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

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 of100 studentsfrom 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 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 1 if the student attended the orientation program.

(A)Write the logistic regression equation relating

E(y) =

e^{₀ + ₁x₁ + ₂x₂}

1 + e^{₀ + ₁x₁ + ₂x₂}

E(y) = ₀ + ₁x₁ + ₂x₂

E(y) =

1 + e^{₀ + ₁x₁ + ₂x₂}

e^{₀ + ₁x₁ + ₂x₂}

E(y) = e^{₀ + ₁x₁ + ₂x₂}

(B) What is the interpretation of

E(y) when x₂= 0?

A, 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.

B, 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.

C, It is an estimate of the GPA for a student who attended the orientation program and returned to Lakeland for the sophomore year.

D, 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.

(C)Use both independent variables and statistical software to compute the estimated logit. (Round your numerical values to two decimal places.)

(x₁,x₂) =

(D)Conduct a test for overall significance using= 0.05.

A, H₀: ₁ = ₂ = 0 H_a: One or more of the parameters is not equal to zero.

B, H₀: ₁ = ₂ = 0 H_a: All the parameters are not equal to zero.

C, H₀: ₀ = 0 H_a: ₀ 0

D, H₀: One or more of the parameters is not equal to zero. H_a: ₁ = ₂ = 0

Find the value of the test statistic. (Round your answer to two decimal places.

Find the p-value. (Round your answer to three decimal places.)p-value =

What is your conclusion at the 0.05 level of significance?

A, Reject H₀. There is insufficient evidence to conclude that there is a significant relationship

B, Do not reject H₀. There is sufficient evidence to conclude that there is a significant relationship.

C, Reject H₀. There is sufficient evidence to conclude that there is a significant relationship.

D, Do not reject H₀. There is insufficient evidence to conclude that there is a significant relationship.