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

DATAfile (Excel): Lakeland DATAfile (CSV): Lakeland A statistical program recommended. 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 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. The dependent variable was coded as y = 1 if the student returned to Lakeland the sophomore year and y = 0 if not. The two independent variables are: *4 = GPA at the end of the first semester So if the student did not attend the orientation program X2 = 1 if the student attended the orientation program. (a) Write the logistic regression equation relating X1 and X2 to y. Ely) = 1 + elo + 1X1 + 2x2 elo + Pq X1 + B2X2 E(Y) = Bo + B1X1 + B2X2 E(Y) = elo + 1*1 + 12*2 Ely) = O elo + 1*1 + 2x2 1 + eo + 1*1 +1242 (b) What is the interpretation of Ely) when x2 = 0? It is an estimate of the GPA for a student who did not attend the orientation program and returned to Lakeland for the sophomore year. For a given GPA, it is an estimate of the probability that a student who attended the orientation program will return to Lakeland for the sophomore year. o For a given GPA, it is an estimate of the probability that a student who did not attend the orientation program will return to Lakeland for the sophomore year. It is an estimate of the GPA for a student who attended the orientation program and returned to Lakeland for the sophomore year. (c) Use both independent variables and statistical software to compute the estimated logit. (Round your numerical values to two decimal places.) g(x1, x2) = -6.89256 +2.5388x, +1.56075x2 (d) Use the estimated logit computed in part (c) to estimate the probability that students with a 1.5 grade point average who did not attend the orientation program will return to Lakeland for their sophomore year. (Round your answer to four decimal places.) What is the estimated probability that students with a 1.5 grade point average who attended the orientation program will return to Lakeland for their sophomore year? (Round your answer to four decimal places.) (e) What is the estimated odds ratio for the orientation program? (Round your answer to four decimal places.) Interpret the estimated odds ratio. (Round your answer to four decimal places.) The odds of students who attended the orientation program continuing are X times greater than for students who did not attend the program