In Problem 9, the first-order interactions between Z and the predictor variables X1, X3, and X4 were not included in the model selection process. Investigate whether this was appropriate, as follows (using the accompanying computer output).
a. Conduct a test to investigate the importance of the interactions, given that X1, X2, X3, X4, and Z ate in the model.
b. In view of your answer in part (a) and in light of the model selected in Problem 9, was it appropriate to exclude the interactions?
c. Why is it necessary to ignore the interaction term X2 × Z?