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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 and years of service. 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
1
48.2
2.18
9
2
55.3
3.31
20
3
53.7
3.18
18
4
61.8
3.62
33
5
56.4
2.62
31
6
52.5
3.75
13
7
54.0
4.25
25
8
55.7
3.43
30
45.1
1.93
10
67.9
4.50
47
11
53.2
2.81
12
46.8
3.06
58.3
5.00
23
14
59.1
4.06
35
15
57.8
4.12
39
16
48.6
2.31
21
17
49.2
3.87
63.0
4.37
40
19
53.0
2.50
50.9
55.4
3.68
22
51.8
3.50
27
60.2
3.00
34
24
50.1
2.43
Hint: For the purposes of this homework assignment, the minimum difference between the R2 or Adjusted R2 values for two acceptable regression models that would favor selecting a model with a larger number of independent variables is 0.05.
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