If the Admissions staff is able to show that the Summer Bridge program has a positive effect on retention, the university administration will consider making the program a requirement for all firstuyear students. The university administration also thinks that that students with lower GPAs have a higher probability of leaving Towson University at the end of the first year. In order to investigate the relationship of these variables to retention, a random sample of 100 students from last year's entering class was selected. The data are contained in the data set named TowsonUni. The dependent variable was coded as y: 1 if the student returned to Towson University for the sophomore year and y=0 if not. The two independent variables are: x1 = GPA at the end of the rst semester = 0 if the student did not attend the Summer Bridge program x 2 1 if the student attended the Summer Bridge program a) [2 points] Write the logistic regression model equation relating X1 and X2 to y {i.e. the general logistic model form ; E ( y]: ? } b) [2 points] What is the interpretation of E l y] when X2=0 ? c) [5 points] Use both independent variables and gretl to compute the estimated logistic regression equation d) [3 points] Conduct a test for overall significance/overall model adequacy using (1 =0.05 . Is the model statistically adequate for predicting a student's Return to the college? Explain e) [3 points] Use (1 =0.05 to determine whether each of the variables is significant. Explain f) [4 points] Use the estimated equation you computed in part {c1 to estimate the probability that