11.22 Consider the sex of the students. Refer to Exercises 11.15 and 11.16. The seventh explanatory variable provided in the GPA data set is a sex indicator variable. This variable (SEX) takes the value 0 for males and 1 for females. If we include it in our model involving the other six variables, it allows the intercept to differ for the two genders. Using b7 to represent the fitted coefficient for the SEX variable, the estimated male intercept is b0 + b7(0) = b0 and the estimated female intercept is b0 + b7(1) = b0 + b7. The difference between these two intercept estimates is (b0 + b7) − b0 = b7, so the coefficient is also an estimate of the difference in intercepts.

  1. (a) Include the variable SEX with the other six explanatory variables and refit the model. Compare the fit of this model, using R2 and s, with the model in Figure 11.10 (pages 627–629).

  2. (b) Does this indicator variable appear to contribute to our explanation of GPA? Report the test results.

  3. (c) Does the coefficient suggest males or females have higher GPA scores? Explain your answer.