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?

ANALYSIS OF VARIANCE Sum of Squares 3100.73976 387.59247 Mean Square F Value Pr> F Source Model Error Corrected Total 17.96 .0001 21 453.26991 21.58428 29 3554.00967 4 64589 83 49667 5.56416 0.8725 Root MSE Dependent Moan Coeff Var R-Square Adj R-Sq 0.8239 PARAMETER ESTIMATES Parameter Standard VariableDF Estimate Error tValue Pr Typo I SS Intercept 24.70798 209151 1 0.27720 1.30212 0.21 0.8335 2271.71350 193.20196 16.105631.53 0.1399 3.48718 4.98736 100655 0.57143 0.08 09360 2.730.0126 76 0.0927 0.28357 13 6078 4973 273 00126 41525208 86.00677 1.70905 89.28986 18.12422 576510 4 0.1734 29.49488 1-0.67663 083801 0.81 0.4285 14.07165 1 53,46722 26.89804 1.99 0.06001 x12 0.70683 1.55573 0.45 06542 x3z 5.76510 1.41 0.1734