122
3. Suppose we have a data set with five predictors, X1
=
GPA, X2 = IQ, X3 Level (1 for College and 0 for High School), X4 = Interac- tion 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 fit the model, and get Bo 50, 120, 82 0.07, 8335, 84 = 0.01, 85=-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.
3. Linear Regression
ii. For a fixed value of IQ and GPA, college graduates earn more, on average, than high school graduates.
iii. For a fixed 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 fixed 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 coefficient for the GPA/IQ interaction term is very small, there is very little evidence of an interaction effect. Justify your answer.
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