The Admissions staff at Towson University is responsible for tracking the retention rate of first-year students. The Admissions staff has noticed that over the past few years, the percentage of students who leave the University at the end of the first-year has increased. In an effort to increase retention rates, last year Townson University started a voluntary 2 week Summer Bridge program to help first-year students in adjusting to college life.

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 first-year students. The university administration also thinks thatthat 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 ofthese 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 asif the student returned to Towson University for the sophomore year andif not. The two independent variables are:

a)Write the logistic regression model equation relatingx1 and x2 to y{i.e. the general logistic model form ;E(y)= ?}

b)What is the interpretation ofE(y)when x2=0?

c)Use both independent variables and gretl to compute theestimated logistic regression equation

d)Conduct a test for overall significance/overall model adequacy using

This question requires the use of grell. Corresponding file is TowsonUni.gdi./ But you are required to show the regression output that helped you to reach your conclusions. The Admissions staff at Towson University is responsible for tracking the retention rate of first-year students. The Admissions staff has noticed that over the past few years, the percentage of students who leave the University at the end of the first-year has increased. In an effort to increase retention rates, last year Townson University started a voluntary 2 week Summer Bridge program to help first-year students in adjusting to college life. 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 first-year 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 Towson Uni. 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 first semester *2 = JO if the student did not attend the Summer Bridge program 11 if the student attended the Summer Bridge program a) Write the logistic regression model equation relating x1 and x2 to y /i.e. the general logistic model form ; E ()') =?) b) What is the interpretation of E (y) when x2 = 0? c) Use both independent variables and gretl to compute the estimated logistic regression equation d) Conduct a test for overall significance/overall model adequacy using a = 0.05. Is the model statistically adequate for predicting a student's Return to the college? Explain e) Use a = 0.05 to determine whether each of the variables is significant. Explain () Use the estimated equation you computed in part (c) to estimate the probability that students with a 2.5 GPA who did not attend the Summer Bridge program will return to Towson University for their sophomore year. What is the estimated probability for students with a 2.5 GPA who attended the Summer Bridge program? g) What is the estimated odds ratio for the Summer Bridge program? Interpret it. h) Would you recommend making the Summer Bridge program a required activity? Why or why not