Question:
Consider the gasoline mileage data in Table B.3.
a. Fit a multiple linear regression model relatmg gasoline mileage $y$ (miles per gallon) to engine displacement $x_{1}$ and the number of carburetor barrels $x_{6}$.
b. Construct the analysis-of-variance table and test for significance of regression.
c. Calculate $R^{2}$ and $R_{\text {Adj }}^{2}$ for this model. Compare this to the $R^{2}$ and the $R_{\text {Adj }}^{2}$ for the simple linear regression model relating mileage to engine displacement in Problem 2.4.
d. Find a $95 %$ CI for $\beta_{1}$.
e. Compute the $t$ statistics for testing $H_{0}$ : $\beta_{1}=0$ and $H_{0}$ : $\beta_{6}=0$. What conclusions can you draw?
f. Find a $95 %$ CI on the mean gasoline mileage when $x_{1}=275$ in. $^{3}$ and $x_{6}=2$ barrels.
g. Find a $95 %$ prediction interval for a new observation on gasoline mileage when $x_{1}=275$ in. ${ }^{3}$ and $x_{6}=2$ barrels.
Transcribed Image Text:
Automobile y x1 X2 X3 X4 Xs X6 X7 X8 X9 X10 X11 Apollo 18.90 350 165 260 8.0:1 2.56:1 4 Omega 1700 350 170 275 8.5:1 2.56:1 Nova Monarch 20.00 250 18.25 351 143 255 105 185 8.25:1 2.73:1 8.0:1 3.00:1 Duster 20.07 225 95 170 8.4:1 2.76:1 Jenson 11.2 440 215 330 8.2:1 2.88:1 4 3 41214 3 200.3 69.9 3910 A 3 199.6 72.9 2860 A 3 196.7 72.2 3510 A 2 3 199.9 74.0 3890 A 3 194.1 71.8 3365 M 184.5 69 4215 A Conv. Skyhawk 22.12 231 Monza Scirocco 21.47 262 34.70 89.7 Corolla 30.40 96.9 110 175 110 200 8.5:1 70 81 8.2:1 75 83 8.0:1 2.56:1 2 2.56:1 2 3.90:1 2 4 9.0:1 4.30:1 2 2222 3345 179.3 65.4 3020 A 179.3 65.4 3180 A 155.7 64 1905 M 165.2 65 2320 M SR-5 Camaro 16.50 350 Datsun 36.50 85.3 155 250 80 83 8.5:1 3.08:1 8.5:1 42 34 195.4 74.4 3885 A 3.89:1 2 4 160.6 62.2 2009 M B210 Capri II 21.50 171 Pacer 19.70 258 Babcat 20.30 140 Granada 17.80 302 Eldorado 14.39 500 Imperial 14.89 440 109 146 8.2:1 110 195 8.0:1 83 109 8.4:1 129 220 8.0:1 190 360 8.5:1 215 330 8.2:1 3.22:1 2 4 3.08:1 3.40:1 3.0:1 212N- 170.4 66.9 2655 M 3 171.5 77 3375 A 2 4 168.8 69.4 2700 M 3 199.9 74 3890 A 2.73:1 4 3 224.1 79.8 5290 A 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 2 3 1976 71 3660 A Starfire 23.54 231 110 175 8.0:1 2.56:1 2 3 179.3 65.4 3050 A Cordoba 21.47 360 180 290 8.4:1 2.45:1 2 3 214.2 76.3 4250 A Trans AM 16.59 400 185 NA 76:1 3.08:1 4 3 196 73 3850 A Corolla E-5 31.90 96.9 Astre 29.40 140 Mark IV 13.27 460 Celica GT 23.90 133.6 Charger SE 19.73 318 Cougar 13.90 351 Elite 13.27 351 Matador Corvette 13.77 360 16.50 350 75 83 9.0:1 86 NA 8.0:1 223 366 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 4.30:1 2 5 165.2 61.8 2275 M 2.92:1 2 4 176.4 65.4 2150 M 165 255 8.5:1 3.00:1 4 3 3.91:1 2 5 2.71:1 2 3.25:1 2 3.26:1 2 3.15:1 2.73:1 228 79.8 5430 A 171.5 63.4 2535 M 3 215.3 76.3 4370 A 3 215.5 78.5 4540 A 4 3 3 216.1 78.5 4715 A 209.3 774 4215 A 4 3 185.2 69 3660 A
