Problem 3.3

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Problem 3.3

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 β₀ = 50, β₁ =
20, β₂ = 0.07, β₃ = 35, β₄ = 0.01, β₅ = −10.

Which answer is correct, and why?

(i) For a fixed value of IQ and GPA, males earn more than females.

(ii) For a fixed value of IQ and GPA, females earn more than males.

(iii) For a fixed value of IQ and GPA, males earn more than females provided that the GPA is high enough.

(iv) For a fixed value of IQ and GPA, females earn more than males provided that the GPA is high enough.

Clear selection

Predict the salary of a female with IQ of 110 and a GPA of 4.0.

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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