F I L E The SAT has gone through many revisions over the years. In 2005, a new writing section was introduced that includes a direct writing measure in the form of an essay.

People argue that female students generally do worse on math tests but better on writing tests. Therefore, the new section may help reduce the usual male lead on the overall average SAT score (The Washington Post, August 30, 2006).

Consider the following portion of data on 20 students who took the SAT test last year; the complete data set can be found on the text website, labeled SATdummy. Information includes each student's score on the math and w riting sections of the exam. Also included are the student's GPA and a dummy that equals 1 for female and 0 for male.

Writing Math GPA Female 620 600 3.44 0 570 550 3.04 0

⋮ ⋮ ⋮ ⋮

540 520 2.84 0

a. Estimate a linear regression model w ith w riting score as the response variable and GPA and the female dummy variable as the explanatory variables.

b. Compute the predicted score for a male student w ith a GPA of 3.5. Repeat the analysis for a female student.

c. Perform a test to determine if there is a statistically significant gender difference in w riting scores at a 5%

level.