Concept explainers
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
- 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 = .05.
- e. Use α = .05 to determine whether each of the independent variables is significant.
- 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?
- g. What is the estimated odds ratio for the orientation program? Interpret it.
- h. Would you recommend making the orientation program a required activity? Why or why not?
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Chapter 15 Solutions
STATISTICS F/BUSINESS+ECONOMICS-TEXT
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