The personnel director for a local manufacturing firm has received complaints from the employees in a certain shop regarding what they perceive to be inequities in the annual salary for employees who have similar performance ratings, years of service and relevant certifications. The personnel director believes that an employee's pay in this particular shop should be positively correlated to their prior performance rating, years of service and relevant certifications. The personnel director has collected the data shown in the following table pertaining to the employees within the shop.
|
Employee
|
Current Annual Salary
(Thousands)
|
Average Performance Rating for Past 3 Years
(5 point scale)
|
Years of Service
|
Number of Relevant Certifications
|
|
1
|
48.2
|
2.18
|
9
|
6
|
|
2
|
55.3
|
3.31
|
20
|
6
|
|
3
|
53.7
|
3.18
|
18
|
7
|
|
4
|
61.8
|
3.62
|
33
|
7
|
|
5
|
56.4
|
2.62
|
31
|
8
|
|
6
|
52.5
|
3.75
|
13
|
6
|
|
7
|
54.0
|
4.25
|
25
|
6
|
|
8
|
55.7
|
3.43
|
30
|
4
|
|
9
|
45.1
|
1.93
|
5
|
6
|
|
10
|
67.9
|
4.5
|
47
|
8
|
|
11
|
53.2
|
2.81
|
25
|
5
|
|
12
|
46.8
|
3.06
|
11
|
6
|
|
13
|
58.3
|
5
|
23
|
8
|
|
14
|
59.1
|
4.06
|
35
|
7
|
|
15
|
57.8
|
4.12
|
39
|
5
|
|
16
|
48.6
|
2.31
|
21
|
4
|
|
17
|
49.2
|
3.87
|
7
|
6
|
|
18
|
63.0
|
4.37
|
40
|
7
|
|
19
|
53.0
|
2.5
|
35
|
6
|
|
20
|
50.9
|
2.81
|
23
|
4
|
|
21
|
55.4
|
3.68
|
33
|
5
|
|
22
|
51.8
|
3.5
|
27
|
4
|
|
23
|
60.2
|
3
|
34
|
8
|
|
24
|
50.1
|
2.43
|
15
|
5
|
The personnel director is interested in creating a linear regression model that can be used to estimate the annual salary an employee might expect to receive based upon his or her past performance, years of service and/or number of relevant certifications. The regression model will be used as a basis for determining whether or not there is any validity to the employees' complaints regarding salary inequities.
Perform each of the following seven regression analyses using a 95% confidence level.
- Annual salary vs. average performance rating for the past 3 years and number of relevant certifications
- Annual salary vs. years of service and number of relevant certifications
- Annual salary vs. average performance rating for the past 3 years, years of service and number of relevant certifications