# vv-4 - SUMMARY OUTPUT Regression Statistics Multiple R R...

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SUMMARY OUTPUT Regression Statistics Multiple R 0.66 R Square 0.43 Without controling for the degrees of freedom. Adjusted R Square 0.42 The % of msft's stock return variability explained by the Standard Error 0.06 Observations 73 >30 by central limit theory and law of large numbers ANOVA Analysis of Variance df SS MS F Regression 1 0.18 0.18 53.46 Residual 71 0.23 0 Tests the n Total 72 0.41 Coefficients Standard Error t Stat P-value Intercept 0 0.01 0.24 0.81 X Variable 1 (beta) 1.04 0.14 7.31 0 Big boy Beta Rule of thumb is t-stat Null is the variable ha P-value is like Sign F For every 1% change in the market, MSFT moves 1.04% in the sa RESIDUAL OUTPUT Observation Predicted Y Residuals ndard Residuals 1 0.02 -0.06 -1.07 2 -0.02 -0.02 -0.37 3 -0.02 0.07 1.16 4 0.03 -0.01 -0.17 5 0 -0.04 -0.67 6 0.04 -0.01 -0.14 7 -0.01 0.08 1.45 8 0.01 -0.07 -1.22 9 -0.02 0.02 0.27 10 0.04 0.04 0.74 11 0 -0.06 -0.98 12 0.03 0.05 0.85 13 0 -0.04 -0.78 14 0.01 0 -0.01 15 0.01 -0.13 -2.23 16 -0.03 -0.03 -0.49 17 0 0.03 0.48 18 0.01 0.03 0.45 19 0.02 0.05 0.85

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20 0.03 0.04 0.65 21 0.03 0.02 0.27 22 0.02 0.01 0.13 23 0.01 0 0.04 24 0.02 0.02 0.31 25 -0.02 -0.06 -1.11 26 0.01 -0.02 -0.4 27 0.05 0.03 0.48 28 0.04 -0.01 -0.12 29 -0.02 -0.02 -0.4 30 -0.03 0.02 0.27 31 0.01 -0.02 -0.36 32 0.04 -0.01 -0.23 33 0.02 0.23 4.09 34 -0.04 -0.04 -0.71 35 -0.01 0.07 1.18 36 -0.06 -0.02 -0.39 37 -0.03 -0.13 -2.25 38 0 0.05 0.85 39 0.05 -0.05 -0.81 40 0.01 -0.02 -0.28 41 -0.09 0.06 1.04 42 -0.01 -0.06 -0.99 43 0.01 0.05 0.9 44 -0.09 0.07 1.25 45 -0.17 0.01 0.19 46 -0.08 -0.01 -0.21 47 0.01 -0.05 -0.85 48 -0.09 -0.03 -0.58 49 -0.11 0.06 1.11 50 0.09 0.05 0.83 51 0.1 0 0.07 52 0.06 -0.02 -0.34 53 0 0.14 2.4 54 0.08 -0.09 -1.57 55 0.04 0.02 0.31 56 0.04 0 0.09 57 -0.02 0.1 1.71 58 0.06 0 0.07 59 0.02 0.02 0.29 60 -0.04 -0.04 -0.68 61 0.03 -0.01 -0.16 62 0.06 -0.04 -0.72 63 0.02 0.03 0.45 64 -0.08 -0.07 -1.19
65 -0.05 -0.05 -0.95 66 0.07 0.05 0.86 67 -0.05 -0.04 -0.67 68 0.09 -0.05 -0.86 69 0.04 0.05 0.86 70 0 -0.05 -0.81 71 0.07 0.04 0.63 72 0.03 -0.03 -0.56 73 0.03 -0.07 -1.24

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entire model Significance F 99.99999997% 0 We are 1-Sign F sure we can reject. null hypothesis that the model has NO explanatory power. Lower 95% Upper 95% We are 95% sure the beta is -0.01 0.01 somewhere between 0.76 0.76 1.32 and 1.32. t>2 we can reject the null for each variable. as NO explanatory power. only for each individual variable. 99.99999997% sure the market ame direction. PROBABILITY OUTPUT has explanatory power. Percentile Y 0.68 -0.16 2.05 -0.16 3.42 -0.15 4.79 -0.12 6.16 -0.11 7.53 -0.11 8.9 -0.09 10.27 -0.09 11.64 -0.08 13.01 -0.08 14.38 -0.08 15.75 -0.08 17.12 -0.07 18.49 -0.06 19.86 -0.06 21.23 -0.06 22.6 -0.05 23.97 -0.05 25.34 -0.04 -0.2 -0.15 -0.1 -0.05 0 -0.2 -0.1 0 0.1 0.2 0.3 X Variable 1 L X Variable 1 Y 0 20 -0.2 -0.1 0 0.1 0.2 0.3 Normal Y
26.71 -0.04 28.08 -0.04 29.45 -0.04 30.82 -0.04 32.19 -0.04 33.56 -0.04 34.93 -0.03 36.3 -0.02 37.67 -0.02 39.04 -0.01 40.41 -0.01 41.78 -0.01 43.15 -0.01 44.52 0 45.89 0 47.26 0 48.63 0.01 50 0.02 51.37 0.02 52.74 0.02 54.11 0.02 55.48 0.03 56.85 0.03 58.22 0.03 59.59 0.03 60.96 0.03 62.33 0.03 63.7 0.03 65.07 0.04 66.44 0.04 67.81 0.04 69.18 0.04 70.55 0.04 71.92 0.04 73.29 0.05 74.66 0.05 76.03 0.05 77.4 0.06 78.77 0.06 80.14 0.07 81.51 0.07 82.88 0.07 84.25 0.07 85.62 0.07 86.99 0.08

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88.36 0.08 89.73 0.08 91.1 0.09 92.47 0.1 93.84 0.11 95.21 0.12 96.58 0.14 97.95 0.14 99.32 0.25
-0.2 -0.15 -0.1 -0.05 0 0.05 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 X Variable 1 Residual Plot X Variable 1 Residuals 0.05 0.1 0.15 Line Fit Plot Column C Column B 40 60 80 100 120 Probability Plot Sample Percentile

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0.1 0.15

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SUMMARY OUTPUT Regression Statistics Multiple R 0.65 R Square 0.42 Adjusted R Square 0.4 Standard Error 5.86 Observations 72 ANOVA df SS MS F ignificance Regression 3 1726.95 575.65 16.75 0 Residual 68 2337.24 34.37 Total 71 4064.19 Coefficients Standard Error t Stat P-value Lower 95% Intercept -0.01 0.7 -0.02 0.99 -1.4 X Variable 1 (mkt-rf) 1.04 0.16 6.48 0 0.72 X Variable 2 (size) -0.08 0.32 -0.26 0.8 -0.71 X Variable 3 (growth) -0.26 0.28 -0.95 0.34 -0.82 RESIDUAL OUTPUT PROBABIL Observation Predicted Y Residuals ndard Residuals Percentile 1 1.51 -5.65 -0.99 0.69 2 -2.32 -1.82 -0.32 2.08 3 -2.41 6.89 1.2 3.47 4 3.77 -1.73 -0.3 4.86 5 0.02 -3.94 -0.69 6.25 6 4.14 -1.31 -0.23 7.64 7 -1.23 8.2 1.43 9.03 8 0.53 -6.87 -1.2 10.42 9 -2.19 1.79 0.31 11.81 10 4.27 3.45 0.6 13.19 11 -0.07 -5.78 -1.01 14.58 12 3.05 4.26 0.74 15.97 13 -0.28 -4.28 -0.75 17.36 14 1.31 -0.41 -0.07 18.75 15 0.26 -11.87 -2.07 20.14 16 -4.16 -2.13 -0.37 21.53 17 -0.82 3.32 0.58 22.92 18 -1.17 4 0.7 24.31 19 2.55 4.25 0.74 25.69

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20 1.8 4.19 0.73 27.08 21 3.16 1.4 0.24 28.47 22 1.84 0.35 0.06 29.86 23 0.1 1.2 0.21 31.25 24 1.57 1.37 0.24 32.64 25 -2.06 -6.72 -1.17 34.03 26 0.83 -2.33 -0.41 35.42 27 4.11 2.86 0.5 36.81 28 3.64 -1.2 -0.21 38.19 29 -1.74 -2.63 -0.46 39.58 30 -2.73 0.68 0.12 40.97 31 1.4 -2.38 -0.41 42.36 32 4.67 -2.45 -0.43 43.75 33 2.86 21.79 3.8 45.14 34 -5.02 -3.75 -0.65 46.53 35 -0.73 6.41 1.12 47.92 36 -7.46 -1.17 -0.2 49.31 37 -2.39 -13.99 -2.44 50.69 38 -1.39 5.57 0.97 52.08 39 5.24 -4.92 -0.86 53.47 40 2.15 -2.65 -0.46 54.86 41 -8.19 5.17 0.9 56.25 42 -2.8 -3.88 -0.68 57.64 43 0.33 6.08 1.06 59.03 44 -11.55 9.23 1.61 60.42 45 -18.33 1.88 0.33 61.81 46 -7.33 -1.51
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