Consider the automobile gasoline mileage data in Table B.3.

a. Build a linear regression model relating gasoline mileage $y$ to vehicle weight $x_{10}$ and the type of transmission $x_{11}$. Does the type of transmission significantly affect the mileage performance?

b. Modify the model developed in part a to include an interaction between vehicle weight and the type of transmission. What conclusions can you draw about the effect of the type of transmission on gasoline mileage? Interpret the parameters in this model.

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Automobile y X1 X2 X3 X4 Xs X6 X7 Xg X9 X10 X11 Apollo Omega Nova 18.90 350 1700 350 20.00 250 165 260 8.0:1 2.56:1 Monarch Duster Jenson 18.25 351 20.07 225 11.2 440 170 275 8.5:1 2.56:1 4 105 185 8.25:1 2.73:1 143 255 8.0:1 3.00:1 44 95 170 8.4:1 2.76:1 215 330 8.2:1 2.88:1 4 121+ 2 3 200.3 69.9 3910 A 3 199.6 72.9 2860 A 3 196.7 72.2 3510 A 3 199.9 74.0 3890 A 3 194.1 71.8 3365 M 3 184.5 69 4215 A Conv. Skyhawk 22.12 231 110 175 8.0:1 2.56:1 2 3 Monza Scirocco 21.47 262 110 200 8.5:1 2.56:1 34.70 89.7 70 81 8.2:1 3.90:1 2 Corolla 30.40 96.9 75 83 9.0:1 4.30:1 2 2222 2 334 in 179.3 65.4 3020 A 3 4 179.3 65.4 3180 A 155.7 64 1905 M 5 165.2 65 2320 M SR-5 Camaro 16.50 350 155 250 8.5:1 3.08:1 Datsun 36.50 85.3 80 83 8.5:1 3.89:1 2 4 42 34 3 195.4 74.4 3885 A 160.6 62.2 2009 M B210 Capri II Pacer Babcat 20.30 140 Granada 17.80 302 21.50 171 109 146 8.2:1 19.70 258 110 195 8.0:1 83 109 129 220 8.0:1 3.22:1 2 4 170.4 66.9 2655 M 3.08:1 1 3 171.5 77 3375 A 8.4:1 3.40:1 2 4 168.8 69.4 2700 M 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 17.80 350 155 250 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 23 1976 71 3660 A Starfire Cordoba 21.47 23.54 231 360 110 175 8.0:1 2.56:1 2 3 179.3 65.4 3050 A 180 290 8.4:1 2.45:1 2 3 214.2 76.3 4250 A Trans AM 16.59 400 185 NA 7.6:1 3.08:1 4 3 196 73 3850 A Corolla E-5 31.90 96.9 75 83 9.0:1 4.30:1 25 165.2 61.8 2275 M Astre 29.40 140 86 NA 8.0:1 2.92:1 2 4 Mark IV 13.27 460 223 366 8.0:1 3.00:1 4 3 Celica GT 23.90 133.6 96 120 8.4:1 3.91:1 25 Charger SE 19.73 318 140 255 8.5:1 2.71:1 2 3 Cougar 13.90 351 148 243 8.0:1 3.25:1 Elite 13.27 351 148 243 8.0:1 Matador 13.77 360 195 295 Corvette 16.50 350 8.25:1 165 255 8.5:1 2 3 3.26:1 2 3 3.15:1 4 3 2.73:1 4 3 176.4 65.4 2150 M 228 79.8 5430 A 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 77.4 4215 A 185.2 69 3660 A