Intro to Statistical Learning (2nd Ed), Solution to Problem 3.3C | Reading Regression Results

Question 3.3C
Suppose we have a data set with fve predictors, X1 = GPA, X2 = IQ, X3 = Level (1 for College and 0 for High School), X4 = Interaction between GPA and IQ, and X5 = Interaction between GPA and Level. The response is starting salary after graduation (in thousands of dollars). Suppose we use least squares to ft the model, and get β^0=50 , β^1=20 , β^2=0.07 , β^3=35 , β^4=0.01 , β^5=−10 .

(a) Which answer is correct, and why?

i. For a fixed value of IQ and GPA, high school graduates earn more, on average, than college graduates.

ii. For a fxed value of IQ and GPA, college graduates earn more, on average, than high school graduates.

iii. For a fxed value of IQ and GPA, high school graduates earn more, on average, than college graduates provided that the GPA is high enough.

iv. For a fxed value of IQ and GPA, college graduates earn more, on average, than high school graduates provided that the GPA is high enough.

(b) Predict the salary of a college graduate with IQ of 110 and a GPA of 4.0.

(c) True or false: Since the coefcient for the GPA/IQ interaction term is very small, there is very little evidence of an interaction effect. Justify your answer.