Chapter B.3, Problem 69E

Gasoline Mileage Ratings. Refer to Exercise B.66 regarding the relationship between gasoline mileage (mpg) and the predictor variables engine displacement (disp) and type of vehicle (car or non-car) for data on 121 vehicles from an issue of Consumer Reports. That exercise considered the regression of mpg on 1/ $\sqrt{disp}$ and car, the indicator variable for vehicle type. Use the technology of your choice to obtain output similar to that in Outputs B.47–B.51 on pages B-86- B-88.

1. a. Obtain the scatterplot of mpg versus 1/ $\sqrt{disp}$ with different plot symbols for non-cars and for cars. Based on this plot does it appear that car is a useful predictor variable? Explain your answer.
2. b. Obtain the regression analysis of mpg on 1/ $\sqrt{disp}$ and car. Conduct the t-tests for the individual utility of the two predictor variables at the 5% level of significance. Interpret your results.
3. c. Based on the output in part (b), obtain the individual regression equations relating mpg to 1/ $\sqrt{disp}$ for the non-cars and for the cars.
4. d. Obtain plots of residuals versus filled values, residuals versus 1/ $\sqrt{disp}$, and residuals versus car, and a normal probability plot of the residuals. Perform a residual analysis to assess the appropriateness of the regression equation, constancy of the conditional standard deviations, and normality of the conditional distributions. Check for outliers and influential observations.
5. e. Provide a plot of mpg versus disp with the regression curves for the cars and for the non-cars. Based on this plot and your residual analysis in part (d), do you feel that this model fits the data well? Does this model fit the data better than the model with only 1/ $\sqrt{disp}$ as a predictor variable? Explain your answers.
6. f. To check for possible interaction between the two predictor variables, perform the regression analysis of mpg on 1/ $\sqrt{disp}$, car, and car – 1/ $\sqrt{disp}$. Is there an interaction between 1/ $\sqrt{disp}$ and car, that is, is the cross-product term car 1/ $\sqrt{disp}$ a useful predictor variable in the regression equation that also contains 1/ $\sqrt{disp}$ and car? Use α = 0.05.