The personnel director for a local manufacturing firm has received complaints fr
ID: 158261 • Letter: T
Question
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
9
45.1
1.93
5
10
67.9
4.50
47
11
53.2
2.81
25
12
46.8
3.06
11
13
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
7
18
63.0
4.37
40
19
53.0
2.50
35
20
50.9
2.81
23
21
55.4
3.68
33
22
51.8
3.50
27
23
60.2
3.00
34
24
50.1
2.43
15
Perform a multiple linear regression analysis to predict an employee’s annual salary based upon his or her average performance rating for the past 3 years and his or her years of service using a 95% level of confidence.
Is the statistical significance of the model as a whole acceptable for a 95% level of confidence?
Is the statistical significance of the linear relationship between the dependent variable and each of the independent variables acceptable for a 95% level of confidence?
What is the regression equation for the model?
What is the predicted annual salary for employee number 13 based upon his or her average performance rating for the past 3 years and years of service, and what does the predicted salary value suggest regarding his or her current annual salary?
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
9
45.1
1.93
5
10
67.9
4.50
47
11
53.2
2.81
25
12
46.8
3.06
11
13
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
7
18
63.0
4.37
40
19
53.0
2.50
35
20
50.9
2.81
23
21
55.4
3.68
33
22
51.8
3.50
27
23
60.2
3.00
34
24
50.1
2.43
15
Explanation / Answer
The hypothesis for the problem will be
Ho : salary doesnt dependent over the year of experience and rating
Ha : salary is dependent over years of experience and raring
Y=Y dash +e
A least sqaure regression selects the line with the lowest total sum of sqaured prediction errors
This is called SSE
Now we have to calculate SSR
SST=SSR+SSE
=SIGMA (Y-Y DASH)^2
R^2= SSR/SST
This R^2 will give the values in between 0 and 1
The equation is y=A+beta *x+e
Beta is calculated by delta y/ delta x
So by these formula and equation. You can solve every question.
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