Consider the multiple regression model fit to the gasoline mileage data in Problem 3.5.

Problem 3.5

Consider the gasoline mileage data in Table B.3.

a. Construct a normal probability plot of the residuals. Does there seem to be any problem with the normality assumption?

b. Construct and interpret a plot of the residuals versus the predicted response.

c. Construct and interpret the partial regression plots for this model.

d. Compute the studentized residuals and the $R$-student residuals for this model. What information is conveyed by these scaled residuals?

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Automobile y x X2 X3 X4 Xs X6 X7 X8 Xg X10 x11 Apollo 18.90 350 165 260 8.0:1 2.56:1 4 Omega 1700 350 170 275 8.5:1 2.56:1 Nova 20.00 250 105 185 8.25:1 2.73:1 Monarch 18.25 351 Duster 20.07 225 Jenson 11.2 440 143 255 8.0:1 3.00:1 95 170 8.4:1 2.76:1 215 330 8.2:1 2.88:1 4 3 412-4 3 200.3 69.9 3910 A 3 199.6 72.9 2860 A 3 196.7 72.2 3510 A 2 3 199.9 74.0 3890 A 3 194.1 71.8 3365 M 184.5 69 4215 A Conv. Skyhawk 22.12 231 110 175 8.0:1 Monza Scirocco 21.47 262 110 200 8.5:1 34.70 89.7 70 81 8.2:1 2.56:1 2 3 2.56:1 2 3 3.90:1 2 4 179.3 65.4 3020 A 179.3 65.4 3180 A 155.7 64 1905 M Corolla 30.40 96.9 75 83 9.0:1 4.30:1 2 5 165.2 65 2320 M SR-5 Camaro 16.50 350 Datsun 36.50 85.3 155 250 80 83 8.5:1 3.08:1 8.5:1 3.89:1 2 4 42 34 195.4 74.4 3885 A 160.6 62.2 2009 M B210 Capri II 21.50 171 Pacer 19.70 258 109 146 8.2:1 110 195 8.0:1 3.22:1 2 4 3.08:1 Babcat 20.30 140 83 109 8.4:1 3.40:1 Granada Eldorado 14.39 500 Imperial 14.89 440 Nova LN 17.80 350 17.80 302 129 220 190 360 8.5:1 215 330 8.2:1 8.5:1 8.0:1 3.0:1 212N- 170.4 66.9 2655 M 3 171.5 77 3375 A 2 4 168.8 69.4 2700 M 3. 199.9 74 3890 A 2.73:1 4 3 224.1 79.8 5290 A 155 250 Valiant 16.41 318 145 255 8.5:1 2.45:1 2.71:1 4 3 3.08:1 4 3 2 3 231.0 79.7 5185 A 196.7 72.2 3910 A 1976 71 3660 A Starfire 23.54 231 110 175 8.0:1 2.56:1 2 3 179.3 65.4 3050 A Cordoba 21.47 360 180 290 8.4:1 2.45:1 2 3 214.2 76.3 4250 A Trans AM 16.59 400 185 NA 76:1 3.08:1 4 3 196 73 3850 A Corolla E-5 31.90 96.9 75 83 9.0:1 4.30:1 2 5 165.2 61.8 2275 M Astre 29.40 140 Mark IV 13.27 460 Celica GT Charger SE 23.90 133.6 19.73 318 Cougar Elite Matador Corvette 13.90 351 13.27 351 13.77 360 16.50 350 86 NA 223 366 8.0:1 96 120 8.4:1 140 255 8.5:1 148 243 8.0:1 148 243 8.0:1 195 295 8.25:1 165 255 8.5:1 8.0:1 2.92:1 3.00:1 4 3 3.91:1 2 5 2.71:1 2 4 176.4 65.4 2150 M 228 79.8 5430 A 171.5 63.4 2535 M 2 3 215.3 76.3 4370 A 3.25:1 2 3 215.5 78.5 4540 A 3.26:1 2 3.15:1 4 3 2.73:1 3 216.1 78.5 4715 A 209.3 77.4 4215 A 4 3 185.2 69 3660 A