Unlike small selective colleges that pay close attention to personal statements, teacher recommendations, etc., large, public state university systems primarily rely on a student's grade point average (GPA) and scores on the SAT or ACT for the college admission decisions. Data were collected for 120 applicants on college admission (Admit equals 1 if admitted, 0 otherwise) along with the student's GPA and SAT scores. A portion of the data is shown in the accompanying table.

a. Estimate the linear probability model and the logistic regression model. (Round coefficient estimates to 4 decimal places.) Variable. Linear Model Logistic Model

Intercept

GPA

SAT

b. Compute the accuracy rates (%) of both models. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)

Linear Model Logistic Model

c-1. Find the preferred model for prediction. multiple choice

• Logistic Model
• Linear Model

c-2. Use the preferred model to predict the probability of admission for a college student with GPA = 3.0 and SAT = 1400. What if GPA = 4.0? (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.) Note: Report the probability between 0 and 1 (not in %).

SAT=1400, GPA=3.0

SAT=1400, GPA=4.0