A university administrator has collected data on total Scholastic Aptitude Test (SAT) score versus freshman grade point average (GPA) for a sample of students who recently finished their first year at the university. The data are listed in file XR15091. Given these data:
a. Determine the least-squares regression equation for estimating the freshman grade point average based on total SAT score, then estimate the freshman grade point average for an applicant who has scored a total of 1100 on his SAT examination.
b. What percentage of the variation in freshman GPA is explained by SAT total?
c. Given an SAT total of 1100, construct and interpret the 99% confidence and prediction intervals associated with freshman GPA.