Seton Hall University is a Roman Catholic university situated in New Jersey, with easy access to New York City. Like most universities, it uses SAT scores and high school GPA as primary criteria for admission. The accompanying table shows a portion of data concerning information on admission (1 for admission and 0 otherwise), SAT score, and GPA for 30 students who had recently applied to Seton Hall.

Admission........... SAT........... GPA

1...................... 1700............ 3.39

1.......................2020............ 2.65

⋮.................................... ⋮..................... ⋮

0...................... 1300............ 2.47

a. Estimate the linear probability model where admission is a function of the SAT score and high school GPA. Analyze the significance of the variables at the 5% level.

b. Use these estimates to predict the probability of admission for an individual with a GPA of 3.5 and an SAT score of 1700.

c. Reestimate the probability of admission for an individual with a GPA of 3.5 and an SAT score of 1800.