Chapter B.1, Problem 30E

Gasoline Mileage Ratings. Refer to Exercise B.24, where the problem is to determine a regression model for relating a vehicle's gasoline mileage, in miles per gallon, to its engine displacement. Obtain output similar to that in Outputs B.15–B.19 on pages B-26–B-29.

1. a. Based on the scatterplot of miles per gallon versus displacement, which transformations should be attempted on miles per gallon? on displacement?
2. b. Based on the plots of powers of miles per gallon versus powers of engine displacement, which pairs of transformed variables would you consider for further analysis? Explain your reasoning.
3. c. For each pair of a power of miles per gallon and a power of engine displacement selected for further analysis in part (b): (i) perform a regression analysis, (ii) obtain a plot of residuals versus filled values and a normal probability plot of the residuals, (iii) perform a residual analysis to assess the assumptions of linearity of the regression equation, constancy of the conditional stand and deviations, and normality of the conditional distributions, and (iv) check for outliers and influential observations.
4. d. For each model considered in part (c), does your analysis in part (c) reveal any violations of the assumptions for regression inferences? Explain your answers.
5. e. For each model considered in part (c), obtain a plot of the regression equation on the scatterplot of the data, as seen in Output B.19 on page B-29. Based on these plots and the results of the residual analyses in parts (c) and (d), select a final model for predicting gasoline mileage based on engine displacement. Do you feel that your model fits the data well? Explain your answer.