Consider the MPG data and multiple linear regression problem in Exercises 6-18 and 6-24.

For Exercises 6-35 to 6-38, using only first-order terms, build regression models using the following techniques:

(a) All possible regression. Find the Cp and S values.

(b) Forward selection

(c) Backward elimination

(d) Comment on the models obtained. Which model would you prefer?

(a) Fit second-order polynomial models.

(b) Check for multicolliearity in the data for each of the polynomial models. Comment on your results.

(c) Test the contribution of the second-order terms in the models when compared to the reduced first-order model.
Comment on your results.