Estimate the parameters in a model for the gasoline mileage data in Table B. 3 using ridge regression.

a. Use the ridge trace to select an appropriate value of \(k\). Is the resulting model adequate?
b. How much inflation in the residual sum of squares has resulted from the use of ridge regression?
c. How much reduction in \(R^{2}\) has resulted from the use of ridge regression?

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Automobile y X1 X2 X4 Xs X6 X7 Xg X10 X11 Apollo 18.90 350 165 260 8.0:1 2.56:1 Omega 1700 350 170 275 8.5:1 2.56:1 Nova 20.00 250 Monarch Duster 18.25 351 20.07 225 105 185 8.25:1 2.73:1 143 255 8.0:1 95 170 8.4:1 3.00:1 2 2.76:1 Jenson 11.2 440 441214 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 3 215 330 8.2:1 2.88:1 4 3 194.1 71.8 3365 M 184.5 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 Corolla 30.40 34.70 89.7 96.9 70 81 8.2:1 75 83 9.0:1 3.90:1 2 4 155.7 64 1905 M 4.30:1 2 5 165.2 65 2320 M SR-5 Camaro 16.50 350 155 250 8.5:1 3.08:1 4 3 Datsun 36.50 85.3 80 83 8.5:1 3.89:1 2 4 34 195.4 74.4 3885 A 160.6 62.2 2009 M B210 Capri II 21.50 171 109 146 8.2:1 3.22:1 Pacer 19.70 258 110 195 8.0:1 3.08:1 Babcat 20.30 140 83 109 8.4:1 3.40:1 Granada 17.80 302 129 220 8.0:1 3.0:1 Eldorado 14.39 500 190 360 8.5:1 2.73:1 Imperial 14.89 440 215 330 8.2:1 2.71:1 43 Nova LN Valiant 17.80 16.41 318 350 Starfire 23.54 231 155 250 145 255 8.5:1 110 175 8.0:1 8.5:1 3.08:1 4 3 2.45:1 2 3 2.56:1 Cordoba 21.47 360 180 290 8.4:1 2.45:1 2122ALLERE 2 4 +3 170.4 66.9 2655 M 3 171.5 77 3375 A 4 168.8 69.4 2700 M 2 3 199.9 74 3890 A 4 3 224.1 79.8 5290 A 231.0 79.7 5185 A 196.7 72.2 3910 A 197.6 71 3660 A 2 3 179.3 65.4 3050 A 2 3 214.2 76.3 4250 A Trans AM 16.59 400 185 NA 76:1 3.08:1 4 196 73 3850 A Corolla E-5 31.90 96.9 75 83 9.0:1 4.30:1 5 165.2 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 Celica GT 23.90 133.6 Charger SE 19.73 318 Cougar Elite Matador Corvette 13.90 351 13.27 351 13.77 360 16.50 350 223 366 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 3.00:1 43 228 79.8 5430 A 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 77.4 4215 A 185.2 69 3660 A