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 firstyear 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
7 2.72 0 0
8 1.74 0 0
9 1.86 0 0
10 3.53 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
x2 = 0 if the student did not attend the orientation program OR 1 if the student attended the orientation program
a. Write the logistic regression equation relating x1 and x2 to y.
b. What is the interpretation of E(y) when x2 = 0?
c. Use both independent variables and Minitab to compute the estimated logit.
d. Conduct a test for overall significance using α = 0.05.
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