Chapter 18 - 419 Chapter 18 18.1 SUMMARY OUTPUT Regression...

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419 Chapter 18 18.1 SUMMARY OUTPUT Regression Statistics Multiple R 0.4924 R Square 0.2425 Adjusted R Square 0.2019 Standard Error 40.24 Observations 60 ANOVA df SS MS F Significance F Regression 3 29030 9677 5.97 0.0013 Residual 56 90694 1620 Total 59 119724 Coefficients Standard Error t Stat P-value Intercept 51.39 23.517 2.19 0.0331 Lot size 0.700 0.559 1.25 0.2156 Trees 0.679 0.229 2.96 0.0045 Distance -0.378 0.195 -1.94 0.0577 a 3 2 1 378 . 679 . 700 . 39 . 51 & x x x y - + + = b The standard error of estimate is e s = 40.24. It is an estimate of the standard deviation of the error variable. c The coefficient of determination is 2 R = .2425; 24.25% of the variation in prices is explained by the model. d The coefficient of determination adjusted for degrees of freedom is .2019. It differs from 2 R because it includes an adjustment for the number of independent variables. e : 0 H = ß1 = ß2 = ß3 0 : 1 H At least one i ß is not equal to zero F = 5.97, p-value = .0013. There is enough evidence to conclude that the model is valid. f 1 b = .700; for each addition thousand square feet the price on average increases by .700 thousand dollars provided that the other variables remain constant. 2 b = .679; for each addition tree the price on average increases by .679 thousand dollars provided that the other variables remain constant. 3 b = -.378; for each addition foot from the lake the price on average decreases by .378 thousand dollars provided that the other variables remain constant. 420 g : 0 H = ßi 0 : 1 H i ß . 0 Lot size: t = 1.25, p-value = .2156 Trees: t = 2.96, p-value = .0045 Distance: t = -1.94, p-value = .0577 Only for the number of trees is there enough evidence to infer a linear relationship with price. 18.2 SUMMARY OUTPUT Regression Statistics Multiple R 0.8734 R Square 0.7629 Adjusted R Square 0.7453 Standard Error 3.75
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Observations 30 ANOVA df SS MS F Significance F Regression 2 1223.18 611.59 43.43 0.0000 Residual 27 380.18 14.08 Total 29 1603.37 Coefficients Standard Error t Stat P-value Intercept 13.01 3.528 3.69 0.0010 Assignment 0.194 0.200 0.97 0.3417 Midterm 1.112 0.122 9.12 0.0000 a 2 1 112 . 1 194 . 01 . 13 & x x y + + = b The standard error of estimate is e s = 3.75. It is an estimate of the standard deviation of the error variable. c The coefficient of determination is 2 R = .7629; 76.29% of the variation in final exam marks is explained by the model. d The coefficient of determination adjusted for degrees of freedom is .7453. It differs from 2 R because it includes an adjustment for the number of independent variables. e : 0 H = ß1 = ß2 0 : 1 H At least one i ß is not equal to zero F = 43.43, p-value = 0. There is enough evidence to conclude that the model is valid. f 1 b = .194; for each addition mark on assignments the final exam mark on average
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Chapter 18 - 419 Chapter 18 18.1 SUMMARY OUTPUT Regression...

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