Suppose we have a data set with five predictors, X1 = GPA, X2 = IQ, X3 = Gender (1 for Female and 0 for Male), X4 = Interaction between GPA and IQ, and X5 = Interaction between GPA and Gender. The response is starting salary after graduation (in thousands of dollars). Suppose we use least squares to fit the model, and get βˆ0 = 50, βˆ1 = 20 , βˆ2 = 0. 07 , βˆ3 = 35 , βˆ4 = 0.01 , βˆ5 = − 10.

Y = 50 + 20(gpa) + 0.07(iq) + 35(gender) + 0.01(gpa * iq) - 10 (gpa * gender)

(A) Which answer is correct, and why?

a. For a fixed value of IQ and GPA, males earn more on average than females.
b. For a fixed value of IQ and GPA, females earn more on average than males.
c. For a fixed value of IQ and GPA, males earn more on average than females provided that the GPA is high enough.
d. For a fixed value of IQ and GPA, females earn more on average than males provided that the GPA is high enough.

(B) Predict the salary of a female with IQ of 110 and a GPA of 4.0.
(C) 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.