(Solved): just (b) please Suppose we have a data set with five predictors: X1=GPAX2=IQX3=Sex(1for ...

Suppose we have a data set with five predictors: $$\begin{array}{l}{X}_1=GPA\\ X_2=IQ\\ X_3=Sex(1\text{ for Female and }0\text{ for Male) }\\ X_4=\text{ Interaction between GPA and IQ }\\ X_5=\text{ Interaction between GPA and Gender }\end{array}$$ The response is starting salary after graduation (in thousands of dollars). Suppose we use least squares to fit the model, and get $${\widehat{?}}_0=50.{\widehat{?}}_1=20.{\widehat{?}}_2=0.07,{\widehat{?}}_3=35.{\widehat{?}}_4=\mathrm{0.01.}{\widehat{?}}_5=?10$$. (a) True or false: Since the coefficient for the GPA:IQ interaction term is very small, there is very little evidence of an interaction effect. Justify your answer. (b) What subset is described by the intercept? In other words, $$\$50.000$$ is the predicted average starting salary for what group of graduates? Is the intercept meaningful in the context of this study? Explain.