Many policy makers and college administrators are interested in learning which factors predict high graduation rates. Data from a random sample of colleges and universities is available in the file "Colleges" (posted on Canvas). GRAD RATE records the percentage of students that successfully complete their degree within 5 years of enrollment. TOPCLASS records the percentage of enrolled students that graduated within the top 10% of their high school class. PHD refers to the percentage of full-time faculty that hold a Ph.D. in their field. RATIO refers to the student-to-faculty ratio on campus. TYPE records whether the college is publicly or privately funded.

(a) Estimate a multiple regression model where GRAD RATE is the dependent variable and TOPCLASS, PHD, RATIO and TYPE will be the independent variables. Let "private" represent the reference category. Write down the estimated regression equation(s).

(b) Identify and interpret the slope coefficient associated with the variable TYPE.

(c) Construct and conduct appropriate hypothesis tests for determining which slope coefficient estimates are statistically significant. Use a 5% level of significance.

(d) Construct and conduct an appropriate hypothesis test for determining whether this model, as a whole, is useful. Use a 5% level of significance.

(e) Identify and interpret the Adjusted-R².

TOPCLASS	PHD	RATIO	GRAD RATE	TYPE
16	76	11.9	15	Public
4	39	9.5	39	Private
18	72	18.9	51	Private
25	85	16.7	69	Private
67	74	14	72	Public
26	63	11.4	44	Public
10	70	17.9	43	Public
17	59	16.6	52	Public
34	74	14.7	61	Public
30	56	15.5	46	Public
18	50	23	48	Private
20	70	12.2	65	Public
24	96	6.7	33	Private
46	79	12.6	54	Public
12	57	19.6	48	Private
21	58	19	68	Private
52	82	13.1	63	Public
24	68	13.3	75	Public
31	63	13.3	65	Public
26	40	17	33	Private
25	73	14.8	39	Private
35	71	17.7	73	Public
24	88	18.9	48	Private
23	78	21.7	41	Private
29	91	19.6	49	Private
98	100	6.5	83	Public
23	72	12.4	60	Public
20	87	19.5	41	Private
47	79	16.1	40	Private
23	72	12.8	47	Public
71	99	9.6	87	Public
95	100	8.2	100	Public
37	100	10.4	73	Public
80	94	8.9	91	Public
60	95	8.2	73	Public
11	77	10.4	43	Public
37	53	11.9	72	Public
52	91	10.5	79	Public
9	38	10.7	67	Public
51	59	10.5	54	Public
20	48	12.3	69	Public
20	71	16.1	54	Public
86	95	11.6	66	Public
18	63	18.6	43	Public
36	88	16.1	78	Public
95	93	15.8	78	Private
85	96	16.1	66	Private
93	97	11.8	77	Private
80	98	13.4	62	Private
95	100	13.9	66	Private
90	96	18.9	69	Private
94	94	21.3	59	Private
26	81	8.9	73	Public
23	86	13.6	62	Public
40	88	13.9	100	Public
45	90	11.4	68	Public
36	87	11.2	65	Public
42	77	14.9	87	Private
35	84	13.6	52	Public
40	93	15.6	66	Public
22	68	10.9	71	Public
42	84	14.2	84	Public
30	55	13.1	55	Public
16	63	27.9	60	Private
56	85	11.3	84	Public
12	75	21.5	40	Private
29	87	19.2	59	Private
16	89	19.1	46	Private
6	48	28.8	59	Private
6	75	21.1	25	Private
10	63	19.4	36	Private
72	40	8.2	88	Private
28	90	19.9	66	Private
29	84	15.9	67	Public
7	76	19.4	52	Private
17	63	12	86	Public
19	71	14.8	82	Public
4	62	15.8	45	Private
20	87	11.2	76	Public
46	91	10.4	91	Public
72	31	8.3	71	Private
16	76	7.9	51	Public
11	61	10.7	66	Public
60	90	12.1	92	Public
14	71	16.9	50	Private
95	96	5.8	99	Public
23	89	16	71	Private
24	90	9.3	75	Public
38	92	7.6	72	Public
71	91	7.2	95	Public
19	89	8.3	96	Public
10	25	27.6	36	Public
22	82	18.3	75	Public
10	52	14.4	84	Public
18	76	12.6	72	Public
12	48	13.8	58	Public
39	90	10.6	57	Public
14	37	16.5	44	Public
33	82	12.8	59	Public
20	65	17.4	68	Public
50	80	23.1	58	Private
34	67	14.4	49	Public
37	50	15.9	33	Private
9	78	14.7	69	Public
83	93	8.4	100	Public
9	45	11.7	82	Public
23	93	13.8	88	Public
18	73	16.8	80	Public
30	93	16.8	94	Public
20	87	17.5	82	Public
66	95	16.6	90	Public
45	80	11.9	72	Public
5	57	10.2	46	Public
48	90	9.8	84	Public
30	94	10.5	79	Public
23	71	11.3	86	Public
70	92	11.3	95	Public
5	39	8.7	58	Public
17	58	17.3	70	Public
25	73	14.2	66	Public
90	97	9.9	100	Public
12	71	27.8	58	Public
8	81	16.1	53	Private
96	99	10.1	94	Public
4	73	17.1	51	Private
1	65	14.2	57	Private
25	79	13	97	Public
11	95	13.3	60	Public
60	99	10.3	92	Public
12	88	16.7	68	Private
10	86	14.5	41	Private
80	94	10.6	91	Public
7	74	15.4	59	Public
21	92	13.2	71	Public
81	94	9	99	Public
49	92	15.2	82	Public
26	79	11.4	62	Public
6	10	15.4	64	Public
10	10	12.1	52	Public
35	64	11.5	75	Public
13	47	13.9	63	Public
40	78	9.2	77	Public
36	82	14.4	72	Public
75	96	3.3	90	Public
25	86	14.7	80	Public
20	80	18.2	29	Private
15	77	12.8	80	Public
20	73	17.9	56	Private
31	63	7.2	64	Public
42	84	11.6	63	Private
50	54	6.8	94	Private
22	89	18.1	63	Private
27	82	18.4	55	Private
31	79	11.2	65	Public
31	84	12.5	60	Public
10	67	15.2	35	Private
53	79	9.8	93	Public
76	93	11.2	96	Public
58	83	10.2	91	Public
20	67	15.9	59	Private
5	65	15	38	Private
10	36	22	84	Public
19	72	11.4	64	Public
12	53	27.2	85	Public
18	29	21.8	75	Public
23	93	14.5	56	Private
17	46	15.1	64	Private
22	53	12.9	54	Public
37	89	13.7	73	Public
44	79	15.3	68	Public
14	62	11.5	46	Public
20	55	12.7	65	Public