Chapter 15.9, Problem 47E

Over the past few years the percentage of students who leave Lakeland College at the end of the first year has increased. Last year Lakeland started a voluntary one-week orientation program to help first-year students adjust to campus life. If Lakeland is able to show that the orientation program has a positive effect on retention, they will consider making the program a requirement for all first-year students. Lakeland’s administration also suspects that students with lower GPAs have a higher probability of leaving Lakeland at the end of the first year. In order to investigate the relation of these variables to retention, Lakeland selected a random sample of 100 students from last year’s entering class. The data are contained in the data set named Lakeland; a portion of the data follows.

Student	GPA	Program	Return
1	3.78	1	1
2	2.38	0	1
3	1.30	0	0
4	2.19	1	0
5	3.22	1	1
6	2.68	1	1
.	.	.	.
.	.	.	.
.	.	.	.
98	2.57	1	1
99	1.70	1	1
100	3.85	1	1

The dependent variable was coded as y = 1 if the student returned to Lakeland for the sophomore year and y = 0 if not. The two independent variables are:

x₁ = GPA at the end of the first semester

$\begin{array}{l}{x}_2=\{\begin{array}{l}\text{0 if the student did not attend the orientation program}\\ \text{1 if the student attended the orientation program}\end{array}\\ \end{array}$

1. a. Write the logistic regression equation relating x₁ and x₂ to y.
2. b. What is the interpretation of E(y) when x₂ = 0?
3. c. Use both independent variables and Minitab to compute the estimated logit.
4. d. Conduct a test for overall significance using α = .05.
5. e. Use α = .05 to determine whether each of the independent variables is significant.
6. f. Use the estimated logit computed in part (c) to estimate the probability that students with a 2.5 grade point average who did not attend the orientation program will return to Lakeland for their sophomore year. What is the estimated probability for students with a 2.5 grade point average who attended the orientation program?
7. g. What is the estimated odds ratio for the orientation program? Interpret it.
8. h. Would you recommend making the orientation program a required activity? Why or why not?