Chapter B.3, Problem 66E

a.

To determine

Explain whether car is a useful predictor variable, based on the mpg versus $\frac{1}{\sqrt{disp}}$ plot in Output B.47.

b.

To determine

Conduct t-tests for the individual utility of the two predictor variables, $\frac{1}{\sqrt{disp}}$ and car at the 5% level of significance using Output B.48.

Interpret the results.

c.

To determine

Find the individual regression equations relating mpg to $\frac{1}{\sqrt{disp}}$ and car for cars and non-cars using Output B.48.

d.

To determine

Perform a residual analysis to assess the assumptions of linearity, constancy of conditional standard deviations, and normality of the conditional distributions, using Outputs B.49 (a)-(d).

Check whether there are outliers and influential observations.

e.

To determine

Explain whether the residual analysis in part d, along with the plot in Output B.50 reveal any violations of the assumptions for regression inferences.

f.

To determine

Identify whether an interaction between $\frac{1}{\sqrt{disp}}$ and car is a useful predictor variable in the regression equation using Output B.51.