Consider the gasoline mileage data in Table B.3.

a. Does the correlation matrix give any indication of multicollinearity?
b. Calculate the variance inflation factors and the condition number of \(\mathbf{X}^{\prime} \mathbf{X}\). Is there any evidence of multicollinearity?

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Automobile y X1 X2 X3 X4 X5 X6 X7 X9 x10 x11 Apollo 18.90 350 165 260 8.0:1 2.56:1 4 Omega 17.00 350 170 275 8.5:1 2.56:1 4 Nova 20.00 250 105 185 8.25:1 2.73:1 1 Monarch 18.25 351 143 255 8.0:1 Duster 20.07 225 95 170 8.4:1 3.00:1 2 3 2.76:1 1 Jenson 11.2 440 215 330 8.2:1 2.88:1 43 333333 200.3 69.9 3910 A 199.6 72.9 2860 A 196.7 72.2 3510 A 199.9 74.0 3890 A 194.1 71.8 3365 M 184.5 69 4215 A Conv. Skyhawk 22.12 231 Monza 21.47 262 Scirocco 34.70 89.7 Corolla 30.40 96.9 110 175 110 200 8.5:1 70 81 75 83 8.0:1 2.56:1 2 2.56:1 8.2:1 9.0:1 3.90:1 2 4.30:1 2222 3343 179.3 65.4 3020 A 179.3 65.4 3180 A 155.7 64 1905 M 5 165.2 65 2320 M SR-5 Camaro 16.50 350 Datsun 36.50 85.3 155 80 83 250 8.5:1 8.5:1 3.08:1 4 3.89:1 2 42 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 Nova LN 17.80 350 155 250 8.5:1 3.08:1 Valiant 16.41 318 145 255 8.5:1 2.45:1 Starfire 23.54 231 110 175 8.0:1 2.56:1 Cordoba 21.47 360 180 290 8.4:1 2.45:1 Trans AM 16.59 400 185 NA 76:1 3.08:1 Corolla E-5 31.90 96.9 75 83 9.0:1 4.30:1 Astre 29.40 140 86 NA 8.0:1 2.92:1 Mark IV 13.27 460 223 366 8.0:1 3.00:1 Celica GT 23.90 133.6 96 120 8.4:1 3.91:1 Charger SE 19.73 318 140 255 8.5:1 2.71:1 Cougar 13.90 351 148 243 8.0:1 3.25:1 Elite 13.27 351 148 243 8.0:1 3.26:1 2 Matador 13.77 360 195 295 8.25:1 Corvette 16.50 350 165 255 8.5:1 3.15:1 2.73:1 212222222222244 4 170.4 66.9 2655 M 3 171.5 77 3375 A 4 168.8 69.4 2700 M 3 199.9 74 3890 A 3 224.1 79.8 5290 A 3 231.0 79.7 5185 A 3 196.7 72.2 3910 A 3 197.6 71 3660 A 3 179.3 65.4 3050 A 3 214.2 76.3 4250 A 3 196 73 3850 A 5 165.2 61.8 2275 M 4 33333333 4 176.4 65.4 2150 M 228 79.8 5430 A 5 171.5 63.4 2535 M 215.3 76.3 4370 A 215.5 78.5 4540 A 216.1 78.5 4715 A 209.3 185.2 69 77.4 4215 A 3660 A