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P436 Ex 11-8 (Modified) (26 pt) The data below presents the highway gasoline performance and engine displacement for 21 Daimler Chrysler vehicles for model year 2005 (U.S. Environmental Protection Agency). TABLE . E11-3 Gasoline Mileage Data Engine MPG Carline Displacement (in') (highway) 300C/SRT-8 215 30.8 CARAVAN 2WD 201 32.5 CROSSFIRE 196 35.4 ROADSTER DAKOTA PICKUP 2WD 226 28.1 DAKOTA PICKUP 4WD 226 24.4 DURANGO 2WD 348 24.1 GRAND 226 28.5 CHEROKEE 2WD GRAND 348 24.2 CHEROKEE 4WD LIBERTY/ 148 32.8 CHEROKEE 2WD LIBERTY/ 226 28 CHEROKEE 4WD NEON/SRT-4/SX 2.0 122 41.3 PACIFICA 2WD 215 30.0 PACIFICA AWD 215 28.2 PT CRUISER 148 34.1 RAM 1500 PICKUP 500 18.7 2WD RAM 1500 PICKUP 348 20.3 4WD SEBRING 4-DR 165 35.1 STRATUS 4-DR 148 37.9 TOWN & COUNTRY 148 33.8 2WD VIPER CONVERTIBLE 500 25.9 WRANGLER/TJ 4WD 148 26.4a. Use R to construct a scatter plot of highway miles per gallon (y) versus engine displacement (x) in cubic inches. Attach the R. code and output. b. Comment on the relationship between highway miles per gallon (y) and engine displacement (x) in cubic inches based on your scatterplot in part (a). c. Use R to calculate the sample correlation coefficient between variables x and Y. Attach the R. code and output d. Use R to fit a simple linear (least square) regression model relating highway miles per gallon ()) to engine displacement (x) in cubic inches. Attach the R. code. e. Give the R. code and output that will show you the fitted regression coefficients , and B, - f. What is the fitted simple linear regression equation for x and I based on your answer in part (e)? g. Do it by hand. For the 11* observation in the data, find the fitted value of y and the corresponding residual for a car, the Neon, with an engine displacement of 122 cubic inches. That is, find yo, and ent.h. Use R to draw the normal probability plot for the residuals of the fitted simple linear regression equation. Attach the R. code and output. . From the normal probability plot in part (h), does the normality assumption for linear models appear to be satisfied? Explain. J. Use R to produce an Analysis of Variance (ANOVA) table for the data Attach the R. code and output. K From your ANOVA table in part (j), what is the value of SSr, the error sum of squares? From your ANOVA table in part (j), what is the value of SS., the regression sum of squares? m. Calculate the sample multiple coefficient of determination by hand. Then interpret this value n. According to your answer in part (m), do you think the fitted regression equation in part (f) is a good model for describing the relationship between highway miles per gallon (y) and engine displacement (x) in cubic inches? Explain. o. Use the following R output to construct, by hand, a two-sided 95% confidence interval for B. Call: Im(formula = y ~ x) Residuals: Min 10. Median 30 Max -6.8035-1.9666-0.4035 1.4280 7.0509 Coefficients: Estimate Std. Error t value Pr(>It[) [Intercept) 39.155505 2.006358 19.516 4.97e-14 * *# X -0.040216 0.007671 -5.243 4.632-05*$ Signif. codes: 0 **** 0.001 "*> 0.01 "*0.0501"1 Residual standard error: 3.743 on 19 degrees of freedom Multiple R-squared: 0.5913, Adjusted R-squared: 0.5698 F-statistic: 27.49 on 1 and 19 DF, p-value: 4.634e-05