Question 3 Perform a regression analysis using compa as the

Question 3)

Perform a regression analysis using compa as the dependent variable and the same independent variables as used in question 2. Show the result, and interpret your findings by answering the same questions.

Note: be sure to include the appropriate hypothesis statements.

A ) Regression hypotheses

Ho:

Ha:

Coefficient hyhpotheses (one to stand for all the separate variables)

Ho:

Ha:

B )Interpretation:

For the Regression as a whole:

What is the value of the F statistic:

What is the p-value associated with this value:

Is the p-value < 0.05?

Do you reject or not reject the null hypothesis:

What does this decision mean for our equal pay question (Do M and F get paid equaly?):

C )For each of the coefficients: Intercept, Midpoint, Age, Perf. rating, Service, Gender, Degree

What is the coefficient\'s p-value for each of the variables:

Is the p-value < 0.05?

Do you reject or not reject each null hypothesis:

What are the coefficients for the significant variables?

Using only the significant variables, what is the equation? Compa =

Is gender a significant factor in compa:

If so, who gets paid more with all other things being equal?

How do we know?

Salary

Compa

Midpoint

Age

Performance Rating

Service

Gender

Raise

Degree

Gender1

66.1

1.159

5.7

25.9

0.834

3.9

35.2

1.135

3.6

55.3

0.971

100

5.5

49.6

1.033

5.7

78.3

1.168

4.5

42.3

1.058

100

5.7

22.8

0.990

5.8

1.164

100

23.3

1.014

4.7

23.6

1.025

100

4.8

60.8

1.067

4.5

40.6

1.014

100

4.7

21.7

0.943

21.8

0.949

4.9

37.4

0.934

5.7

1.000

33.5

1.081

5.6

1.000

4.6

1.162

4.8

1.135

6.3

43.7

0.911

3.8

25.3

1.098

3.3

48.9

1.019

3.8

25.8

1.122

23.3

1.013

6.2

42.3

1.057

3.9

75.2

1.122

4.4

80.9

1.208

5.4

1.020

4.3

24.2

1.054

3.9

27.5

0.886

5.6

63.6

1.115

5.5

28.6

0.922

4.9

22.4

0.976

5.3

23.6

1.026

4.3

24.3

1.057

6.2

1.105

4.5

34.8

1.123

5.5

24.3

1.057

6.3

42.8

1.071

4.3

0.998

100

5.7

75.4

1.125

5.5

60.7

1.065

5.2

57.9

1.206

5.2

62.2

1.091

3.9

62.2

1.091

5.5

70.1

1.230

5.3

61.7

1.083

6.6

61.4

1.077

4.6

ID	Salary	Compa	Midpoint	Age	Performance Rating	Service	Gender	Raise	Degree	Gender1	Gr
1	66.1	1.159	57	34	85	8	0	5.7	0	M	E
2	25.9	0.834	31	52	80	7	0	3.9	0	M	B
3	35.2	1.135	31	30	75	5	1	3.6	1	F	B
4	55.3	0.971	57	42	100	16	0	5.5	1	M	E
5	49.6	1.033	48	36	90	16	0	5.7	1	M	D
6	78.3	1.168	67	36	70	12	0	4.5	1	M	F
7	42.3	1.058	40	32	100	8	1	5.7	1	F	C
8	22.8	0.990	23	32	90	9	1	5.8	1	F	A
9	78	1.164	67	49	100	10	0	4	1	M	F
10	23.3	1.014	23	30	80	7	1	4.7	1	F	A
11	23.6	1.025	23	41	100	19	1	4.8	1	F	A
12	60.8	1.067	57	52	95	22	0	4.5	0	M	E
13	40.6	1.014	40	30	100	2	1	4.7	0	F	C
14	21.7	0.943	23	32	90	12	1	6	1	F	A
15	21.8	0.949	23	32	80	8	1	4.9	1	F	A
16	37.4	0.934	40	44	90	4	0	5.7	0	M	C
17	57	1.000	57	27	55	3	1	3	1	F	E
18	33.5	1.081	31	31	80	11	1	5.6	0	F	B
19	23	1.000	23	32	85	1	0	4.6	1	M	A
20	36	1.162	31	44	70	16	1	4.8	0	F	B
21	76	1.135	67	43	95	13	0	6.3	1	M	F
22	43.7	0.911	48	48	65	6	1	3.8	1	F	D
23	25.3	1.098	23	36	65	6	1	3.3	0	F	A
24	48.9	1.019	48	30	75	9	1	3.8	0	F	D
25	25.8	1.122	23	41	70	4	0	4	0	M	A
26	23.3	1.013	23	22	95	2	1	6.2	0	F	A
27	42.3	1.057	40	35	80	7	0	3.9	1	M	C
28	75.2	1.122	67	44	95	9	1	4.4	0	F	F
29	80.9	1.208	67	52	95	5	0	5.4	0	M	F
30	49	1.020	48	45	90	18	0	4.3	0	M	D
31	24.2	1.054	23	29	60	4	1	3.9	1	F	A
32	27.5	0.886	31	25	95	4	0	5.6	0	M	B
33	63.6	1.115	57	35	90	9	0	5.5	1	M	E
34	28.6	0.922	31	26	80	2	0	4.9	1	M	B
35	22.4	0.976	23	23	90	4	1	5.3	0	F	A
36	23.6	1.026	23	27	75	3	1	4.3	0	F	A
37	24.3	1.057	23	22	95	2	1	6.2	0	F	A
38	63	1.105	57	45	95	11	0	4.5	0	M	E
39	34.8	1.123	31	27	90	6	1	5.5	0	F	B
40	24.3	1.057	23	24	90	2	0	6.3	0	M	A
41	42.8	1.071	40	25	80	5	0	4.3	0	M	C
42	23	0.998	23	32	100	8	1	5.7	1	F	A
43	75.4	1.125	67	42	95	20	1	5.5	0	F	F
44	60.7	1.065	57	45	90	16	0	5.2	1	M	E
45	57.9	1.206	48	36	95	8	1	5.2	1	F	D
46	62.2	1.091	57	39	75	20	0	3.9	1	M	E
47	62.2	1.091	57	37	95	5	0	5.5	1	M	E
48	70.1	1.230	57	34	90	11	1	5.3	1	F	E
49	61.7	1.083	57	41	95	21	0	6.6	0	M	E
50	61.4	1.077	57	38	80	12	0	4.6	0	M	E

Here regression hypothesis is,

H0 : 1 = 2 = · · · = p = 0 Vs H1 : j 0

for at least for at least one j , j = 1,2,......p

Here we use F-statistics.

Coefficient hypothesis :

H0 : j = 0 Vs H1 : j 0

Here we use t-statistics.

All the given questions we are done using MINITAB.

START --> STAT --> Regression --> Regression --> Response : Compa --> predictors : mid point,age, performance rating, service, gender, raise, degree. --> result : select second option --> ok

Output :

Regression Analysis: Compa versus Midpoint, Age, ...

The regression equation is
Compa = 0.940 + 0.00331 Midpoint - 0.00088 Age - 0.00061 Performance Rating
+ 0.00051 Service + 0.0362 Gender + 0.0091 Raise - 0.0133 Degree

Predictor Coef SE Coef T P
Constant 0.9402 0.1136 8.28 0.000
Midpoint 0.0033087 0.0009027 3.67 0.001
Age -0.000883 0.002010 -0.44 0.663
Performance Rating -0.000610 0.001425 -0.43 0.671
Service 0.000508 0.002541 0.20 0.843
Gender 0.03620 0.02550 1.42 0.163
Raise 0.00908 0.01934 0.47 0.641
Degree -0.01328 0.02240 -0.59 0.557

S = 0.0780344 R-Sq = 28.8% R-Sq(adj) = 16.9%

Analysis of Variance

Source DF SS MS F P
Regression 7 0.103243 0.014749 2.42 0.035
Residual Error 42 0.255753 0.006089
Total 49 0.358996

What is the value of the F statistic:

F = 2.42

What is the p-value associated with this value:

Is the p-value < 0.05?

P-value = 0.035

yes P-value < 0.05

reject H0 at 5% level of significance.

C )For each of the coefficients: Intercept, Midpoint, Age, Perf. rating, Service, Gender, Degree

Intercept = 0.940