Chapter 3, page 120
1. 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 = 50, = 20, =0 .07, = 35, =0 .01, =−10.
(a) Which answer is correct, and why?
i. For a fixed value of IQ and GPA, males earn more on average than females.
ii. For a fixed value of IQ and GPA, females earn more on average than males.
iii. For a fixed value of IQ and GPA, males earn more on average than females provided that the GPA is high enough.
iv. 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.
Chapter 3, page 123
2. This question should be answered using the Carseats data set. Use R to model the data.
(a) Fit a multiple regression model to predict Sales using Price, Urban, and US.
(b) Provide an interpretation of each coefficient in the model. Be careful—some of the variables in the model are qualitative!
(c) Write out the model in equation form, being careful to handle the qualitative variables properly.
(d) For which of the predictors can you reject the null hypothesis H0: βj = 0?
(e) On the basis of your response to the previous question, fit a smaller model that only uses the predictors for which there is evidence of association with the outcome.
(f) How well do the models in (a) and (e) fit the data?
Note: No need to answer (g) and (h)
