The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature (x1), the number of days in the month (x2), the average product purity (x3), and the tons of product produced (x4). The past year€™s historical data are available and are presented in the following table:
(a) Fit a multiple linear regression model to these data.
(b) Estimate σ2.
(c) Compute the standard errors of the regression coefficients.
(d) Predict power consumption for a month in which X1 =75OF, x2 = 24 days, x3 = 90%, and x4 = 98 tons.
y: Miles/gallon
x1: Displacement (cubic inches)
x2: Horsepower (foot-pounds)
x3: Torque (foot-pounds)
x4: Compression ratio
x5: Rear axle ratio
x6: Carburetor (barrels)
x7: No. of transmission speeds
x8: Overall length (inches)
x9: Width (inches)
x10: Weight (pounds)
x11: Type of transmission (A€”automatic, M€”manual)

Transcribed Image Text:

X2 X3 X4 240 25 24 91 100 236 31 21 90 95 270 45 24 88 110 274 60 25 87 88 301 65 25 91 94 316 72 26 94 99 300 80 25 87 97 296 84 25 86 96 267 75 24 88 110 276 60 25 91 105 288 50 25 90 100 261 38 23 89 98 Automobile X6 X7 X1 X2 X4 X5 X9 X10 X11 Apollo 200.3 3910 18.90 350 165 260 8.0:1 2.56:1 4 69.9 105 Nova 20.00 250 185 8.25:1 2.73:1 3. 196.7 72.2 3510 Monarch 18.25 351 255 74.0 3890 143 8.0:1 3.00:1 2 199.9 A Duster 20.07 225 95 170 8.4:1 2.76:1 3. 194.1 71.8 3365 8.2:1 4215 Jenson Conv. 11.2 440 215 330 2.88:1 4 184.5 69 A Skyhawk 22.12 231 110 175 8.0:1 2.56:1 179.3 65.4 3020 A Scirocco 155.7 34.70 89.7 70 81 8.2:1 3.90:1 64 1905 M Corolla SR-5 30.40 96.9 75 83 9.0:1 4.30:1 165.2 65 2320 Camaro 16.50 350 155 250 8.5:1 3.08:1 4 3. 195.4 74.4 3885 A. 3.89:1 62.2 2009 Datsun B210 36.50 85.3 80 83 8.5:1 4 160.6 M Capri II 21.50 171 109 146 8.2:1 3.22:1 4 170.4 66.9 2655 3.08:1 3375 Pacer 19.70 258 110 195 8.0:1 1. 171.5 77 A Granada 17.80 302 129 220 8.0:1 3.0:1 199.9 74 3890 A Eldorado 14.39 500 190 360 8.5:1 2.73:1 4 224.1 79.8 5290 A Imperial 14.89 231.0 79.7 440 215 330 8.2:1 2.71:1 4 5185 350 72.2 3910 Nova LN 17.80 155 250 8.5:1 3.08:1 196.7 A Starfire 179.3 65.4 23.54 231 110 175 8.0:1 2.56:1 3. 3050 A Cordoba 214.2 76.3 21.47 360 180 290 8.4:1 2.45:1 4250 Trans Am 7.6:1 3.08:1 16.59 400 185 NA 4 196 73 3850 Corolla E-5 31.90 96.9 75 83 9.0:1 4.30:1 2 165.2 61.8 2275 Mark IV 13.27 460 223 366 8.0:1 3.00:1 3 228 79.8 5430 A Celica GT 23.90 133.6 96 120 8.4:1 3.91:1 2 171.5 63.4 2535 Charger SE 76.3 19.73 318 140 255 8.5:1 2.71:1 215.3 4370 243 Cougar 13.90 351 148 8.0:1 3.25:1 215.5 78.5 4540 185.2 3660 Corvette 16.50 350 165 255 8.5:1 2.73:1 4 3. 69 2.