Hi, I have this question on modeling the salary on female and male Let X1 = GPA,

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Hi, I have this question on modeling the salary on female and male

Let X1 = GPA,
X2 = IQ,
X3 = Sex (1 for Female and 0 for Male),
X4 = Interaction between GPA and IQ,
X5 = Interaction between GPA and Gender.

Let the response be starting salary after graduation (in thousands of dollars). Suppose we use least squares to fit the model, and estimate

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

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

2. Provide the estimated equation of a line for females. Simplify it as much as possible.

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

4. 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.