In Exercise 4.7, we discussed the data in Appendix D, Table D.7, that relate gas mileage (MPG) to certain characteristics of the automobile. Here we focus on displacement (DISP) and type of transmission, where we define the indicator { 1 if automatic 0 if manual.

a. Fit the model MPG=+B,DISP+

e, noting the parameter estimates, the residual mean square, and R.

b. Fit a model that is a quadratic function of DISP, and compare with the linear model.

c. Construct a scatter-plot of MPG versus DISP using type of transmission as the plotting symbol.

d. Fit the model MPG = B+BDISP+B+e, and write the separate equations for the two types of transmissions. Test the hypothesis H: B = 0. Note that this is testing whether, in the context of this model, there is a difference in the types of transmissions.

e. Fit the model MPG = B+ BDISP + Bz + BDISP+z+e, that allows for different slopes. Write the separate equations for the two transmissions. Discuss the conclusion with respect to differences in transmissions and contrast these results with those of part d.