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 (Washington Post, August 30, 2006). Consider the following portion of data on 20 students who took the SAT test last year; the entire data set, labeled SATdummy, can be found on the text website. Information includes each student’s score on the writing and math sections of the exam. Also included are the student’s GPA and the values of a Gender dummy variable with 1 for females and 0 for males.

a. Estimate a linear regression model with Writing as the response variable and GPA and Gender as the explanatory variables.
b. Compute the predicted writing score for a male student with a GPA of 3.5. Repeat the computation for a female student.
c. Perform a test to determine if there is a statistically significant gender difference in writing scores at a 5%level.

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Writing 620 570 Math 600 550 GPA 3.44 3.04 Gender 540 520 2.84 0