In Problem 3.6 a regression model was developed for the gasoline mileage data using the regressor vehicle length \(x_{8}\) and vehicle weight \(x_{10}\). Calculate the PRESS statistic for this model. What conclusions can you draw about the potential performance of this model as a predictor?

Data From Problem 3.6

In Problem 2.4 you were asked to compute a $95 %$ CI on mean gasoline prediction interval on mileage when the engine displacement $x_{1}=275$ in. $^{3}$ Compare the lengths of these intervals to the lengths of the confidence and prediction intervals from Problem 3.5 above. Does this tell you anything about the benefits of adding $x_{6}$ to the model?

Data From Problem 2.4

Table B. 3 presents data on the gasoline mileage performance of 32 different automobiles.

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Automobile Apollo Omega 1700 350 Nova 20.00 250 y X1 X2 X3 X4 18.90 350 165 260 8.0:1 170 275 8.5:1 105 185 8.25:1 Monarch 18.25 351 143 255 8.0:1 X5 X6 X X X X1011 2.56:1 4 3 2.56:1 4 3 2.73:1 1 3 3.00:1 2 3 200.3 69.9 3910 A 199.6 72.9 2860 A 196.7 72.2 3510 A 199.9 74.0 3890 A Duster 20.07 225 Jenson 11.2 440 215 95 170 8.4:1 330 8.2:1 2.76:1 1 3 194.1 71.8 3365 M 2.88:1 4 3 1845 69 4215 A Conv. Skyhawk 22.12 231 110 175 8.0:1 2.56:1 2 3 179.3 65.4 3020 A Monza 21.47 262 110 200 8.5:1 2.56:1 2 3 179.3 65.4 3180 A Scirocco 34.70 89.7 70 81 8.2:1 3.90:1 2 4 155.7 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 8.5:1 80 83 8.5:1 3.08:1 4 3 195.4 74.4 3885 A 3.89:1 2 4 160.6 62.2 2009 M B210 Capri II 21.50 171 109 146 8.2:1 3.22:1 2 4 170.4 66.9 2655 M Pacer 19.70 258 110 195 8.0:1 3.08:1 1 3 171.5 77 3375 A Babcat 20.30 140 83 109 8.4:1 3.40:1 2 4 168.8 69.4 2700 M Granada 1780 302 129 220 8.0:1 3.0:1 2 3 199.9 74 3890 A Eldorado 14.39 500. 190 360 8.5:1 2.73:1 4 3 224.1 79.8 5290 A Imperial 14.89 440 215 330 8.2:1 2.71:1 4 3 231.0 79.7 5185 A Nova LN 1780 350 155 250 8.5:1 3.08:1 4 3 196.7 72.2 3910 A Valiant 16.41 318 145 255 8.5:1 2.45:1 2 3 1976 71 3660 A Starfire 23.54 231 110 175 8.0:1 Cordoba 21.47 360 180 290 Trans AM 16.59 400 185 NA 8.4:1 7.6:1 2.56:1 2 3 2.45:1 2 3 3.08:1 4 3 179.3 65.4 3050 A 214.2 76.3 4250 A 196 73 3850 A Corolla E-5 31.90 96.9 75 83 9.0:1 4.30:1 25 165.2 61.8 2275 M Astre 29.40 140 86 NA 8.0:1 2.92:1 2 4 176.4 65.4 2150 M Mark IV 13.27 460 223 366 8.0:1 3.00:1 4 3 228 79.8 5430 A Celica GT 23.90 133.6 Charger SE 19.73 318 19.73 318 Cougar Elite Matador Corvette 13.90 351 13.27 351 13.77 360 16.50 350 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 3.91:1 2 5 2.71:1 2 3 3.25:1 2 3 3.26:1 2 3 3.15:1 4 3 2.73:1 4 3 171.5 63.4 2535 M 215.3 76.3 4370 A 215.5 78.5 4540 A 216.1 78.5 4715 A 209.3 774 185.2 69 4215 A 3660 A