We want to examine what factors account for differences in salary in a university department by characteristics of the faculty member: the number of years since each faculty member received their Ph.D. (X1), the number of publications (X2), gender of the professor (1=F, 0=M), and number of citations in the scientific literature (X4).

Table 2: Salary Differentiation

Case	Time	Pubs	Cites	Salary	Gender
1	3	18	50	51876	1
2	6	3	26	54511	1
3	3	2	50	53425	1
4	8	17	34	61863	0
5	9	11	41	52926	1
6	6	6	37	47034	0
7	16	38	48	66432	0
8	10	48	56	61100	0
9	2	9	19	41934	0
10	5	22	29	47454	0
11	5	30	28	49832	1
12	6	21	31	47047	0
13	7	10	25	39115	1
14	11	27	40	59677	0
15	18	37	61	61458	0
16	6	8	32	54528	0
17	9	13	36	60327	1
18	7	6	69	56600	0
19	7	12	47	52542	1
20	3	29	29	50455	1
21	7	29	35	51647	1
22	5	7	35	62895	0
23	7	6	18	53740	0
24	13	69	90	75822	0
25	5	11	60	56596	0
26	8	9	30	55682	1
27	8	20	27	62091	1
28	7	41	35	42162	1
29	2	3	14	52646	1
30	13	27	56	74199	0
31	5	14	50	50729	0
32	3	23	25	70011	0
33	1	1	35	37939	0
34	3	7	1	39652	0
35	9	19	69	68987	0
36	3	11	69	55579	0
37	9	31	27	54671	0
38	3	9	50	57704	0
39	4	12	32	44045	1
40	10	32	33	51122	0
41	1	26	45	47082	0
42	11	12	54	60009	0
43	5	9	47	58632	0
44	1	6	29	38340	0
45	21	39	69	71219	0
46	7	16	47	53712	1
47	5	12	43	54782	1
48	16	50	55	83503	0
49	5	18	33	47212	0
50	4	16	28	52840	1
51	5	5	42	53650	0
52	11	20	24	50931	0
53	16	50	31	66784	1
54	3	6	27	49751	1
55	4	19	83	74343	1
56	4	11	49	57710	1
57	5	13	14	52676	0
58	6	3	36	41195	1
59	4	8	34	45662	1
60	8	11	70	47606	1
61	3	25	27	44301	1
62	4	4	28	58582	1

After analyzing Table 2, answer the following questions:

1. What number is in the denominator of the t-test that is testing the significance of the variance uniquely accounted for by number of publications
2. What number is in the denominator of the t-test that is testing the significance of the variance uniquely accounted for by number of citations?
3. What number is in the denominator of the t-test that is testing the significance of the variance uniquely accounted for by years since the Ph.D.?
4. What number is in the denominator of the t-test that is testing the significance of the variance uniquely accounted for by gender?
5. Which predictor variable has the strongest relationship with salary and how do you know this?
6. Is there a problem with multicollinearity? How do you know?