3. Use any math/stat software (e.g., www.numbergeneratororglrandomnumbergenerator) of your choice to nd a random number generator to randomly select 20 rows of Table 8.3 for Problem 2.4 of Textbook and then do (a), (b), (c), (d), (e), (1'). List which rows of Table 33 data you selected and provide intermediate steps in your calculations. State assumptions for all steps in your analyses. 2.4- Table B3 presents data on the gasoline mileage performance of 32 different automobiles. 3. Fit a simple linear regression model relating gasoline mileagey [miles per gallon] to engine displacement X1 [cubic inches]. b. Construct the analysis-ofvariance table and test for signicance of regression. c. What percent of the total variability in gasoline mileage is accounted for by the linear relationship with engine displacement? (1. Find a 95% Cl on the mean gasoline mileage if the engine displacement is 2'75 in.3 e. Suppose that we wish to predict the gasoline mileage obtained from a car with a 275-in.3 engine. Give a point estimate of mileage. Find a 95% prediction interval on the mileage. f. Compare the two intervals obtained in parts d and e. Explain the difference between them. Which one is wider, and why? TABLE B.3 Gasoline Mileage Performance for 32 Antomobiles Automobile y X1 X2 X3 X4 X5 X6 X7 X8 X9 *10 *11 Apollo 18.90 350 165 260 8.0 : 1 2.56 : 1 4 3 200.3 69.9 3910 A Omega 17.00 350 170 275 8.5 : 1 2.56 : 1 4 3 199.6 72.9 2860 A Nova 20.00 250 105 185 8.25 : 1 2.73 : 1 1 3 196.7 72.2 3510 A Monarch 18.25 351 143 255 8.0 : 1 3.00 : 1 2 3 199.9 74.0 3890 A Duster 20.07 225 95 170 8.4 : 1 2.76 :1 1 3 194.1 71.8 3365 M Jenson Conv. 11.2 440 215 330 8.2 : 1 2.88 : 1 4 3 184.5 69 4215 A 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 34.70 89.7 70 0 81 8.2:1 3.90 :1 2 4 155.7 64 1905 M Corolla SR-5 30.40 96.9 75 83 9.0 : 1 4.30 : 1 2 5 165.2 65 2320 M Camaro 16.50 350 155 250 8.5 : 1 3.08 : 14 3 195.4 74.4 3885 A Datsun B210 36.50 85.3 80 3 8.5 : 1 3.89 : 1 2 4 160.6 62.2 2009 M Capri II 21.50 171 109 146 8.2 : 1 3.22 : 1 2 4 170.4 66.9 2655 M Pacer 19.70 258 110 195 8.0 : 1 3.08 : 1 1 3 171.5 77 3375 A Babcat 20.30 140 83 109 8.4 : 1 3.40 : 1 2 4 168.8 69.4 2700 M Granada 17.80 302 129 220 8.0 : 1 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 2 3 197.6 71 3660 A Starfire 23.54 231 110 175 8.0 : 1 2.56 :1 23 179.3 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 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 2 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 MMar'kN 13.2? 460 223 366 3.0 : 1 3.00:1 4 3 223 ?9.3 5430 A CelicaG'I' 23.90 133.6 96 120 3.4:1 3.91:1 2 5 1?1.5 63.4 2535 M Charger SE 19.?3 313 140 255 3.5 : 1 231:1 2 3 215.3 ?6.3 43?0 A Cougar 13.90 351 143 243 3.0 : 1 3.25:1 2 3 215.5 ?3.5 4540 A Elite 13.2? 351 143 243 3.0 : 1 3.26:1 2 3 216.1 T35 4?15 A Matador 135'? 360 195 295 3.25:1 3.15:1 4 3 209.3 3'14 4215 A Corvette 16.50 350 165 255 3.5 : 1 2.?3 : 1 4 3 135.2 69 3660 A y: M iles f gallon x1: Displacement [cubic in.) x2: Horsepower [Ftlb] x3: Torque [ftlb) x4: Compression ratio x5: Rear axle ratio x5: Carburetor [barrels] x7: No. of transmission speeds x3: Overall length [in] x.;: Width n.) x10: Weight [11:] x11: Type of tranission [A automatic: M manual] Source: Motor Trend. 1975