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Chapter 17 - Chapter 17 17.1 1 2 3 4 5 6 7 8 9 10 11 12 13...

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Chapter 17 17.1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 A B C D E F 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 29,030 9,677 5.97 0.0013 Residual 56 90,694 1,620 Total 59 119,724 Coefficients Standard Error t Stat P-value Intercept 51.39 23.52 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 x 378 . x 679 . x 700 . 39 . 51 y ˆ - + + = b The standard error of estimate is ε 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 : H 0 = β 1 = β 2 = β 3 0 : H 1 At least one i β 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. g : H 0 = β i 0 : H 1 i β 0 5
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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. h 1 2 3 4 5 6 7 8 9 10 11 12 13 A B C D Prediction Interval Price Predicted value 103.87 Prediction Interval Lower limit 35.50 Upper limit 172.24 Interval Estimate of Expected Value Lower limit 91.86 Upper limit 115.88 We predict that the lot in question will sell for between $35,500 and $172,240 i 1 2 3 4 5 6 7 8 9 10 11 12 13 A B C D Prediction Interval Price Predicted value 64.80 Prediction Interval Lower limit -7.18 Upper limit 136.78 Interval Estimate of Expected Value Lower limit 39.29 Upper limit 90.30 Estimated average price lies between $39,290 and $90,300. 6
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17.2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 A B C D E F SUMMARY OUTPUT Regression Statistics Multiple R 0.8734 R Square 0.7629 Adjusted R Square 0.7453 Standard Error 3.75 Observations 30 ANOVA df SS MS F Significance F Regression 2 1223.2 611.59 43.43 0.0000 Residual 27 380.2 14.08 Total 29 1603.4 Coefficients Standard Error t Stat P-value Intercept 13.01 3.53 3.69 0.0010 Assignment 0.194 0.200 0.97 0.3417 Midterm 1.11 0.122 9.12 0.0000 a 2 1 x 11 . 1 x 194 . 01 . 13 y ˆ + + = b The standard error of estimate is ε 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 : H 0 = β 1 = β 2 0 : H 1 At least one i β is not equal to zero F = 43.43, p-value = 0. There is enough evidence to conclude that the model is valid.
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