Question

Q) 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
7	2.72	0	0
8	1.74	0	0
9	1.86	0	0
10	3.53	1	1
11	3.12	0	1
12	1.21	0	0
13	3.01	1	1
14	2.70	0	0
15	2.47	1	1
16	2.37	0	1
17	2.28	1	0
18	2.76	0	0
19	2.24	0	0
20	3.10	1	1
21	2.86	0	1
22	2.62	0	1
23	3.07	1	1
24	2.18	0	1
25	3.30	1	1
26	2.43	1	0
27	2.38	0	0
28	1.23	0	0
29	2.63	1	1
30	4.00	1	1
31	2.21	1	0
32	1.73	0	0
33	2.62	1	0
34	2.65	1	1
35	2.82	1	1
36	3.77	1	1
37	2.38	1	1
38	3.11	1	1
39	2.82	0	1
40	2.16	1	0
41	2.66	1	0
42	3.33	1	1
43	2.77	1	0
44	4.00	1	1
45	2.33	0	0
46	3.41	0	0
47	1.98	1	0
48	3.06	1	1
49	3.98	1	1
50	3.24	1	1
51	3.22	0	0
52	3.05	1	1
53	2.66	0	0
54	2.88	1	1
55	2.60	1	1
56	3.12	1	1
57	3.12	1	1
58	2.72	1	1
59	3.38	1	1
60	3.29	0	1
61	3.49	1	1
62	2.89	1	1
63	2.46	1	1
64	1.90	1	1
65	2.77	1	1
66	2.61	0	0
67	2.44	1	0
68	3.10	1	1
69	3.87	1	1
70	3.25	1	1
71	2.44	1	1
72	2.66	1	1
73	3.06	1	1
74	2.75	0	1
75	3.65	1	1
76	1.66	0	0
77	3.41	1	1
78	2.91	1	1
79	2.15	0	1
80	1.54	0	0
81	3.45	1	1
82	1.98	0	0
83	2.22	0	0
84	2.51	0	0
85	2.99	1	1
86	3.48	1	1
87	2.75	1	1
88	3.71	1	1
89	2.11	0	0
90	2.86	1	1
91	2.87	1	1
92	2.64	0	1
93	1.61	0	0
94	3.48	1	1
95	3.04	1	1
96	2.25	0	1
97	2.54	0	0
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

            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. Insert a minitab output here.

d) Conduct a test for overall significance using a = 0.05. Insert a minitab output here.

e) Use a = 0.05 to determine whether each of the independent variables is significant.

f) Use the estimated logit computed in part (c) to compute an estimate of 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?

Answer 1