The admissions officer of a university is trying to develop a formal system to decide which students to admit to the university. She believes that determinants of success include the standard variables—high school grades and SAT scores. However, she also believes that students who have participated in extracurricular activities are more likely to succeed than those who have not. To investigate the issue, she randomly sampled 100 fourth-year students and recorded the following variables:

GPA for the first 3 years at the university (range: 0 to 12)

GPA from high school (range: 0 to 12)

SAT score (range: 400 to 1600)

Number of hours on average spent per week in organized extracurricular activities in the last year of high school

a. Develop a model that helps the admissions officer decide which students to admit and use the computer to generate the usual statistics.

b. What is the coefficient of determination? Interpret its value.

c. Test the overall validity of the model.

d. Test to determine whether each of the independent variables is linearly related to the dependent variable in this model.

e. Determine the 95% interval of the GPA for the first 3 years of university for a student whose high school GPA is 10, whose SAT score is 1200, and who worked an average of 2 hours per week on organized extracurricular activities in the last year of high school.

f. Find the 90% interval of the mean GPA for the first 3 years of university for all students whose high school GPA is 8, whose SAT score is 1100, and who worked an average of 10 hours per week on organized extracurricular activities in the last year of high school.