0.07588 0.10720 -0.02119 -0.37522 0.29622 0.11869 0.09907

0.5 Stock Random Industry Random

0.1 0.01



SS 2 3.438999416 37 0.548033658 39 3.987033074

Coefficients Standard Error -0.021423527 0.021616345 3.006318797 1.856435223 -1.293186386 1.863567292



SS 2 1.48769667 17 0.267950731 19 1.755647401

Coefficients Standard Error -0.060652437 0.03358933 0.835775754 2.977698112 0.867432923 3.00575536

SUMMARY OUTPUT Regression Statistics

Multiple R R Square Adjusted R Square Standard Error Observations

0.947946432 0.898602438 0.886673313 0.114342085 20


SS 2 1.96970512 17 0.222259911 19 2.191965031

Coefficients Standard Error 0.010121213 0.02797532 3.853114475 2.329593717 -2.10816525 2.32890988



SS 1 1.146283555 38 0.004264964 39 1.150548519

Coefficients Standard Error 0.001748561 0.001860176 0.994324825 0.009838936


RESIDUAL OUTPUT Observation 1 2 3 4 5 6 7 8 9 10 11 12

Predicted Y 0.147095172 -0.185443165 -0.241892575 0.334743231 0.07299174 -0.128050103 0.105973634 0.113337116 0.19989625 -0.115626625 0.230621283 0.154032544

Residuals -0.001246474 0.009831554 0.010819001 -0.003659931 0.016111605 -0.002058562 -0.007820651 0.003262435 -0.003691056 -0.014670343 -0.000158338 0.015014626

13 14 15 16 17 18 19 20 21 22 23 24

0.032821212 0.213824835 0.270626984 -0.050881108 0.140279246 0.191868764 -0.040601715 0.278487896 0.047512165 0.088014916 -0.014522553 0.320552289

0.004198292 0.000772743 -0.009437844 0.007597783 0.002026339 0.019505077 -0.01511179 -0.002256866 0.010003142 0.002821106 0.000156001 0.001174978

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

0.24740871 0.25757743 0.29633236 0.142540313 -0.060997012 -0.143734063 -0.211355303 0.26444815 0.044672784 0.083657206 0.114833153 -0.029948964 -0.368343125 0.298123021 0.132979474 0.106084068

0.001446474 0.005110541 0.022714849 -0.012553393 -0.011168861 -0.018855007 0.020034081 -0.016173478 0.003012539 -0.007781895 -0.00763726 0.008757749 -0.006879428 -0.001907871 -0.014286527 -0.007015343

1.0420015

Regression on Full Data Set


t Stat P-value Lower 95% Upper 95%Lower 95.0% Upper 95.0% -0.99108 0.328084 -0.0652224 0.022375 -0.06522 0.022375 1.619404 0.113854 -0.75517623 6.767814 -0.75518 6.767814 -0.69393 0.49206 -5.06913236 2.48276 -5.06913 2.48276

Regression on 1971 to 1990


t Stat -1.80571 0.280678 0.288591

P-value Lower 95% Upper 95%Lower 95.0% Upper 95.0% 0.088703 -0.13151973 0.010215 -0.13152 0.010215 0.782344 -5.44661805 7.11817 -5.44662 7.11817 0.776384 -5.4741565 7.209022 -5.47416 7.209022

Regression on 1991 to 2010


t Stat 0.361791 1.653986 -0.90522

P-value Lower 95% Upper 95%Lower 95.0% Upper 95.0% 0.721966 -0.04890155 0.069144 -0.0489 0.069144 0.116475 -1.0618986 8.768128 -1.0619 8.768128 0.378002 -7.02173555 2.805405 -7.02174 2.805405

Industry Returns Against S&P 500 Returns


t Stat P-value Lower 95% Upper 95%Lower 95.0% Upper 95.0% 0.939998 0.353156 -0.00201717 0.005514 -0.00202 0.005514 101.0602 8.34E-48 0.97440694 1.014243 0.974407 1.014243

S&P ReturnStock Return 0.146176 0.10744 -0.18826 -0.20158 -0.24503 -0.52248 0.334895 0.43227 0.07165 -0.05039 -0.13054 -0.37331 0.10482 0.27566 0.112225 0.20091 0.199279 0.23306 -0.11805 -0.27492 0.230179 0.27318 0.153153 0.43995


Stock Returns versus S&P and Residuals

ANOVA df Regression

SS 2 3.438999


0.03125 0.213287 0.270413 -0.05293 0.139321 0.191205 -0.04259 0.278319 0.046025 0.086759 -0.01636 0.320623

0.11354 0.45988 0.33915 -0.39223 0.22408 0.21501 -0.13159 0.35984 -0.05446 0.20876 -0.16123 0.67425

Residual Total

37 0.548034 0.014812 39 3.987033

0.247062 0.257289 0.296265 0.141595 -0.0631 -0.14631 -0.21432 0.264199 0.043169 0.082376 0.11373 -0.03188 -0.3722 0.298066 0.13198 0.104931

0.42950 0.46644 0.40817 0.35882 -0.16301 -0.20730 -0.19424 0.43350 0.21498 0.06276 0.19643 -0.29032 -0.62574 0.56938 0.40864 0.24785

b * 0 = (b 0 + b 2 γ 0 ) and b * 1 = (b 1 + b 2 γ 1 )

Coefficients Standard Error t Stat P-value Lower 95% Intercept -0.02368 0.021369 -1.10835 0.274863 -0.06698 X Variable 1 -1.29319 1.863567 -0.69393 0.49206 -5.06913 X Variable 2 1.720471 0.113028 15.22168 1.64E-17 1.491456

b(0) = b(1) =

-0.02368 1.720471

SUMMARY OUTPUT Regression Statistics Multiple R 0.92777 R Square 0.860757 Adjusted R Square 0.857093 Standard Error0.12087 Observations 40

Stock Returns versus S&P Returns


SS MS F Significance F 1 3.431867 3.431867 234.9044 7.44E-18 38 0.555166 0.01461 39 3.987033

Coefficients Standard Error t Stat P-value Lower 95% Intercept -0.02368 0.021223 -1.11599 0.271433 -0.06665 X Variable 1 1.720471 0.112254 15.32659 7.44E-18 1.493225

s S&P and Residuals

Significance F

Upper 95%Lower 95.0% Upper 95.0% 0.019614 -0.06698 0.019614 2.48276 -5.06913 2.48276 1.949487 1.491456 1.949487

s S&P Returns

Significance F

Upper 95%Lower 95.0% Upper 95.0% 0.019279 -0.06665 0.019279 1.947718 1.493225 1.947718

Annual Stock Against S&P500 and Industry Returns; 1971 to 2010 b0 =

DATE 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

0.03 b1 = Stock Return 0.30335 -0.16693 -0.35542 0.56112 0.09266 -0.18279 0.08344 0.11417 0.19288 -0.20901 0.46529 0.26144 0.08462 0.39854 0.42666 -0.23613 0.08345 0.46660 -0.15002 0.46888 -0.08639 0.05387 -0.17635 0.55110 0.58767 0.49014 0.41706 0.16288 -0.27923 -0.26047 -0.42351 0.43990 -0.04446 0.07893 0.09529 -0.03719 -0.35815 0.49065 0.29852 0.17781

S&P Return 0.146176 -0.18826 -0.24503 0.334895 0.07165 -0.13054 0.10482 0.112225 0.199279 -0.11805 0.230179 0.153153 0.03125 0.213287 0.270413 -0.05293 0.139321 0.191205 -0.04259 0.278319 0.046025 0.086759 -0.01636 0.320623 0.247062 0.257289 0.296265 0.141595 -0.0631 -0.14631 -0.21432 0.264199 0.043169 0.082376 0.11373 -0.03188 -0.3722 0.298066 0.13198 0.10493

1.1 b2 = Industry Return 0.15529 -0.20214 -0.23339 0.33927 0.04997 -0.11245 0.11341 0.10090 0.21554 -0.12420 0.23265 0.15951 0.03841 0.21825 0.26306 -0.05486 0.13717 0.19386 -0.04624 0.30287 0.03572 0.08153 -0.02592 0.31768 0.25854 0.26550 0.29353 0.14462 -0.05263 -0.13519 -0.21259 0.26938 0.04913 0.07842 0.11230 -0.00878 -0.37721 0.29601 0.13849 0.09842

0.5 Stock Random Industry Random

0.1 0.01



SS MS 2 3.207408 1.603704 37 0.37171 0.010046 39 3.579118

Coefficients Standard Error t Stat -0.024556047 0.018054 -1.36017 1.270436474 1.738658 0.730699 0.38513495 1.702774 0.226181

SUMMARY OUTPUT Regression Statistics Multiple R 1 R Square 1 Adjusted R Square 1 Standard Error 7.39726E-17 Observations 20 ANOVA df Regression Residual Total


SS MS 2 1.261398 0.630699 17 9.3E-32 5.47E-33 19 1.261398

Coefficients Standard Error t Stat -0.03 1.88E-17 -1.6E+15 1.1 2.94E-16 3.74E+15 0.5 2.69E-16 1.86E+15

-2.11133

F Significance F 159.6325 6.37E-19

P-value Lower 95%Upper 95%Lower 95.0% Upper 95.0% 0.182005 -0.06114 0.012024 -0.06114 0.012024 0.469565 -2.25242 4.793293 -2.25242 4.793293 0.822306 -3.06501 3.835284 -3.06501 3.835284

F Significance F 1.15E+32 2.4E-265

P-value Lower 95%Upper 95%Lower 95.0% Upper 95.0% 1.9E-249 -0.03 -0.03 -0.03 -0.03 1E-255 1.1 1.1 1.1 1.1 1.5E-250 0.5 0.5 0.5 0.5

WN Weekly Stock Prices, 2010 and Heteroskedasticity Closing Week Ending Price 1/4/2010 0.98 1/11/2010 1.35 1/19/2010 1.24 1/25/2010 1.2 2/1/2010 1.16 2/8/2010 1.24 2/16/2010 1.38 2/22/2010 1.29 3/1/2010 1.97 3/8/2010 2.3 3/15/2010 1.82 3/22/2010 2.34 3/29/2010 2.16 4/5/2010 3.54 4/12/2010 4.55 4/19/2010 5.47 4/26/2010 5.43 5/3/2010 4.8 5/10/2010 5.45 5/17/2010 4.8 5/24/2010 4.65 6/1/2010 5.28 6/7/2010 4.86 6/14/2010 4.77 6/21/2010 3.83 6/28/2010 3.37 7/6/2010 3.22 7/12/2010 3.2 7/19/2010 3.51 7/26/2010 3.43 8/2/2010 3.36 8/9/2010 3.17 8/16/2010 3.09 8/23/2010 3.52 8/30/2010 3.8 9/7/2010 3.78 9/13/2010 4 9/20/2010 4.07 9/27/2010 4.16 10/4/2010 5.14 10/11/2010 5.21 10/18/2010 5.25 10/25/2010 5.16

t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

SUMMARY OUTPUT Regression Statistics Multiple R 0.79215114 R Square 0.62750343 Adjusted R Square 0.6200535 Standard Error 1.57507506 Observations 52 ANOVA df

SS MS 1 208.9615 208.9615 50 124.0431 2.480861 51 333.0046

F 84.2294235

CoefficientsStandard Error t Stat 0.81047511 0.443225 1.828587 0.13356698 0.014553 9.177659

P-value 0.07342955 2.6589E-12



RESIDUAL OUTPUT Observation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Predicted Y 0.94404209 1.07760907 1.21117604 1.34474302 1.47831 1.61187697 1.74544395 1.87901093 2.0125779 2.14614488 2.27971186 2.41327884 2.54684581 2.68041279 2.81397977 2.94754674 3.08111372 3.2146807 3.34824767

Residuals 0.035958 0.272391 0.028824 -0.14474 -0.31831 -0.37188 -0.36544 -0.58901 -0.04258 0.153855 -0.45971 -0.07328 -0.38685 0.859587 1.73602 2.522453 2.348886 1.585319 2.101752

eT 0.03595791 eeT 0.00129297 0.00979461 0.00103645 -0.00520466 -0.01144576 -0.01337192 -0.0131406 -0.0211796 -0.00153101 0.00553231 -0.01653028 -0.00263495 -0.01391017 0.03090896 0.06242366 0.09070215 0.08446104

11/1/2010 5.55 11/8/2010 5.28 11/15/2010 7.24 11/22/2010 7.83 11/29/2010 9.18 12/6/2010 10.3 12/13/2010 11.05 12/20/2010 11.77 12/27/2010 9.7 Date Adj Close

44 45 46 47 48 49 50 51 52 T

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

3.48181465 3.61538163 3.7489486 3.88251558 4.01608256 4.14964953 4.28321651 4.41678349 4.55035047 4.68391744 4.81748442 4.9510514 5.08461837 5.21818535 5.35175233 5.4853193 5.61888628 5.75245326 5.88602023 6.01958721 6.15315419 6.28672116 6.42028814 6.55385512 6.6874221 6.82098907 6.95455605 7.08812303 7.22169 7.35525698 7.48882396 7.62239093 7.75595791

1.318185 0.05700477 1.034618 0.07557462 1.531051 0.04739919 0.977484 0.03720271 0.753917 0.05505341 -0.31965 0.0351483 -0.91322 0.984245 0.0271093 -1.19678 -0.01149393 -1.35035 -0.03283736 -1.17392 -0.04303383 -1.38748 -0.04855578 -1.59105 -0.04221162 -1.91462 -0.04989104 -2.12819 -0.05721088 -1.83175 -0.06884568 -1.68532 -0.0765251 -1.83889 -0.06586599 -1.75245 -0.06060056 -1.81602 -0.06612251 -1.85959 -0.06301456 -1.01315 -0.06530029 -1.07672 -0.06686687 -1.17029 -0.03643091 -1.39386 -0.03871664 -1.13742 -0.04208112 -1.54099 -0.05012012 0.285444 -0.04089932 0.741877 -0.05541075 1.95831 0.01026397 2.944743 0.02667635 3.561176 0.07041673 4.147609 0.1058868 1.944042 3.435193 0.12805245

0.14913935 0.06990369

Goldfeldt-Quant Test Closing Price

t 0.98 1.35 1.24 1.2 1.16 1.24

1 2 3 4 5 6

Closing Price t 5.21 5.25 5.16 5.55 5.28 7.24

41 42 43 44 45 46

SUMMARY OUTPUT Regression Statistics Multiple R 0.844356 R Square 0.712938 Adjusted R Square 0.684232

1.38 1.29 1.97 2.3 1.82 2.34

7 8 9 10 11 12

7.83 9.18 10.3 11.05 11.77 9.7

47 48 49 50 51 52

Standard Error 0.260007 Observations 12 ANOVA df Regression Residual Total

1 10 11

SS 1.67898619 0.67603881 2.355025

CoefficientsStandard Error Intercept 0.818182 0.16002353 X Variable 1 0.108357 0.02174292

RESIDUAL OUTPUT ObservationPredicted Y 1 0.926538 2 1.034895 3 1.143252 4 1.251608 5 1.359965 6 1.468322 7 1.576678 8 1.685035 9 1.793392 10 1.901748 11 2.010105 12 2.118462

df2\df1 3 4 5 6 7 8 9

1

2

Residuals 0.05346154 0.3151049 0.09674825 -0.05160839 -0.19996503 -0.22832168 -0.19667832 -0.39503497 0.17660839 0.39825175 -0.1901049 0.22153846

3

10.13

9.55

9.28

7.71

6.94

6.59

6.61

5.79

5.41

5.99

5.14

4.76

5.59

4.74

4.35

5.32

4.46

4.07

5.12

4.26

3.86

10 11 12 13 14 15 16 17 18 19 20 22 24 26 28 30 35 40 45 50 60 70 80 100 200 500 1000 >1000 df2/df1

4.96

4.1

3.71

4.84

3.98

3.59

4.75

3.89

3.49

4.67

3.81

3.41

4.6

3.74

3.34

4.54

3.68

3.29

4.49

3.63

3.24

4.45

3.59

3.2

4.41

3.55

3.16

4.38

3.52

3.13

4.35

3.49

3.1

4.3

3.44

3.05

4.26

3.4

3.01

4.23

3.37

2.98

4.2

3.34

2.95

4.17

3.32

2.92

4.12

3.27

2.87

4.08

3.23

2.84

4.06

3.2

2.81

4.03

3.18

2.79

4

3.15

2.76

3.98

3.13

2.74

3.96

3.11

2.72

3.94

3.09

2.7

3.89

3.04

2.65

3.86

3.01

2.62

3.85

3

2.61

1.04

1

3

2

2.61

3

(eeT)-1

7.2917E+18 9.6233E+17 -1.534E+18 -1.55E+18 5.7858E+17

1.5981E+16 -2.284E+17 -1.175E+17 2.706E+18 -9.598E+17 3.9911E+17 3.0315E+18 1.5829E+17 6.2408E+16 7.0225E+16 -9.54E+16 6.4085E+15 1.326E+17 -5.86E+16 -2.999E+17 -2.331E+17 -7.859E+16 -8.212E+16 4.2892E+16 -1.134E+17 -1.571E+17 1.5158E+16 -9.227E+16 -1.394E+17 -7.914E+15 4.8806E+16 5.3527E+16 3.9165E+15 -4.041E+16 -1.654E+17 -6.46E+16 -1.531E+17 2.1675E+17 7.4251E+15 1.8084E+17 3.5306E+16 1.6466E+17 -1.41E+15 -2.106E+17 -6.706E+16 1.2311E+18 -2.01E+17 -3.986E+16 1.1944E+17 -6.092E+15 1.6638E+15 -8.554E+16


Lower 95% -0.079768262 0.10433543

Upper 95% Lower 95.0% Upper 95.0% 1.700718488 -0.07976826 1.700718488 0.162798523 0.10433543 0.162798523

0.272390933

0.028823956

0.009794609 0.07419682 0.007851384 -0.039426686 -0.086704757 -0.101295916 -0.099543619 -0.160441236 -0.011597835 0.041908739 -0.125221342 -0.01996049 -0.105373292 0.234143762 0.472876171 0.687093397 0.639815326

0.001036449 0.007851384 0.00083082 -0.004172066 -0.009174953 -0.010718966 -0.01053354 -0.016977625 -0.001227264 0.004434713 -0.013250715 -0.002112186 -0.011150427 0.024776704 0.050038971 0.072707082 0.067704195

-0.14474302 -0.318309997 -0.371876974 -0.365443951 -0.589010928 -0.00520466 -0.03942669 -0.00417207 0.020950542 0.046073151 0.053826597 0.052895461 0.085255221 0.006162855 -0.02226945 0.066540083 0.0106066 0.055993231 -0.12441925 -0.25127681 -0.3651075 -0.3399849

-0.011445762 -0.086704757 -0.009174953 0.046073151 0.101321254 0.118372159 0.116324463 0.187488067 0.013552973 -0.048973622 0.146330881 0.023325386 0.12313689 -0.273615203 -0.552592596 -0.80292209 -0.747673986

-0.013371919 -0.101295916 -0.010718966 0.053826597 0.118372159 0.138292484 0.135900191 0.219039602 0.015833742 -0.057215176 0.170956255 0.027250712 0.14385905 -0.319660691 -0.645585952 -0.938042285 -0.873496723

-0.013140601 -0.099543619 -0.01053354 0.052895461 0.116324463 0.135900191 0.133549281 0.215250481 0.015559838 -0.056225422 0.167998918 0.026779307 0.141370462 -0.314130947 -0.634418094 -0.921815285 -0.858386283

-0.021179602 -0.160441236 -0.016977625 0.085255221 0.187488067 0.219039602 0.215250481 0.346933873 0.025078851 -0.090622346 0.270775308 0.043162035 0.227856411 -0.506306261 -1.022534889 -1.485752534 -1.383519688

0.431826604 0.572498277 0.359061737 0.281820664 0.417044518 0.266257893 0.205360276 -0.087069635 -0.248751898 -0.325992971 -0.367823223 -0.319764468 -0.377938176 -0.433387974 -0.521524685 -0.579698393 -0.498952726 -0.459065698 -0.50089595 -0.477352378 -0.494667446 -0.506534696 -0.275974015 -0.293289083 -0.318775879 -0.379673496 -0.309823466 -0.419751451 0.077752344 0.202080561 0.533425888 0.802121299 0.970032066

1.129771104 0.529539439

-0.589543746 -0.781593296 -0.490202779 -0.38475075 -0.569362761 -0.363503948 -0.280364537 0.118870302 0.339604193 0.445056223 0.502164245 0.436552866 0.515973508 0.591675379 0.712002487 0.791423129 0.681186513 0.626731443 0.683839466 0.651697015 0.67533611 0.691537665 0.376768714 0.400407809 0.435203213 0.518342624 0.422981087 0.573058354 -0.106150033 -0.275886965 -0.728250397 -1.095082125 -1.324319372 0.119550502 -0.60033746 -1.320225431 -1.54240031 0.056034984 -0.28138652 -0.618808033 -0.72294449

0.045695174 0.060580817 0.037995317 0.029821795 0.044130959 0.028174968 0.021730883 -0.009213564 -0.026322513 -0.034496035 -0.038922443 -0.033836945 -0.03999279 -0.045860396 -0.055186876 -0.061342721 -0.052798349 -0.04857757 -0.053003978 -0.050512636 -0.052344888 -0.05360066 -0.029203112 -0.031035364 -0.033732334 -0.040176419 -0.032785005 -0.044417402 0.008227624 0.021383829 0.056446242 0.084879144 0.102647183

-0.2294639 -0.30421398 -0.19079813 -0.14975379 -0.221609 -0.14148405 -0.10912429 0.046267039 0.132181716 0.173226057 0.195453805 0.169916356 0.200828686 0.230293585 0.277127647 0.308039976 0.265133365 0.243938207 0.266165955 0.253655378 0.262856254 0.26916227 0.146646997 0.155847874 0.169391041 0.2017508 0.16463391 0.223047413 -0.04131602 -0.10738151 -0.2834517 -0.426231 -0.51545538

-0.504622983 -0.669008778 -0.419591575 -0.329329372 -0.487348966 -0.311143063 -0.239979459 0.101747643 0.290685945 0.380948149 0.429830053 0.373669658 0.441650162 0.506447566 0.609442169 0.677422673 0.583065078 0.536453983 0.585335887 0.557823392 0.578057396 0.5919252 0.322497107 0.342731111 0.372514415 0.443678019 0.362052824 0.490512228 -0.090859663 -0.236146858 -0.62334965 -0.937341143 -1.133557937

-0.57934535 -0.768072675 -0.481722863 -0.378095026 -0.559513472 -0.357215768 -0.275514569 0.116813989 0.33372945 0.437357287 0.493477409 0.429001028 0.507047788 0.581440109 0.699685703 0.777732463 0.669402808 0.615889745 0.672009868 0.640423442 0.66365361 0.679574898 0.370251069 0.393481237 0.427674722 0.509375922 0.415664025 0.563145135 -0.104313765 -0.271114453 -0.715652543 -1.076138525 -1.301410244 -1.515718645 -0.710438423

-0.933770394 -1.237955088 -0.776425576 -0.609401528 -0.901806004 -0.575749005 -0.444065612 0.188277069 0.537894505 0.704918553 0.795371181 0.691450202 0.817243485 0.937146659 1.127731145 1.253524428 1.078922138 0.992671487 1.083124114 1.032214119 1.069655763 1.095317189 0.596758888 0.634200532 0.689312504 0.820995897 0.669954044 0.907659403 -0.168129607 -0.436973645 -1.153465989 -1.734485819 -2.097571606 -2.442987066 -1.145062036

MS 1.678986189 0.067603881

F Significance F 24.83564791 0.000550542

t Stat 5.112884393 4.98353769

P-value Lower 95% 0.000455387 0.461627171 0.000550542 0.059910407

Upper 95% Lower 95.0% Upper 95.0% 1.174736465 0.461627171 1.174736465 0.15680288 0.059910407 0.15680288

R= F= RSS 0.002858136 0.099291095 0.009360224 0.002663426 0.039986015 0.052130789 0.038682362 0.156052624 0.031190524 0.158604455 0.036139871 0.04907929

14.70450845 2.82 df =

(52-28-2*1)/2 = 11

0.676038811

4

5

6

7

8

9

10

9.12

9.01

8.94

8.89

8.85

8.81

8.79

6.39

6.26

6.16

6.09

6.04

6

5.96

5.19

5.05

4.95

4.88

4.82

4.77

4.74

4.53

4.39

4.28

4.21

4.15

4.1

4.06

4.12

3.97

3.87

3.79

3.73

3.68

3.64

3.84

3.69

3.58

3.5

3.44

3.39

3.35

3.63

3.48

3.37

3.29

3.23

3.18

3.14

3.48

3.33

3.22

3.14

3.07

3.02

2.98

3.36

3.2

3.09

3.01

2.95

2.9

2.85

3.26

3.11

3

2.91

2.85

2.8

2.75

3.18

3.03

2.92

2.83

2.77

2.71

2.67

3.11

2.96

2.85

2.76

2.7

2.65

2.6

3.06

2.9

2.79

2.71

2.64

2.59

2.54

3.01

2.85

2.74

2.66

2.59

2.54

2.49

2.96

2.81

2.7

2.61

2.55

2.49

2.45

2.93

2.77

2.66

2.58

2.51

2.46

2.41

2.9

2.74

2.63

2.54

2.48

2.42

2.38

2.87

2.71

2.6

2.51

2.45

2.39

2.35

2.82

2.66

2.55

2.46

2.4

2.34

2.3

2.78

2.62

2.51

2.42

2.36

2.3

2.25

2.74

2.59

2.47

2.39

2.32

2.27

2.22

2.71

2.56

2.45

2.36

2.29

2.24

2.19

2.69

2.53

2.42

2.33

2.27

2.21

2.16

2.64

2.49

2.37

2.29

2.22

2.16

2.11

2.61

2.45

2.34

2.25

2.18

2.12

2.08

2.58

2.42

2.31

2.22

2.15

2.1

2.05

2.56

2.4

2.29

2.2

2.13

2.07

2.03

2.53

2.37

2.25

2.17

2.1

2.04

1.99

2.5

2.35

2.23

2.14

2.07

2.02

1.97

2.49

2.33

2.21

2.13

2.06

2

1.95

2.46

2.31

2.19

2.1

2.03

1.97

1.93

2.42

2.26

2.14

2.06

1.98

1.93

1.88

2.39

2.23

2.12

2.03

1.96

1.9

1.85

2.38

2.22

2.11

2.02

1.95

1.89

1.84

2.37

4

2.21

5

2.1

6

2.01

7

1.94

8

1.88

9

1.83

10

-3.31396E+17 8.58835E+18 -1.7027E+18 4.04038E+16 -2.70376E+17 -5.62334E+17 1.47101E+17 -6.43224E+16 4.7838E+17 -9.676E+16 -2.16673E+15 -2.7569E+16 -6.92202E+16 1.09759E+16 -1.49355E+16 -3.76883E+18 5.31937E+17 -1.85256E+17 1.35414E+17 -6.66191E+16 -1.05155E+17 6.9143E+16 -1.72406E+18 3.77323E+17 -1.72463E+16 5.93284E+16 1.11595E+17 -2.96965E+16 -7.66099E+16 -4.83736E+17 7.34615E+16 -1.45799E+15 -2.36287E+16 -2.52982E+16 -2.31494E+16

-1.08271E+16 2.01536E+15 2.83975E+15 -1.77958E+17 4.05344E+16 -2.8213E+16 -1.71038E+17 -1.76287E+16 -5.53653E+15 -1.84419E+15 2.43738E+15 -2.06641E+15 -4.3305E+15 6.14798E+15 2.08925E+16 9.48364E+15 -1.53126E+15 -3.37965E+15 -1.4934E+16 1.65453E+16 -9.39192E+14 2.8989E+15 1.48537E+16 1.17858E+14 5.78687E+15 -5.30067E+15 -1.82015E+15 -5.92184E+15 8.9644E+15 1.01843E+16 -3.39685E+15 1.01333E+16 -8.02099E+15 -5.58564E+14 -7.63055E+15 -5.16039E+15 -1.52811E+16 -2.25083E+15 9.6812E+15 1.19444E+16 -4.45251E+16 1.62105E+15 1.86532E+15 -6.40122E+15 -4.61375E+14 -4.20569E+14 7.30325E+15

-2.97327E+17 -2.70427E+17 -2.25449E+17 3.9615E+18 -6.45093E+17 2.68569E+17 2.0991E+18 1.53417E+17 -1.19756E+17 1.22012E+17 -1.22145E+17 8.36913E+15 1.20938E+17 -3.30887E+16 -2.92069E+17 -3.50734E+17 -7.57807E+16 -1.82148E+17 -7.63512E+16 -4.06009E+16 -1.6706E+17 2.02829E+17 3.78172E+16 -2.6437E+17 5.8327E+16 -1.90756E+16 9.47392E+16 -1.04755E+17 6.30261E+16 -1.73364E+17 -2.42926E+17 -2.19589E+17 2.46587E+17 8.60434E+16 1.58221E+17 -3.05665E+16 1.13101E+17 -2.67611E+16 -2.25511E+17 1.0813E+17 1.5299E+18 -3.52626E+17 -7.20159E+16 1.20663E+17 9.0375E+15 -1.24705E+16 -6.45664E+16

3.76191E+16 5.77254E+16 5.5001E+16 -5.2964E+17 1.21941E+17 -8.5623E+16 -4.5221E+17 -2.318E+16 1.51272E+16 -2.5338E+16 3.28808E+16 -1.323E+15 -2.2363E+16 1.41491E+15 5.86919E+16 6.37992E+16 2.78481E+16 3.97943E+16 3.36988E+16 6.60304E+15 4.02729E+16 -3.9952E+16 -3.8016E+15 5.66825E+16 -8.1694E+15 -3.4477E+15 -1.9502E+16 2.60554E+16 -1.117E+16 3.16267E+16 4.57659E+16 4.10808E+16 -5.2248E+16 -1.7383E+16 -3.6492E+16 -4.9686E+14 -1.7006E+16 7.14824E+15 5.4096E+16 -1.6702E+16 -3.1177E+17 8.01297E+16 9.63164E+15 -2.6622E+16 -1.9126E+15 1.90841E+15 1.0362E+16

6.71378E+15 3.181E+15 -8.07192E+15 5.42421E+16 2.21788E+16 -1.00368E+16 -3.10055E+16 -6.15588E+15 -2.45399E+15 -1.5031E+14 4.31767E+14 4.06288E+14 5.14141E+15 -1.2076E+15 -2.20338E+15 -4.58473E+15 -2.47845E+15 -7.0703E+15 4.19233E+15 6.68274E+15 -1.44594E+15 1.56026E+15 1.70793E+15 -4.37408E+15 4.00917E+15 -3.81745E+14 -2.46344E+14 -2.16514E+15 -5.95247E+14 1.21775E+15 -1.23197E+15 -1.69023E+15 3.50071E+15 3.12006E+14 5.04812E+15 -4.52223E+15 -1.81512E+14 -7.58354E+14 -3.71353E+15 1.83837E+15 3.69309E+16 -3.3298E+15 -8.22964E+14 1.48419E+15 -9.08767E+14 -6.06981E+14 -2.63927E+15

-8.92541E+15 1.08172E+15 8.3033E+15 -1.85643E+17 2.41556E+16 -1.66853E+16 -1.17225E+17 -6.68836E+14 -4.58189E+15 -5.32762E+15 4.35121E+15 -2.08572E+15 -5.88614E+15 2.51065E+15 1.59598E+16 1.44255E+16 6.29505E+15 3.94519E+15 -4.768E+15 1.75935E+16 9.23661E+14 -2.30177E+15 3.71409E+15 7.5908E+15 2.37811E+15 -1.1453E+15 -2.36078E+15 3.12482E+15 1.50631E+15 9.25852E+15 2.87655E+15 8.53515E+15 -1.13419E+16 -1.75217E+15 -8.62756E+15 -1.76599E+15 -8.14519E+15 2.04788E+13 1.14934E+16 4.13006E+14 -7.18882E+16 1.16673E+16 2.36072E+15 -7.04016E+15 1.88016E+14 3.1238E+12 5.3386E+15

2.7158E+16 9.29037E+15 1.77944E+14 -2.08556E+17 9.58472E+16 -2.46509E+16 -2.68159E+17 -1.33924E+16 -3.70652E+15 -5.94032E+15 8.96669E+15 -6.10797E+14 -6.68923E+15 2.27875E+15 2.38128E+16 2.30496E+16 4.47406E+15 2.50834E+15 5.77046E+15 1.22188E+16 1.09395E+16 -7.3195E+15 9.67131E+15 1.33039E+16 1.41935E+15 -3.95429E+15 -7.36069E+15 -3.8408E+14 2.42288E+15 1.34928E+16 9.42101E+15 1.6953E+16 -1.59031E+16 -3.20152E+15 -9.79622E+15 -7.95258E+15 -1.56057E+16 -3.02138E+14 1.25362E+16 5.15418E+15 -6.84266E+16 2.00662E+16 4.25365E+15 -9.61745E+15 -1.67701E+15 -1.42589E+14 1.20036E+15

-7.16616E+15 -8.08356E+15 -9.37601E+15 5.82509E+16 -1.83275E+15 4.83386E+15 1.13947E+16 -2.19755E+15 -2.7086E+15 3.32006E+15 -3.69745E+15 7.28925E+14 4.34451E+15 -3.1745E+14 -5.5513E+15 -9.20558E+15 -4.603E+15 -3.68186E+15 -5.06701E+15 2.99224E+15 -4.48424E+15 6.806E+15 4.27031E+15 -7.13899E+15 2.79729E+15 -7.89348E+14 1.37393E+15 -3.8079E+15 4.17633E+15 -3.98602E+15 -6.82225E+15 -4.15793E+15 7.32525E+15 9.51044E+14 4.21792E+15 -6.76523E+14 3.5509E+14 -1.41717E+15 -7.88036E+15 5.23085E+15 4.53319E+16 -8.87998E+15 -2.36255E+15 2.21453E+15 -4.58563E+14 -4.7554E+14 -8.55277E+14

-0.042577905 -0.001531012 -0.011597835 -0.001227264 0.006162855 0.013552973 0.015833742 0.015559838 0.025078851 0.001812878 -0.006550829 0.019573568 0.003120059 0.016471084 -0.036599423 -0.073916104 -0.107400775 -0.100010657

0.153855118 -0.459711859 -0.073278835 -0.386845812 0.005532308 0.041908739 0.004434713 -0.022269455 -0.048973622 -0.057215176 -0.056225422 -0.090622346 -0.006550829 0.023671397 -0.070729022 -0.011274324 -0.059518208 0.132251892 0.267095598 0.388092344 0.361388176

-0.016530278 -0.125221342 -0.013250715 0.066540083 0.146330881 0.170956255 0.167998918 0.270775308 0.019573568 -0.070729022 0.211334993 0.03368715 0.177837607 -0.395162434 -0.798069088 -1.159601675 -1.079810878

-0.002634954 -0.01996049 -0.002112186 0.0106066 0.023325386 0.027250712 0.026779307 0.043162035 0.003120059 -0.011274324 0.03368715 0.005369788 0.028347611 -0.06298955 -0.127213541 -0.184842437 -0.172123651

-0.013910167 -0.105373292 -0.011150427 0.055993231 0.12313689 0.14385905 0.141370462 0.227856411 0.016471084 -0.059518208 0.177837607 0.028347611 0.149649683 -0.332527713 -0.671572158 -0.975800479 -0.908656821

0.859587211

1.736020234

0.03090896 0.234143762 0.024776704 -0.124419249 -0.273615203 -0.319660691 -0.314130947 -0.506306261 -0.036599423 0.132251892 -0.395162434 -0.06298955 -0.332527713 0.738890173 1.492260791 2.16826856 2.019072606

0.062423659 0.472876171 0.050038971 -0.251276812 -0.552592596 -0.645585952 -0.634418094 -1.022534889 -0.073916104 0.267095598 -0.798069088 -0.127213541 -0.671572158 1.492260791 3.013766253 4.379029893 4.07771411

-0.067499575 -0.089488211 -0.05612557 -0.044051883 -0.065188961 -0.041619239 -0.032100225 0.013610007 0.038882846 0.050956534 0.057495094 0.049982945 0.05907618 0.067743635 0.081520439 0.090613673 0.077992176 0.071757365 0.078295925 0.074615788 0.077322337 0.079177327 0.043137983 0.045844531 0.049828417 0.059347431 0.04842905 0.065612086 -0.012153605 -0.031587567 -0.083380737 -0.125380988 -0.151627415 -0.176596504 -0.082773239

0.243909489 0.323365353 0.202809563 0.159181332 0.235560094 0.150390981 0.115994057 -0.049179717 -0.140503034 -0.184131265 -0.207758331 -0.180613207 -0.213471579 -0.244791401 -0.294573836 -0.327432209 -0.281824471 -0.259295001 -0.282922066 -0.269623903 -0.279404008 -0.28610701 -0.155878957 -0.165659062 -0.18005482 -0.214451744 -0.174998211 -0.237089056 0.043917013 0.11414157 0.301296016 0.453063786 0.547905161 0.638130883 0.299100826

-0.728790083 -0.966200468 -0.605985437 -0.475626335 -0.703842483 -0.449361179 -0.346584789 0.146946682 0.41981646 0.550175562 0.620772122 0.539663769 0.637843041 0.731425194 0.880172771 0.978352043 0.842078267 0.774761269 0.84535783 0.805623544 0.834846037 0.854874293 0.465758995 0.494981488 0.537995337 0.640771727 0.522886425 0.70841095 -0.131221969 -0.341049643 -0.900258329 -1.353733287 -1.637114858 -1.906705073 -0.893699202

SUMMARY OUTPUT Regression Statistics Multiple R 0.926270961 R Square 0.857977893 Adjusted R Square0.843775683

-0.116170352 -0.154013963 -0.096595087 -0.07581563 -0.112193663 -0.07162892 -0.055246192 0.023423546 0.066919443 0.0876989 0.09895211 0.086023303 0.101673242 0.116590393 0.140301005 0.155950944 0.134228677 0.123498236 0.134751445 0.128417734 0.133075848 0.136268385 0.074242759 0.078900873 0.085757352 0.10214008 0.083348967 0.112921885 -0.020917 -0.054363881 -0.143502676 -0.215787339 -0.260958833 -0.303931962 -0.14245714

-0.613274134 -0.813054086 -0.509934482 -0.400237785 -0.592280821 -0.378135754 -0.291649805 0.123655084 0.353273983 0.462970681 0.522377423 0.454125047 0.536742537 0.61549157 0.7406621 0.82327959 0.708605717 0.651958715 0.711365457 0.677929204 0.702519823 0.719373525 0.391934455 0.416525074 0.452721067 0.539207016 0.440006974 0.596125169 -0.110422797 -0.286992001 -0.757564022 -1.139161506 -1.37762604 -1.604485199 -0.752044542

1.362720198 1.80663942 1.133095268 0.889344721 1.316072199 0.840233105 0.648057791 -0.274766652 -0.784989234 -1.028739781 -1.16074399 -1.00908442 -1.192663862 -1.367647432 -1.645781467 -1.829360909 -1.574550873 -1.448678919 -1.580683129 -1.506386407 -1.561027768 -1.598477384 -0.870894382 -0.925535743 -1.005964719 -1.198140033 -0.977713486 -1.324614498 0.24536397 0.637707959 1.683338229 2.53126344 3.061141383 3.565231709 1.671073718

2.752146388 3.648684565 2.288396439 1.796118429 2.657936202 1.69693273 1.308815934 -0.55491806 -1.585362342 -2.077640352 -2.344235731 -2.037944433 -2.408701026 -2.762097416 -3.323816235 -3.694572828 -3.179959102 -2.925748411 -3.19234379 -3.042294313 -3.152647871 -3.228281025 -1.75885617 -1.869209728 -2.031643893 -2.419760688 -1.974587772 -2.675188209 0.495536475 1.287913438 3.39966578 5.112133467 6.182273668 7.200333262 3.374896404

Standard Error Observations

0.99703653 12

ANOVA df

MS 60.05404825 0.994081841


Coefficients Standard Error t Stat -22.34061772 3.887670671 -5.746530406 0.648041958 0.083376383 7.772488245

P-value Lower 95% 0.000186049 -31.00288774 1.51466E-05 0.4622678


1 10 11


SS 60.05404825 9.940818415 69.99486667

RESIDUAL OUTPUT Observation 1 2 3 4 5 6 7 8 9 10 11 12

Predicted Y 4.229102564 4.877144522 5.52518648 6.173228438 6.821270396 7.469312354 8.117354312 8.76539627 9.413438228 10.06148019 10.70952214 11.3575641

Residuals 0.980897436 0.372855478 -0.36518648 -0.623228438 -1.541270396 -0.229312354 -0.287354312 0.41460373 0.886561772 0.988519814 1.060477855 -1.657564103

RSS 0.96215978 0.139021207 0.133361165 0.388413686 2.375514434 0.052584156 0.082572501 0.171896253 0.785991775 0.977171422 1.124613282 2.747518754 9.940818415

11

12

13

14

15

16

17

8.76

8.74

8.73

8.71

8.7

8.69

8.68

5.94

5.91

5.89

5.87

5.86

5.84

5.83

4.7

4.68

4.66

4.64

4.62

4.6

4.59

4.03

4

3.98

3.96

3.94

3.92

3.91

3.6

3.57

3.55

3.53

3.51

3.49

3.48

3.31

3.28

3.26

3.24

3.22

3.2

3.19

3.1

3.07

3.05

3.03

3.01

2.99

2.97

2.94

2.91

2.89

2.86

2.85

2.83

2.81

2.82

2.79

2.76

2.74

2.72

2.7

2.69

2.72

2.69

2.66

2.64

2.62

2.6

2.58

2.63

2.6

2.58

2.55

2.53

2.51

2.5

2.57

2.53

2.51

2.48

2.46

2.44

2.43

2.51

2.48

2.45

2.42

2.4

2.38

2.37

2.46

2.42

2.4

2.37

2.35

2.33

2.32

2.41

2.38

2.35

2.33

2.31

2.29

2.27

2.37

2.34

2.31

2.29

2.27

2.25

2.23

2.34

2.31

2.28

2.26

2.23

2.21

2.2

2.31

2.28

2.25

2.23

2.2

2.18

2.17

2.26

2.23

2.2

2.17

2.15

2.13

2.11

2.22

2.18

2.15

2.13

2.11

2.09

2.07

2.18

2.15

2.12

2.09

2.07

2.05

2.03

2.15

2.12

2.09

2.06

2.04

2.02

2

2.13

2.09

2.06

2.04

2.01

1.99

1.98

2.08

2.04

2.01

1.99

1.96

1.94

1.92

2.04

2

1.97

1.95

1.92

1.9

1.89

2.01

1.97

1.94

1.92

1.89

1.87

1.86

1.99

1.95

1.92

1.89

1.87

1.85

1.83

1.95

1.92

1.89

1.86

1.84

1.82

1.8

1.93

1.89

1.86

1.84

1.81

1.79

1.77

1.91

1.88

1.84

1.82

1.79

1.77

1.75

1.89

1.85

1.82

1.79

1.77

1.75

1.73

1.84

1.8

1.77

1.74

1.72

1.69

1.67

1.81

1.77

1.74

1.71

1.69

1.66

1.64

1.8

1.76

1.73

1.7

1.68

1.65

1.63

1.79

11

1.75

12

1.72

13

1.69

14

1.67

15

1.64

16

6.22748E+18 1.08891E+17 -5.89749E+17 -1.95119E+18 6.51217E+16 -7.61306E+16 6.38642E+17 -1.00515E+17 -1.08931E+17 -2.05349E+17 2.10424E+16 -5.29037E+15 -1.87652E+18 -3.91443E+17 -6.69736E+16 2.02775E+17 -7.56534E+16 -1.17373E+16 -1.19466E+18 6.23873E+16 1.21414E+17 4.41891E+17 -7.06062E+15 1.4437E+16 2.73822E+17 -1.32218E+17 -9.8614E+16 -8.60908E+16 1.90757E+16 -1.5554E+15

1.62

17

1.23417E+17 1.66363E+16 9.70913E+15 -2.1322E+16 1.12782E+16

3.74011E+16 -5.19186E+16 -1.9724E+16 2.64501E+18 -4.43686E+17 2.64056E+17 2.11894E+18 9.43641E+16 4.65065E+16 8.25056E+16 -7.00129E+16 4.69932E+15 1.29004E+17 -4.9929E+16 -2.46189E+17 -2.16341E+17 -7.26917E+16 -7.64125E+16 -6.81104E+15 -1.59705E+17 -8.19458E+16 4.57454E+16 -7.135E+16 -1.21516E+17 2.58364E+16 2.47527E+16 4.21763E+16 -9.69368E+15 -1.34172E+16 -1.41774E+17 -4.40274E+16 -1.49604E+17 1.79607E+17 2.59548E+16 1.26987E+17 5.91574E+15 1.44207E+17 -2.0041E+16 -1.85876E+17 -2.0659E+16 1.17811E+18 -1.89722E+17 -2.79059E+16 1.12788E+17 -9.10959E+15 3.15337E+15 -8.12623E+16

-4.18374E+16 -1.21756E+16 -3.49263E+16 1.45495E+17 1.81827E+16 -2.43706E+16 -3.30934E+17 -6.92412E+15 -4.96793E+15 6.65211E+15 -7.02589E+14 -2.69562E+14 -1.87114E+15 4.59306E+15 1.11504E+16 -9.59958E+15 2.23505E+15 -1.46992E+16 -1.92857E+16 1.79404E+16 3.30991E+15 2.21607E+16 1.96084E+16 -1.41056E+16 -2.87324E+15 -5.57574E+15 3.10952E+14 -1.70955E+16 1.86882E+16 1.7101E+15 -1.89099E+16 2.43503E+15 3.67996E+15 4.86838E+15 -2.23847E+15 -6.45901E+15 -6.69269E+15 -6.16172E+15 -3.94723E+15 3.10557E+16 1.46274E+16 -8.29461E+15 -5.16628E+15 -5.71163E+15 2.52619E+15 -2.98806E+15 2.2985E+15

9.06237E+15 1.96262E+16 -9.29001E+15 -2.42643E+17 1.34307E+17 -4.56528E+16 -3.9168E+17 -1.8383E+16 -1.37121E+16 -5.27777E+15 7.48059E+15 -3.19214E+14 -5.75577E+15 5.44689E+15 2.79308E+16 1.73072E+16 1.56137E+15 -3.77784E+14 -4.70323E+15 2.12157E+16 1.09442E+16 4.14682E+15 1.86069E+16 5.31553E+15 5.88435E+15 -8.39501E+15 -5.95718E+15 -7.45214E+15 1.19004E+16 1.61995E+16 1.10376E+15 1.67434E+16 -1.62398E+16 -1.58386E+15 -1.3609E+16 -1.12531E+16 -2.43141E+16 -1.16169E+15 1.43542E+16 1.81492E+16 -6.33754E+16 1.66533E+16 3.41178E+15 -1.22787E+16 -1.55843E+15 -1.4429E+15 3.76419E+15

3.92293E+16 6.55926E+16 4.27447E+16 -9.09694E+17 3.03433E+17 -1.11155E+17 -9.20679E+17 -3.17215E+16 -2.74993E+16 -2.78061E+16 3.33842E+16 -6.30866E+15 -3.88857E+16 1.51502E+16 1.05043E+17 9.31884E+16 1.69121E+16 1.31739E+16 1.10678E+16 3.41203E+15 4.53529E+16 -3.41193E+16 1.98794E+16 5.81667E+16 -1.22544E+15 -1.03466E+16 -2.81197E+16 7.98377E+15 2.08428E+15 5.37607E+16 5.59754E+16 6.6561E+16 -7.02402E+16 -1.18788E+16 -3.65199E+16 -2.45999E+16 -5.93031E+16 1.377E+15 5.40704E+16 1.08912E+16 -3.44783E+17 8.31473E+16 2.41212E+16 -3.72293E+16 -7.56973E+15 -1.17983E+15 2.00869E+16

3.73612E+15 -6.83478E+15 1.86419E+15 1.52124E+16 4.97506E+15 -6.45585E+13 2.23846E+16 2.67717E+15 3.77611E+15 -1.4329E+15 1.08701E+15 -1.48613E+15 3.22916E+15 -2.45927E+15 2.12554E+15 1.96774E+15 9.11848E+14 4.67534E+15 3.55974E+15 -3.41818E+15 5.7737E+15 -5.60709E+15 -2.37285E+13 3.62884E+15 3.78533E+14 -1.84087E+14 -3.67706E+15 4.31434E+15 7.33874E+14 -1.41496E+15 5.17327E+15 2.58545E+15 1.64148E+14 -2.59028E+15 2.72699E+15 -2.42005E+15 3.59598E+15 -7.35398E+14 -1.27692E+15 -3.03095E+15 -6.09223E+14 6.5893E+15 8.00593E+14 -2.92095E+14 -1.23759E+15 -2.82096E+13 -1.48998E+15

-1.26001E+15 -1.45095E+15 1.27052E+14 -6.39026E+15 1.59183E+15 -6.23678E+15 -3.38225E+16 -3.77378E+15 -1.65877E+15 -5.42618E+14 1.18851E+15 -3.85893E+14 2.88665E+14 -4.83587E+14 2.29633E+15 1.0946E+15 1.73772E+15 4.61382E+14 -1.28618E+14 4.72806E+15 1.97118E+15 3.56813E+14 1.58516E+14 -8.1585E+13 4.73377E+14 -1.2129E+15 -1.71172E+14 -1.50343E+14 -3.47817E+13 5.99757E+14 2.66936E+14 1.32476E+15 -5.85015E+14 -1.36246E+14 -1.09886E+15 -7.36702E+14 7.29472E+14 -6.07921E+14 1.73471E+15 1.16192E+15 -3.43175E+15 1.65499E+15 2.8239E+14 -7.9989E+14 2.6035E+14 -2.97146E+14 -1.90954E+14

-2.79321E+15 -4.80477E+15 -9.65658E+14 5.7009E+16 -2.47734E+16 7.11529E+15 6.13004E+16 2.27203E+15 1.90628E+15 1.60446E+15 -1.87888E+15 2.64272E+14 1.7151E+15 -1.23689E+15 -6.28895E+15 -5.0659E+15 -3.27829E+14 -3.79679E+14 1.94766E+14 -2.63607E+15 -2.37623E+15 3.75192E+14 -2.7397E+15 -2.23043E+15 -7.92983E+14 1.23889E+15 1.63166E+15 7.57236E+14 -1.77887E+15 -3.42288E+15 -1.36973E+15 -3.98853E+15 3.83812E+15 7.10259E+14 2.72579E+15 2.4976E+15 5.57842E+15 -1.5532E+14 -3.41542E+15 -2.34362E+15 1.75299E+16 -4.19509E+15 -9.46389E+14 2.5409E+15 4.69438E+14 9.48056E+13 -1.14922E+15

2.522453257

2.34888628

1.585319303

2.101752326

1.31818535

1.034618373

1.531051396

0.090702147 0.687093397 0.072707082 -0.365107504 -0.80292209 -0.938042285 -0.921815285 -1.485752534 -0.107400775 0.388092344 -1.159601675 -0.184842437 -0.975800479 2.16826856 4.379029893 6.362770434 5.924955848

0.084461041 0.639815326 0.067704195 -0.339984895 -0.747673986 -0.873496723 -0.858386283 -1.383519688 -0.100010657 0.361388176 -1.079810878 -0.172123651 -0.908656821 2.019072606 4.07771411 5.924955848 5.517266757

0.057004769 0.431826604 0.045695174 -0.229463905 -0.504622983 -0.589543746 -0.57934535 -0.933770394 -0.067499575 0.243909489 -0.728790083 -0.116170352 -0.613274134 1.362720198 2.752146388 3.99889384 3.723734761

0.075574621 0.572498277 0.060580817 -0.30421398 -0.669008778 -0.781593296 -0.768072675 -1.237955088 -0.089488211 0.323365353 -0.966200468 -0.154013963 -0.813054086 1.80663942 3.648684565 5.301572001 4.936777204

0.04739919 0.359061737 0.037995317 -0.190798129 -0.419591575 -0.490202779 -0.481722863 -0.776425576 -0.05612557 0.202809563 -0.605985437 -0.096595087 -0.509934482 1.133095268 2.288396439 3.325060929 3.096267482

0.037202714 0.281820664 0.029821795 -0.149753788 -0.329329372 -0.38475075 -0.378095026 -0.609401528 -0.044051883 0.159181332 -0.475626335 -0.07581563 -0.400237785 0.889344721 1.796118429 2.609776484 2.430200901

0.055053408 0.417044518 0.044130959 -0.221609004 -0.487348966 -0.569362761 -0.559513472 -0.901806004 -0.065188961 0.235560094 -0.703842483 -0.112193663 -0.592280821 1.316072199 2.657936202 3.86200558 3.596265618

3.99889384 5.301572001 3.325060929 2.609776484 3.86200558 2.465658756 1.901721508 -0.80630101 -2.303545964 -3.018830408 -3.406195929 -2.961151875 -3.499864592 -4.013352776 -4.82953535 -5.368248067 -4.620509622 -4.251139166 -4.638504687 -4.420481426 -4.580826154 -4.690721817 -2.555634081 -2.715978808 -2.951997134 -3.515934383 -2.869094068 -3.887072904 0.720019024 1.87134999 4.939745431 7.427976623 8.98290011 10.46215 4.903755302

3.723734761 4.936777204 3.096267482 2.430200901 3.596265618 2.295999741 1.770866336 -0.750820407 -2.145041735 -2.811108316 -3.171819681 -2.757398574 -3.259043116 -3.737198795 -4.497220828 -4.998865369 -4.302577908 -3.958623389 -4.319334754 -4.116313412 -4.265625012 -4.367958886 -2.379783971 -2.529095571 -2.748873759 -3.274007164 -2.671675154 -3.619608089 0.670475381 1.742584647 4.599847485 6.91686648 8.36479755 9.742262033 4.566333793

2.513237294 3.331948534 2.08974468 1.640200478 2.427205332 1.549624918 1.195199874 -0.506746578 -1.447739764 -1.897283966 -2.140736659 -1.861033982 -2.199605833 -2.52232449 -3.035281465 -3.373853316 -2.903912322 -2.671769224 -2.915221917 -2.778197977 -2.878971932 -2.948039502 -1.606172891 -1.706946846 -1.855280381 -2.209705425 -1.803177203 -2.442959722 0.452519806 1.176111888 3.104546641 4.668357954 5.645601125 6.575284716 3.081927452

3.331948534 4.417362842 2.770499125 2.174511572 3.217890833 2.054430152 1.584547738 -0.671824153 -1.919354928 -2.515342481 -2.838102232 -2.467283715 -2.916148606 -3.343995973 -4.024053619 -4.47291851 -3.849889714 -3.542123767 -3.864883518 -3.68322271 -3.816824752 -3.908391747 -2.129399171 -2.263001212 -2.459655824 -2.929538238 -2.390579535 -3.238777367 0.599932488 1.559241657 4.115882593 6.189120494 7.484710035 8.717247006 4.085894985

2.08974468 2.770499125 1.737612616 1.363818781 2.01820952 1.288505641 0.993802927 -0.421357334 -1.203788627 -1.577582461 -1.7800122 -1.547440774 -1.828961634 -2.097300641 -2.523821889 -2.805342749 -2.414589081 -2.221563215 -2.423992954 -2.310058209 -2.393851267 -2.451280618 -1.335525007 -1.419318065 -1.542656683 -1.837359396 -1.499333142 -2.031309219 0.376268035 0.977931359 2.581415549 3.881717108 4.694290088 5.467317508 2.562607802

1.640200478 2.174511572 1.363818781 1.070435177 1.584053904 1.011323339 0.780016837 -0.330715281 -0.944830581 -1.238214185 -1.397097401 -1.214556554 -1.435516872 -1.646131006 -1.980899345 -2.201859663 -1.895164611 -1.743662315 -1.902545531 -1.813120337 -1.878887899 -1.923963094 -1.048227937 -1.113995499 -1.210801612 -1.442108114 -1.176797797 -1.594335606 0.295325556 0.767559548 2.026103503 3.046685232 3.684458163 4.291192544 2.011341664

2.427205332 3.217890833 2.01820952 1.584053904 2.344118377 1.496578884 1.154286352 -0.489399866 -1.398181415 -1.832337031 -2.067455965 -1.797327938 -2.124309957 -2.435981461 -2.931379132 -3.25836115 -2.804506956 -2.580310472 -2.815429406 -2.683096005 -2.780420314 -2.847123595 -1.551191133 -1.648515442 -1.791771292 -2.134063824 -1.741451686 -2.35933347 0.43702936 1.135851777 2.998273255 4.508552912 5.452343553 6.350202651 2.976428356

Upper 95% Lower 95.0% Upper 95.0% -13.67834769 -31.00288774 -13.67834769 0.833816116 0.4622678 0.833816116

18

19

20

22

24

26

28

8.67

8.67

8.66

8.65

8.64

8.63

8.62

5.82

5.81

5.8

5.79

5.77

5.76

5.75

4.58

4.57

4.56

4.54

4.53

4.52

4.5

3.9

3.88

3.87

3.86

3.84

3.83

3.82

3.47

3.46

3.44

3.43

3.41

3.4

3.39

3.17

3.16

3.15

3.13

3.12

3.1

3.09

2.96

2.95

2.94

2.92

2.9

2.89

2.87

2.8

2.79

2.77

2.75

2.74

2.72

2.71

2.67

2.66

2.65

2.63

2.61

2.59

2.58

2.57

2.56

2.54

2.52

2.51

2.49

2.48

2.48

2.47

2.46

2.44

2.42

2.41

2.39

2.41

2.4

2.39

2.37

2.35

2.33

2.32

2.35

2.34

2.33

2.31

2.29

2.27

2.26

2.3

2.29

2.28

2.25

2.24

2.22

2.21

2.26

2.24

2.23

2.21

2.19

2.17

2.16

2.22

2.2

2.19

2.17

2.15

2.13

2.12

2.18

2.17

2.16

2.13

2.11

2.1

2.08

2.15

2.14

2.12

2.1

2.08

2.07

2.05

2.1

2.08

2.07

2.05

2.03

2.01

2

2.05

2.04

2.03

2

1.98

1.97

1.95

2.02

2

1.99

1.97

1.95

1.93

1.91

1.99

1.97

1.96

1.93

1.91

1.9

1.88

1.96

1.95

1.93

1.91

1.89

1.87

1.85

1.91

1.89

1.88

1.85

1.83

1.82

1.8

1.87

1.85

1.84

1.81

1.79

1.77

1.76

1.84

1.82

1.81

1.78

1.76

1.74

1.73

1.81

1.8

1.78

1.76

1.74

1.72

1.7

1.78

1.76

1.75

1.72

1.7

1.68

1.66

1.75

1.74

1.72

1.7

1.67

1.65

1.64

1.73

1.72

1.7

1.68

1.65

1.63

1.62

1.71

1.69

1.68

1.65

1.63

1.61

1.59

1.66

1.64

1.62

1.6

1.57

1.55

1.53

1.62

1.61

1.59

1.56

1.54

1.52

1.5

1.61

1.6

1.58

1.55

1.53

1.51

1.49

1.61

18

1.59

19

1.57

20

1.54

22

1.52

24

1.5

26

1.48

28

-2.70663E+16 -8.15251E+16 1.35897E+17 -1.46168E+16 1.07147E+17 8.47806E+16 -1.32122E+17 -1.63111E+15 -7.65122E+15 5.24446E+15 -3.98962E+15 9.35484E+15 1.16408E+16 -1.3321E+16 -1.39768E+16 2.907E+16 -3.19159E+16 -3.69597E+16 -2.55335E+16 -2.58251E+16 5.69828E+16 8.81838E+15 1.80527E+16 -2.46717E+16 1.13639E+16 -1.94349E+16 -2.42828E+16 2.47922E+16 1.70769E+15 -1.46227E+15 -8.38192E+15 -2.3932E+15 3.74782E+15 3.09116E+15 -3.88907E+15

2.09576E+15 1.22391E+15 6.9997E+14 -1.83252E+15 5.92408E+15 -2.30396E+15 -1.9224E+16 -4.20035E+14 9.71355E+14 -6.12196E+14 8.0462E+14 -2.32005E+14 2.79792E+14 -1.85076E+14 1.72783E+15 1.97431E+15 6.3346E+14 4.10322E+14 1.17546E+15 6.32537E+14 9.52605E+14 -1.13145E+15 3.17972E+14 1.28746E+15 2.84642E+14 -3.22256E+14 -8.43251E+14 4.62606E+14 8.04656E+13 3.30117E+14 1.54275E+15 1.20169E+15 -9.08663E+14 -3.78168E+14 -2.35984E+14 -8.00205E+14 -9.21141E+13 -7.04357E+13 8.16803E+14 1.21407E+14 -3.47703E+15 1.83507E+15 3.03126E+14 -6.49102E+14 -2.61084E+14 -5.10778E+13 -6.43593E+13

4.50953E+15 1.81084E+15 2.48118E+15 -4.89954E+16 1.0482E+16 -3.09971E+15 -2.11842E+16 -3.35888E+14 -5.03395E+14 -9.94046E+14 1.02675E+15 -3.22027E+14 -1.68451E+15 6.01952E+14 3.75743E+15 3.64163E+15 4.6944E+14 1.24644E+15 -5.54465E+14 1.03097E+15 8.62323E+14 -1.85799E+15 6.53169E+14 3.10848E+15 -1.73923E+13 1.08171E+14 -8.14993E+14 1.17092E+15 -8.40479E+14 1.873E+15 1.67615E+15 2.03814E+15 -3.02483E+15 -7.74582E+14 -1.87856E+15 -1.78046E+14 -1.90483E+15 7.18212E+13 2.35705E+15 -3.03592E+14 -1.64756E+16 4.016E+15 9.55395E+14 -1.27982E+15 -5.57073E+13 2.57655E+14 7.15686E+14

-5.36746E+15 -6.4951E+15 -4.01808E+15 4.0413E+16 -1.55823E+16 5.52546E+15 2.68297E+16 4.1684E+15 -1.82016E+15 2.01614E+15 -2.24968E+15 2.55873E+14 1.25261E+15 -5.22914E+13 -4.2131E+15 -5.49963E+15 -1.59873E+15 -1.59463E+15 -2.08998E+15 3.11338E+15 -3.51045E+15 3.67658E+15 3.33085E+14 -5.0453E+15 8.73415E+14 2.21719E+14 2.27398E+15 -2.05194E+15 1.2628E+15 -2.38948E+15 -4.76611E+15 -3.54724E+15 3.85269E+15 1.29185E+15 2.19854E+15 7.58126E+14 1.73124E+15 -5.45016E+14 -3.22026E+15 1.75772E+15 2.02699E+16 -5.87006E+15 -1.12875E+15 1.83777E+15 3.31514E+14 -3.11102E+14 -1.23495E+14

-1.03266E+15 2.32503E+15 1.38002E+15 5.15323E+15 9.13208E+15 -2.39541E+15 -2.38941E+16 -1.14504E+15 5.16762E+14 -3.24911E+14 1.00146E+15 -1.4353E+14 -1.19804E+14 1.22586E+14 2.06395E+15 9.23058E+14 5.88652E+14 -6.98532E+14 9.69058E+14 -2.00988E+15 1.53051E+15 -9.7423E+14 1.10452E+15 8.02327E+14 6.849E+14 -7.61543E+14 -8.13092E+14 9.22575E+13 9.05366E+14 4.01692E+14 1.10667E+15 1.74237E+15 -8.99027E+14 -3.35303E+14 -5.36421E+14 -1.14451E+15 -4.80756E+14 -1.55801E+14 8.75665E+14 7.57804E+14 -4.21233E+15 1.26541E+15 2.67791E+14 -5.83579E+14 -1.19707E+14 -6.8685E+12 3.52918E+14

-2.89846E+15 -3.59024E+15 -8.06437E+14 4.23762E+16 -1.65648E+16 5.47909E+15 3.80333E+16 3.39271E+15 8.64733E+14 1.46904E+15 -1.46863E+15 2.76192E+14 2.00886E+15 -7.33999E+14 -4.71964E+15 -4.72663E+15 -6.30715E+14 -1.4321E+15 -9.4144E+14 -1.9329E+15 -1.62801E+15 1.71338E+15 -1.61541E+15 -3.03006E+15 -7.7699E+14 3.45019E+14 1.30861E+15 -3.76502E+14 -1.20551E+14 -2.74678E+15 -1.94545E+15 -3.22744E+15 2.94117E+15 8.83653E+14 2.54029E+15 1.475E+15 3.37526E+15 -3.59305E+14 -3.32076E+15 -5.22591E+14 1.51204E+16 -3.80587E+15 -1.26034E+15 1.99615E+15 1.76243E+14 1.12094E+13 -5.84361E+14

1.5535E+15 1.05524E+15 -4.8019E+14 6.37303E+16 -6.13842E+15 3.02075E+15 3.15426E+16 -7.45246E+14 -5.16968E+14 1.17637E+15 -1.11065E+15 1.75716E+14 1.84125E+15 -1.66538E+14 -3.64085E+15 -3.11014E+15 -2.47039E+15 -1.75608E+15 7.48993E+14 -4.18219E+15 -1.97739E+15 8.47317E+14 -7.14433E+14 -2.20319E+15 1.03152E+15 -8.58918E+13 6.36815E+14 -1.25154E+15 4.36903E+14 -1.80385E+15 -1.52082E+15 -1.89341E+15 3.51466E+15 5.54313E+14 1.37688E+15 -2.64655E+14 1.17634E+15 -1.93588E+14 -3.58898E+15 -9.90085E+13 2.06117E+16 -4.73994E+15 -6.4075E+14 1.55413E+15 -2.68617E+14 -1.41593E+14 -1.03672E+15

1.9997E+15 5.73812E+15 3.31539E+15 -3.37065E+16 1.1026E+16 -6.43658E+15 -4.26543E+16 -4.22597E+15 -6.3431E+14 -1.88173E+15 1.70818E+15 4.78693E+12 -2.5456E+15 1.30033E+15 5.46598E+15 4.18745E+15 1.43214E+15 1.28614E+15 9.60757E+14 -6.66701E+14 1.56702E+15 -1.15718E+15 1.0974E+15 2.91977E+15 9.37421E+13 -1.07643E+15 -1.13943E+15 4.39044E+14 5.29816E+14 3.01685E+15 1.71714E+15 3.52687E+15 -3.39293E+15 -5.9118E+14 -2.93241E+15 -5.75838E+14 -3.95827E+15 6.11612E+14 4.21292E+15 9.98297E+13 -2.20977E+16 3.80656E+15 1.30938E+15 -2.07199E+15 -1.11E+13 -6.79611E+13 1.58161E+15

0.977484419 0.035148297 0.266257893 0.028174968 -0.141484047 -0.311143063 -0.363503948 -0.357215768 -0.575749005 -0.041619239 0.150390981 -0.449361179 -0.07162892 -0.378135754 0.840233105 1.69693273 2.465658756 2.295999741

0.753917442 -0.319649535 -0.913216512 -1.196783488 -1.350350465 -1.173917442 0.027109296 0.205360276 0.021730883 -0.109124288 -0.239979459 -0.280364537 -0.275514569 -0.444065612 -0.032100225 0.115994057 -0.346584789 -0.055246192 -0.291649805 0.648057791 1.308815934 1.901721508 1.770866336

-0.011493929 -0.087069635 -0.009213564 0.046267039 0.101747643 0.118870302 0.116813989 0.188277069 0.013610007 -0.049179717 0.146946682 0.023423546 0.123655084 -0.274766652 -0.55491806 -0.80630101 -0.750820407

-0.032837357 -0.248751898 -0.026322513 0.132181716 0.290685945 0.339604193 0.33372945 0.537894505 0.038882846 -0.140503034 0.41981646 0.066919443 0.353273983 -0.784989234 -1.585362342 -2.303545964 -2.145041735

-0.043033833 -0.325992971 -0.034496035 0.173226057 0.380948149 0.445056223 0.437357287 0.704918553 0.050956534 -0.184131265 0.550175562 0.0876989 0.462970681 -1.028739781 -2.077640352 -3.018830408 -2.811108316

-0.048555781 -0.367823223 -0.038922443 0.195453805 0.429830053 0.502164245 0.493477409 0.795371181 0.057495094 -0.207758331 0.620772122 0.09895211 0.522377423 -1.16074399 -2.344235731 -3.406195929 -3.171819681

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1.549624918 2.054430152 1.288505641 1.011323339 1.496578884 0.955475789 0.736942553 -0.31245244 -0.892654911 -1.169837213 -1.31994654 -1.147486009 -1.356244401 -1.555227949 -1.871509628 -2.08026802 -1.790509359 -1.64737336 -1.797482687 -1.712995754 -1.775131483 -1.817717524 -0.990342432 -1.052478162 -1.143938424 -1.36247166 -1.111812376 -1.506292808 0.279017015 0.725173183 1.91421751 2.878440421 3.480994096 4.054223239 1.900270853

1.195199874 1.584547738 0.993802927 0.780016837 1.154286352 0.736942553 0.56839151 -0.24098936 -0.688489857 -0.902275946 -1.018052769 -0.885036835 -1.046048704 -1.199521399 -1.443464186 -1.604476055 -1.380990029 -1.270591618 -1.386368441 -1.321205077 -1.36912933 -1.401975233 -0.763834614 -0.811758866 -0.882300642 -1.050851685 -0.857522357 -1.16177854 0.215201174 0.559313991 1.476404064 2.220093126 2.684832734 3.126954819 1.46564724

-0.506746578 -0.671824153 -0.421357334 -0.330715281 -0.489399866 -0.31245244 -0.24098936 0.102175825 0.291909233 0.382551285 0.431638898 0.375242164 0.443508749 0.508578838 0.612006872 0.680273457 0.585518779 0.538711531 0.587799144 0.560170868 0.580490023 0.594416187 0.323854265 0.344173419 0.37408206 0.44554514 0.363576443 0.49257644 -0.091242026 -0.23714063 -0.625972879 -0.941285736 -1.138328265 -1.325781308 -0.62141215

-1.447739764 -1.919354928 -1.203788627 -0.944830581 -1.398181415 -0.892654911 -0.688489857 0.291909233 0.833964397 1.092922442 1.233162341 1.072040791 1.267073681 1.452974405 1.748461111 1.943494001 1.67278647 1.539061415 1.679301314 1.60036925 1.658419663 1.698205746 0.925229133 0.983279546 1.068726454 1.272891509 1.038712638 1.407256665 -0.260672129 -0.677494302 -1.788361024 -2.689187949 -3.252124764 -3.787665083 -1.775331336

-1.897283966 -2.515342481 -1.577582461 -1.238214185 -1.832337031 -1.169837213 -0.902275946 0.382551285 1.092922442 1.432290718 1.61607714 1.404925012 1.660518443 1.90414404 2.291383655 2.546977087 2.192210939 2.016962315 2.200748737 2.097307122 2.173383031 2.225523269 1.212526203 1.288602111 1.400581524 1.668142791 1.361247983 1.844230277 -0.341614608 -0.887866113 -2.34367307 -3.524219825 -4.261956689 -4.963790048 -2.326597474

-2.140736659 -2.838102232 -1.7800122 -1.397097401 -2.067455965 -1.31994654 -1.018052769 0.431638898 1.233162341 1.61607714 1.823446379 1.585199964 1.873590231 2.148476993 2.585405811 2.873796077 2.473507606 2.275771705 2.483140944 2.366426071 2.452263768 2.511094455 1.368113229 1.453950925 1.580299136 1.882192907 1.535918455 2.08087531 -0.385449372 -1.001793917 -2.644404816 -3.976435108 -4.808835728 -5.600725833 -2.625138141

-1.861033982 -2.467283715 -1.547440774 -1.214556554 -1.797327938 -1.147486009 -0.885036835 0.375242164 1.072040791 1.404925012 1.585199964 1.378082161 1.62879216 1.867762985 2.247603903 2.498313902 2.150326006 1.978425726 2.158700678 2.057235445 2.131857828 2.183001862 1.189359372 1.263981755 1.373821662 1.636270835 1.335239637 1.80899395 -0.335087633 -0.87090232 -2.298894263 -3.456885195 -4.180526672 -4.868950627 -2.282144918

30

35

40

45

50

60

70

8.62

8.6

8.59

8.59

8.58

8.57

8.57

5.75

5.73

5.72

5.71

5.7

5.69

5.68

4.5

4.48

4.46

4.45

4.44

4.43

4.42

3.81

3.79

3.77

3.76

3.75

3.74

3.73

3.38

3.36

3.34

3.33

3.32

3.3

3.29

3.08

3.06

3.04

3.03

3.02

3.01

2.99

2.86

2.84

2.83

2.81

2.8

2.79

2.78

2.7

2.68

2.66

2.65

2.64

2.62

2.61

2.57

2.55

2.53

2.52

2.51

2.49

2.48

2.47

2.44

2.43

2.41

2.4

2.38

2.37

2.38

2.36

2.34

2.33

2.31

2.3

2.28

2.31

2.28

2.27

2.25

2.24

2.22

2.21

2.25

2.22

2.2

2.19

2.18

2.16

2.15

2.19

2.17

2.15

2.14

2.12

2.11

2.09

2.15

2.12

2.1

2.09

2.08

2.06

2.05

2.11

2.08

2.06

2.05

2.04

2.02

2

2.07

2.05

2.03

2.01

2

1.98

1.97

2.04

2.01

1.99

1.98

1.97

1.95

1.93

1.98

1.96

1.94

1.92

1.91

1.89

1.88

1.94

1.91

1.89

1.88

1.86

1.84

1.83

1.9

1.87

1.85

1.84

1.82

1.8

1.79

1.87

1.84

1.82

1.8

1.79

1.77

1.75

1.84

1.81

1.79

1.77

1.76

1.74

1.72

1.79

1.76

1.74

1.72

1.7

1.68

1.66

1.74

1.72

1.69

1.67

1.66

1.64

1.62

1.71

1.68

1.66

1.64

1.63

1.6

1.59

1.69

1.66

1.63

1.61

1.6

1.58

1.56

1.65

1.62

1.59

1.57

1.56

1.53

1.52

1.62

1.59

1.57

1.55

1.53

1.5

1.49

1.6

1.57

1.54

1.52

1.51

1.48

1.46

1.57

1.54

1.52

1.49

1.48

1.45

1.43

1.52

1.48

1.46

1.43

1.41

1.39

1.36

1.48

1.45

1.42

1.4

1.38

1.35

1.32

1.47

1.43

1.41

1.38

1.36

1.33

1.31

1.46

30

1.42

35

1.4

40

1.37

45

1.35

50

1.32

60

4.14401E+15 2.24866E+16 -3.46521E+15 9.52554E+15 4.47413E+16 -2.38912E+17 -6.78921E+15 9.91659E+15 5.78869E+16 -5.88194E+15 5.97381E+15 -2.74001E+16 1.22532E+16 -4.62731E+16 6.68831E+16 5.52246E+16 -2.91508E+16 3.54161E+16 -1.04131E+16 4.92053E+14 -4.14029E+16 -3.57479E+15 -1.22629E+16 4.92627E+16 -1.67088E+16 2.62853E+16 9.10472E+16 -8.42377E+15 4.19547E+15 -1.71719E+16

1.3

70

9.0615E+16 -1.95183E+15 -7.68951E+16 -1.06185E+16 -9.06761E+15

-3.19553E+15 -4.23205E+15 -4.16293E+15 -1.11546E+16 1.914E+15 1.11146E+14 2.72775E+16 3.74413E+15 -2.5561E+15 8.15359E+14 -1.84564E+15 -1.85466E+14 -1.41837E+15 1.60356E+15 -1.99115E+15 -2.05317E+15 -1.90963E+15 -2.77899E+15 -5.01933E+15 1.70802E+15 -4.59314E+15 3.13561E+15 1.03049E+15 -1.15041E+15 -9.92899E+13 3.14617E+14 1.57605E+15 -1.79343E+15 5.23334E+14 4.41239E+14 -3.78433E+15 -1.94824E+15 5.21772E+14 1.17311E+15 -1.308E+15 5.86966E+14 -2.47782E+15 -2.67661E+14 -2.81419E+14 1.06586E+15 1.63366E+15 -2.29971E+15 -2.0197E+14 -1.27713E+14 6.14415E+14 -2.17384E+13 1.24714E+15

1.094E+16 6.24816E+15 4.76767E+15 2.11053E+16 -5.32223E+15 2.0473E+15 2.92504E+16 -2.7487E+14 3.03674E+15 -4.36338E+14 1.40552E+15 -3.04848E+14 1.38379E+15 -9.8875E+14 -9.21584E+14 1.47083E+15 -2.60444E+14 -4.34846E+14 7.24456E+15 -7.88937E+15 1.35074E+15 -5.08159E+15 -2.17439E+15 4.26531E+15 4.21443E+14 2.14964E+13 -1.18725E+15 2.49499E+15 -2.2411E+15 -1.09345E+15 4.76263E+15 1.51992E+15 1.97379E+13 -7.55416E+14 1.24392E+15 -8.6651E+14 5.87185E+14 1.11667E+15 -9.79526E+14 -4.70954E+15 4.70179E+15 3.82219E+15 1.04671E+15 1.12866E+15 -5.38446E+14 7.61338E+14 -1.9318E+15

1.22901E+16 1.34814E+16 1.3861E+16 1.86883E+17 -5.62552E+16 1.87485E+16 2.09313E+17 3.85408E+14 1.28199E+16 -1.58009E+15 1.88507E+15 2.85599E+15 3.97206E+15 -4.37682E+15 -1.12291E+16 3.71777E+15 1.34072E+14 4.65793E+15 1.40847E+16 -2.6366E+16 4.10851E+15 -1.16585E+16 -1.49453E+16 6.38321E+15 -5.20415E+15 2.29079E+15 -2.22243E+15 6.97059E+15 -8.17685E+15 -6.75655E+15 1.09361E+16 5.41894E+13 3.81192E+15 -1.23772E+15 4.82427E+15 2.64646E+15 1.0382E+16 3.26324E+15 -4.99774E+14 -1.74212E+16 1.18796E+15 -1.05502E+14 -5.33447E+14 5.09486E+15 -6.39449E+14 1.57237E+15 -2.4467E+15

-2.64347E+15 -1.80206E+15 -2.41624E+15 -1.21178E+16 -8.94225E+15 3.29932E+15 8.29974E+15 2.55294E+15 8.38557E+13 1.17132E+15 -1.40483E+15 2.21157E+14 -2.27932E+15 1.42738E+15 -1.34149E+15 -3.49508E+15 1.80649E+14 2.80404E+13 -4.13663E+15 -8.67992E+14 -2.16335E+15 2.08787E+15 3.9152E+14 -5.32134E+14 -1.62608E+15 1.23308E+15 2.04148E+15 -7.20994E+14 -7.84022E+14 -4.81541E+14 -3.1415E+15 -2.13428E+15 4.83519E+14 6.31412E+14 -3.24921E+14 4.0578E+15 7.12135E+14 -9.05254E+14 7.06916E+14 8.55837E+12 -4.95748E+15 -2.11915E+15 -5.37228E+14 7.43291E+14 9.85429E+14 -5.21426E+13 1.3432E+15

3.04901E+15 1.04485E+15 3.92601E+14 5.32187E+15 -2.56408E+15 1.79462E+15 2.29406E+16 1.02987E+15 2.43142E+14 -4.65281E+14 -5.94494E+14 -1.93733E+14 1.0899E+15 -1.69323E+14 -1.16568E+15 -1.07282E+15 -4.55463E+14 3.3941E+14 7.78607E+14 -8.28677E+14 -1.6719E+15 7.9505E+13 -5.22268E+14 -7.87886E+14 5.68464E+14 -1.3173E+14 3.31501E+14 3.86786E+14 6.87531E+13 -8.34427E+14 -2.03978E+14 -5.64921E+14 9.6307E+14 1.47589E+14 4.32386E+13 -1.95386E+14 6.44405E+14 -2.14995E+14 -8.10099E+14 -6.6312E+14 1.0856E+16 -1.69554E+15 7.31326E+13 6.0177E+14 -2.91207E+14 2.3182E+14 -6.1933E+14

8.90004E+14 6.18507E+15 3.00257E+15 -6.67355E+16 2.80272E+16 -1.06591E+16 -1.02619E+17 -5.39497E+15 -1.77136E+15 -2.16247E+15 2.99458E+15 3.28381E+14 -2.87844E+15 1.91054E+15 9.00618E+15 7.53409E+15 1.66899E+15 1.69009E+15 -7.64828E+13 1.49898E+15 3.96979E+15 -8.76502E+14 3.81329E+15 3.85641E+15 3.85322E+14 -1.30474E+15 -2.27341E+15 -8.25926E+14 1.74582E+15 4.55319E+15 1.8938E+15 5.56966E+15 -5.61813E+15 -9.05268E+14 -5.13825E+15 -1.43746E+15 -5.40017E+15 -1.24757E+14 6.01366E+15 3.19282E+15 -3.34521E+16 5.87112E+15 1.50074E+15 -3.5953E+15 -1.50573E+14 -2.9834E+14 1.80901E+15

-4.11651E+15 -2.48572E+15 -4.76796E+15 4.92561E+16 2.20391E+15 -2.50702E+13 -2.3749E+16 -3.17757E+14 -1.58904E+15 1.65452E+15 -7.84568E+14 -3.91174E+13 2.12368E+15 -7.38494E+14 -2.41103E+15 -3.9428E+15 -5.31974E+14 -1.5752E+15 1.47177E+15 1.39797E+15 9.32335E+14 2.53528E+15 1.26977E+15 -4.02631E+15 1.64691E+15 -9.25E+14 -1.08359E+14 -2.10915E+15 2.75739E+15 -1.64733E+15 -2.75904E+15 -1.05644E+15 3.04972E+15 6.45185E+14 2.2199E+15 -1.64437E+15 8.29223E+14 -4.41496E+14 -2.59015E+15 3.05261E+15 2.38742E+16 -3.87624E+15 -1.20078E+15 6.18738E+14 -5.54142E+13 -3.80498E+14 -1.3182E+15

-1.387484419 -1.591051396 -1.914618373 -0.04989104 -0.377938176 -0.03999279 0.200828686 0.441650162 0.515973508 0.507047788 0.817243485 0.05907618 -0.213471579 0.637843041 0.101673242 0.536742537 -1.192663862 -2.408701026 -3.499864592 -3.259043116

-0.057210883 -0.433387974 -0.045860396 0.230293585 0.506447566 0.591675379 0.581440109 0.937146659 0.067743635 -0.244791401 0.731425194 0.116590393 0.61549157 -1.367647432 -2.762097416 -4.013352776 -3.737198795

-0.068845675 -0.521524685 -0.055186876 0.277127647 0.609442169 0.712002487 0.699685703 1.127731145 0.081520439 -0.294573836 0.880172771 0.140301005 0.7406621 -1.645781467 -3.323816235 -4.82953535 -4.497220828

-2.12818535 -1.831752326 -1.685319303 -1.83888628 -0.076525097 -0.579698393 -0.061342721 0.308039976 0.677422673 0.791423129 0.777732463 1.253524428 0.090613673 -0.327432209 0.978352043 0.155950944 0.82327959 -1.829360909 -3.694572828 -5.368248067 -4.998865369

-0.065865985 -0.498952726 -0.052798349 0.265133365 0.583065078 0.681186513 0.669402808 1.078922138 0.077992176 -0.281824471 0.842078267 0.134228677 0.708605717 -1.574550873 -3.179959102 -4.620509622 -4.302577908

-0.06060056 -0.459065698 -0.04857757 0.243938207 0.536453983 0.626731443 0.615889745 0.992671487 0.071757365 -0.259295001 0.774761269 0.123498236 0.651958715 -1.448678919 -2.925748411 -4.251139166 -3.958623389

-0.06612251 -0.50089595 -0.05300398 0.266165955 0.585335887 0.683839466 0.672009868 1.083124114 0.078295925 -0.28292207 0.84535783 0.134751445 0.711365457 -1.58068313 -3.19234379 -4.63850469 -4.31933475

-2.199605833 -2.916148606 -1.828961634 -1.435516872 -2.124309957 -1.356244401 -1.046048704 0.443508749 1.267073681 1.660518443 1.873590231 1.62879216 1.925113013 2.207559022 2.656503161 2.952824013 2.541527812 2.338354274 2.551426062 2.431501589 2.519699779 2.580148281 1.405735649 1.493933839 1.623756562 1.933952259 1.578155435 2.138098327 -0.396049035 -1.029342743 -2.717124609 -4.085785059 -4.941076274 -5.754742956 -2.69732811

-2.52232449 -3.343995973 -2.097300641 -1.646131006 -2.435981461 -1.555227949 -1.199521399 0.508578838 1.452974405 1.90414404 2.148476993 1.867762985 2.207559022 2.531444544 3.046256235 3.386052271 2.914412096 2.68142963 2.925762583 2.788243201 2.889381528 2.958698827 1.611980385 1.713118712 1.861988581 2.217695132 1.809697012 2.451792814 -0.454155997 -1.180364396 -3.115771855 -4.685237493 -5.666014115 -6.599059195 -3.093070881

-3.035281465 -4.024053619 -2.523821889 -1.980899345 -2.931379132 -1.871509628 -1.443464186 0.612006872 1.748461111 2.291383655 2.585405811 2.247603903 2.656503161 3.046256235 3.665763513 4.074662771 3.507106659 3.226743302 3.520765457 3.355279203 3.476985705 3.56039984 1.939803622 2.061510124 2.240655177 2.668700618 2.177729241 2.950405989 -0.546516233 -1.420411285 -3.749416301 -5.63805909 -6.818293082 -7.941088522 -3.722098703

-3.373853316 -4.47291851 -2.805342749 -2.201859663 -3.25836115 -2.08026802 -1.604476055 0.680273457 1.943494001 2.546977087 2.873796077 2.498313902 2.952824013 3.386052271 4.074662771 4.529172882 3.898308465 3.586671851 3.913490841 3.729545348 3.864827656 3.957546258 2.156179899 2.291462208 2.490590077 2.966382042 2.420645039 3.279510367 -0.607477635 -1.578851708 -4.167646647 -6.266958955 -7.578842684 -8.826880852 -4.137281895

-2.903912322 -3.849889714 -2.414589081 -1.895164611 -2.804506956 -1.790509359 -1.380990029 0.585518779 1.67278647 2.192210939 2.473507606 2.150326006 2.541527812 2.914412096 3.507106659 3.898308465 3.355316586 3.087087555 3.368384222 3.210060331 3.326499288 3.4063032 1.85584754 1.972286498 2.143678026 2.553197356 2.083475569 2.822710318 -0.522862622 -1.358934874 -3.587138894 -5.394039879 -6.523192503 -7.597392558 -3.561003621

-2.671769224 -3.542123767 -2.221563215 -1.743662315 -2.580310472 -1.64737336 -1.270591618 0.538711531 1.539061415 2.016962315 2.275771705 1.978425726 2.338354274 2.68142963 3.226743302 3.586671851 3.087087555 2.840301154 3.099110545 2.953443302 3.060573955 3.133998223 1.70748831 1.814618963 1.972309195 2.349090937 1.916919413 2.597058629 -0.481064201 -1.250299585 -3.300377641 -4.962832256 -6.001718729 -6.990045623 -3.276331661

-2.91522192 -3.86488352 -2.42399295 -1.90254553 -2.81542941 -1.79748269 -1.38636844 0.587799144 1.679301314 2.200748737 2.483140944 2.158700678 2.551426062 2.925762583 3.520765457 3.913490841 3.368384222 3.099110545 3.381502752 3.222562251 3.339454693 3.419569409 1.863075335 1.979967777 2.152026807 2.563141054 2.091589885 2.833703662 -0.52489897 -1.36422739 -3.60110939 -5.41504754 -6.54859777 -7.62698141 -3.57487233

80

100

200

500

1000

>1000

8.56

8.55

8.54

8.53

8.53

8.54

5.67

5.66

5.65

5.64

5.63

5.63

4.42

4.41

4.39

4.37

4.37

4.36

3.72

3.71

3.69

3.68

3.67

3.67

3.29

3.27

3.25

3.24

3.23

3.23

2.99

2.97

2.95

2.94

2.93

2.93

2.77

2.76

2.73

2.72

2.71

2.71

df1/df2 3 4 5 6 7 8 9

2.6

2.59

2.56

2.55

2.54

2.54

2.47

2.46

2.43

2.42

2.41

2.41

2.36

2.35

2.32

2.31

2.3

2.3

2.27

2.26

2.23

2.22

2.21

2.21

2.2

2.19

2.16

2.14

2.14

2.13

2.14

2.12

2.1

2.08

2.07

2.07

2.08

2.07

2.04

2.02

2.02

2.01

2.03

2.02

1.99

1.97

1.97

1.96

1.99

1.98

1.95

1.93

1.92

1.92

1.96

1.94

1.91

1.89

1.88

1.88

1.92

1.91

1.88

1.86

1.85

1.84

1.86

1.85

1.82

1.8

1.79

1.78

1.82

1.8

1.77

1.75

1.74

1.73

1.78

1.76

1.73

1.71

1.7

1.69

1.74

1.73

1.69

1.67

1.66

1.66

1.71

1.7

1.66

1.64

1.63

1.62

1.65

1.63

1.6

1.57

1.57

1.56

1.61

1.59

1.55

1.53

1.52

1.51

1.57

1.55

1.51

1.49

1.48

1.47

1.54

1.52

1.48

1.46

1.45

1.44

1.5

1.48

1.44

1.41

1.4

1.39

1.47

1.45

1.4

1.37

1.36

1.35

1.45

1.43

1.38

1.35

1.34

1.33

1.41

1.39

1.34

1.31

1.3

1.28

1.35

1.32

1.26

1.22

1.21

1.19

1.3

1.28

1.21

1.16

1.14

1.12

1.29

1.26

1.19

1.13

1.11

1.08

1.28

80

1.25

100

1.17

200

1.11

500

1.08

1000

1.03

>1000

10 11 12 13 14 15 16 17 18 19 20 22 24 26 28 30 35 40 45 50 60 70 80 100 200 500 1000 >1000 df1\df2

8.33352E+16 -6.24436E+16 -5.43074E+16 1.97972E+16 5.95164E+16 8.91578E+16 1.56259E+17 1.71752E+16 -9.67623E+15 -7.56148E+15 -7.63813E+15 1.30617E+16 2.16787E+16 3.93245E+15 9.33403E+15 3.15453E+16 -1.21362E+16 -2.92887E+16 3.37169E+16 2.03095E+16 -7.0345E+16 -2.25076E+16 1.65771E+16 1.30763E+16 -1.11109E+15 -1.06455E+16 -2.96111E+16 -2.2486E+16 1.8434E+16 -8.07314E+15 -8.08319E+15 -1.32098E+16 1.11397E+16 1.97371E+16 -1.4001E+16

1.89893E+15 9.89376E+14 4.01895E+15 3.80094E+16 -2.86643E+16 1.00045E+16 7.44381E+16 1.09992E+15 2.13005E+15 7.06945E+14 -1.41912E+15 2.1213E+14 4.12992E+14 -1.71231E+14 -5.06268E+15 -2.54821E+15 -1.67108E+15 -3.97034E+14 2.37791E+14 -8.97624E+15 -2.6833E+15 -1.62448E+15 -3.28452E+15 1.48582E+13 -7.28377E+14 1.17598E+15 1.07651E+15 1.2556E+15 -2.21063E+15 -2.74248E+15 9.52044E+13 -2.38201E+15 2.2728E+15 2.88893E+14 1.62541E+15 1.72761E+15 2.45319E+15 8.18409E+14 -2.16535E+15 -4.30308E+15 1.01724E+16 -3.25164E+15 4.1045E+14 2.47158E+15 2.61099E+14 4.82959E+14 -3.9142E+14

-2.34606E+15 6.8876E+14 4.41195E+14 -2.64389E+16 5.79363E+15 -4.67056E+15 -2.73292E+16 -2.32287E+15 -6.89355E+14 -3.40529E+14 5.43232E+14 1.12729E+14 -1.15312E+15 9.28871E+14 2.35521E+15 1.75312E+15 3.62125E+14 3.68439E+14 -1.03468E+15 1.77124E+15 3.14207E+14 8.46797E+14 1.22872E+15 3.4476E+14 -2.49802E+14 -1.87716E+14 3.89798E+13 -7.5021E+14 1.07981E+15 1.71199E+15 -4.22762E+14 1.28226E+15 -1.57988E+15 1.41431E+14 -2.24014E+15 5.51468E+13 -1.88144E+15 -1.21388E+14 2.48445E+15 1.31426E+15 -1.30941E+16 1.1608E+13 3.08966E+14 -1.22779E+15 3.29574E+14 -7.90781E+13 1.23474E+15

2.1178E+15 6.65854E+13 5.83433E+14 -3.32692E+16 8.95543E+15 -3.22987E+15 -2.55194E+16 -6.65915E+14 -6.72452E+14 -4.20626E+14 7.26989E+14 -1.78157E+14 -5.7467E+14 4.0019E+14 2.86166E+15 1.95789E+15 1.6538E+14 -1.01745E+14 -1.24927E+15 1.87096E+15 3.19787E+14 -1.70932E+14 1.87745E+15 1.14535E+15 3.18871E+14 -3.67424E+14 -5.16487E+14 -4.13042E+12 2.33879E+13 1.14903E+15 4.3712E+14 1.70136E+15 -1.58428E+15 -4.6813E+14 -1.03464E+15 -1.64222E+14 -1.78655E+15 -3.13604E+14 1.17123E+15 9.45889E+14 -9.5136E+15 2.24113E+15 5.44441E+14 -9.77584E+14 -7.14445E+12 -3.559E+13 4.63834E+14

-1.68606E+15 -2.08324E+15 -3.20856E+15 4.83905E+15 7.69595E+15 -1.47645E+15 -2.01955E+16 7.77592E+13 -1.5448E+15 7.49757E+14 -6.46221E+14 -6.07535E+12 4.6247E+14 1.04697E+14 1.20604E+14 -1.59458E+15 -7.70756E+14 -9.57772E+14 -1.96572E+15 2.28921E+15 -6.23856E+14 2.43131E+15 1.72584E+15 -1.72474E+15 8.25479E+14 -3.58277E+14 2.05831E+14 -1.97626E+15 1.85747E+15 -7.07622E+13 -1.97639E+15 -1.81858E+14 4.82959E+14 2.91391E+14 6.10995E+13 -1.3239E+15 -1.44704E+15 -6.36033E+14 -8.45033E+14 2.7159E+15 7.59215E+15 -1.67419E+15 -5.36818E+14 -2.12989E+14 -4.42927E+13 -3.27374E+14 -1.4996E+14

9.06913E+14 -1.69082E+15 1.25855E+15 2.86014E+16 -1.71583E+16 7.08987E+15 5.59505E+16 2.46086E+15 1.21813E+15 9.79035E+14 -1.01922E+15 2.57119E+14 1.03688E+14 -1.20422E+14 -4.05712E+15 -3.0995E+15 -5.59925E+14 -3.64813E+14 -2.85309E+14 -6.31486E+14 -1.66002E+15 -2.9534E+14 -2.45337E+15 -6.12459E+14 -1.24835E+15 1.46448E+15 9.56398E+14 9.9971E+14 -2.41101E+15 -2.18983E+15 -2.20657E+14 -2.67457E+15 1.94298E+15 1.47192E+14 1.24641E+15 3.03451E+15 2.50106E+15 4.98895E+14 -1.79155E+15 -2.74489E+15 3.74501E+15 -1.80516E+15 -3.06587E+13 1.99548E+15 5.03712E+14 3.72955E+14 -3.53968E+14

-2.62394E+15 -2.48403E+15 1.05697E+15 5.17874E+16 -3.01019E+16 9.98448E+15 8.07642E+16 4.52084E+15 2.27896E+15 3.90699E+14 -1.95253E+15 4.09242E+14 2.3251E+14 -6.89669E+14 -5.40833E+15 -2.58196E+15 -6.76448E+14 -7.34711E+14 8.77322E+14 -6.54078E+15 -3.61077E+15 -8.43487E+14 -4.0646E+15 -1.35752E+15 -1.89669E+15 1.305E+15 1.45973E+15 8.5968E+14 -2.07562E+15 -2.35242E+15 -4.11127E+14 -3.26382E+15 2.95161E+15 7.59397E+14 2.04754E+15 2.18799E+15 3.07527E+15 1.19054E+15 -2.02493E+15 -3.91537E+15 7.10192E+15 -3.2481E+15 -4.67419E+14 2.10679E+15 4.44364E+14 3.30236E+14 2.37245E+13

-7.7838E+15 -6.0072E+15 -6.9032E+15 6.65762E+16 -6.6559E+15 4.18437E+15 1.88685E+16 6.90517E+14 -1.2341E+15 2.85053E+15 -2.2573E+15 6.90584E+13 2.24645E+15 -6.2624E+14 -4.3991E+15 -6.8381E+15 -1.7653E+15 -3.1302E+15 -2.2047E+15 1.43341E+15 -1.2001E+15 4.10885E+15 1.54456E+15 -5.9786E+15 5.57224E+14 -8.4652E+13 1.55679E+15 -2.6652E+15 2.39093E+15 -2.9964E+15 -5.2148E+15 -3.4285E+15 4.58048E+15 1.45458E+15 3.67052E+15 -4.0402E+14 2.18663E+15 -1.5893E+15 -4.6633E+15 3.66395E+15 2.67605E+16 -5.6875E+15 -1.8875E+15 1.63797E+15 9.29369E+13 -3.9395E+14 -8.3599E+14

-1.752453257 -1.816020234 -1.859587211 -1.013154188 -1.076721165 -1.170288141 -1.393855118 -0.063014557 -0.477352378 -0.050512636 0.253655378 0.557823392 0.651697015 0.640423442 1.032214119 0.074615788 -0.269623903 0.805623544 0.128417734 0.677929204 -1.506386407 -3.042294313 -4.420481426 -4.116313412

-0.065300292 -0.494667446 -0.052344888 0.262856254 0.578057396 0.67533611 0.66365361 1.069655763 0.077322337 -0.279404008 0.834846037 0.133075848 0.702519823 -1.561027768 -3.152647871 -4.580826154 -4.265625012

-0.06686687 -0.506534696 -0.05360066 0.26916227 0.5919252 0.691537665 0.679574898 1.095317189 0.079177327 -0.28610701 0.854874293 0.136268385 0.719373525 -1.598477384 -3.228281025 -4.690721817 -4.367958886

-0.036430907 -0.275974015 -0.029203112 0.146646997 0.322497107 0.376768714 0.370251069 0.596758888 0.043137983 -0.155878957 0.465758995 0.074242759 0.391934455 -0.870894382 -1.75885617 -2.555634081 -2.379783971

-0.038716643 -0.293289083 -0.031035364 0.155847874 0.342731111 0.400407809 0.393481237 0.634200532 0.045844531 -0.165659062 0.494981488 0.078900873 0.416525074 -0.925535743 -1.869209728 -2.715978808 -2.529095571

-0.042081116 -0.318775879 -0.033732334 0.169391041 0.372514415 0.435203213 0.427674722 0.689312504 0.049828417 -0.18005482 0.537995337 0.085757352 0.452721067 -1.005964719 -2.031643893 -2.951997134 -2.748873759

-0.050120117 -0.379673496 -0.040176419 0.2017508 0.443678019 0.518342624 0.509375922 0.820995897 0.059347431 -0.214451744 0.640771727 0.10214008 0.539207016 -1.198140033 -2.419760688 -3.515934383 -3.274007164

-2.778197977 -3.68322271 -2.310058209 -1.813120337 -2.683096005 -1.712995754 -1.321205077 0.560170868 1.60036925 2.097307122 2.366426071 2.057235445 2.431501589 2.788243201 3.355279203 3.729545348 3.210060331 2.953443302 3.222562251 3.071092418 3.182490574 3.258839664 1.775505356 1.886903512 2.050875265 2.442665942 1.993279055 2.700511318 -0.500227182 -1.30010472 -3.431846733 -5.160524498 -6.240794557 -7.268491018 -3.406842892

-2.878971932 -3.816824752 -2.393851267 -1.878887899 -2.780420314 -1.775131483 -1.36912933 0.580490023 1.658419663 2.173383031 2.452263768 2.131857828 2.519699779 2.889381528 3.476985705 3.864827656 3.326499288 3.060573955 3.339454693 3.182490574 3.29792949 3.377048002 1.839908505 1.955347421 2.125266944 2.531269098 2.065581539 2.798467335 -0.518371991 -1.347263596 -3.55633058 -5.347712909 -6.467167752 -7.532141988 -3.530419771

-2.948039502 -3.908391747 -2.451280618 -1.923963094 -2.847123595 -1.817717524 -1.401975233 0.594416187 1.698205746 2.225523269 2.511094455 2.183001862 2.580148281 2.958698827 3.56039984 3.957546258 3.4063032 3.133998223 3.419569409 3.258839664 3.377048002 3.458064595 1.88404857 2.002256907 2.176252861 2.591995152 2.115135581 2.86560357 -0.530807921 -1.379584933 -3.641648226 -5.47600646 -6.622317426 -7.712840776 -3.615115808

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-1.07189E+15 -7.77667E+15 -7.7554E+15 7.20554E+16 8.15237E+13 6.64619E+15 2.26983E+16 3.71562E+15 -1.04859E+15 2.50005E+15 -1.18798E+15 -1.73999E+14 4.52573E+15 -2.15162E+15 -5.50768E+15 -6.11776E+15 1.97835E+14 6.01787E+14 6.66304E+14 -2.35175E+14 2.52395E+15 3.08641E+15 6.17789E+14 -4.79774E+15 8.16218E+14 -5.97338E+13 3.90424E+14 -1.47057E+15 8.42268E+14 -2.91853E+15 -2.8331E+15 -2.87533E+15 3.82049E+15 8.4576E+14 3.95601E+15 -1.73883E+15 3.62136E+15 -1.23473E+15 -4.89088E+15 2.08655E+15 3.14661E+16 -4.35498E+15 -2.40599E+15 1.41617E+15 -3.72786E+14 -1.36984E+14 -2.3771E+15

2.97633E+15 4.18359E+15 -6.30072E+14 -2.03584E+16 2.25078E+16 -6.4982E+15 -4.8884E+16 -3.16198E+15 -1.90268E+15 -6.54973E+14 1.25783E+15 -4.04821E+13 -9.88747E+14 7.96238E+14 4.25325E+15 2.94427E+15 -2.76339E+14 1.0857E+14 -3.17412E+14 -8.16698E+13 1.69626E+15 -1.93574E+14 2.54275E+15 1.34268E+15 8.20675E+14 -8.08433E+14 -9.25791E+14 -8.64432E+14 1.37966E+15 2.38207E+15 3.48934E+14 2.61432E+15 -2.49166E+15 -3.97161E+14 -1.56622E+15 -1.4637E+15 -3.54345E+15 -1.71083E+14 1.76406E+15 2.17866E+15 -6.69032E+15 2.27959E+15 6.97686E+14 -1.65778E+15 -3.67436E+14 -1.34056E+14 4.51366E+14

-1.0627E+15 -1.31455E+15 -1.54271E+15 3.39848E+16 -1.23573E+16 5.19725E+15 3.94278E+16 7.34857E+14 1.05804E+15 9.95798E+14 -1.38478E+15 2.3233E+14 1.69689E+15 -9.39473E+14 -3.85357E+15 -3.30708E+15 -9.47276E+14 -9.89019E+14 1.16169E+15 -1.62532E+15 -1.45473E+15 1.41363E+14 -1.49167E+15 -1.91859E+15 3.74587E+13 2.42228E+14 5.58715E+14 7.12099E+13 -3.77967E+14 -2.06948E+15 -7.62832E+14 -2.02701E+15 2.99834E+15 3.83786E+14 2.22594E+15 4.24404E+14 2.37E+15 -7.93347E+13 -2.71889E+15 -1.03089E+15 1.75321E+16 -3.53455E+15 -4.17353E+14 1.71647E+15 -6.79578E+13 -4.78005E+12 -1.01611E+15

1.9003E+15 1.4171E+15 2.17784E+15 -2.79411E+16 1.5844E+15 -7.87174E+14 -2.05715E+15 -2.08942E+14 4.75471E+14 -8.61087E+14 5.62146E+14 -1.02131E+14 -1.06031E+15 2.42111E+14 1.2716E+15 2.16079E+15 4.88246E+14 1.08698E+15 5.7926E+14 3.03211E+13 3.57734E+14 -1.43801E+15 -7.82808E+14 1.87499E+15 -4.54045E+14 5.11397E+14 -2.91344E+14 1.05317E+15 -9.29563E+14 1.00286E+15 1.50017E+15 8.39523E+14 -1.56531E+15 -4.02035E+14 -9.99069E+14 3.65694E+14 -8.34085E+14 7.03312E+14 1.47101E+15 -1.38131E+15 -1.10558E+16 1.96946E+15 5.86166E+14 -5.12927E+14 -3.77586E+13 2.00878E+14 4.86502E+14

4.147609067

1.94404209

0.149139354 1.129771104 0.119550502 -0.600337465 -1.320225431 -1.54240031 -1.515718645 -2.442987066 -0.176596504 0.638130883 -1.906705073 -0.303931962 -1.604485199 3.565231709 7.200333262 10.46215 9.742262033

0.069903691 0.529539439 0.056034984 -0.281386524 -0.618808033 -0.72294449 -0.710438423 -1.145062036 -0.082773239 0.299100826 -0.893699202 -0.14245714 -0.752044542 1.671073718 3.374896404 4.903755302 4.566333793

6.575284716 8.717247006 5.467317508 4.291192544 6.350202651 4.054223239 3.126954819 -1.325781308 -3.787665083 -4.963790048 -5.600725833 -4.868950627 -5.754742956 -6.599059195 -7.941088522 -8.826880852 -7.597392558 -6.990045623 -7.626981409 -7.268491018 -7.532141988 -7.712840776 -4.202167495 -4.465818464 -4.853897706 -5.781166126 -4.717582195 -6.391420247 1.18390992 3.077015665 8.122304301 12.21364285 14.77036605 17.20266097 8.063126599

3.081927452 4.085894985 2.562607802 2.011341664 2.976428356 1.900270853 1.46564724 -0.62141215 -1.775331336 -2.326597474 -2.625138141 -2.282144918 -2.69732811 -3.093070881 -3.722098703 -4.137281895 -3.561003621 -3.276331661 -3.574872327 -3.406842892 -3.530419771 -3.615115808 -1.969614384 -2.093191263 -2.275089404 -2.709713017 -2.211196427 -2.995747616 0.554915055 1.442240064 3.80703706 5.724704376 6.923076119 8.063126599 3.779299648

-2.78934E+16 7.13638E+15 -2.39524E+15 6.42071E+15 1.73338E+16 1.43916E+16 4.01827E+15 -2.47624E+15 -1.69804E+15 7.9805E+15

-2.28998E+13 -5.31433E+14 -2.15802E+12 -7.58924E+15 1.32771E+15 -6.67666E+14 -1.11206E+16 4.37651E+14 1.34446E+13 -2.50583E+14 1.5605E+14 2.03853E+14 -7.85659E+14 1.70058E+14 6.14868E+14 4.82528E+14 4.15438E+14 4.42855E+14 -6.07545E+13 2.29961E+15 9.55605E+13 2.07426E+14 9.53983E+13 5.19284E+14 -4.76899E+14 1.50455E+14 3.14189E+13 2.94984E+12 -1.26033E+14 4.67768E+14 -5.10246E+13 1.72795E+14 -8.66292E+14 -2.11411E+13 -4.17818E+14 7.08269E+14 -1.40129E+14 -4.26582E+12 6.30221E+14 2.1224E+14 -5.6739E+15 1.36009E+15 -3.21073E+13 -4.24595E+14 1.72841E+14 2.17331E+13 3.3827E+14

1.23087E+15 1.27567E+15 2.33816E+15 -9.39395E+15 -9.05395E+15 3.08739E+15 2.77758E+16 -9.48362E+13 1.12789E+15 1.80887E+14 -2.58682E+14 2.61813E+14 1.03899E+14 -1.01301E+14 -1.551E+15 -4.70455E+14 -1.12587E+14 8.74365E+14 2.30464E+14 -2.52089E+15 -1.37061E+13 -9.44723E+14 -1.51803E+15 5.20496E+14 -8.41613E+14 8.48113E+14 8.78545E+13 7.0075E+14 -9.93111E+14 -8.15861E+14 4.69133E+14 -5.831E+14 6.38839E+14 -1.07031E+14 1.22093E+14 1.4022E+15 1.22964E+15 5.44822E+14 9.30734E+12 -1.87259E+15 -3.30487E+14 -3.01551E+14 2.70048E+14 8.84455E+14 1.58673E+14 1.71131E+14 -6.2254E+13

Weighted Regression Pt

Pt/√t

t

0.98 1.35 1.24 1.2 1.16 1.24 1.38 1.29 1.97 2.3 1.82 2.34 2.16 3.54 4.55 5.47 5.43 4.8 5.45 4.8 4.65 5.28 4.86 4.77 3.83 3.37 3.22 3.2 3.51 3.43 3.36 3.17 3.09 3.52 3.8 3.78 4 4.07 4.16 5.14 5.21 5.25 5.16 5.55

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

1/√t √t 0.98 1 1 SUMMARY OUTPUT 0.954594 0.707107 1.414214 0.715914 0.6 0.518768 0.506228 0.521591 0.456084

0.57735 0.5 0.447214 0.408248 0.377964 0.353553

1.732051 2 2.236068 2.44949 2.645751 2.828427

Regression Statistics Multiple R 0.951378 R Square 0.905119 Adjusted R Square 0.883222 Standard Error 0.286538 Observations 52

0.656667 0.333333 3 0.727324 0.316228 3.162278 ANOVA 0.548751 0.301511 3.316625 0.6755 0.288675 3.464102 Regression 0.599076 0.27735 3.605551 Residual 0.946105 0.267261 3.741657 Total

df

SS MS 2 39.16174 19.58087 50 4.105199 0.082104 52 43.26694

1.174805 0.258199 3.872983 1.3675 0.25 4 Coefficients Standard Error t Stat 1.316968 0.242536 4.123106 Intercept 0 #N/A #N/A 1.131371 0.235702 4.242641 X Variable 1 0.88793 0.178537 4.973372 1.250316 0.229416 4.358899 X Variable 2 0.130644 0.010246 12.75124 1.073313 1.014713 1.1257 1.01338

0.223607 0.218218 0.213201 0.208514

4.472136 4.582576 4.690416 4.795832 RESIDUAL OUTPUT

0.973672 0.204124 4.898979 0.766 0.660911 0.619689 0.604743 0.651791 0.626229 0.603474 0.560382 0.5379 0.603675 0.642317 0.63 0.657596 0.660241 0.666133 0.812705 0.813665 0.810093 0.786893 0.836694

0.2 0.196116 0.19245 0.188982 0.185695 0.182574 0.179605 0.176777 0.174078 0.171499 0.169031 0.166667 0.164399 0.162221 0.160128 0.158114 0.156174 0.154303 0.152499 0.150756

5ObservationPredicted Y Residuals 5.09902 1 1.018574 -0.03857 5.196152 2 0.81262 0.141974 5.291503 3 0.738929 -0.02301 5.385165 4 0.705253 -0.10525 5.477226 5 0.689224 -0.17046 5.567764 6 0.682507 -0.17628 5.656854 7 0.681258 -0.15967 5.744563 8 0.683448 -0.22736 5.830952 9 0.687909 -0.03124 5.91608 10 0.693921 0.033403 6 11 0.701019 -0.15227 6.082763 12 0.708888 -0.03339 6.164414 13 0.717312 -0.11824 6.244998 14 0.726135 0.21997 6.324555 15 0.735245 0.43956 6.403124 16 0.744559 0.622941 6.480741 17 0.754014 0.562954 6.557439 18 0.763563 0.367808 6.63325 19 0.77317 0.477146

5.28 7.24 7.83 9.18 10.3 11.05 11.77 9.7

45 46 47 48 49 50 51 52

0.787096 1.06748 1.142123 1.325019 1.471429 1.562706 1.64813 1.345148

0.149071 0.147442 0.145865 0.144338 0.142857 0.141421 0.140028 0.138675

6.708204 6.78233 6.855655 6.928203 7 7.071068 7.141428 7.211103

9.708456

Pt

Pt/√t

t

0.98 1.35 1.24 1.2 1.16 1.24 1.38 1.29 1.97 2.3 1.82 2.34

1 2 3 4 5 6 7 8 9 10 11 12

1/√t

√t

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

0.782806 0.792449 0.802083 0.811694 0.821271 0.830807 0.840294 0.849729 0.859107 0.868425 0.877681 0.886873 0.896 0.905062 0.914059 0.922989 0.931853 0.940652 0.949386 0.958055 0.96666 0.975202 0.983681 0.992099 1.000456 1.008752 1.01699 1.025169 1.033291 1.041356 1.049366 1.057321 1.065222

0.290507 0.222264 0.323617 0.201687 0.152401 -0.06481 -0.17938 0.06416 -0.23004 -0.25436 -0.21663 -0.25145 -0.2834 -0.33562 -0.36716 -0.31038 -0.28067 -0.30185 -0.28306 -0.28914 -0.29192 -0.15395 -0.16154 -0.17359 -0.20521 -0.16376 -0.22166 0.05049 0.116954 0.291728 0.430072 0.51334 0.590809 0.279926 0.080206

SUMMARY OUTPUT

0.98

1

1

0.954594 0.715914 0.6 0.518768 0.506228 0.521591

0.707107 0.57735 0.5 0.447214 0.408248 0.377964

1.414214 1.732051 2 2.236068 2.44949 2.645751


0.456084 0.353553 2.828427 0.656667 0.333333 3

ANOVA

0.727324 0.316228 3.162278 0.548751 0.301511 3.316625 0.6755 0.288675 3.464102

Regression Residual

df

SS 2 5.357167 10 0.110111

Total

12 5.467278

Coefficients Standard Error Intercept 0 #N/A X Variable 1 0.925946 0.093592 X Variable 2 0.091777 0.018668 Pt

t

5.21 5.25 5.16 5.55 5.28 7.24 7.83 9.18 10.3 11.05 11.77 9.7

41 42 43 44 45 46 47 48 49 50 51 52

Pt/√t 1/√t √t 0.813665 0.156174 6.403124 0.810093 0.786893 0.836694 0.787096 1.06748 1.142123

0.154303 0.152499 0.150756 0.149071 0.147442 0.145865

6.480741 6.557439 6.63325 6.708204 6.78233 6.855655

1.325019 0.144338 6.928203 1.471429 0.142857 7 1.562706 0.141421 7.071068 1.64813 0.140028 7.141428 1.345148 0.138675 7.211103


SS 2 16.3812 10 0.208417 12 16.58962

Coefficients Standard Error Intercept 0 #N/A X Variable 1 -22.1917 3.809163 X Variable 2 0.644839 0.082145

ln(Pt) t -0.0202 0.300105

1 2

0.215111 0.182322 0.14842 0.215111 0.322083 0.254642

3 4 5 6 7 8

0.678034 0.832909

9 10

0.598837 0.850151 0.770108 1.264127

11 12 13 14

1.515127

15

P-value Lower 95%Upper 95%Lower 95.0% Upper 95.0% #N/A #N/A #N/A #N/A #N/A 8.15E-06 0.529328 1.246532 0.529328 1.246532

1.699279 1.691939 1.568616

16 17 18

2.46E-17 0.110065 0.151223 0.110065 0.151223

1.695616

19

1.568616 1.536867 1.663926 1.581038

20 21 22 23

1.562346

24

1.342865 1.214913 1.169381 1.163151 1.255616 1.23256 1.211941 1.153732 1.128171 1.258461 1.335001 1.329724 1.386294 1.403643 1.425515 1.637053 1.65058 1.658228 1.640937 1.713798

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44


Regression

Observation

1.663926 1.979621 2.057963 2.217027 2.332144 2.40243 2.465554 2.272126


45 46 47 48 49 50 51 52

t Stat P-value Lower 95%Upper 95%Lower 95.0% Upper 95.0% #N/A #N/A #N/A #N/A #N/A #N/A 9.893456 1.75E-06 0.717411 1.134482 0.717411 1.134482 4.91632 0.000608 0.050183 0.133372 0.050183 0.133372


t Stat P-value Lower 95%Upper 95%Lower 95.0% Upper 95.0% #N/A #N/A #N/A #N/A #N/A #N/A -5.82587 0.000167 -30.679 -13.7043 -30.679 -13.7043 7.849992 1.39E-05 0.461808 0.82787 0.461808 0.82787

SUMMARY OUTPUT Regression Statistics Multiple R 0.838243 R Square 0.702652 Adjusted R Square 0.696705 Standard Error0.34221 Observations 52 ANOVA df Regression Residual Total

SS MS 1 13.83665 13.83665 50 5.855395 0.117108 51 19.69205


Coefficients Standard Error t Stat P-value Lower 95%Upper 95%Lower 95.0% Upper 95.0% Intercept 0.385296 0.096298 4.001095 0.000208 0.191877 0.578716 0.191877 0.578716 X Variable 1 0.03437 0.003162 10.86982 9.02E-15 0.028019 0.040721 0.028019 0.040721

RESIDUAL OUTPUT ObservationPredicted Y Residuals 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0.419666 0.454037 0.488407 0.522777 0.557147 0.591517 0.625887 0.660258 0.694628 0.728998 0.763368 0.797738 0.832108 0.866479 0.900849 0.935219 0.969589 1.003959 1.038329 1.072699

-0.43987 -0.15393 -0.2733 -0.34046 -0.40873 -0.37641 -0.3038 -0.40562 -0.01659 0.103911 -0.16453 0.052413 -0.062 0.397648 0.614279 0.76406 0.72235 0.564657 0.657286 0.495916

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

1.10707 1.14144 1.17581 1.21018 1.24455 1.27892 1.313291 1.347661 1.382031 1.416401 1.450771 1.485141 1.519511 1.553882 1.588252 1.622622 1.656992 1.691362 1.725732 1.760103 1.794473 1.828843 1.863213 1.897583 1.931953 1.966323 2.000694 2.035064 2.069434 2.103804 2.138174 2.172544

0.429798 0.522486 0.405229 0.352166 0.098315 -0.06401 0.161153 -0.14391 -0.18451 -0.12641 -0.18384 -0.23883 -0.33141 -0.39134 -0.29542 -0.25325 -0.2929 -0.2707 -0.28772 -0.30022 -0.12305 -0.14389 -0.17061 -0.22228 -0.18379 -0.26803 0.013298 0.057269 0.181963 0.26271 0.298626 0.32738 0.099582 0.042119

WN Weekly Stock Prices, 2010 and Heteroskedasticity Closing Week Ending Price 1/4/2010 0.98 1/11/2010 1.35 1/19/2010 1.24 1/25/2010 1.2 2/1/2010 1.16 2/8/2010 1.24 2/16/2010 1.38 2/22/2010 1.29 3/1/2010 1.97 3/8/2010 2.3 3/15/2010 1.82 3/22/2010 2.34 3/29/2010 2.16 4/5/2010 3.54 4/12/2010 4.55 4/19/2010 5.47 4/26/2010 5.43 5/3/2010 4.8 5/10/2010 5.45 5/17/2010 4.8 5/24/2010 4.65 6/1/2010 5.28 6/7/2010 4.86 6/14/2010 4.77 6/21/2010 3.83 6/28/2010 3.37 7/6/2010 3.22 7/12/2010 3.2 7/19/2010 3.51 7/26/2010 3.43 8/2/2010 3.36 8/9/2010 3.17 8/16/2010 3.09 8/23/2010 3.52 8/30/2010 3.8 9/7/2010 3.78 9/13/2010 4 9/20/2010 4.07 9/27/2010 4.16 10/4/2010 5.14 10/11/2010 5.21 10/18/2010 5.25 10/25/2010 5.16

t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43


1 50 51

SS MS 208.9615283 208.9615283 124.0430717 2.480861434 333.0046

Coefficients Standard Error t Stat 0.81047511 0.443224891 1.828586639 0.13356698 0.014553491 9.177658932


RESIDUAL OUTPUT Observation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Predicted Y 0.94404209 1.07760907 1.21117604 1.34474302 1.47831 1.61187697 1.74544395 1.87901093 2.0125779 2.14614488 2.27971186 2.41327884 2.54684581 2.68041279 2.81397977 2.94754674 3.08111372 3.2146807 3.34824767

Residuals 0.03595791 0.272390933 0.028823956 -0.144743021 -0.318309997 -0.371876974 -0.365443951 -0.589010928 -0.042577905 0.153855118 -0.459711859 -0.073278835 -0.386845812 0.859587211 1.736020234 2.522453257 2.34888628 1.585319303 2.101752326

11/1/2010 5.55 11/8/2010 5.28 11/15/2010 7.24 11/22/2010 7.83 11/29/2010 9.18 12/6/2010 10.3 12/13/2010 11.05 12/20/2010 11.77 12/27/2010 9.7 Date Adj Close

44 45 46 47 48 49 50 51 52 T

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

3.48181465 3.61538163 3.7489486 3.88251558 4.01608256 4.14964953 4.28321651 4.41678349 4.55035047 4.68391744 4.81748442 4.9510514 5.08461837 5.21818535 5.35175233 5.4853193 5.61888628 5.75245326 5.88602023 6.01958721 6.15315419 6.28672116 6.42028814 6.55385512 6.6874221 6.82098907 6.95455605 7.08812303 7.22169 7.35525698 7.48882396 7.62239093 7.75595791

1.31818535 1.034618373 1.531051396 0.977484419 0.753917442 -0.319649535 -0.913216512 0.984244555 -1.196783488 -1.350350465 -1.173917442 -1.387484419 -1.591051396 -1.914618373 -2.12818535 -1.831752326 -1.685319303 -1.83888628 -1.752453257 -1.816020234 -1.859587211 -1.013154188 -1.076721165 -1.170288141 -1.393855118 -1.137422095 -1.540989072 0.285443951 0.741876974 1.958309997 2.944743021 3.561176044 4.147609067 1.94404209 3.435193485

(eeT)-1

7.2917E+18 9.6233E+17 -1.534E+18 -1.55E+18 5.7858E+17 1.5981E+16 -2.284E+17 -1.175E+17

2.706E+18 -9.598E+17 3.9911E+17 3.0315E+18 1.5829E+17 6.2408E+16 7.0225E+16 -9.54E+16 6.4085E+15 1.326E+17 -5.86E+16 -2.999E+17 -2.331E+17 -7.859E+16 -8.212E+16 4.2892E+16 -1.134E+17 -1.571E+17 1.5158E+16 -9.227E+16 -1.394E+17 -7.914E+15 4.8806E+16 5.3527E+16 3.9165E+15 -4.041E+16 -1.654E+17 -6.46E+16 -1.531E+17 2.1675E+17 7.4251E+15 1.8084E+17 3.5306E+16 1.6466E+17 -1.41E+15 -2.106E+17 -6.706E+16

y

X 0.98 1

1

X

T

=

1

1

1

1.35 1.24 1.2 1.16 1.24 1.38 1.29 1.97 2.3 1.82 2.34 2.16 3.54 4.55 5.47 5.43

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

2 1 2 3 3 4 XT(eeT)-1 = 5 1.075E+19 -7.79247E+17 7.94581E+18 6 7.781E+19 -5.26601E+18 6.42865E+19 7 XT(eeT)-1 X = 8 2.089E+19 1.14326E+20 9 1.731E+20 1.07236E+21 10 T T -1 -1 11 ( X (ee ) X ) = 4.106E-19 -4.37802E-20 12 -6.628E-20 7.99888E-21 13 XT(eeT)-1 y = 14 3.22E+19 15 2.835E+20 16 T T -1 -1 T T -1 17 ( X (ee ) X ) X (ee ) y = 0.810475113 = b0

4.8 5.45 4.8 4.65 5.28 4.86 4.77 3.83 3.37 3.22 3.2 3.51 3.43 3.36 3.17 3.09 3.52 3.8 3.78 4 4.07 4.16 5.14 5.21 5.25 5.16 5.55 5.28 7.24 7.83

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

0.133566977 = b1

9.18 10.3 11.05 11.77 9.7

1 1 1 1 1

48 49 50 51 52


P-value Lower 95% 0.07342955 -0.079768262 2.6589E-12 0.10433543

Upper 95% Lower 95.0% Upper 95.0% 1.700718488 -0.079768262 1.700718488 0.162798523 0.10433543 0.162798523

eT 0.03595791 eeT

0.272390933

0.00129297 0.00979461 0.00103645 -0.00520466 -0.01144576 -0.01337192 -0.0131406 -0.0211796 -0.00153101 0.00553231 -0.01653028 -0.00263495 -0.01391017 0.03090896 0.06242366 0.09070215 0.08446104

0.009794609 0.07419682 0.007851384 -0.039426686 -0.086704757 -0.101295916 -0.099543619 -0.160441236 -0.011597835 0.041908739 -0.125221342 -0.01996049 -0.105373292 0.234143762 0.472876171 0.687093397 0.639815326

0.028823956 -0.144743021 -0.318309997 -0.371876974 -0.365443951 0.001036449 0.007851384 0.00083082 -0.004172066 -0.009174953 -0.010718966 -0.01053354 -0.016977625 -0.001227264 0.004434713 -0.013250715 -0.002112186 -0.011150427 0.024776704 0.050038971 0.072707082 0.067704195

-0.005204657 -0.039426686 -0.004172066 0.020950542 0.046073151 0.053826597 0.052895461 0.085255221 0.006162855 -0.022269455 0.066540083 0.0106066 0.055993231 -0.124419249 -0.251276812 -0.365107504 -0.339984895

-0.011445762 -0.086704757 -0.009174953 0.046073151 0.101321254 0.118372159 0.116324463 0.187488067 0.013552973 -0.048973622 0.146330881 0.023325386 0.12313689 -0.273615203 -0.552592596 -0.80292209 -0.747673986

-0.013371919 -0.101295916 -0.010718966 0.053826597 0.118372159 0.138292484 0.135900191 0.219039602 0.015833742 -0.057215176 0.170956255 0.027250712 0.14385905 -0.319660691 -0.645585952 -0.938042285 -0.873496723

-0.013140601 -0.099543619 -0.01053354 0.052895461 0.116324463 0.135900191 0.133549281 0.215250481 0.015559838 -0.056225422 0.167998918 0.026779307 0.141370462 -0.314130947 -0.634418094 -0.921815285 -0.858386283

1.129771104 0.529539439

-0.589543746 -0.781593296 -0.490202779 -0.38475075 -0.569362761 -0.363503948 -0.280364537 0.118870302 0.339604193 0.445056223 0.502164245 0.436552866 0.515973508 0.591675379 0.712002487 0.791423129 0.681186513 0.626731443 0.683839466 0.651697015 0.67533611 0.691537665 0.376768714 0.400407809 0.435203213 0.518342624 0.422981087 0.573058354 -0.106150033 -0.275886965 -0.728250397 -1.095082125 -1.324319372 0.119550502 -0.600337465 -1.320225431 -1.54240031 0.056034984 -0.281386524 -0.618808033 -0.72294449

-0.57934535 -0.768072675 -0.481722863 -0.378095026 -0.559513472 -0.357215768 -0.275514569 0.116813989 0.33372945 0.437357287 0.493477409 0.429001028 0.507047788 0.581440109 0.699685703 0.777732463 0.669402808 0.615889745 0.672009868 0.640423442 0.66365361 0.679574898 0.370251069 0.393481237 0.427674722 0.509375922 0.415664025 0.563145135 -0.104313765 -0.271114453 -0.715652543 -1.076138525 -1.301410244 -1.515718645 -0.710438423

-3.31396E+17 -6.43224E+16 -1.49355E+16 6.9143E+16 -7.66099E+16 -1.08271E+16 2.01536E+15 2.83975E+15

8.58835E+18 -1.7027E+18 4.04038E+16 -2.70376E+17 4.7838E+17 -9.67602E+16 -2.16673E+15 -2.7569E+16 -3.76883E+18 5.31937E+17 -1.85256E+17 1.35414E+17 -1.72406E+18 3.77323E+17 -1.72463E+16 5.93284E+16 -4.83736E+17 7.34615E+16 -1.45799E+15 -2.36287E+16 -2.97327E+17 3.76191E+16 6.71378E+15 -8.92541E+15 -2.70427E+17 5.77254E+16 3.181E+15 1.08172E+15 -2.25449E+17 5.5001E+16 -8.07192E+15 8.3033E+15

-5.62334E+17 -6.92202E+16 -6.66191E+16 1.11595E+17 -2.52982E+16 2.7158E+16 9.29037E+15 1.77944E+14

0.05700477 0.07557462 0.04739919 0.03720271 0.05505341 0.0351483 0.0271093 -0.01149393 -0.03283736 -0.04303383 -0.04855578 -0.04221162 -0.04989104 -0.05721088 -0.06884568 -0.0765251 -0.06586599 -0.06060056 -0.06612251 -0.06301456 -0.06530029 -0.06686687 -0.03643091 -0.03871664 -0.04208112 -0.05012012 -0.04089932 -0.05541075 0.01026397 0.02667635 0.07041673 0.1058868 0.12805245

0.431826604 0.572498277 0.359061737 0.281820664 0.417044518 0.266257893 0.205360276 -0.087069635 -0.248751898 -0.325992971 -0.367823223 -0.319764468 -0.377938176 -0.433387974 -0.521524685 -0.579698393 -0.498952726 -0.459065698 -0.50089595 -0.477352378 -0.494667446 -0.506534696 -0.275974015 -0.293289083 -0.318775879 -0.379673496 -0.309823466 -0.419751451 0.077752344 0.202080561 0.533425888 0.802121299 0.970032066

0.14913935 0.06990369

0.045695174 0.060580817 0.037995317 0.029821795 0.044130959 0.028174968 0.021730883 -0.009213564 -0.026322513 -0.034496035 -0.038922443 -0.033836945 -0.03999279 -0.045860396 -0.055186876 -0.061342721 -0.052798349 -0.04857757 -0.053003978 -0.050512636 -0.052344888 -0.05360066 -0.029203112 -0.031035364 -0.033732334 -0.040176419 -0.032785005 -0.044417402 0.008227624 0.021383829 0.056446242 0.084879144 0.102647183

-0.229463905 -0.30421398 -0.190798129 -0.149753788 -0.221609004 -0.141484047 -0.109124288 0.046267039 0.132181716 0.173226057 0.195453805 0.169916356 0.200828686 0.230293585 0.277127647 0.308039976 0.265133365 0.243938207 0.266165955 0.253655378 0.262856254 0.26916227 0.146646997 0.155847874 0.169391041 0.2017508 0.16463391 0.223047413 -0.04131602 -0.107381514 -0.283451704 -0.426231 -0.515455377

-0.504622983 -0.669008778 -0.419591575 -0.329329372 -0.487348966 -0.311143063 -0.239979459 0.101747643 0.290685945 0.380948149 0.429830053 0.373669658 0.441650162 0.506447566 0.609442169 0.677422673 0.583065078 0.536453983 0.585335887 0.557823392 0.578057396 0.5919252 0.322497107 0.342731111 0.372514415 0.443678019 0.362052824 0.490512228 -0.090859663 -0.236146858 -0.62334965 -0.937341143 -1.133557937

(eeT)-1

7.2917E+18 9.6233E+17 -1.534E+18 -1.55E+18 5.7858E+17 1.5981E+16 -2.284E+17 -1.175E+17

2.706E+18 -9.598E+17 3.9911E+17 3.0315E+18 1.5829E+17 6.2408E+16 7.0225E+16 -9.54E+16 6.4085E+15 1.326E+17 -5.86E+16 -2.999E+17 -2.331E+17 -7.859E+16 -8.212E+16 4.2892E+16 -1.134E+17 -1.571E+17 1.5158E+16 -9.227E+16 -1.394E+17 -7.914E+15 4.8806E+16 5.3527E+16 3.9165E+15 -4.041E+16 -1.654E+17 -6.46E+16 -1.531E+17 2.1675E+17 7.4251E+15 1.8084E+17 3.5306E+16 1.6466E+17 -1.41E+15 -2.106E+17 -6.706E+16 1.2311E+18 -2.01E+17 -3.986E+16 1.1944E+17 -6.092E+15 1.6638E+15 -8.554E+16

-1.77958E+17 4.05344E+16 -2.8213E+16 -1.71038E+17 -1.76287E+16 -5.53653E+15 -1.84419E+15 2.43738E+15 -2.06641E+15 -4.3305E+15 6.14798E+15 2.08925E+16 9.48364E+15 -1.53126E+15 -3.37965E+15 -1.4934E+16 1.65453E+16 -9.39192E+14 2.8989E+15 1.48537E+16 1.17858E+14 5.78687E+15 -5.30067E+15 -1.82015E+15 -5.92184E+15 8.9644E+15 1.01843E+16 -3.39685E+15 1.01333E+16 -8.02099E+15 -5.58564E+14 -7.63055E+15 -5.16039E+15 -1.52811E+16 -2.25083E+15 9.6812E+15 1.19444E+16 -4.45251E+16 1.62105E+15 1.86532E+15 -6.40122E+15 -4.61375E+14 -4.20569E+14 7.30325E+15

3.9615E+18 -6.45093E+17 2.68569E+17 2.0991E+18 1.53417E+17 -1.19756E+17 1.22012E+17 -1.22145E+17 8.36913E+15 1.20938E+17 -3.30887E+16 -2.92069E+17 -3.50734E+17 -7.57807E+16 -1.82148E+17 -7.63512E+16 -4.06009E+16 -1.6706E+17 2.02829E+17 3.78172E+16 -2.6437E+17 5.8327E+16 -1.90756E+16 9.47392E+16 -1.04755E+17 6.30261E+16 -1.73364E+17 -2.42926E+17 -2.19589E+17 2.46587E+17 8.60434E+16 1.58221E+17 -3.05665E+16 1.13101E+17 -2.67611E+16 -2.25511E+17 1.0813E+17 1.5299E+18 -3.52626E+17 -7.20159E+16 1.20663E+17 9.0375E+15 -1.24705E+16 -6.45664E+16

-5.29639E+17 1.21941E+17 -8.56226E+16 -4.52206E+17 -2.31797E+16 1.51272E+16 -2.53377E+16 3.28808E+16 -1.32297E+15 -2.23627E+16 1.41491E+15 5.86919E+16 6.37992E+16 2.78481E+16 3.97943E+16 3.36988E+16 6.60304E+15 4.02729E+16 -3.99518E+16 -3.8016E+15 5.66825E+16 -8.16937E+15 -3.44766E+15 -1.95023E+16 2.60554E+16 -1.11696E+16 3.16267E+16 4.57659E+16 4.10808E+16 -5.22481E+16 -1.73828E+16 -3.64921E+16 -4.96864E+14 -1.70062E+16 7.14824E+15 5.4096E+16 -1.67023E+16 -3.11774E+17 8.01297E+16 9.63164E+15 -2.66222E+16 -1.91257E+15 1.90841E+15 1.0362E+16

5.42421E+16 2.21788E+16 -1.00368E+16 -3.10055E+16 -6.15588E+15 -2.45399E+15 -1.5031E+14 4.31767E+14 4.06288E+14 5.14141E+15 -1.2076E+15 -2.20338E+15 -4.58473E+15 -2.47845E+15 -7.0703E+15 4.19233E+15 6.68274E+15 -1.44594E+15 1.56026E+15 1.70793E+15 -4.37408E+15 4.00917E+15 -3.81745E+14 -2.46344E+14 -2.16514E+15 -5.95247E+14 1.21775E+15 -1.23197E+15 -1.69023E+15 3.50071E+15 3.12006E+14 5.04812E+15 -4.52223E+15 -1.81512E+14 -7.58354E+14 -3.71353E+15 1.83837E+15 3.69309E+16 -3.3298E+15 -8.22964E+14 1.48419E+15 -9.08767E+14 -6.06981E+14 -2.63927E+15

-1.85643E+17 2.41556E+16 -1.66853E+16 -1.17225E+17 -6.68836E+14 -4.58189E+15 -5.32762E+15 4.35121E+15 -2.08572E+15 -5.88614E+15 2.51065E+15 1.59598E+16 1.44255E+16 6.29505E+15 3.94519E+15 -4.768E+15 1.75935E+16 9.23661E+14 -2.30177E+15 3.71409E+15 7.5908E+15 2.37811E+15 -1.1453E+15 -2.36078E+15 3.12482E+15 1.50631E+15 9.25852E+15 2.87655E+15 8.53515E+15 -1.13419E+16 -1.75217E+15 -8.62756E+15 -1.76599E+15 -8.14519E+15 2.04788E+13 1.14934E+16 4.13006E+14 -7.18882E+16 1.16673E+16 2.36072E+15 -7.04016E+15 1.88016E+14 3.1238E+12 5.3386E+15

-2.08556E+17 9.58472E+16 -2.46509E+16 -2.68159E+17 -1.33924E+16 -3.70652E+15 -5.94032E+15 8.96669E+15 -6.10797E+14 -6.68923E+15 2.27875E+15 2.38128E+16 2.30496E+16 4.47406E+15 2.50834E+15 5.77046E+15 1.22188E+16 1.09395E+16 -7.3195E+15 9.67131E+15 1.33039E+16 1.41935E+15 -3.95429E+15 -7.36069E+15 -3.8408E+14 2.42288E+15 1.34928E+16 9.42101E+15 1.6953E+16 -1.59031E+16 -3.20152E+15 -9.79622E+15 -7.95258E+15 -1.56057E+16 -3.02138E+14 1.25362E+16 5.15418E+15 -6.84266E+16 2.00662E+16 4.25365E+15 -9.61745E+15 -1.67701E+15 -1.42589E+14 1.20036E+15

1

1

1

1

1

1

1

4

7

8

-1.566E+18 -1.09977E+17 -4.24984E+17 -9.58837E+17 -1.111E+19 7.79295E+17 -4.09192E+18 -5.35372E+18

5.33112E+16 1.04285E+18

OLS Estmators

5

6

9

10

8.82516E+18 -7.28153E+17 7.01433E+19 -4.72809E+18

-0.589010928 -0.042577905 -0.021179602 -0.160441236 -0.016977625 0.085255221 0.187488067 0.219039602 0.215250481 0.346933873 0.025078851 -0.090622346 0.270775308 0.043162035 0.227856411 -0.506306261 -1.022534889 -1.485752534 -1.383519688

-0.001531012 -0.011597835 -0.001227264 0.006162855 0.013552973 0.015833742 0.015559838 0.025078851 0.001812878 -0.006550829 0.019573568 0.003120059 0.016471084 -0.036599423 -0.073916104 -0.107400775 -0.100010657

0.153855118 -0.459711859 -0.073278835 -0.386845812 0.005532308 0.041908739 0.004434713 -0.022269455 -0.048973622 -0.057215176 -0.056225422 -0.090622346 -0.006550829 0.023671397 -0.070729022 -0.011274324 -0.059518208 0.132251892 0.267095598 0.388092344 0.361388176

-0.016530278 -0.125221342 -0.013250715 0.066540083 0.146330881 0.170956255 0.167998918 0.270775308 0.019573568 -0.070729022 0.211334993 0.03368715 0.177837607 -0.395162434 -0.798069088 -1.159601675 -1.079810878

-0.002634954 -0.01996049 -0.002112186 0.0106066 0.023325386 0.027250712 0.026779307 0.043162035 0.003120059 -0.011274324 0.03368715 0.005369788 0.028347611 -0.06298955 -0.127213541 -0.184842437 -0.172123651

-0.013910167 -0.105373292 -0.011150427 0.055993231 0.12313689 0.14385905 0.141370462 0.227856411 0.016471084 -0.059518208 0.177837607 0.028347611 0.149649683 -0.332527713 -0.671572158 -0.975800479 -0.908656821

0.859587211 0.03090896 0.234143762 0.024776704 -0.124419249 -0.273615203 -0.319660691 -0.314130947 -0.506306261 -0.036599423 0.132251892 -0.395162434 -0.06298955 -0.332527713 0.738890173 1.492260791 2.16826856 2.019072606

-0.933770394 -1.237955088 -0.776425576 -0.609401528 -0.901806004 -0.575749005 -0.444065612 0.188277069 0.537894505 0.704918553 0.795371181 0.691450202 0.817243485 0.937146659 1.127731145 1.253524428 1.078922138 0.992671487 1.083124114 1.032214119 1.069655763 1.095317189 0.596758888 0.634200532 0.689312504 0.820995897 0.669954044 0.907659403 -0.168129607 -0.436973645 -1.153465989 -1.734485819 -2.097571606 -2.442987066 -1.145062036

-0.067499575 -0.089488211 -0.05612557 -0.044051883 -0.065188961 -0.041619239 -0.032100225 0.013610007 0.038882846 0.050956534 0.057495094 0.049982945 0.05907618 0.067743635 0.081520439 0.090613673 0.077992176 0.071757365 0.078295925 0.074615788 0.077322337 0.079177327 0.043137983 0.045844531 0.049828417 0.059347431 0.04842905 0.065612086 -0.012153605 -0.031587567 -0.083380737 -0.125380988 -0.151627415 -0.176596504 -0.082773239

0.243909489 0.323365353 0.202809563 0.159181332 0.235560094 0.150390981 0.115994057 -0.049179717 -0.140503034 -0.184131265 -0.207758331 -0.180613207 -0.213471579 -0.244791401 -0.294573836 -0.327432209 -0.281824471 -0.259295001 -0.282922066 -0.269623903 -0.279404008 -0.28610701 -0.155878957 -0.165659062 -0.18005482 -0.214451744 -0.174998211 -0.237089056 0.043917013 0.11414157 0.301296016 0.453063786 0.547905161 0.638130883 0.299100826

-0.728790083 -0.966200468 -0.605985437 -0.475626335 -0.703842483 -0.449361179 -0.346584789 0.146946682 0.41981646 0.550175562 0.620772122 0.539663769 0.637843041 0.731425194 0.880172771 0.978352043 0.842078267 0.774761269 0.84535783 0.805623544 0.834846037 0.854874293 0.465758995 0.494981488 0.537995337 0.640771727 0.522886425 0.70841095 -0.131221969 -0.341049643 -0.900258329 -1.353733287 -1.637114858 -1.906705073 -0.893699202

-0.116170352 -0.154013963 -0.096595087 -0.07581563 -0.112193663 -0.07162892 -0.055246192 0.023423546 0.066919443 0.0876989 0.09895211 0.086023303 0.101673242 0.116590393 0.140301005 0.155950944 0.134228677 0.123498236 0.134751445 0.128417734 0.133075848 0.136268385 0.074242759 0.078900873 0.085757352 0.10214008 0.083348967 0.112921885 -0.020917 -0.054363881 -0.143502676 -0.215787339 -0.260958833 -0.303931962 -0.14245714

-0.613274134 -0.813054086 -0.509934482 -0.400237785 -0.592280821 -0.378135754 -0.291649805 0.123655084 0.353273983 0.462970681 0.522377423 0.454125047 0.536742537 0.61549157 0.7406621 0.82327959 0.708605717 0.651958715 0.711365457 0.677929204 0.702519823 0.719373525 0.391934455 0.416525074 0.452721067 0.539207016 0.440006974 0.596125169 -0.110422797 -0.286992001 -0.757564022 -1.139161506 -1.37762604 -1.604485199 -0.752044542

1.362720198 1.80663942 1.133095268 0.889344721 1.316072199 0.840233105 0.648057791 -0.274766652 -0.784989234 -1.028739781 -1.16074399 -1.00908442 -1.192663862 -1.367647432 -1.645781467 -1.829360909 -1.574550873 -1.448678919 -1.580683129 -1.506386407 -1.561027768 -1.598477384 -0.870894382 -0.925535743 -1.005964719 -1.198140033 -0.977713486 -1.324614498 0.24536397 0.637707959 1.683338229 2.53126344 3.061141383 3.565231709 1.671073718

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0.149139354 1.129771104 0.119550502 -0.600337465 -1.320225431 -1.54240031 -1.515718645 -2.442987066 -0.176596504 0.638130883 -1.906705073 -0.303931962 -1.604485199 3.565231709 7.200333262 10.46215 9.742262033

0.069903691 0.529539439 0.056034984 -0.281386524 -0.618808033 -0.72294449 -0.710438423 -1.145062036 -0.082773239 0.299100826 -0.893699202 -0.14245714 -0.752044542 1.671073718 3.374896404 4.903755302 4.566333793

5.645601125 7.484710035 4.694290088 3.684458163 5.452343553 3.480994096 2.684832734 -1.138328265 -3.252124764 -4.261956689 -4.808835728 -4.180526672 -4.941076274 -5.666014115 -6.818293082 -7.578842684 -6.523192503 -6.001718729 -6.548597768 -6.240794557 -6.467167752 -6.622317426 -3.608020422 -3.834393617 -4.167602093 -4.963763455 -4.050560317 -5.487733367 1.016516161 2.641954508 6.973886649 10.4867483 12.68197481 14.77036605 6.923076119

6.575284716 8.717247006 5.467317508 4.291192544 6.350202651 4.054223239 3.126954819 -1.325781308 -3.787665083 -4.963790048 -5.600725833 -4.868950627 -5.754742956 -6.599059195 -7.941088522 -8.826880852 -7.597392558 -6.990045623 -7.626981409 -7.268491018 -7.532141988 -7.712840776 -4.202167495 -4.465818464 -4.853897706 -5.781166126 -4.717582195 -6.391420247 1.18390992 3.077015665 8.122304301 12.21364285 14.77036605 17.20266097 8.063126599

3.081927452 4.085894985 2.562607802 2.011341664 2.976428356 1.900270853 1.46564724 -0.62141215 -1.775331336 -2.326597474 -2.625138141 -2.282144918 -2.69732811 -3.093070881 -3.722098703 -4.137281895 -3.561003621 -3.276331661 -3.574872327 -3.406842892 -3.530419771 -3.615115808 -1.969614384 -2.093191263 -2.275089404 -2.709713017 -2.211196427 -2.995747616 0.554915055 1.442240064 3.80703706 5.724704376 6.923076119 8.063126599 3.779299648

-5.14232E+16 -2.26218E+14 3.81079E+16 5.5559E+15 4.35053E+15 1.9003E+15 1.4171E+15 2.17784E+15

-2.78934E+16 7.13638E+15 -2.39524E+15 6.42071E+15 1.73338E+16 1.43916E+16 4.01827E+15 -2.47624E+15 -1.69804E+15 7.9805E+15 -2.28998E+13 1.23087E+15 -5.31433E+14 1.27567E+15 -2.15802E+12 2.33816E+15

-2.79411E+16 1.5844E+15 -7.87174E+14 -2.05715E+15 -2.08942E+14 4.75471E+14 -8.61087E+14 5.62146E+14 -1.02131E+14 -1.06031E+15 2.42111E+14 1.2716E+15 2.16079E+15 4.88246E+14 1.08698E+15 5.7926E+14 3.03211E+13 3.57734E+14 -1.43801E+15 -7.82808E+14 1.87499E+15 -4.54045E+14 5.11397E+14 -2.91344E+14 1.05317E+15 -9.29563E+14 1.00286E+15 1.50017E+15 8.39523E+14 -1.56531E+15 -4.02035E+14 -9.99069E+14 3.65694E+14 -8.34085E+14 7.03312E+14 1.47101E+15 -1.38131E+15 -1.10558E+16 1.96946E+15 5.86166E+14 -5.12927E+14 -3.77586E+13 2.00878E+14 4.86502E+14 #N/A

-7.58924E+15 1.32771E+15 -6.67666E+14 -1.11206E+16 4.37651E+14 1.34446E+13 -2.50583E+14 1.5605E+14 2.03853E+14 -7.85659E+14 1.70058E+14 6.14868E+14 4.82528E+14 4.15438E+14 4.42855E+14 -6.07545E+13 2.29961E+15 9.55605E+13 2.07426E+14 9.53983E+13 5.19284E+14 -4.76899E+14 1.50455E+14 3.14189E+13 2.94984E+12 -1.26033E+14 4.67768E+14 -5.10246E+13 1.72795E+14 -8.66292E+14 -2.11411E+13 -4.17818E+14 7.08269E+14 -1.40129E+14 -4.26582E+12 6.30221E+14 2.1224E+14 -5.6739E+15 1.36009E+15 -3.21073E+13 -4.24595E+14 1.72841E+14 2.17331E+13 3.3827E+14

-9.39395E+15 -9.05395E+15 3.08739E+15 2.77758E+16 -9.48362E+13 1.12789E+15 1.80887E+14 -2.58682E+14 2.61813E+14 1.03899E+14 -1.01301E+14 -1.551E+15 -4.70455E+14 -1.12587E+14 8.74365E+14 2.30464E+14 -2.52089E+15 -1.37061E+13 -9.44723E+14 -1.51803E+15 5.20496E+14 -8.41613E+14 8.48113E+14 8.78545E+13 7.0075E+14 -9.93111E+14 -8.15861E+14 4.69133E+14 -5.831E+14 6.38839E+14 -1.07031E+14 1.22093E+14 1.4022E+15 1.22964E+15 5.44822E+14 9.30734E+12 -1.87259E+15 -3.30487E+14 -3.01551E+14 2.70048E+14 8.84455E+14 1.58673E+14 1.71131E+14 -6.2254E+13

#N/A

Ramsey Test Closing Predicted Y Price 0.9440421 0.98 1.0776091 1.35 1.211176 1.24 1.344743 1.2 1.47831 1.16 1.611877 1.24 1.745444 1.38 1.8790109 1.29 2.0125779 1.97 2.1461449 2.3 2.2797119 1.82 2.4132788 2.34 2.5468458 2.16 2.6804128 3.54 2.8139798 4.55 2.9475467 5.47 3.0811137 5.43 3.2146807 4.8 3.3482477 5.45 3.4818147 4.8 3.6153816 4.65 3.7489486 5.28 3.8825156 4.86 4.0160826 4.77 4.1496495 3.83 4.2832165 3.37 4.4167835 3.22 4.5503505 3.2 4.6839174 3.51 4.8174844 3.43 4.9510514 3.36 5.0846184 3.17 5.2181853 3.09 5.3517523 3.52 5.4853193 3.8 5.6188863 3.78 5.7524533 4 5.8860202 4.07 6.0195872 4.16 6.1531542 5.14 6.2867212 5.21 6.4202881 5.25 6.5538551 5.16

Predicted Y2

t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

0.89121547 1.1612413

SUMMARY OUTPUT

1.46694741 1.80833379 2.18540045 2.59814738 3.04657459 3.53068207


4.05046982 4.60593785

ANOVA

5.19708616 5.82391474 6.48642359 7.18461272

df

SS MS 2 224.9469 112.4735 49 108.0577 2.205259 51 333.0046

F 51.0024

Coefficients Standard Error t Stat Intercept 2.022529 0.614239 3.292738 X Variable 1 -0.04579 0.068015 -0.6732 X Variable 2 0.154345 0.057327 2.692353

P-value 0.001846 0.503985 0.009683


7.91848212 8.6880318 9.49326175 10.334172 11.2107625 12.1230333 13.0709843 14.0546156 15.0739272 16.1289191 17.2195913 18.3459437 19.5079764 20.7056894 21.9390826 23.2081561 24.5129099 25.853344 27.2294583 28.641253 30.0887279 31.571883 33.0907185 34.6452342 36.2354302 37.8613065 39.522863 41.2200998 42.9530169

6.6874221 6.8209891 6.954556 7.088123 7.22169 7.355257 7.488824 7.6223909 7.7559579

5.55 5.28 7.24 7.83 9.18 10.3 11.05 11.77 9.7

44 45 46 47 48 49 50 51 52

44.7216143 46.5258919 48.3658498 50.241488 52.1528065 54.0998052 56.0824842 58.1008435 60.1548831


Lower 95%Upper 95%Lower 95.0% Upper 95.0% 0.788169 3.25689 0.788169 3.25689 -0.18247 0.090893 -0.18247 0.090893 0.039142 0.269549 0.039142 0.269549

New Privately Owned Single Housing Units Started Not Seasonally Adjusted, Not Annulaized, ('000's) Jan 2007 Feb 2007 Mar 2007 Apr 2007 May 2007 Jun 2007 Jul 2007 Aug 2007 Sep 2007 Oct 2007 Nov 2007 Dec 2007 Jan 2008 Feb 2008 Mar 2008 Apr 2008 May 2008 Jun 2008 Jul 2008 Aug 2008 Sep 2008 Oct 2008 Nov 2008 Dec 2008 Jan 2009 Feb 2009 Mar 2009 Apr 2009 May 2009 Jun 2009 Jul 2009 Aug 2009 Sep 2009 Oct 2009 Nov 2009 Dec 2009 Jan 2010 Feb 2010 Mar 2010 Apr 2010 May 2010 Jun 2010 Jul 2010 Aug 2010 Sep 2010 Oct 2010 Nov 2010 Dec 2010

75.4 82.9 101.3 111.4 111.4 110.1 100.1 86.6 78.6 77.4 58.6 52.3 48.5 51.9 61.5 62.6 66.1 65.2 59.9 54.4 48.7 45.8 31.3 26.1 22.7 24.6 31.0 35.0 39.5 49.2 49.3 43.4 45.6 39.4 35.2 30.1 31.7 35.2 47.4 52.2 44.5 45.5 40.7 39.1 39.2 36.0 33.0 26.6

Jan Avg Feb Avg Mar Avg Apr Avg May Avg Jun Avg Jul Avg Aug Avg Sep Avg Oct Avg Nov Avg Dec Avg Average

Monthly Additive Multiplicative Averages Adjustments Adjustments 44.6 -9.3 0.82795449 48.7 -5.2 0.90364523 60.3 6.5 1.12003715 65.3 11.5 1.21290922 65.4 11.5 1.2143023 67.5 13.7 1.25377293 62.5 8.7 1.16090086 55.9 2.0 1.03784537 53.0 -0.8 0.98490829 49.7 -4.2 0.92221964 39.5 -14.3 0.7341537 33.8 -20.1 0.62735082 53.8 0.0 1.0

Not Seasonally Adjusted, Not Annulaized, ('000's) Jan 2007 75.4 Jan 2009 22.7 Feb 2007 82.9 Feb 2009 24.6 Mar 2007 101.3 Mar 2009 31.0 Apr 2007 111.4 Apr 2009 35.0 May 2007 111.4 May 2009 39.5 Jun 2007 110.1 Jun 2009 49.2 Jul 2007 100.1 Jul 2009 49.3 Aug 2007 86.6 Aug 2009 43.4 Sep 2007 78.6 Sep 2009 45.6 Oct 2007 77.4 Oct 2009 39.4 Nov 2007 58.6 Nov 2009 35.2 Dec 2007 52.3 Dec 2009 30.1 Jan 2008 48.5 Jan 2010 31.7 Feb 2008 51.9 Feb 2010 35.2 Mar 2008 61.5 Mar 2010 47.4 Apr 2008 62.6 Apr 2010 52.2 May 2008 66.1 May 2010 44.5 Jun 2008 65.2 Jun 2010 45.5 Jul 2008 59.9 Jul 2010 40.7 Aug 2008 54.4 Aug 2010 39.1 Sep 2008 48.7 Sep 2010 39.2 Oct 2008 45.8 Oct 2010 36.0 Nov 2008 31.3 Nov 2010 33.0 Dec 2008 26.1 Dec 2010 26.6

Seasonal Adjustments Month Additive Jan 2007 84.6625 Feb 2007 88.0875 Mar 2007 94.8375 Apr 2007 99.9375 May 2007 99.8625 Jun 2007 96.4375 Jul 2007 91.4375 Aug 2007 84.5625 Sep 2007 79.4125 Oct 2007 81.5875 Nov 2007 72.9125 Dec 2007 72.3625 Jan 2008 57.7625 Feb 2008 57.0875 Mar 2008 55.0375 Apr 2008 51.1375 May 2008 54.5625 Jun 2008 51.5375 Jul 2008 51.2375 Aug 2008 52.3625 Sep 2008 49.5125 Oct 2008 49.9875 Nov 2008 45.6125 Dec 2008 46.1625

Seasonal Adjustments Month Additive Multiplicative Jan 2007 84.7 91.06781 Feb 2007 88.1 91.73954 Mar 2007 94.8 90.44343 Apr 2007 99.9 91.84529 May 2007 99.9 91.73992 Jun 2007 96.4 87.81494 Jul 2007 91.4 86.22614 Aug 2007 84.6 83.4421 Sep 2007 79.4 79.80438 Oct 2007 81.6 83.92795 Nov 2007 72.9 79.8198 Dec 2007 72.4 83.36643 Jan 2008 57.8 58.5781 Feb 2008 57.1 57.43404 Mar 2008 55.0 54.90889 Apr 2008 51.1 51.61145 May 2008 54.6 54.43455 Jun 2008 51.5 52.00304 Jul 2008 51.2 51.59786 Aug 2008 52.4 52.41629 Sep 2008 49.5 49.44623 Oct 2008 50.0 49.66279 Nov 2008 45.6 42.63412 Dec 2008 46.2 41.60352 Jan 2009 32.0 27.41697 Feb 2009 29.8 27.22307 Mar 2009 24.5 27.67765 Apr 2009 23.5 28.85624 May 2009 28.0 32.52897 Jun 2009 35.5 39.24156 Jul 2009 40.6 42.46702 Aug 2009 41.4 41.8174 Sep 2009 46.4 46.29873 Oct 2009 43.6 42.72301 Nov 2009 49.5 47.94636 Dec 2009 50.2 47.97953 Jan 2010 41.0 38.28713 Feb 2010 40.4 38.95334 Mar 2010 40.9 42.32002 Apr 2010 40.7 43.03702 May 2010 33.0 36.64656 Jun 2010 31.8 36.29046 Jul 2010 32.0 35.05898 Aug 2010 37.1 37.67421 Sep 2010 40.0 39.80066 Oct 2010 40.2 39.03625 Nov 2010 47.3 44.94972 Dec 2010 46.7 42.40052

easonal Adjustments Multiplicative 91.06781 91.73954 90.44343 91.84529 91.73992 87.81494 86.22614 83.4421 79.80438 83.92795 79.8198 83.36643 58.5781 57.43404 54.90889 51.61145 54.43455 52.00304 51.59786 52.41629 49.44623 49.66279 42.63412 41.60352

Seasonal Adjustments Month Additive Multiplicative Jan 2009 31.9625 27.41697 Feb 2009 29.7875 27.22307 Mar 2009 24.5375 27.67765 Apr 2009 23.5375 28.85624 May 2009 27.9625 32.52897 Jun 2009 35.5375 39.24156 Jul 2009 40.6375 42.46702 Aug 2009 41.3625 41.8174 Sep 2009 46.4125 46.29873 Oct 2009 43.5875 42.72301 Nov 2009 49.5125 47.94636 Dec 2009 50.1625 47.97953 Jan 2010 40.9625 38.28713 Feb 2010 40.3875 38.95334 Mar 2010 40.9375 42.32002 Apr 2010 40.7375 43.03702 May 2010 32.9625 36.64656 Jun 2010 31.8375 36.29046 Jul 2010 32.0375 35.05898 Aug 2010 37.0625 37.67421 Sep 2010 40.0125 39.80066 Oct 2010 40.1875 39.03625 Nov 2010 47.3125 44.94972 Dec 2010 46.6625 42.40052

Stochastic Processes and Stock Prices: Simulations Initial Stock Price= Sigma =

100 mu = 0.07

0.005 Hit F9 to generate another random process

[0,1] Normally distributed variable Arithmetic [0,1] Brownian Motion Geometric [0,1] Brownian Motion Geometric Brownian Motion Weiner Process

-0.8499

-0.5

0.0114 -1.2259

1.15932 0.0457 1.343757

-0.1724 -1.6854

-0.8848

0.18

100 99.1501

98.65

98.661 97.4352

98.5945

99.8115 98.1261 97.2414

97.421

97.8608

98.788

-11.02 -25.8203 -21.3688 14.6459 1.68791

1.9918

2.86708

5.5252

-4.879 -10.5354

98.64 99.98391

100 42.7471 21.354

21.597

100 94.2244 90.981

91.053 83.5656

90.6299

90.92 99.88744

98.6892 87.7067 82.4396

83.485

86.0931 91.8657

100 94.6967 91.895

92.429 85.2537

92.9242 93.689 103.4454

102.717 91.7437 86.6663

88.205

91.4168 98.0353

Weiner Process

Geometric Brownian Motion 120

140

100

120 100 S(t)

80 S(t)

0.43946 0.92712

60 40

80 60 40

20

20

0

0

1

20

39

58

77

96 115 134 153 172 191 t

1

21

41

61

81 101 121 141 161 181 t

Notice the drift on the Weiner Process - the Y-Axis scale has a higher maximum if mu > 0. Note: The first two random variables are not driven off the input variables mu and sigma.

-0.652 -1.66891 -0.64201 -1.6782 -0.47211 -0.2652

-0.156 -0.0271

0.6346 0.564554

95.825

94.147

93.6748 93.4096 92.6166

92.037 92.02027

91.9296 91.10122

90.6036

91.1223

90.302 90.1462 90.1192

90.754 91.31834

1.922748 -1.28615 -0.46042

0.3122

0.16483 0.12112 0.02507

0.0105 0.010366

0.00943 0.001618

0.00081

0.00123

0.0002 0.00019 0.00018

0.0003 0.000466

87.76715

78.0901

74.6584

66.384

64.2257 63.0447 59.6404

57.27 57.20203

56.8401 53.63789

51.8016

53.7169

50.72 50.1695 50.0745

52.349 54.45933

94.13099

84.1721

80.8764

72.273

70.2742 69.3276 65.9129

63.61 63.85337

63.7674 60.47655

58.6989

61.1744

58.051 57.7086 57.8881

60.821 63.58987

98.13596

96.467

161 181 201

-0.793 -0.5795 -0.01688 -0.09068 -0.82837 -0.49764

0.51867 -0.8201

0.8782 -0.4802 0.76805 0.71521

-0.025

2.1614 -0.83868 -0.5298

0.00424 -2.58808

95.336

94.4973

93.967

93.9717

0.0009 0.00046 0.00081 0.00138 0.00135 0.00426

0.00069

0.0003

0.00032 -0.00051

57.912 55.9976 59.0906 62.1243 62.0158 72.1457

68.0321

65.555

65.5748

54.7089

82.2678

79.67

80.0933

67.1565 65.3343

92.197 91.7163 92.4843 93.1995 93.1746

67.96 66.0432 70.0404 74.0053 74.2464

86.807

-0.4644

2.3809 1.232557 -0.07134

91.3837 90.9192 93.3001 -0.0003

-0.0009

94.5327 94.46136

0.45582

94.893

95.3484 95.3179 96.8713

-0.00208 -0.00193 -0.0028 -0.00403

52.959 62.5634 68.20101 67.86128 77.57

0.4312

84.9837 84.98422

-0.0304 1.55338 -0.0039

-0.01

69.941

72.2084 72.0548 80.3316

88.028

91.3371 91.5996 102.633

1.25396 0.33485 -1.1136 -0.66678286 -0.82611986

-0.4744097 -0.17696171 -1.10235431 -1.49605483 -2.00512187

0.21255462

1.40599717 -1.01923247

98.1253 98.4601 97.3466

96.6797677

95.8536479

95.110934

94.6365243

94.4595625

90.0685861

91.4745833

-0.0225

-0.03 0.00341

0.00113558

0.00019746

5.0803E-05

2.6701E-05

2.1976E-05 -2.2494E-06

1.1158E-06 -1.1215E-06 -1.3599E-06 -3.2719E-06

6.2927E-08

87.7016 89.7816 83.0488

79.2616123

74.808053

71.0181563

68.6984672

67.8527264

62.8137983

56.5684229

49.1605956

49.8975161

55.0582119

51.2668709

103.31204

97.9958898

93.497581

90.8969898

90.2279788

83.9460864

75.9785396

66.3598628

67.6922177

75.0677486

70.248907

112.611

115.86 107.709

-0.7427139

93.3572082

91.8611534

89.8560315

90.4553508

-1.32666051

0.56799575

1.16426193

89.1286903

89.6966861

90.860948

1.01894844 -0.45296293

0.31371984

91.8798965

91.7406534

0.46423801

1.29655564 -0.03601079 -1.38762568

92.4703107

90.6645725

91.1288105

92.4253661

92.3893553

-2.0556E-08 -3.2231E-08 -6.9757E-08 -1.4084E-07 -7.7043E-08 -1.0121E-07 -2.0418E-07 -1.4545E-07

1.1719E-07

1.716E-07

3.9408E-07

3.7989E-07 -1.4726E-07

46.7202887

48.6152963

52.7432897

56.6426902

54.874872

56.0932749

60.2333845

59.0327245

52.0232256

53.7415758

58.8472922

58.6991394

53.2656293

64.3398065

67.2850597

73.3642347

79.1831039

77.096319

79.2031384

85.475241

84.1913293

74.5664193

77.4154925

85.1952615

85.4067435

77.8895085

91.4269335

1.01729759 -0.28764023 -1.80573826 92.757951

91.0017297

-0.9017381 -1.04776664

0.34113083 -0.55088141 -0.91742688 -0.89878495 -0.98957143 -0.01430641

-1.8845134 -0.77979376 -0.11709521

90.0999916

89.0522249

89.3933557

88.8424743

87.9250475

87.0262625

86.0366911

86.0223847

84.1378713

-1.447E-08

6.9116E-10

9.2694E-10

4.1631E-10

3.4376E-11

3.4793E-12

3.6285E-14

3.5765E-14 -3.1635E-14 -6.9662E-15 -6.1505E-15 -1.0773E-14

1.3954E-14

50.0073304

46.4708827

47.5939235

45.7935567

42.9451413

40.3264899

37.6276281

37.5899649

32.9443965

31.1943074

30.9396632

32.6110874

27.7707551

73.4914886

68.6366009

70.6476674

68.3159586

64.3877574

60.764672

56.9821789

57.2104812

50.3914331

47.9536836

47.8006365

50.6354706

43.3359908

83.3580775

83.2409823

0.75161966 -2.29526923 83.992602

81.6973327

-0.64435506 -0.47537508

-1.3357848

0.79175852

1.40331287 -1.54136938

0.89834686

0.28004133

79.2418178

80.0335763

81.4368892

79.8955198

80.7938667

81.073908

81.1446733

80.8274527

80.5493277

81.0661808

4.9628E-15

2.6036E-15 -8.7425E-16 -1.5665E-15 -3.7647E-15

2.0381E-15

3.869E-15

4.9525E-15

5.3029E-15

3.6207E-15

2.6137E-15

3.9646E-15 -9.4481E-17

26.5459883

25.6771729

23.3850621

24.7177237

27.2690523

24.4800032

26.0688436

26.58491

26.7169269

26.1302041

25.6264017

26.5705339

24.7329086

41.6323968

40.4716763

37.0436683

39.3509666

43.6303251

39.3641925

42.1291905

43.1785462

43.6104729

42.8665535

42.2507933

44.0269898

41.1874947

81.0529777

80.5776026

0.0707653 -0.31722062 -0.27812504

0.51685314 -1.02383095 80.0423498

-1.1090698 -0.65955389 -1.22289196 78.93328

78.2737261

77.0508342

0.57066129 -0.90980957 -3.08006652 -0.27164722 77.6214955

76.7116859

73.6316194

73.3599722

1.23881182

2.52547801

0.96050252 -0.73281709 -0.49981601

-0.1307168

74.598784

77.124262

78.0847645

76.7214146

77.3519474

76.8521314

1.0305E-17

3.5083E-18 -7.8197E-19 -1.2282E-18 -1.1077E-19

2.3041E-19

1.6782E-19

3.7572E-19

1.3246E-18

2.5969E-18

6.9385E-19

3.4705E-19

3.0169E-19

22.8854149

21.8528431

20.0600163

20.8775597

19.5893924

15.7901063

15.4926893

16.8961381

20.1633892

21.565692

20.4873275

19.7829292

19.6027375

38.3019113

36.7570861

33.9106319

35.4695606

33.4478735

27.0959307

26.7188217

29.2852822

35.1234338

37.7544637

36.0463827

34.9815016

34.8366231

0.26412382

0.54816038 -0.17792212

0.08305342

0.20251765 -0.45022541 -0.47743951 -1.83004568

0.98774216

0.28216668

0.97057177

0.04261876

1.19691394

76.9855384

77.5336988

77.3557767

77.4388301

77.6413478

77.1911224

76.7136828

75.8713793

76.153546

77.1241178

77.1667365

78.3636505

3.8137E-19

5.9042E-19

4.8537E-19

5.2568E-19

6.3214E-19

3.4754E-19

1.8161E-19 -1.5074E-19 -2.9964E-19 -3.8419E-19 -7.5707E-19 -7.8933E-19 -1.7341E-18

19.9685372

20.7496446

20.4928198

20.6123067

20.9065926

20.2579796

19.5921309

17.2364238

18.4703502

18.8387972

20.1631856

20.2234285

21.9908341

35.6645746

37.2454248

36.9688093

37.3707497

38.0942952

37.0974696

36.0579727

31.8814648

34.3350518

35.1955065

37.8586104

38.1620572

41.7051961

74.8836372

0.55096901

0.75802185 -0.27341841 -2.51646728

78.9146195

79.6726413

0.2379442

0.309041

1.00438224

0.26281612

0.45004409

0.39788324

0.14836042

79.3992229

76.8827556

77.1206998

77.4297408

78.4341231

78.6969392

79.1469833

79.5448665

79.693227

0.10541358 -1.51975868

-2.6895E-18 -4.7283E-18 -3.4355E-18

5.2098E-18

6.4494E-18

8.4425E-18

1.6922E-17

2.1369E-17

3.0987E-17

4.3316E-17

4.9742E-17

5.4986E-17 -2.8579E-17

22.8555406

24.1010424

23.6441519

19.8253832

20.158362

20.5991963

22.0995847

22.5099165

23.2303365

23.8864382

24.1357969

24.3145525

21.8607312

43.5623637

46.1665305

45.5183617

38.3579992

39.1977436

40.255718

43.4043128

44.4318226

46.0836869

47.6227625

48.361115

48.9634955

44.2427681

79.7986405

78.2788819

-0.13028227

1.8913395

1.53439014

1.32843444 -0.69205792 -0.15555264

1.71312532

-0.3348289

2.13166631 -0.57442741 -0.33196648

0.91815357 -1.07924569

78.1485996

80.0399391

81.5743292

82.9027637

83.7682784

83.4334495

85.5651158

85.5768755

-2.4856E-17 -7.1867E-17 -1.8214E-16

-4.241E-16

82.2107057

82.0551531

84.9906884

-1.306E-16 -1.1028E-16 -2.9921E-16 -1.9903E-16 -6.2328E-16 -2.6525E-16

84.6587219

-1.772E-16 -3.3989E-16

84.4976298 2.6935E-17

21.6622729

24.7287352

27.5326685

30.2157604

28.7868764

28.4751255

32.1030066

31.3593248

36.4058074

34.9709734

34.1676993

36.4357881

33.7845732

44.0608735

50.5501508

56.5640281

62.3874197

59.7350884

59.384361

67.285831

66.0565806

77.0710942

74.4046454

73.0599784

78.3003031

72.9667806

-0.730695 -0.79848072

1.19665738

0.8582389 -1.94925983

0.48581691

0.18426316

1.60841126 -1.94153402

82.7265571

81.6474262

81.0016515

81.4874685

81.6717316

83.2801429

-5.664E-18 -7.3948E-18 -2.5652E-18

2.0299E-19

7.1903E-20

1.0683E-19

1.2652E-19

3.3002E-19 -3.1072E-19

29.8453545

27.6739084

26.4507842

27.3657708

27.7210323

31.0245926

27.0820953

66.7549993

62.2083992

59.7569678

62.1339776

63.2560897

71.1492789

62.4191931

83.0740906

0.30557655 -0.65310997 -1.07913093 -0.64577467 83.3796671

83.7669348

82.9684541

84.1651115

85.0233504

7.2537E-18

1.4618E-18

3.211E-18

5.9668E-18

32.0999873

30.3550224

33.0072753

35.0510203

30.5803161

31.2414862

69.6759793

66.2186389

72.3653789

77.2312923

67.7183051

69.5292055

81.3386088

-0.53481131

0.70930369

0.09436961 -0.23008436

0.37568685

0.13754989

0.94606223

0.96835015

80.8037975

81.5131012

81.6074708

81.7530733

81.8906232

82.8366854

83.8050356

1.59689213

0.68104335 -1.80939236

84.5490228

82.0490198

83.6459119

84.3269552

-1.4454E-19 -2.4707E-19 -2.7039E-19 -2.0817E-19 -2.8638E-19 -3.2577E-19 -6.3398E-19 -1.2479E-18 -2.1763E-18

3.2645E-18

8.4775E-18

1.4251E-17 -1.1535E-17

26.0869719

27.4149171

27.596616

27.1557077

27.8793238

28.1490561

30.0763209

32.185714

33.9063324

28.4629028

31.8291975

33.383343

29.4119072

60.4269996

63.8213183

64.5663353

63.8532348

65.8833216

66.8541791

71.789496

77.2095134

81.7447661

68.9651685

77.508222

81.7002494

72.3416178

81.3773865

0.7439872 -2.50000304

82.5175629

0.18417753 -0.26022299

0.76581499

0.49885323

0.20944327 -1.44320608

1.33534673

0.57524118 -1.27848174 -0.60817093 -0.75688306 -1.31084382

1.58783106

82.7017404

83.2073324

83.7061856

83.9156289

82.4724228

83.8077696

84.3830107

82.4963581

81.739475

80.4286312

82.0164622

-1.3659E-17 -1.0105E-17 -1.7843E-17 -2.6744E-17 -3.2345E-17

1.4336E-17

3.3479E-17

5.2737E-17 -1.4686E-17 -5.7545E-18

-1.399E-18

4.3488E-19

1.1254E-18

82.4415174

83.104529

29.793553

29.2557583

30.8668708

31.9637738

32.4358477

29.3191181

32.1918742

33.5145928

30.6455428

29.3682824

27.8527986

25.4108026

28.3981089

73.647634

72.6807388

77.0676384

80.2063896

81.798934

74.3095731

81.9995744

85.7967339

78.8452616

75.9378508

72.3802477

66.3653029

74.5390051

0.90995298 -0.59694474

1.89256194

0.46749248 -0.92495801 -0.60146723 -0.73155177

1.29206909

0.38187858

0.7715534

0.41392253 -0.80533743 -1.80010319

82.9264152

82.3294705

84.2220324

84.6895249

83.7645669

83.1630997

82.4315479

83.723617

84.1054956

84.877049

85.2909715

84.4856341

2.1494E-18

8.6634E-19

2.5059E-18

3.6775E-18

2.7596E-19

1.0998E-19

2.9524E-20

6.7671E-20

9.3514E-20

1.6566E-19

2.3424E-19

4.5597E-20 -3.6482E-20

30.2658273

29.0271945

33.139054

34.2414514

32.094667

30.7714458

29.2353488

32.0027996

32.8698192

34.6938912

35.7138369

33.7562161

29.7597664

79.8395707

76.9559456

88.2975585

91.6921647

86.3742734

83.2282776

79.4699165

87.4286801

90.247408

95.7330524

99.0414244

94.0817958

83.359064

82.6855309

Ornstein-Uhlenbeck Process Simulation r0 = k= σ=

0.05 0 0.02

rt = rt-1 + k(r0 - rt-1) + e t

Hit F9 to generate another random process

[0,1] Normally distributed variable Ornstein-Uhlenbeck Process

0.00922

-0.01

0.0116 -0.0031 -0.00623 0.0305 -0.02624

0.00888 0.01684 0.01753 -0.0107 -0.01255 0.00168

0.05 0.05922

0.049

0.0606 0.05748

0.06436

0.05125 0.0817 0.055477

0.0812 0.09873

0.088

0.07544 0.07712

Ornstein-Uhlenbeck (Vasicek) Process 0.6 0.5

r(t)

0.4 0.3 0.2 0.1 0 1

20

39

58

77

96

115

134

153

172

191

t Notice that as k gets closer to 1, the process becomes more mean reverting. As k approaches 0, the process looks like Brownian motion.

-0.00358 -0.00677 0.073542

0.06677

0.011

0.0201

0.07777

0.0979

0.0286 0.01781 0.12649

-0.0042 -0.0042 0.012794

0.1443 0.14012

0.136

0.14875

0.01262 0.005146 -0.02752

0.03682 -0.0034

0.16137 0.166521

0.17583

0.139

-0.0379 -0.0227 -0.0003 0.012528

0.1725 0.13456 0.11186

0.1116 0.124113

0.0005

-0.026 0.01482

0.1246 0.09869

-0.0277 -0.0148 0.02914

0.01954

0.0032

0.01485

0.01323 0.00104

0.1135 0.08576 0.07091 0.10005

0.11959

0.1228

0.13761

0.15084 0.15188 0.14208

-0.0098

-0.00857 0.005095 -0.0094 0.13351 0.138605

0.1292

0.00392

-0.0001 0.00478

0.1331 0.13296 0.13774

-0.0073 0.04818 0.02319

0.02747697

0.02478608 -0.01886236

0.13044 0.17862 0.20181

0.22928971

0.25407579

0.23521343

0.0098968

-0.0318259

0.01504965

0.02703555

0.02015233 -0.02761557 -0.03058794

0.03452155

0.24511023

0.21328433

0.22833397

0.25536952

0.27552186

0.25183989

0.24790628

0.21731834

-0.00756133

0.01589886

0.00323862 -0.00993219 -0.02778546

0.01533044

0.24427856

0.26017743

0.26341605

0.24102883

0.25348385

0.2256984

0.05546587 -0.04328438 0.2964947

0.25321032

0.02255691

0.01442443

0.00702754

0.27576723

0.29019166

0.2972192

-0.0227211 -0.00846014 0.27449811

0.26603797

-0.00804388

0.02281653

0.01989133 -0.00488908 -0.01182766

0.00014724

-0.0227141 -0.00212528

0.25799409

0.28081062

0.30070196

0.28413245

0.26141835

0.29581288

0.28398521

0.25929307

0.0302499

-0.0082639

0.01661676 -0.02240502

0.03744127

0.28954297

0.28127907

0.29789583

0.31293209

0.27549081

0.01373038 -0.03512939 -0.00675502

0.02077431

0.02112204

0.32666246

0.30555236

0.3266744

0.29153307

0.28477805

0.03388211 -0.02074025

0.01744816

-0.0160042

0.02469024 -0.04223246

0.01616464

0.00281973

0.36055651

0.35726441

0.34126021

0.36595045

0.33988263

0.34270235

0.33981626

0.32371799

0.01911256 -0.00622796 -0.00239482

0.02064891 -0.01090523

0.00088572 -0.00457182

0.01949271 -0.02285796

0.02049838 -0.01359739 -0.03567627 -0.02351654

0.36181492

0.37384104

0.36382153

0.37874242

0.37638284

0.35558696

0.35319213

0.36293581

0.35924971

0.35588447

0.36278545

0.32710918

0.30359264

0.02010076

0.0224902

0.0165166 -0.02133508 -0.00266771

0.00252376 -0.00505156 -0.02696929 -0.00345449

0.00531649

0.00444032

-0.0131488

0.01800304

0.3236934

0.3461836

0.3627002

0.34122118

0.31106234

0.31550265

0.30235385

0.32035689

0.34136513

0.33869742

0.33616962

0.30920033

0.30574584

-0.00282935 -0.00389262 0.31752754

0.31363492

0.03538106

0.01095578

0.01449803

0.00532265 -0.00951012 -0.00450914

0.00965511

-0.0054678

0.0143896

0.0004951

0.00928456

0.34901598

0.35997176

0.37446979

0.37979245

0.37542829

0.36996049

0.38435009

0.38484519

0.39412976

0.37028232

0.36577319

0.04151668

0.02079516

0.01675441

0.02467294

0.02018568

0.43564644

0.4564416

0.473196

0.49786894

0.51805463

0.0121678 -0.02707985 -0.01584133 0.53022243

0.50314258

0.48730125

0.04736141

0.00171291 -0.03189088 -0.00740667

0.01685944

0.53466266

0.53637557

0.51393746

0.50448469

0.49707802

0.00410227 -0.04415172 -0.00073261 -0.00020818 -0.01846545 -0.00684099 0.51803972

0.473888

0.47315539

0.47294721

0.45448176

0.44764077

0.05551203 -0.01279057 -0.01716034 0.5031528

0.49036223

0.47320189

0.01606073 -0.00426015 -0.00944509

0.00225407

0.48926262

0.47781145

0.48500247

0.47555738

0.04214756

0.00387786

0.02315259

0.00975167 -0.02085732 -0.00320772

0.519959

0.52383687

0.54698945

0.55674113

0.53588381

0.53267609

0.01456551 -0.01048297 -0.00289632 0.5472416

0.53675863

0.53386231

0.00044712 0.53430943

0.0116744 -0.01267622 0.54598383

0.53330761

0.00502833 0.53833594

0.0002835 0.53861944

0.01691666 -0.00971148 -0.00414819 0.5555361

0.54582462

0.54167643

0.0145956 0.55627203

-0.0247814 -0.02870572 -0.04367802 0.53149064

0.50278491

0.45910689

0.0069918 0.46609869

0.00332085 -0.03665274 -0.03067732 0.46941955

0.43276681

0.40208949

0.012368 0.41445749

0.03351135

0.00123573 -0.02479439

0.01886825

0.00359542 -0.01526495

0.02732849

0.00592983

0.44796884

0.44920457

0.44327842

0.44687385

0.45893739

0.46486723

0.42441017

0.4316089

0.0205083 -0.00591331 0.48537552

0.47946222

0.01266028 -0.00453855 0.4921225

0.48758394

0.04704151 0.53462546

Pairs Trading and the Ornstein-Uhlenbeck Process D Diff. Date Adj Close Adj Close Diff. 1/3/2012 117925 78.37 370 65 12/1/2011 114755 76.3 305 -55 11/1/2011 118500 78.76 360 200 10/3/2011 116950 77.86 160 -80 9/1/2011 106800 71.04 240 -29 8/1/2011 109769 73 269 24 7/1/2011 111500 74.17 245 225 6/1/2011 116105 77.39 20 -150 5/2/2011 118775 79.07 170 370 4/1/2011 124750 83.3 -200 -55 3/1/2011 125300 83.63 -145 -525 2/1/2011 131300 87.28 380 580 1/3/2011 122425 81.75 -200 -485 12/1/2010 120450 80.11 285 -395 11/1/2010 120200 79.68 680 720 10/1/2010 119300 79.56 -40 -520 9/1/2010 124500 82.68 480 -25 8/2/2010 118675 78.78 505 685 7/1/2010 117000 78.12 -180 -645 6/1/2010 120000 79.69 465 380 5/3/2010 105910 70.55 85 260 4/1/2010 115325 77 -175 -70 3/1/2010 121800 81.27 -105 290 2/1/2010 119800 80.13 -395 -350 1/4/2010 114600 76.43 -45 -665 12/1/2009 99200 65.72 620 610 11/2/2009 100600 67.06 10 -500 10/1/2009 99000 65.66 510 -800 9/1/2009 101000 66.46 1310 -960 8/3/2009 100850 65.72 2270 685 7/1/2009 97000 63.61 1585 -1535 6/1/2009 90000 57.92 3120 680 5/1/2009 91600 59.44 2440 390 4/1/2009 94000 61.3 2050 -50 3/2/2009 86700 56.4 2100 420 2/2/2009 78600 51.28 1680 1848 1/2/2009 89502 59.78 -168 -348 12/1/2008 96600 64.28 180 1150 11/3/2008 104000 69.98 -970 -1260 10/1/2008 115490 76.8 290 1540 9/2/2008 130600 87.9 -1250 -790 8/1/2008 116600 78.04 -460 -40 7/1/2008 114450 76.58 -420 -810 6/2/2008 120750 80.24 390 680

m - Diff. -2.68852 62.31148 7.311475 207.3115 127.3115 98.31148 122.3115 347.3115 197.3115 567.3115 512.3115 -12.6885 567.3115 82.31148 -312.689 407.3115 -112.689 -137.689 547.3115 -97.6885 282.3115 542.3115 472.3115 762.3115 412.3115 -252.689 357.3115 -142.689 -942.689 -1902.69 -1217.69 -2752.69 -2072.69 -1682.69 -1732.69 -1312.69 535.3115 187.3115 1337.311 77.31148 1617.311 827.3115 787.3115 -22.6885

m-Diff.Lag 62.31148 7.311475 207.3115 127.3115 98.31148 122.3115 347.3115 197.3115 567.3115 512.3115 -12.6885 567.3115 82.31148 -312.689 407.3115 -112.689 -137.689 547.3115 -97.6885 282.3115 542.3115 472.3115 762.3115 412.3115 -252.689 357.3115 -142.689 -942.689 -1902.69 -1217.69 -2752.69 -2072.69 -1682.69 -1732.69 -1312.69 535.3115 187.3115 1337.311 77.31148 1617.311 827.3115 787.3115 -22.6885 657.3115

SUMMARY OUTPUT Regression Statistics Multiple R 0.385676 R Square 0.148746 Adjusted R Square 0.133812 Standard Error632.475 Observations 59 ANOVA df Regression Residual Total

1 57 58

Coefficients Intercept -0.49198 X Variable 1 0.29731

RESIDUAL OUTPUT ObservationPredicted Y 1 18.03385 2 1.681798 3 61.14382 4 37.35901 5 28.73702 6 35.87246 7 102.7672 8 58.17071 9 168.1754 10 151.8234 11 -4.2644 12 168.1754 13 23.98005 14 -93.4574 15 120.6058 16 -33.9954 17 -41.4282 18 162.2292 19 -29.5358 20 83.44207

5/1/2008 4/1/2008 3/3/2008 2/1/2008 1/2/2008 12/3/2007 11/1/2007 10/1/2007 9/4/2007 8/1/2007 7/2/2007 6/1/2007 5/1/2007 4/2/2007 3/1/2007 2/1/2007 1/3/2007

134650 133850 133400 140000 136000 141600 140100 132500 118510 118390 110000 109475 109490 109200 108990 106190 110050

89.96 -290 89.14 140 89.46 -790 93.49 -235 91 -500 94.72 -480 93.8 -600 88.28 80 79.04 -50 77.8 1690 72.08 1880 72.1 1325 72.5 740 72.56 360 72.8 -210 70.46 500 73.35 25 m = 367.311

-430 930 -555 265 -20 120 -680 130 -1740 -190 555 585 380 570 -710 475

657.3115 227.3115 1157.311 602.3115 867.3115 847.3115 967.3115 287.3115 417.3115 -1322.69 -1512.69 -957.689 -372.689 7.311475 577.3115 -132.689

227.3115 1157.311 602.3115 867.3115 847.3115 967.3115 287.3115 417.3115 -1322.69 -1512.69 -957.689 -372.689 7.311475 577.3115 -132.689

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59

160.7427 139.931 226.1509 122.0924 -75.6188 105.7403 -42.9147 -280.763 -566.18 -362.523 -818.894 -616.723 -500.772 -515.638 -390.768 158.6615 55.19761 397.1042 22.4935 480.351 245.4761 233.5837 -7.2375 194.9334 67.09002 343.5884 178.5813 257.3685 251.4223 287.0995 84.92862 123.5789 -393.741 -450.23 -285.222 -111.296 1.681798 171.1485 -39.9416

dr = k ( m  r )dt  sdz D Diff. = k(m - Diff.) + e k = .29731

SS MS F Significance F 3984260 3984260 9.960038 0.002555 22801403 400024.6 26785664 Standard Error t Stat P-value Lower 95% Upper 95%Lower 95.0% Upper 95.0% 82.34302 -0.00597 0.995254 -165.381 164.3971 -165.381 164.3971 0.094206 3.155953 0.002555 0.108666 0.485955 0.108666 0.485955

Residuals 46.96615 -56.6818 138.8562 -117.359 -57.737 -11.8725 122.2328 -208.171 201.8246 -206.823 -520.736 411.8246 -508.98 -301.543 599.3942 -486.005 16.42816 522.7708 -615.464 296.5579

Lag. Residuals -56.6818 138.8562 -117.359 -57.737 -11.8725 122.2328 -208.171 201.8246 -206.823 -520.736 411.8246 -508.98 -301.543 599.3942 -486.005 16.42816 522.7708 -615.464 296.5579 99.2573

Regression of Residuals on Lagged Residuals SUMMARY OUTPUT Regression Statistics Multiple R 0.194424 R Square 0.037801 Adjusted R Square 0.020619 Standard Error 619.6202 Observations 58 ANOVA df Regression Residual Total

SS MS F Significance F 1 844645.9 844645.9 2.200004 0.143617 56 21500038 383929.3 57 22344684

Coefficients Standard Error t Stat P-value Lower 95%Upper 95% Intercept 11.39687 81.36019 0.140079 0.8891 -151.587 174.3809 X Variable 1 -0.19248 0.129768 -1.48324 0.143617 -0.45243 0.067479

99.2573 -209.931 63.84909 -472.092 -589.381 504.2597 -457.085 -519.237 -393.82 1047.523 -716.106 1296.723 890.7723 465.6378 810.7675 1689.338 -403.198 752.8958 -1282.49 1059.649 -1035.48 -273.584 -802.762 485.0666 -497.09 586.4116 -733.581 7.631526 -271.422 -167.099 -764.929 6.421066 -1346.26 260.2295 840.2224 696.296 378.3182 398.8515 -670.058

-209.931 63.84909 -472.092 -589.381 504.2597 -457.085 -519.237 -393.82 1047.523 -716.106 1296.723 890.7723 465.6378 810.7675 1689.338 -403.198 752.8958 -1282.49 1059.649 -1035.48 -273.584 -802.762 485.0666 -497.09 586.4116 -733.581 7.631526 -271.422 -167.099 -764.929 6.421066 -1346.26 260.2295 840.2224 696.296 378.3182 398.8515 -670.058 0

Lower 95.0% Upper 95.0% -151.587 174.3809 -0.45243 0.067479

Cox, Ingersoll and Ross (CIR) Process Simulation r0 = k= σ=

0.05 0.1 0.05

rt = rt-1 + k(r0 - rt-1) + rt.5e t [0,1] Normally distributed variable Ornstein-Uhlenbeck Process

Hit F9 to generate another random process -0.047

0.0181 -0.0121

0.05 0.05241 0.0415

0.01077

0.046 0.04383

0.11457 0.0194

0.02984 -0.01574 -0.0619

0.06844 0.0717 0.077499

0.07037

-0.0186

0.0519 0.04746

0.0013 -0.01724 0.048

-0.0908

0.04443 0.02585

Cox, Ingersoll and Ross (CIR) Process 0.16 0.14 0.12 r(t)

0.1 0.08 0.06 0.04 0.02 0 1

20

39

58

77

96

115

134

153

172

191

t Notice that as k gets closer to 1, the process becomes more mean reverting. As k approaches 0, the process looks like Brownian motion.

-0.0277 0.023808

0.00854 -0.02793 -0.0132

0.03759 -0.0408 0.02677

0.0175 0.032547 -0.03895 0.000575

0.07136

0.09822 -0.0869

0.02774

0.03415

0.0396 0.047166

0.05549

0.07808

0.02532

0.0257

0.0282 0.03488

0.03899 0.040205

-0.096

0.0252 -0.02713

0.051 0.06355 0.03799

0.0561

0.0441 0.039003

-0.0376 0.02135

-0.053

0.04323

0.0208 -0.04522

0.0327 0.03826 0.03537 0.02963 0.03906 0.02967

-0.0208

-0.0383 0.04293

0.03915

0.0444

0.03539

0.0623 0.04857

-0.045 0.10019 0.069516 0.068905 -0.0294 -0.02058 0.01386 0.0388 0.05965 0.075666 0.092053

0.0789

0.07025

0.0719

-0.1157 0.0387

0.11911 0.00506 -0.0323 -0.03219821 -0.00937053

0.05165275

0.01028439

0.05606653

0.06326

0.05575849

0.05761112

0.07030727

0.0632 0.05376

0.04591599

0.04431647

-0.0432752 -0.05072914 -0.04826767 0.0568019

0.04403136

0.0344999

0.00925156

-0.0311473

0.04625715

0.03776831

0.03293829

0.04303963

0.07044695 -0.03900289 -0.04235031

-0.0062295

0.08061743

0.06702645

0.02695041 -0.00436893

-0.0172711 -0.01865088

0.05913231

0.03292842 -0.04337274

0.05835059

0.03886718

0.05587399

0.07113009

0.07620482

0.06549397

0.07263838

0.07924925

0.04809404

0.03899707

0.07237829

0.05917148

0.06411436

0.05506474

0.0279755 -0.07208764 -0.08046707

0.00652219

0.01746078 -0.03771375

0.07664576

0.0817262

0.04027053

0.04474742

0.05794531

0.03778088

0.03729487

0.0156574 -0.06470482 0.04158912

0.02923469

0.03085762 -0.06437911 0.0365873

0.02561426

0.03349429 -0.01868565 0.03341341

0.03165646

-0.0516844

0.0406022

0.02429499

0.03319409

0.0811234 -0.06413067 0.04965476

0.03539882

0.12707237 -0.00521285 -0.10684187 0.06076707

0.05840534

0.03174412

0.02248201

0.04023773

-0.0242796

0.00799585

0.03857176

0.07311554

0.0375753

0.04661759

0.0417136

0.04417531

0.05286476

0.06938925

0.08460231

0.02108841 -0.00070811 -0.02152357

0.05178069

-0.0204238

-0.0114184

0.05603324 -0.06441549

0.08973613

0.09207976

0.08918376

0.07916609

0.07303675

0.08587623

0.08765691

0.07751876

0.06341188

0.00557073 -0.03619343 0.0634735

0.05300759

0.00691713

0.0377654

0.05429939

0.06266963

-0.03066865 -0.07427348 -0.04820834 -0.06030833 0.05372511

0.03613699

0.02835901

0.02036711

0.02652112

0.06619058

0.0411199

0.08400884

0.08349711 -0.08361584

0.00304042

0.04014684

0.04356576

0.02711531

0.0403032

0.04952798

0.06827125

0.08826089

0.05937645

0.0682215

0.0777784

0.05959359

-0.05392719 -0.00487249 -0.05302156 0.05996092

0.05777171

0.04425041

0.09083061 -0.08593267 0.0639323

0.04081113

0.00667054 -0.01822587

0.01011407 -0.06379261 -0.03753186 -0.04885895 -0.02539661

0.03692196

0.04307759

0.04301081

0.02797218

0.03998702

0.03047975

0.02587929

0.0204314

0.01975811

0.01892573

0.1730972

0.05555836

0.04074286 -0.01821879 -0.02732585

0.03334027

0.06661261

0.07929064

0.08783419

0.0786513

0.06812268

0.05271041 -0.06581624 0.080068

0.05843765

0.06675731

0.02715821 -0.06155927

0.04633854

0.0201108

0.07373171

0.07873297

0.06894394

0.07233008

0.05858651

0.07380985 0.08994768

0.02069364 -0.00224775 -0.01317526 -0.01158305 -0.03847506 -0.06086467 0.0921592

0.08726091

0.07964285

0.07340971

0.06064422

0.04459123

0.02903828

0.04921069 -0.02407126

0.02340436 -0.05773858

0.07185676

0.05126402

0.06227968

0.06003109

0.06061619

0.05504452

0.04488131

0.09204066 -0.00696856 0.08221531

0.07699567

0.0346993

0.04374882

0.08863611

0.12221741

0.02432803 -0.02122118

0.03123042

0.03233169

0.00677017 -0.01182888

0.09872175

0.08392449

0.09320596

0.11594566

0.15096709

0.15032291

0.13520584

0.13857373

0.13223659

0.14689736

0.13206285

0.11971143

-0.06709592

0.0464665

0.00104429

0.02855445 -0.00663431

0.03682447

0.03871263

0.00456325 -0.02943164

0.11677652

0.06010087 -0.01494888

0.05056564

0.11149165

0.12085781

0.11413508

0.11736837

0.11464465

0.12128797

0.11574839

0.13101696

0.14466953

0.13976281

0.10835868

0.09916037

0.12951671

-0.04796643 0.11285435

0.05201542 -0.12563347

0.06571248

0.01969708 -0.04909704

0.12404287

0.08783204

0.08988636

0.07239082

0.07117791

-0.0377426

0.10773075

-0.0882337

0.07083359

0.08542471 -0.00220751

0.06953032

0.0589907

0.08425728

0.05521986

0.07134299

0.09202573

0.10396472

0.08715349

WN Weekly Stock Prices, 2010 and Serial Correlation Closing Week Ending Price 1/4/2010 0.98 1/11/2010 1.35 1/19/2010 1.24 1/25/2010 1.2 2/1/2010 1.16 2/8/2010 1.24 2/16/2010 1.38 2/22/2010 1.29 3/1/2010 1.97 3/8/2010 2.3 3/15/2010 1.82 3/22/2010 2.34 3/29/2010 2.16 4/5/2010 3.54 4/12/2010 4.55 4/19/2010 5.47 4/26/2010 5.43 5/3/2010 4.8 5/10/2010 5.45 5/17/2010 4.8 5/24/2010 4.65 6/1/2010 5.28 6/7/2010 4.86 6/14/2010 4.77 6/21/2010 3.83 6/28/2010 3.37 7/6/2010 3.22 7/12/2010 3.2 7/19/2010 3.51 7/26/2010 3.43 8/2/2010 3.36 8/9/2010 3.17 8/16/2010 3.09 8/23/2010 3.52 8/30/2010 3.8 9/7/2010 3.78 9/13/2010 4 9/20/2010 4.07 9/27/2010 4.16 10/4/2010 5.14 10/11/2010 5.21 10/18/2010 5.25 10/25/2010 5.16

t 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43



Coefficients Standard Error t Stat P-value Lower 95% Intercept 0.810475 0.443225 1.828587 0.07343 -0.07977 X Variable 1 0.133567 0.014553 9.177659 2.66E-12 0.104335

RESIDUAL OUTPUT ObservationPredicted Y Residuals Difference 1 0.944042 0.035958 NA SUMMARY OUTPUT 2 1.077609 0.272391 0.035958 0.236433 3 4 5 6 7 8

1.211176 0.028824 0.272391 -0.24357 Regression Statistics 1.344743 -0.14474 0.028824 -0.17357 Multiple R 1.47831 -0.31831 -0.14474 -0.17357 R Square 1.611877 -0.37188 -0.31831 -0.05357 Adjusted R Square 1.745444 -0.36544 -0.37188 0.006433 Standard Error 1.879011 -0.58901 -0.36544 -0.22357 Observations

9 2.012578 -0.04258 10 2.146145 0.153855 11 12 13 14 15

2.279712 -0.45971 2.413279 -0.07328 2.546846 -0.38685 2.680413 0.859587 2.81398

1.73602

16 2.947547 2.522453 17 3.081114 2.348886 18 3.214681 1.585319 19 3.348248 2.101752

-0.58901 -0.04258 0.153855 -0.45971 -0.07328 -0.38685 0.859587 1.73602 2.522453 2.348886 1.585319

0.546433 0.196433 ANOVA -0.61357 0.386433 Regression -0.31357 Residual 1.246433 Total 0.876433 0.786433 Coefficients -0.17357 Intercept -0.76357 X Variable 1 0.516433

11/1/2010 5.55 11/8/2010 5.28 11/15/2010 7.24 11/22/2010 7.83 11/29/2010 9.18 12/6/2010 10.3 12/13/2010 11.05 12/20/2010 11.77 12/27/2010 9.7 Date Adj Close

44 45 46 47 48 49 50 51 52 T

20 21 22 23

3.481815 3.615382 3.748949 3.882516

1.318185 1.034618 1.531051 0.977484

24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

4.016083 4.14965 4.283217 4.416783 4.55035 4.683917 4.817484 4.951051 5.084618 5.218185 5.351752 5.485319 5.618886 5.752453 5.88602 6.019587 6.153154 6.286721 6.420288 6.553855 6.687422 6.820989 6.954556 7.088123 7.22169 7.355257 7.488824 7.622391 7.755958

0.753917 -0.31965 -0.91322 -1.19678 -1.35035 -1.17392 -1.38748 -1.59105 -1.91462 -2.12819 -1.83175 -1.68532 -1.83889 -1.75245 -1.81602 -1.85959 -1.01315 -1.07672 -1.17029 -1.39386 -1.13742 -1.54099 0.285444 0.741877 1.95831 2.944743 3.561176 4.147609 1.944042

2.101752 1.318185 1.034618 1.531051 0.977484 0.753917 -0.31965 -0.91322 -1.19678 -1.35035 -1.17392 -1.38748 -1.59105 -1.91462 -2.12819 -1.83175 -1.68532 -1.83889 -1.75245 -1.81602 -1.85959 -1.01315 -1.07672 -1.17029 -1.39386 -1.13742 -1.54099 0.285444 0.741877 1.95831 2.944743 3.561176 4.147609

-0.78357 -0.28357 0.496433 RESIDUAL OUTPUT -0.55357 -0.22357Observation -1.07357 1 -0.59357 2 -0.28357 3 -0.15357 4 0.176433 5 -0.21357 6 -0.20357 7 -0.32357 8 -0.21357 9 0.296433 10 0.146433 11 -0.15357 12 0.086433 13 -0.06357 14 -0.04357 15 0.846433 16 -0.06357 17 -0.09357 18 -0.22357 19 0.256433 20 -0.40357 21 1.826433 22 0.456433 23 1.216433 24 0.986433 25 0.616433 26 0.586433 27 -2.20357 28 29 30 31 32 33 34 35 36 37 38 39 40 41

42 43 44 45 46 47 48 49 50 51 52

Significance F


SUMMARY OUTPUT Regression Statistics 0.91477 0.836804 0.833474 0.642748 51

df


Coefficients Standard Error t Stat P-value Lower 95%Upper 95%Lower 95.0% Upper 95.0% 0.034719 0.09003 0.385636 0.701436 -0.1462 0.215642 -0.1462 0.215642 0.929314 0.058628 15.85095 6.35E-21 0.811496 1.047131 0.811496 1.047131

RESIDUAL OUTPUT Predicted Y Residuals 0.068135 0.204256 0.287856 -0.25903 0.061505 -0.20625 -0.09979 -0.21852 -0.26109 -0.11079 -0.31087 -0.05457 -0.30489 -0.28412 -0.51266 0.470079 -0.00485 0.158704 0.177699 -0.63741 -0.3925 0.319219 -0.03338 -0.35347 -0.32478 1.184369 0.833545 0.902475 1.648026 0.874427 2.378869 -0.02998 2.217571 -0.63225 1.507978 0.593775 1.987906 -0.66972 1.259726 -0.22511 0.996204 0.534848 1.457546 -0.48006 0.943108 -0.18919 0.735345 -1.05499 -0.26234 -0.65088 -0.81395 -0.38284 -1.07747 -0.27288 -1.22018 0.046263 -1.05622 -0.33127 -1.25469 -0.33636 -1.44387 -0.47075 -1.74456 -0.38362 -1.94303 0.11128 -1.66755 -0.01777 -1.53147 -0.30742 -1.67418 -0.07827 -1.59386 -0.22216 -1.65293 -0.20665 -1.69342 0.680266 -0.90682 -0.1699 -0.96589 -0.2044

-1.05285 -1.26061 -1.0223 -1.39734 0.299986 0.724155 1.854603 2.771308 3.344168 3.889148

-0.34101 0.123187 -0.51869 1.682787 0.441891 1.234155 1.09014 0.789868 0.803441 -1.94511

-2.4E-16 1.944042

New Privately Owned Single Housing Units Started Not Seasonally Adjusted, Not Annulaized, ('000's) Jan 2007 Feb 2007 Mar 2007 Apr 2007 May 2007 Jun 2007 Jul 2007 Aug 2007 Sep 2007 Oct 2007 Nov 2007 Dec 2007 Jan 2008 Feb 2008 Mar 2008 Apr 2008 May 2008 Jun 2008 Jul 2008 Aug 2008 Sep 2008 Oct 2008 Nov 2008 Dec 2008 Jan 2009 Feb 2009

75.4 82.9 101.3 111.4 111.4 110.1 100.1 86.6 78.6 77.4 58.6 52.3 48.5 51.9 61.5 62.6 66.1 65.2 59.9 54.4 48.7 45.8 31.3 26.1 22.7 24.6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

SUMMARY OUTPUT

Mar 2009 Apr 2009 May 2009 Jun 2009 Jul 2009 Aug 2009

31.0 35.0 39.5 49.2 49.3 43.4

27 28 29 30 31 32

Sep 2009 Oct 2009

45.6 39.4

33 34

9 74.28549 10 72.96626

Nov 2009 Dec 2009 Jan 2010 Feb 2010

35.2 30.1 31.7 35.2

35 36 37 38

11 12 13 14

Mar 2010

47.4

39

15 66.37014 -4.870137

Apr 2010 May 2010 Jun 2010

52.2 44.5 45.5

40 41 42

16 65.05091 -2.450912 17 63.73169 2.368313 18 62.41246 2.787538

Jul 2010 Aug 2010 Sep 2010 Oct 2010 Nov 2010

40.7 39.1 39.2 36.0 33.0

43 44 45 46 47

19 20 21 22 23

Regression Statistics Multiple R 0.770641 R Square 0.593887 Adjusted R Square 0.585059 Standard Error15.4379 Observations 48 ANOVA df Regression Residual Total

1 46 47

SS MS F 16032.14 16032.1447 67.2690015 10963.13 238.328864 26995.27

Coefficients Standard Error t Stat Intercept 86.15851 4.527095 19.0317421 X Variable 1 -1.31922 0.160846 -8.2017682

P-value 1.9328E-23 1.4936E-10

RESIDUAL OUTPUT ObservationPredicted Y Residuals 1 84.83929 -9.439286 NA 89.1001148 2 83.52006 -0.620061 -9.4392857 0.38447538 3 4 5 6 7 8

82.20084 80.88161 79.56239 78.24316 76.92394 75.60471

71.64704 70.32781 69.00859 67.68936

61.09324 59.77401 58.45479 57.13556 55.81634

19.09916 -0.6200608 364.778071 30.51839 19.099164 931.372071 31.83761 30.518389 1013.63366 31.85684 31.837614 1014.85819 23.17606 31.856839 537.129935 10.99529 23.176064 120.896375 4.314514 4.433739 -13.04704 -18.02781 -20.50859 -15.78936

-1.193237 -5.374012 -9.754787 -11.33556 -24.51634

10.995289 4.3145137 4.4337386 -13.047036 -18.027812 -20.508587 -15.789362 -4.8701368 -2.4509119 2.3683131 2.787538 -1.1932371 -5.3740122 -9.7547872 -11.335562

18.6150283 19.658038 170.225161 325.001989 420.602125 249.303943 23.7182322 6.00696892 5.6089068 7.77036807 1.42381473 28.8800067 95.155874 128.494973 601.050799

Dec 2010

26.6

48

24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

54.49711 53.17789 51.85866 50.53944 49.22021 47.90099 46.58176 45.26254 43.94331 42.62409 41.30486 39.98564 38.66641 37.34719 36.02796 34.70874 33.38951 32.07029 30.75106 29.43184 28.11261 26.79339 25.47416 24.15494 22.83571

-28.39711 -30.47789 -27.25866 -19.53944 -14.22021 -8.400988 2.618237 4.037462 -0.543313 2.975912 -1.904863 -4.785638 -8.566413 -5.647188 -0.827964 12.69126 18.81049 12.42971 14.74894 11.26816 10.98739 12.40661 10.52584 8.845061 3.764286 0.210008

-24.516337 -28.397112 -30.477888 -27.258663 -19.539438 -14.220213 -8.4009878 2.6182371 4.037462 -0.5433131 2.9759119 -1.9048632 -4.7856383 -8.5664134 -5.6471884 -0.8279635 12.691261 18.810486 12.429711 14.748936 11.268161 10.987386 12.406611 10.525836 8.8450608 =

806.395996 928.901629 743.034688 381.789625 202.214451 70.5765967 6.85516542 16.3010995 0.29518909 8.85605136 3.62850389 22.9023339 73.3834381 31.8907374 0.6855236 161.068116 353.834396 154.497722 217.531118 126.971454 120.722652 153.923995 110.793221 78.2351004 14.1698469 10963.1278 DW =


Lower 95%Upper 95%Lower 95.0%Upper 95.0% 77.04594 95.27108 77.0459405 95.27108 -1.64299 -0.99546 -1.6429919 -0.99546

(Difference)^2 SUMMARY OUTPUT 77.77873 388.8478 130.3987 1.740354 0.00037 75.35586 148.3713

Regression Statistics Multiple R 0.894664 R Square 0.800424 Adjusted R Square 0.795989 Standard Error6.943929 Observations 47

44.63276 0.014215

ANOVA

305.5775 24.80812 6.154245 22.27108


SS MS 1 8702.315 8702.315 45 2169.817 48.21816 46 10872.13


119.2295 5.852649 23.22493 0.17575 15.84657 17.47888 19.19119 2.49885 173.7328


Coefficients Standard Error t Stat P-value Lower 95%Upper 95% 0.27224 1.01289 0.268775 0.789331 -1.76783 2.312305 0.891532 0.066363 13.43421 2.35E-17 0.757871 1.025194

RESIDUAL OUTPUT

15.06042 4.329625 10.36341 59.58643 28.29415 33.86338 121.4233 2.014199 20.9835 12.38494 23.82197 8.298865 14.29426 8.521874 23.22493 182.7694 37.44491 40.71429 5.378804 12.1158 0.078835 2.014199 3.537315 2.825005 25.81428 2302.34 0.210008

Observation Predicted Y 1 -8.14319 2 -0.28056 3 17.29976 4 27.48036 5 28.65649 6 28.67363 7 20.93444 8 10.07489 9 4.118767 10 4.22506 11 -11.3596 12 -15.8001 13 -18.0118 14 -13.8045 15 -4.06964 16 -1.91283 17 2.383667 18 2.757419 19 -0.79157 20 -4.51886 21 -8.42447 22 -9.83378 23 -21.5849 24 -25.0447 25 -26.8998 26 -24.0297 27 -17.1478 28 -12.4055 29 -7.21751 30 2.606482 31 3.871767 32 -0.21214 33 2.925361 34 -1.42601 35 -3.99431 36 -7.36499 37 -4.76241 38 -0.46592 39 11.58691 40 17.04239 41 11.35373 42 13.42139 43 10.31817 44 10.06785 45 11.33313 46 9.65636 47 8.157895 48 4.07E-14

Residuals 7.523126 19.37973 13.21863 4.357251 3.200344 -5.49757 -9.93916 -5.76038 0.314971 -17.2721 -6.6682 -4.70845 2.222462 8.934346 1.618732 4.28114 0.403871 -3.95066 -4.58244 -5.23592 -2.9111 -14.6826 -6.81225 -5.43319 -0.35889 4.490295 2.927583 4.004549 9.835748 1.43098 -4.41508 3.188053 -4.83022 -3.35963 -4.5721 1.717804 3.934447 13.15718 7.22358 -4.61268 3.39521 -2.15323 0.669219 2.338764 -0.8073 -0.8113 -4.39361 3.764286

Lower 95.0% Upper 95.0% -1.76783 2.312305 0.757871 1.025194

VIX Contracts and Serial Correlation %Date Close %http://finance.yahoo.com/q/hp?s=^VIX&a=00&b=2&c=2006&d=08&e=28&f=2009&g=d 1 31 2006 12.95 1 SUMMARY OUTPUT 2 28 2006 12.34 2 3 31 2006 11.39 3 Regression Statistics 4 28 2006 11.59 4 Multiple R 0.750395 5 31 2006 16.44 5 R Square 0.563093 6 30 2006 13.08 6 Adjusted R Square 0.55269 7 31 2006 14.95 7 Standard Error8.25066 8 31 2006 12.31 8 Observations 44 9 29 2006 11.98 9 10 31 2006 11.1 10 ANOVA 11 30 2006 10.91 11 df SS MS F Significance F 12 29 2006 11.56 12 Regression 1 3684.826 3684.826 54.1302 4.5E-09 1 31 2007 10.42 13 Residual 42 2859.083 68.07339 2 28 2007 15.42 14 Total 43 6543.909 3 30 2007 14.64 15 4 30 2007 14.22 16 Coefficients Standard Error t Stat P-value Lower 95% 5 31 2007 13.05 17 Intercept 6.950307 2.530685 2.746413 0.008834 1.843177 6 29 2007 16.23 18 X Variable 1 0.720663 0.097952 7.357323 4.5E-09 0.522988 7 31 2007 23.52 19 8 31 2007 23.38 20 9 28 2007 18 21 10 31 2007 18.53 22 RESIDUAL OUTPUT 11 30 2007 22.87 23 12 31 2007 22.5 24 ObservationPredicted Y Residuals Lag Res. Squ.Res. (Difference)^2 1 31 2008 26.2 25 1 7.67097 5.27903 NA 27.86816 NA 2 29 2008 26.54 26 2 8.391633 3.948367 5.27903 15.5896 1.770664 3 31 2008 25.61 27 3 9.112296 2.277704 3.948367 5.187936 2.791115 4 30 2008 20.79 28 4 9.832959 1.757041 2.277704 3.087193 0.27109 5 30 2008 17.83 29 5 10.55362 5.886378 1.757041 34.64944 17.05142 6 30 2008 23.95 30 6 11.27429 1.805715 5.886378 3.260605 16.65181 7 31 2008 22.94 31 7 11.99495 2.955051 1.805715 8.732329 1.320975 8 29 2008 20.65 32 8 12.71561 -0.40561 2.955051 0.164521 11.29406 9 30 2008 39.39 33 9 13.43627 -1.45627 -0.40561 2.120736 1.103893 10 31 2008 59.89 34 10 14.15694 -3.05694 -1.45627 9.34487 2.562122 11 28 2008 55.28 35 11 14.8776 -3.9676 -3.05694 15.74186 0.829307 12 31 2008 40 36 12 15.59826 -4.03826 -3.9676 16.30758 0.004993 1 29 2009 42.63 37 13 16.31893 -5.89893 -4.03826 34.79734 3.462067 2 27 2009 46.35 38 14 17.03959 -1.61959 -5.89893 2.623074 18.31272 3 31 2009 44.14 39 15 17.76025 -3.12025 -1.61959 9.735983 2.25199 4 30 2009 36.5 40 16 18.48092 -4.26092 -3.12025 18.15541 1.301112 5 29 2009 28.92 41 17 19.20158 -6.15158 -4.26092 37.84194 3.574607 6 30 2009 26.35 42 18 19.92224 -3.69224 -6.15158 13.63266 6.048338 7 31 2009 25.92 43 19 20.64291 2.877094 -3.69224 8.277668 43.15619

8

31 2009

26.01

44

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

21.36357 22.08423 22.8049 23.52556 24.24622 24.96689 25.68755 26.40821 27.12887 27.84954 28.5702 29.29086 30.01153 30.73219 31.45285 32.17352 32.89418 33.61484 34.33551 35.05617 35.77683 36.4975 37.21816 37.93882

44 38.65948

2.877094 2.016431 -4.08423 -4.2749 -0.65556 -1.74622 1.233115 0.852452 -0.79821 -6.33887 -10.0195 -4.6202 -6.35086 -9.36153 8.65781 28.43715 23.10648 7.10582 9.015157 12.01449 9.083831 0.723168 -7.5775 -10.8682 -12.6495 -12.0188

2.016431 -4.08423 -4.2749 -0.65556 -1.74622 1.233115 0.852452 -0.79821 -6.33887 -10.0195 -4.6202 -6.35086 -9.36153 8.65781 28.43715 23.10648 7.10582 9.015157 12.01449 9.083831 0.723168 -7.5775 -10.8682 -12.0188

0.509319

=

4.065992 16.68096 18.27473 0.429757 3.049291 1.520572 0.726674 0.637141 40.18133 100.3911 21.34626 40.33347 87.63819 74.95767 808.6713 533.9096 50.49268 81.27306 144.3481 82.51598 0.522972 57.41844 118.1169 144.4521

0.740741 37.21809 0.036352 13.0996 1.189546 8.876448 0.144904 2.724689 30.69895 13.54728 29.15284 2.995195 9.064093 324.6965 391.2222 28.41597 256.0212 3.645567 8.996022 8.588786 69.90069 68.90101 10.82846 1.324026

160.0095 0.397736 2859.083 1456.185 DW = 0.509319

SUMMARY OUTPUT Regression Statistics Multiple R 0.738055 R Square 0.544725 Adjusted R Square 0.53362 Standard Error 5.606371 Observations 43 ANOVA

Significance F


Upper 95%Lower 95.0% Upper 95.0% 12.05744 1.843177 12.05744 0.918338 0.522988 0.918338


Coefficients Standard Error t Stat P-value Lower 95% Intercept -0.34526 0.855554 -0.40356 0.688636 -2.07309 X Variable 1 0.756341 0.107988 7.003954 1.63E-08 0.538255

RESIDUAL OUTPUT (Difference)^2

ObservationPredicted Y Residuals 1 3.647481 0.300886 2 2.641046 -0.36334 3 1.377456 0.379585 4 0.983657 4.90272 5 4.106842 -2.30113 6 1.020471 1.93458 7 1.889761 -2.29537 8 -0.65204 -0.80423 9 -1.4467 -1.61023 10 -2.65735 -1.31025 11 -3.34612 -0.69214 12 -3.39957 -2.49936 13 -4.80686 3.187271 14 -1.57023 -1.55003 15 -2.70524 -1.55568 16 -3.56797 -2.58361 17 -4.99795 1.30571 18 -3.13786 6.014951 19 1.830799 0.185632

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

1.179844 -3.43433 -3.57854 -0.84109 -1.666 0.587391 0.29948 -0.94898 -5.13961 -7.92345 -3.83971 -5.14868 -7.42577 6.202989 21.1629 17.13111 5.029156 6.473265 8.741785 6.525206 0.201697 -6.07643 -8.56529 -9.43559

-5.26408 -0.84056 2.922982 -0.90513 2.899117 0.265061 -1.09769 -5.38989 -4.87993 3.303246 -2.51115 -4.21285 16.08358 22.23416 1.94358 -10.0253 3.986001 5.541229 0.342046 -5.80204 -7.77919 -4.79173 -3.45353 -3.2139

Significance F


Month 1 2006 2 2006 3 2006 4 2006 5 2006 6 2006 7 2006 8 2006 9 2006 10 2006 11 2006 12 2006 1 2007 2 2007

Pt 12.95 12.34 11.39 11.59 16.44 13.08 14.95 12.31 11.98 11.1 10.91 11.56 10.42 15.42

t 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Month 4 2007 5 2007 6 2007 7 2007 8 2007 9 2007 10 2007 11 2007 12 2007 1 2008 2 2008 3 2008 4 2008 5 2008

Pt 14.22 13.05 16.23 23.52 23.38 18 18.53 22.87 22.5 26.2 26.54 25.61 20.79 17.83

t 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Month 7 2008 8 2008 9 2008 10 2008 11 2008 12 2008 1 2009 1 2009 2 2009 3 2009 4 2009 5 2009 6 2009 7 2009

3 2007 14.64 15

6 2008 23.95 30

8 2009

Pt 22.94 20.65 39.39 59.89 55.28 40 42.63 44.84 46.35 44.14 36.5 28.92 26.35 25.92

t 31 32 33 34 35 36 37 38 39 40 41 42 43 44

26.01 45

Exponential Weighted Moving Average w=

0.5

12

14

17

13

14

19

22

17

12

13

15

14

14

16.5

19.25

18.125

11

18

14.5625 16.28125

16

22 Data

16.14063 19.07031 Exponential Weighted Moving Average

AR(1) Process Simulation b0 =

0.01

b1 =

0.01

xt = b 0 + b 1xt-1 + e t.


[0,1] Normally distributed variable AR(1) Process

0.01

0.9172

-0.771 -1.4731 1.05745

0.19415

-0.584 0.143629

-1.8968 -1.3941 0.62891

1.0809

1.10952

-1.6124

0.9273

-0.751 -1.4706 1.05275

0.21468

-0.572 0.147909 -1.88532 -1.4029 0.62489

1.0972

1.13049

-1.5911

AR(1) Process 4 3

2 S(t)

1 0 -1 -2 -3 -4 1

20

39

58

77

96

115

134

153

172

191

t Notice that as b1 gets closer to 0, the process becomes more mean reverting. As b1 increases from 1 or decreases from -1, the process explodes.

0.636946

0.93183

0.40835 -0.8086

0.76346 -0.3283 0.32997 -1.2351 -0.48279 -0.78465 -0.14891

0.631035

0.94814

0.42783 -0.7943

0.76552 -0.3107 0.33686 -1.2217 -0.48501

ocess explodes.

-0.7795

-0.1467

0.2956 -0.30274 -0.9292 0.37461 1.62791 0.30413

-0.2897 -0.9221 0.37539 1.64167

2.2749 0.646232 2.3014 0.679245

0.9772 1.41226 1.71953

0.60465

0.1304 -0.96691 -0.30857

-0.0512

-2.6141

-0.65074

0.0418 1.99696 1.36902 1.00089 1.43227 1.74385

0.025 1.98654 1.33905

0.63209

0.1467 -0.95544 -0.30812

-0.0443

-2.6046

-0.66679 0.962492

0.95916

0.4426 -0.17022 1.56157

-0.5618

0.4622

-0.5361

-0.1556 1.57001

-0.795 1.30322 -0.4278 -0.73125551 -0.20562739 -0.27582776

3.47171183

1.20587318

1.14957751

0.77941178

0.59779352

0.53932235

0.08774384

0.34415407

-0.7903 1.30532 -0.4047 -0.72530294 -0.20288042 -0.26785656

3.47903326

1.25066351

1.17208414

0.80113262

0.61580485

0.5554804

0.10329864

0.35518706

-0.5260538

0.4233699

0.32781009

1.29355594

0.08724272

0.03254179 -0.39508729

0.22756021

0.30088802 -0.59091927

1.40595317

1.67168447

0.81947962

-0.51250193

0.42824489

0.34209253

1.30697686

0.11031249

0.04364492 -0.38465084

0.2337137

0.31322516 -0.57778701

1.4101753

1.69578622

0.84643748

0.69094026

1.09172841 -1.08117838 -0.09581166

0.47951593 -0.05335207 -0.12678707 -0.20781522 -0.27264851 -1.09182088 -0.26573143

1.48174051

1.02066228

0.70940464

1.10882246 -1.06009016 -0.09641256

0.48855181 -0.03846655 -0.11717173 -0.19898694 -0.26463838 -1.08446727 -0.26657611

1.48907475

1.04555303

0.15389916 -1.64028761 -0.78500878

1.50146212 -0.43595956 -1.06676052 -1.03090507

0.43127633

-1.0082073

1.09423906 -1.24298285

2.58209064 -0.59800196

0.17435469 -1.62854406 -0.79129422

1.50354918 -0.41092407 -1.06086976 -1.03151377

0.43096119 -0.99389769

1.09430009 -1.22203985

2.57987024 -0.56220325

-2.59796001 -2.90183843 -1.29660179

-0.4499158 -0.03755143 -1.41194286 -0.67436324 -0.99817427

0.00989582

1.20714291 -0.35126925 -1.27542202

0.34858094

-2.59358205 -2.91777425 -1.31577953 -0.45307359 -0.03208217 -1.40226368 -0.67838588 -0.99495813

0.00994623

1.21724237 -0.32909682 -1.26871299

0.34589381

1.30224164

0.89846 -0.72348634 -0.74793397

0.39397141 -0.43452618

0.67299402

0.86696698 -0.48609911

0.44687104

0.62281749 -0.16895039

0.07486018

1.31570058

0.921617 -0.70427017 -0.74497668

0.39652164 -0.42056096

0.67878841

0.88375486 -0.46726156

0.45219842

0.63733947

0.08333441

-0.152577

1.51357997

-1.4413019

0.58622982

0.12961949 -1.24663502

0.86209182

1.54476725

0.46034293 -0.53931523

1.28177942

0.03339403

0.35283489

0.60119631

1.52441331 -1.41605777

0.58206924

0.14544019 -1.23518062

0.85974001

1.56336465

0.48597658 -0.52445546

1.28653486

0.05625938

0.36339748

0.61483029

0.09183559 -2.23957626 0.1079839 -2.22849642

1.23597744 -0.26878871 -1.13237368

0.29021544

0.70200907 -0.85403518

1.22369247 -0.24655179

0.28896705

0.71489874

-1.1248392

-0.8368862

1.0035205

-0.3660815 -0.30633278 -0.55678747

1.00515164 -0.34602998 -0.29979308

-0.5497854

0.1120559 0.11655804

-0.00650904

1.20286566

0.23258066 -0.59133318 -1.80786713 -1.62054321

0.48083572 -0.93279893 -1.47361554 -1.51137549 -1.09261533

0.22169428

1.63114817

0.00465654

1.21291223

0.25470978 -0.57878609

0.47454992 -0.91805343 -1.47279608 -1.51610345 -1.09777636

0.22071651

1.64335534

-1.803655 -1.62857976

-0.91774902 -0.93154361

1.18090609 -0.46822503

0.75187117

-0.5627502 -1.08621706 -0.19775269

-1.0370348 -0.73140625

1.21102695 -1.73084926

0.60618315

-0.89131546 -0.93045676

1.18160153 -0.44640901

0.75740708 -0.54517613 -1.08166882 -0.19856938

-1.0290205 -0.73169645

1.21370999 -1.70871216

0.59909603

-0.82072112

0.22250001

0.2329666 -0.07150096 -0.35042228

0.98189112

0.25911139 -0.53354518 -0.40909478 -0.80810455

-0.80473015

0.22445271

0.24521113 -0.05904885 -0.34101277

0.98848099

0.2789962 -0.52075521 -0.40430233 -0.80214758

0.01863444

-1.4826664

0.88943444

0.02061296 -1.47246027

0.88470984

1.14818267 -1.07444352

1.43959441

1.16702977 -1.05277322

1.43906668 -0.63680183

-0.6611925 -0.02879118 -0.45441104 -0.85469604 -0.0251592 -0.44466263 -0.84914266

0.89837456

0.07320538

0.83115896

0.63620866 -1.22624074 -0.56728339

0.89988313

0.09220421

0.842081

0.65462947 -1.20969445 -0.56938034

WN Weekly Stock Prices, 2010 and AR(1) Forecasting Week Closing Closing Ending Price t Price t-1 t 1/4/2010 0.98 NA 1 1/11/2010 1.35 0.98 2 1/19/2010 1.24 1.35 3 1/25/2010 1.2 1.24 4 2/1/2010 1.16 1.2 5 2/8/2010 1.24 1.16 6 2/16/2010 1.38 1.24 7 2/22/2010 1.29 1.38 8 3/1/2010 1.97 1.29 9 3/8/2010 2.3 1.97 10 3/15/2010 1.82 2.3 11 3/22/2010 2.34 1.82 12 3/29/2010 2.16 2.34 13 4/5/2010 3.54 2.16 14 4/12/2010 4.55 3.54 15 4/19/2010 5.47 4.55 16 4/26/2010 5.43 5.47 17 5/3/2010 4.8 5.43 18 5/10/2010 5.45 4.8 19 5/17/2010 4.8 5.45 20 5/24/2010 4.65 4.8 21 6/1/2010 5.28 4.65 22 6/7/2010 4.86 5.28 23 6/14/2010 4.77 4.86 24 6/21/2010 3.83 4.77 25 6/28/2010 3.37 3.83 26 7/6/2010 3.22 3.37 27 7/12/2010 3.2 3.22 28 7/19/2010 3.51 3.2 29 7/26/2010 3.43 3.51 30 8/2/2010 3.36 3.43 31 8/9/2010 3.17 3.36 32 8/16/2010 3.09 3.17 33 8/23/2010 3.52 3.09 34 8/30/2010 3.8 3.52 35 9/7/2010 3.78 3.8 36 9/13/2010 4 3.78 37 9/20/2010 4.07 4 38 9/27/2010 4.16 4.07 39 10/4/2010 5.14 4.16 40 10/11/2010 5.21 5.14 41 10/18/2010 5.25 5.21 42 10/25/2010 5.16 5.25 43


SS MS F 1 300.59 300.59 706.9306 49 20.83502 0.425204 50 321.425

Coefficients Standard Error t Stat P-value Intercept 0.193612 0.183188 1.056903 0.295739 X Variable 1 0.994669 0.03741 26.58817 9.03E-31

RESIDUAL OUTPUT ObservationPredicted YResiduals 1 1.168388 0.181612 2 1.536415 -0.29641 3 1.427001 -0.227 4 1.387215 -0.22721 5 1.347428 -0.10743 6 1.427001 -0.047 7 1.566255 -0.27626 8 1.476735 0.493265 9 2.15311 0.14689 10 2.48135 -0.66135 11 2.003909 0.336091 12 2.521137 -0.36114 13 2.342097 1.197903 14 3.714739 0.835261 15 4.719355 0.750645 16 5.63445 -0.20445 17 5.594663 -0.79466 18 4.968022 0.481978 19 5.614557 -0.81456

11/1/2010 5.55 11/8/2010 5.28 11/15/2010 7.24 11/22/2010 7.83 11/29/2010 9.18 12/6/2010 10.3 12/13/2010 11.05 12/20/2010 11.77 12/27/2010 9.7 Date Adj Close

5.16 5.55 5.28 7.24 7.83 9.18 10.3 11.05 11.77

44 45 46 47 48 49 50 51 52 T

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

4.968022 4.818822 5.445463 5.027702 4.938182 4.003193 3.545646 3.396445 3.376552 3.684899 3.605326 3.535699 3.346712 3.267139 3.694846 3.973353 3.95346 4.172287 4.241914 4.331434 5.306209 5.375836 5.415623 5.326103 5.714024 5.445463 7.395014 7.981868 9.324671 10.4387 11.1847

-0.31802 0.461178 -0.58546 -0.2577 -1.10818 -0.63319 -0.32565 -0.19645 0.133448 -0.2549 -0.24533 -0.3657 -0.25671 0.252861 0.105154 -0.19335 0.04654 -0.10229 -0.08191 0.808566 -0.09621 -0.12584 -0.25562 0.223897 -0.43402 1.794537 0.434986 1.198132 0.975329 0.6113 0.585298

51 11.90086

-2.20086

WN Weekly Stock Returns, 2010 and AR(1) Forecas


Lower 95%Upper 95%Lower 95.0% Upper 95.0% -0.17452 0.561743 -0.17452 0.561743 0.91949 1.069847 0.91949 1.069847

Week Ending 1/4/2010 1/11/2010 1/19/2010 1/25/2010 2/1/2010 2/8/2010 2/16/2010 2/22/2010 3/1/2010 3/8/2010 3/15/2010 3/22/2010 3/29/2010 4/5/2010 4/12/2010 4/19/2010 4/26/2010 5/3/2010 5/10/2010 5/17/2010 5/24/2010 6/1/2010 6/7/2010 6/14/2010 6/21/2010 6/28/2010 7/6/2010 7/12/2010 7/19/2010 7/26/2010 8/2/2010 8/9/2010 8/16/2010 8/23/2010 8/30/2010 9/7/2010 9/13/2010 9/20/2010 9/27/2010 10/4/2010 10/11/2010 10/18/2010 10/25/2010

Return t NA 0.377551 -0.08148 -0.03226 -0.03333 0.068966 0.112903 -0.06522 0.527132 0.167513 -0.2087 0.285714 -0.07692 0.638889 0.285311 0.202198 -0.00731 -0.11602 0.135417 -0.11927 -0.03125 0.135484 -0.07955 -0.01852 -0.19706 -0.1201 -0.04451 -0.00621 0.096875 -0.02279 -0.02041 -0.05655 -0.02524 0.139159 0.079545 -0.00526 0.058201 0.0175 0.022113 0.235577 0.013619 0.007678 -0.01714

Return t-1 NA NA 0.377551 -0.081481 -0.032258 -0.033333 0.068966 0.112903 -0.065217 0.527132 0.167513 -0.208696 0.285714 -0.076923 0.638889 0.285311 0.202198 -0.007313 -0.116022 0.135417 -0.119266 -0.03125 0.135484 -0.079545 -0.018519 -0.197065 -0.120104 -0.04451 -0.006211 0.096875 -0.022792 -0.020408 -0.056548 -0.025237 0.139159 0.079545 -0.005263 0.058201 0.0175 0.022113 0.235577 0.013619 0.007678

t 1 SUMMARY OUTPUT 2 3 Regression Statistics 4 Multiple R 5 R Square 6 Adjusted R Square 7 Standard Error 8 Observations 9 10 ANOVA 11 12 Regression 13 Residual 14 Total 15 16 Coefficients 17 Intercept 18 X Variable 1 19 20 21 22 RESIDUAL OUTPUT 23 24Observation 25 1 26 2 27 3 28 4 29 5 30 6 31 7 32 8 33 9 34 10 35 11 36 12 37 13 38 14 39 15 40 16 41 17 42 18 43 19

11/1/2010 11/8/2010 11/15/2010 11/22/2010 11/29/2010 12/6/2010 12/13/2010 12/20/2010 12/27/2010 Date

0.075581 -0.04865 0.371212 0.081492 0.172414 0.122004 0.072816 0.065158 -0.17587

-0.017143 0.075581 -0.048649 0.371212 0.081492 0.172414 0.122004 0.072816 0.065158

44 45 46 47 48 49 50 51 52

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

010 and AR(1) Forecasting SUMMARY OUTPUT Regression Statistics 0.007797 6.08E-05 -0.02077 0.166446 50

df

SS MS F Significance F 1 8.09E-05 8.09E-05 0.002918 0.957141 48 1.329809 0.027704 49 1.32989

Coefficients Standard Error t Stat P-value Lower 95%Upper 95%Lower 95.0% Upper 95.0% 0.052097 0.025161 2.07055 0.043802 0.001508 0.102686 0.001508 0.102686 -0.00766 0.141779 -0.05402 0.957141 -0.29272 0.277406 -0.29272 0.277406

RESIDUAL OUTPUT Predicted Y Residuals 0.049205 -0.13069 0.052721 -0.08498 0.052344 -0.08568 0.052352 0.016613 0.051569 0.061334 0.051232 -0.11645 0.052597 0.474535 0.04806 0.119453 0.050814 -0.25951 0.053695 0.232019 0.049909 -0.12683 0.052686 0.586203 0.047204 0.238107 0.049912 0.152286 0.050548 -0.05786 0.052153 -0.16818 0.052986 0.082431 0.05106 -0.17033 0.05301 -0.08426

0.052336 0.051059 0.052706 0.052239 0.053606 0.053017 0.052438 0.052145 0.051355 0.052272 0.052253 0.05253 0.05229 0.051031 0.051488 0.052137 0.051651 0.051963 0.051928 0.050293 0.051993 0.052038 0.052228 0.051518 0.05247 0.049254 0.051473 0.050776 0.051163 0.051539 0.051598

0.083148 -0.1306 -0.07122 -0.2493 -0.17371 -0.09753 -0.05865 0.04473 -0.07415 -0.07268 -0.1088 -0.07777 0.086868 0.028514 -0.05675 0.006064 -0.03415 -0.02985 0.183649 -0.03667 -0.04432 -0.06918 0.023353 -0.10017 0.318743 0.032238 0.120941 0.071228 0.021653 0.013619 -0.22747


0

b1 =

0.99

xt = b 0 + b 1xt-1 + e t.


[0,1] Normally distributed variable AR(1) Process

0

-0.1487

-1.052

0.5833 0.37367 -0.43346 0.7878 0.968145

0.24272 -0.3954 0.14467

0.3626

0.06223

-0.1487

-1.199

-0.604 -0.2243

1.33732 0.92852

1.4159

1.46395

-0.6555 0.1389 1.105657

1.0639

0 -0.1487 -1.0521 0.58332 0.37367 -0.4335 0.78784 0.96815 0.24272 -0.3954 0.14467 0.36261 0.06223 0.61992 -0.2016 0.13912 0.01431 1.16295 -0.5477 -0.0892 -1.3178 -1.7719 0.12683 2.203 -1.2081

0 -0.1487 -1.1993 -0.604 -0.2243 -0.6555 0.1389 1.10566 1.33732 0.92852 1.0639 1.41587 1.46395 2.06922 1.84694 1.96759 1.96222 3.10555 2.52675 2.41228 1.07033 -0.7122 -0.5783 1.63049 0.40606

S(t)

AR(1) Process 9 8 7 6 5 4 3 2 1 0 -1 -2

1

21

41 t

Notice that as b1 gets closer to 0, the process becomes more mean reverting.

3.59351 -0.4123 0.57516 -0.8504 1.44305 -0.803 -2.2595 0.59267 -0.4657 1.43934 -0.5137 0.16731 1.33693 1.08291 1.28611 -0.2266 -0.4487 -0.4155

3.99551 3.54323 4.08296 3.19174 4.60287 3.75379 1.45673 2.03484 1.54875 2.97261 2.42921 2.57223 3.88344 4.92752 6.16435 5.87606 5.36861 4.89941

0.61992 -0.20159

0.13912

0.01431

1.1629 -0.54774 -0.0892

2.06922 1.846938

1.96759

1.96222

3.1055

-1.3178 -1.7719 0.126825

2.203 -1.20813

2.52675 2.41228 1.07033 -0.7122 -0.57829

1.63049 0.406058

ecomes more mean reverting. As b1 increases from 1 or decreases from -1, the process explodes.

3.59351 -0.41232 3.99551

3.54323

0.5752

-0.8504 1.44305

-0.803

4.083 3.19174 4.60287

3.7538

-2.25952

0.5927 -0.4657 1.43934

-0.5137 0.16731 1.33693

1.08291

1.2861 -0.22665 -0.44868

1.456735

2.0348 1.54875 2.97261 2.42921 2.57223 3.88344

4.92752

6.1643

5.87606

-0.4155

1.6809 0.455074 -1.51844

5.36861 4.89941 6.53132 6.921077 5.333426

0.5854 -0.27961 5.8655

0.2179

5.5272 5.68982

0.61044 0.73786 0.67651 -0.9652

1.39762161 -0.23489853

6.24336 6.91879 7.52611 6.48564

7.81840643

7.50532383

0.10288241 7.533153


5 "True Value"

b1 =

0.5 "True Value"

xt = b 0 + b 1xt-1 + e t. et

xt

0 -1.125 0.57887 0.64055 1.4211 0.63031 1.45323 0.25498 -1.136 1.69815 1.02491 -2.0807 -0.3196 1.3585 -0.1496 -0.0457 -0.5811 0.25748 0.61932 -1.9653 -0.0054 -0.152 -2.0746 -0.5366 -0.0818 0.17078 -0.9348 -1.488

5 6.37505 8.7664 10.0237 11.433 11.3468 12.1266 11.3183 9.52318 11.4597 11.7548 8.79665 9.07871 10.8979 10.2993 10.104 9.47089 9.99292 10.6158 8.34264 9.16589 9.43094 7.64085 8.28378 9.06008 9.70082 8.91561 7.96977

xt-1 6.375047 8.766398 10.02375 11.43297 11.3468 12.12663 11.31829 9.523177 11.45974 11.75478 8.796648 9.078712 10.89785 10.29934 10.10401 9.470887 9.992924 10.61579 8.342635 9.165895 9.430936 7.640853 8.283785 9.060076 9.700821 8.915608

rt

t 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27


Regression of xt on xt-1

ANOVA df

SS MS FSignificance F 1 14.08 14.08 12.521 0.001 39 43.86 1.125 40 57.95



Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 5.481 1.257 4.36 9E-05 2.938 8.0235 2.9384 8.024 0.449 0.127 3.539 0.0011 0.192 0.7059 0.1924 0.706

RESIDUAL OUTPUT Observation Predicted Residuals Y 1 8.344 0.422 2 9.418 0.606

N/A 0.275 0.3751 0.1434 0.1406 -0.008 0.0687 -0.067 -0.159 0.2034 0.0257 -0.252 0.0321 0.2004 -0.055 -0.019 -0.063 0.0551 0.0623 -0.214 0.0987 0.0289 -0.19 0.0841 0.0937 0.0707 -0.081 -0.106

-0.222 0.12245 -0.0003 1.39268 -0.8308 -1.2396 -0.0883 1.48977 0.08896 2.0048 0.40331 -0.7233 -1.7759 0.5216 -0.4548

8.76293 9.50391 9.75168 11.2685 9.80343 8.66211 9.24278 11.1112 10.6445 12.3271 11.5669 10.0601 8.25419 9.64869 9.36955

7.969766 8.762926 9.503913 9.751676 11.26852 9.803429 8.662114 9.242777 11.11115 10.64454 12.32707 11.56685 10.0601 8.254187 9.648694

28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

9.983 10.62 10.58 10.93 10.56 9.758 10.63 10.76 9.432 9.559 10.38 10.11 10.02 9.735 9.969 10.25 9.228 9.598 9.717 8.913 9.201 9.55 9.838 9.485 9.06 9.417 9.749 9.861 10.54 9.884 9.371 9.632 10.47 10.26 11.02 10.68 9.999

1.45 0.731 1.549 0.391 -1.04 1.702 1.127 -1.96 -0.35 1.339 -0.08 -0 -0.55 0.258 0.647 -1.91 -0.06 -0.17 -2.08 -0.63 -0.14 0.151 -0.92 -1.52 -0.3 0.087 0.002 1.408 -0.74 -1.22 -0.13 1.479 0.173 2.065 0.549 -0.62 -1.75

0.0995 0.0846 0.0261 0.1555 -0.13 -0.116 0.067 0.2021 -0.042 0.1581 -0.062 -0.13 -0.18 0.1689 -0.029

40 9.188 41 9.815

xt

t 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

5 6.37505 8.7664 10.0237 11.433 11.3468 12.1266 11.3183 9.52318 11.4597 11.7548 8.79665 9.07871 10.8979 10.2993 10.104 9.47089 9.99292 10.6158 8.34264 9.16589

xt-1 6.375047 8.766398 10.02375 11.43297 11.3468 12.12663 11.31829 9.523177 11.45974 11.75478 8.796648 9.078712 10.89785 10.29934 10.10401 9.470887 9.992924 10.61579 8.342635

t 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

0.46 -0.44

xt

xt-1

7.641 8.284 9.06 9.701 8.916 7.97 8.763 9.504 9.752 11.27 9.803 8.662 9.243 11.11 10.64 12.33 11.57 10.06 8.254 9.649 9.37

9.431 7.641 8.284 9.06 9.701 8.916 7.97 8.763 9.504 9.752 11.27 9.803 8.662 9.243 11.11 10.64 12.33 11.57 10.06 8.254 9.649

21 9.43094

9.165895

rt-1 0.275 0.3751 0.1434 0.1406 -0.008 0.0687 -0.067 -0.159 0.2034 0.0257 -0.252 0.0321 0.2004 -0.055 -0.019 -0.063 0.0551 0.0623 -0.214 0.0987 0.0289 -0.19 0.0841 0.0937 0.0707 -0.081

t 0 1 2 SUMMARY OUTPUT 3 Regression 4 Statistics 5 Multiple 0 R.0786 6 R Square 0.0062 7 Adjusted-0.019 R Square 8 Standard0.1355 Error 9 Observations41 10 11 ANOVA 12 df SS MS F Significance F 13 Regression 1 0.004 0.004 0.242 0.6254 14 Residual 39 0.716 0.018 15 Total 40 0.721 16 17 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% 18 Intercept0.0162 0.022 0.754 0.456 -0.027 0.0598 -0.027 0.0598 19 X Variable 0.0754 1 0.153 0.492 0.625 -0.235 0.3853 -0.235 0.3853 20 21 22 23 RESIDUAL OUTPUT 24 25 Observation PredictedResiduals Y 26 1 0.037 0.338 27 2 0.0445 0.099

-0.106 0.0995 0.0846 0.0261 0.1555 -0.13 -0.116 0.067 0.2021 -0.042 0.1581 -0.062 -0.13 -0.18 0.1689

28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

0.027 0.0268 0.0157 0.0214 0.0112 0.0043 0.0316 0.0182 -0.003 0.0186 0.0313 0.0121 0.0148 0.0115 0.0204 0.0209 8E-05 0.0237 0.0184 0.0019 0.0226 0.0233 0.0216 0.0101 0.0082 0.0237 0.0226 0.0182 0.028 0.0064 0.0074 0.0213 0.0315 0.0131 0.0281 0.0116 0.0064

0.114 -0.034 0.053 -0.088 -0.17 0.199 -0.006 -0.27 0.035 0.182 -0.086 -0.031 -0.077 0.044 0.042 -0.235 0.099 0.005 -0.208 0.082 0.071 0.047 -0.102 -0.116 0.091 0.061 0.003 0.137 -0.158 -0.123 0.06 0.181 -0.073 0.145 -0.09 -0.142 -0.186

40 0.0027 0.166 41 0.029 -0.058

Sample Price Data, Returns and Regression Results SUMMARY OUTPUT PRICEt

TIME 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

30 30.125 30.25 30.125 32 34 31 32 30.5 30.75 30.875 31 30.875 31 31.125 30.25 33 30 35.125 33 32.125 32.25 32.375 32.125 32.25 34.25 36.375 38.5 34.375 33.875 33.625

ERRORt2

RETURNt RETURNt-1 ERRORt N.A. 0.00417 0.00415 -0.00413 0.06224 0.0625 -0.08824 0.03226 -0.04688 0.0082 0.00407 0.00405 -0.00403 0.00405 0.00403 -0.02811 0.09091 -0.09091 0.17083 -0.0605 -0.02652 0.00389 0.00388 -0.00772 0.00389 0.06202 0.06204 0.05842 -0.10714 -0.01455 -0.00738

0.022478 0.003066 VARP

0.00417 0.00415 -0.00413 0.06224 0.0625 -0.08824 0.03226 -0.04688 0.0082 0.00407 0.00405 -0.00403 0.00405 0.00403 -0.02811 0.09091 -0.09091 0.17083 -0.0605 -0.02652 0.00389 0.00388 -0.00772 0.00389 0.06202 0.06204 0.05842 -0.10714 -0.01455

F

ERRORt-12 ERRORt-22

‑0.00189 ‑0.01018 0.05261 0.08157 ‑0.06905 ‑0.01375 ‑0.04077 ‑0.01992 ‑0.00023 ‑0.00204 ‑0.01013 ‑0.00554 ‑0.00206 ‑0.03421 0.07091 ‑0.05944 0.12367 0.00554 ‑0.06052 ‑0.01542 ‑0.00229 ‑0.01389 ‑0.00729 0.05585 0.08102 0.07741 ‑0.08972 ‑0.06873 ‑0.02151

0.0000035 0.000104 0.002768 0.006654 0.004768 0.000189 0.001662 0.000397 0 0.000004 0.000103 0.000031 0.000004 0.001171 0.005028 0.003533 0.015295 0.000031 0.003663 0.000238 0.000005 0.000193 0.000053 0.00312 0.006564 0.005992 0.00805 0.004723 0.000463

0.000004 0.000104 0.002768 0.006654 0.004768 0.000189 0.001662 0.000397 0 0.000004 0.000103 0.000031 0.000004 0.001171 0.005028 0.003533 0.015295 0.000031 0.003663 0.000238 0.000005 0.000193 0.000053 0.00312 0.006564 0.005992 0.00805 0.004723

0.000004 0.000104 0.002768 0.006654 0.004768 0.000189 0.001662 0.000397 0 0.000004 0.000103 0.000031 0.000004 0.001171 0.005028 0.003533 0.015295 0.000031 0.003663 0.000238 0.000005 0.000193 0.000053 0.00312 0.006564 0.005992 0.00805

0.001861 0.002352 0.003493 0.003813 0.002679 0.002169 0.002193 0.001909 0.001842 0.001861 0.001864 0.001848 0.002051 0.002934 0.003318 0.00516 0.004427 0.002499 0.002502 0.001883 0.001877 0.001884 0.002406 0.003536 0.004015 0.004285 0.00404

4 4 3 5 5 2 4 3 4 4 4 3 4 4 3 5 2 7 2 3 4 4 3 4 5 5 5 1 3 3

1

2

3

4

5

6

1 2 1 1 2 1 3 2 4 5 6 3 7 8 4 3 2 1 3 4 9 10 5 11 4 5 6 1 6 7 7

Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Residual Total Coefficients Intercept X Variable 1

RESIDUAL OUTPUT Observation 1 2 3 4 5 6 7 8 9 10 11

0.095154 0.003172 VARS

-.15 to -.10

-.1 to -.05

1

-.05 to 0

3

0 to .05

7

.05 to .10

11

.10 to .15

6

12 10 8 6

Series1

4 2 0 -.15 to - -.1 to - -.05 to 0 0 to .05 .10 .05 1

2

3

4

.05 to .10

.10 to .15

.15 to .20

5

6

7

.15 to .20

0

1

12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

SUMMARY OUTPUT Regression Statistics 0.432081 0.186694 0.156572 0.052637 29

df

SS 1 0.017172 27 0.074808 28 0.091981

RETURNt

on RETURNt-1


Coefficients Standard Error t Stat P-value Lower 95%Upper 95%Lower 95.0% Upper 95.0% 0.007844 0.009825 0.798369488 0.431623 -0.01232 0.028005 -0.01232 0.028005 -0.43247 0.173714 -2.489546024 0.019247 -0.7889 -0.07604 -0.7889 -0.07604

RESIDUAL OUTPUT Predicted Y Residuals 0.006041 -0.00189 0.00605 -0.01018 0.00963 0.05261 -0.01907 0.081573 -0.01919 -0.06905 0.046006 -0.01375 -0.00611 -0.04077 0.028119 -0.01992 0.004298 -0.00023 0.006084 -0.00203 0.006093 -0.01012

Squared Residuals 3.57571E-06 0.000103624 0.002767764 0.006654086 0.00476859 0.000188939 0.001662427 0.000396749 5.20296E-08 4.13798E-06 0.000102472

3.58E-06 0.000104 0.002768 0.006654 0.004769 0.000189 0.001662 0.000397 5.2E-08 4.14E-06

3.58E-06 0.000104 0.002768 0.006654 0.004769 0.000189 0.001662 0.000397 5.2E-08

SUMMARY OUTPUT Regression Statistics Multiple R 0.276006 R Square 0.076179 Adjusted R Square -0.00081 Standard Error 0.003583 Observations 27

Two Lag Periods

0.009587 0.006093 0.006102 0.020001 -0.03147 0.04716 -0.06603 0.034009 0.019313 0.006162 0.006166 0.011183 0.006162 -0.01898 -0.01899 -0.01742 0.054179 0.014137

-0.00554 -0.00206 -0.03421 0.070909 -0.05944 0.12367 0.005535 -0.06053 -0.01542 -0.00228 -0.01389 -0.00729 0.055858 0.081017 0.077406 -0.08972 -0.06873 -0.02152

3.06607E-05 4.25535E-06 0.001170427 0.005028074 0.003532935 0.015294217 3.06308E-05 0.003663735 0.000237883 5.20773E-06 0.000192831 5.31882E-05 0.003120111 0.006563826 0.005991703 0.00804958 0.004723703 0.000462972

0.000102 3.07E-05 4.26E-06 0.00117 0.005028 0.003533 0.015294 3.06E-05 0.003664 0.000238 5.21E-06 0.000193 5.32E-05 0.00312 0.006564 0.005992 0.00805 0.004724

4.14E-06 0.000102 3.07E-05 4.26E-06 0.00117 0.005028 0.003533 0.015294 3.06E-05 0.003664 0.000238 5.21E-06 0.000193 5.32E-05 0.00312 0.006564 0.005992 0.00805


SS 2 2.54E-05 24 0.000308 26 0.000334

MS 1.27E-05 1.28E-05

F Significance F 0.98953 0.386415

Coefficients Standard Error t Stat P-value Lower 95%Upper 95% Intercept 0.001842 0.000953 1.932465 0.065188 -0.00013 0.003809 X Variable 1 0.177997 0.202383 0.879504 0.38785 -0.2397 0.595695 X Variable 2 0.168676 0.201527 0.836987 0.410857 -0.24726 0.584608

RESIDUAL OUTPUT ObservationPredicted Y Residuals 1 0.001861 0.000907 2 0.002352 0.004302 3 0.003493 0.001276 4 0.003813 -0.00362 5 0.00268 -0.00102 6 0.002169 -0.00177 7 0.002193 -0.00219 8 0.001909 -0.0019 9 0.001842 -0.00174 10 0.001861 -0.00183 11 0.001864 -0.00186 12 0.001848 -0.00068 13 0.002051 0.002977 14 0.002934 0.000599 15 0.003319 0.011976 16 0.00516 -0.00513 17 0.004427 -0.00076 18 0.002499 -0.00226 19 0.002502 -0.0025 20 0.001883 -0.00169 21 0.001877 -0.00182

22 23 24 25 26 27

0.001884 0.002406 0.003536 0.004015 0.004285 0.00404

0.001236 0.004158 0.002455 0.004034 0.000439 -0.00358

Lower 95.0% Upper 95.0% -0.00013 0.003809 -0.2397 0.595695 -0.24726 0.584608

Linear Probability Model Defense Dummy

Firm 1 2 3 4 5 6 7 8 9 10

x1,i 1 1 1 1 1 0 0 0 0 0

x2,i 1,000 1200 1400 1500 1600 1800 1100 1000 900 700

x3,i 48 63 55 49 44 62 60 58 66 74

x4,i 0.18 0.03 0.16 0.07 0.14 0.02 0 0.11 0.05 0

Linear Probability Model Results 0.2 0.35 0.1 0.3 0.2 0.03 0 0.02 0.04 0.05


SS 4 2.307222 5 0.192778 9 2.5

Coefficients Standard Error Intercept -0.55993 1.220861 X Variable 1 0.000196 0.000249 X Variable 2 0.002589 0.015221 X Variable 3 3.661388 1.674945 X Variable 4 3.041962 0.595926

RESIDUAL OUTPUT ObservationPredicted YResiduals 1 1.027972 -0.02797 2 1.013129 -0.01313 3 0.747146 0.252854 4 1.030099 -0.0301 5 0.988875 0.011125 6 0.118212 -0.11821 7 -0.18878 0.188785 8 0.250011 -0.25001 9 0.092258 -0.09226 10 -0.07892 0.078918

Model Results


t Stat -0.45863 0.789187 0.170088 2.185976 5.104598

P-value Lower 95%Upper 95%Lower 95.0% Upper 95.0% 0.665745 -3.69825 2.578397 -3.69825 2.578397 0.46576 -0.00044 0.000835 -0.00044 0.000835 0.871609 -0.03654 0.041715 -0.03654 0.041715 0.080504 -0.64419 7.966971 -0.64419 7.966971 0.003756 1.510086 4.573838 1.510086 4.573838

0.038556 0.014622

Mean and variance

-0.03856 0.029857

Mean and variance

Using the Offset Function to Invert Matrices of Varying Sizes 3 First, enter dimension of the square matrix (between 2 and 6) TRUE OK Then, enter elements of matrix. 3 12 33 5 44 22 66 Enter 1 15 23 7 7 3 33 Cell Values 2 3 3 6 55 1 On Left for 12 15 18 33 3 22 Matrix to Invert. 2 7 3 9 33 33 7 3 6 33 2 4 Do not enter values into yellow regions. They can be protected. -0.10619 0.185841 -0.25664 #N/A #N/A #N/A 0.068584 -0.05752 0.019912 #N/A #N/A #N/A 0.002212 -0.06637 0.484513 #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A Inverse Matrix #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A #N/A Let A1 = n, the number of rows and columns of the matrix to invert. A1 must be between 2 and 6 in this example. Input matrix elements in grey Cells A3:F8. Inputs beyond the nth row and nth column will not affect results. Inverse matrix will also be n x n in Range A10:F15. Ignore cells beyond the nth row and nth column. Instructions for revising this file. To increase the potential matrix sizes, move all ranges far enough apart from each other so as to prevent interference. Adjust Cell H2 accordingly. Set an n x n range for the largest matrix to invert in the new file. Make sure that this and all other ranges are not conflicting with one another. Highlight an n x n range into which the inverse matrix will be placed just as though you were going through the standard MINVERSE routine. Now begin the MINVERSE routine, selecting the paste function, Math&Trig and MINVERSE. Instead of entering the range as normal, enter the following instead: OFFSET(A3:B4,0,0,H2,H2). Then simultaneously hit Ctrl-Shft-Enter. Actually, be certain to replace A101:B102 with the two upper/left most cells in the matrix to invert and make appropriate adjustments for Cell H2.

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