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mont4e_sm_ch12_sec05

# mont4e_sm_ch12_sec05 - Section 12-5 12-51 a The regression...

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Section 12-5 12-51. a) The regression equation is mpg = 49.9 - 0.0104 cid - 0.0012 rhp - 0.00324 etw + 0.29 cmp - 3.86 axle + 0.190 n/v Predictor Coef SE Coef T P Constant 49.90 19.67 2.54 0.024 cid -0.01045 0.02338 -0.45 0.662 rhp -0.00120 0.01631 -0.07 0.942 etw -0.0032364 0.0009459 -3.42 0.004 cmp 0.292 1.765 0.17 0.871 axle -3.855 1.329 -2.90 0.012 n/v 0.1897 0.2730 0.69 0.498 S = 2.22830 R-Sq = 89.3% R-Sq(adj) = 84.8% b) There appears to be an outlier. Otherwise, the normality assumption is not violated. Standardized Residual Score 3 2 1 0 -1 -2 -3 2 1 0 -1 -2 Normal Probability Plot of the Residuals (response is mpg) c) The plots do not show any violations of the assumptions. 12-32

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Fitted Value Standardized Residual 40 35 30 25 20 2 1 0 -1 -2 -3 Residuals Versus the Fitted Values (response is mpg) cid 500 400 300 200 100 2 1 0 -1 -2 -3 Residuals Versus cid (response is mpg) etw 6000 5500 5000 4500 4000 3500 3000 2 1 0 -1 -2 -3 Residuals Versus etw (response is mpg) cmp 10.00 9.75 9.50 9.25 9.00 8.75 8.50 2 1 0 -1 -2 -3 Residuals Versus cmp (response is mpg) 12-33
axle Standardized Residual 4.25 4.00 3.75 3.50 3.25 3.00 2.75 2.50 2 1 0 -1 -2 -3 Residuals Versus axle (response is mpg) n/v 40 35 30 25 20 2 1 0 -1 -2 -3 Residuals Versus n/v (response is mpg) d) 0.036216, 0.000627, 0.041684, 0.008518, 0.026788, 0.040384, 0.003136, 0.196794, 0.267746, 0.000659, 0.075126, 0.000690, 0.041624, 0.070352, 0.008565, 0.051335, 0.001813, 0.019352, 0.000812, 0.098405, 0.574353 None of the values is greater than 1 so none of the observations are influential. 12-52. a) 2 = R 852 . 0 b) The residual plots look reasonable. There is some increase in variability at the middle of the predicted values. c) Normality assumption is reasonable. The residual plots appear reasonable too. Residual Percent 20 10 0 -10 -20 99 95 90 80 70 60 50 40 30 20 10 5 1 Normal Probability Plot of the Residuals (response is y) 12-34

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x1 Residual 90 80 70 60 50 40 30 20 10 5 0 -5 -10 -15 Residuals Versus x1 (response is y) x2 26 25 24 23 22 21 10 5 0 -5 -10 -15 Residuals Versus x2 (response is y) x3 94 93 92 91 90 89 88 87 86 85 10 5 0 -5 -10 -15 Residuals Versus x3 (response is y) x4 110 105 100 95 90 10 5 0 -5 -10 -15 Residuals Versus x4 (response is y) 12-53. a) % 8 . 97 2 = R b) Assumption of normality appears adequate. Residual Percent 5 4 3 2 1 0 -1 -2 -3 -4 99 95 90 80 70 60 50 40 30 20 10 5 1 Normal Probability Plot of the Residuals (response is Rating Pts) c) Model appears adequate. Some suggestion of nonconstant variance in the plot of x (percentage of TDs) 7 Fitted Value 120 110 100 90 80 70 4 3 2 1 0 -1 -2 -3 -4 -5 Residuals Versus the Fitted Values (response is Rating Pts) Pct Comp 70.0 67.5 65.0 62.5 60.0 57.5 55.0 4 3 2 1 0 -1 -2 -3 -4 -5 Residuals Versus Pct Comp (response is Rating Pts) 12-35
Pct TD Residual 10 9 8 7 6 5 4 3 2 4 3 2 1 0 -1 -2 -3 -4 -5 Residuals Versus Pct TD (response is Rating Pts) Pct Int 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 4 3 2 1 0 -1 -2 -3 -4 -5 Residuals Versus Pct Int (response is Rating Pts) d) No, none of the observations has a Cook’s distance greater than 1.

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mont4e_sm_ch12_sec05 - Section 12-5 12-51 a The regression...

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