QUESTION 4 Regression Analysis Guide to marks: 20 marks - 12 for (a), 3 for (b),
ID: 3141312 • Letter: Q
Question
QUESTION 4 Regression Analysis
Guide to marks: 20 marks - 12 for (a), 3 for (b), 3 for (c), 2 for (d)
A training agency is reviewing part of its operations. It runs one scheme whereby young people who are unemployed are put through a training course which provides them with a variety of IT skills including word-processing, spreadsheets, database systems, email and the internet. On completion of the course participants take a standard test and receive a score out of 40.
The agency is trying to assess the wages its trainees receive from the companies they go to work for in relation to the ability test score they received and the number of years of prior relevant experience. The data appear below:
Score/40
Years
Wage ($ )
37
0
1,084
29
1
932
24
2
852
32
1
968
36
1
1,044
27
0
792
31
0
912
22
2
820
38
3
1,292
21
1
724
30
3
900
34
5
1,192
28
0
836
25
1
800
33
2
1,112
35
1
1,080
29
2
892
34
2
924
32
1
968
26
1
864
Wage represents the gross weekly wage ($) of trainees once they have found employment.
Score is the test score received.
Years represent the number of years of relevant job experience.
(a) Using Excel, perform three regression analyses to regress (1) Wages against Score, (2) then against Years, (3) then against both of them simultaneously. Paste your results into Word. State the cost equation from each. Analyse and comment on the results of each regression as you perform it and determine the best one to use as a basis for future use.
(b) If you had to settle for the results of a simple regression, which one would you use and why?
(c) How do you explain the difference between the simple regression results and the multiple regression results?
(d) If the multiple regression were adopted, what would be the predicted Wage for a trainee who had a test score of 30 and had 2 years relevant job experience?
Score/40
Years
Wage ($ )
37
0
1,084
29
1
932
24
2
852
32
1
968
36
1
1,044
27
0
792
31
0
912
22
2
820
38
3
1,292
21
1
724
30
3
900
34
5
1,192
28
0
836
25
1
800
33
2
1,112
35
1
1,080
29
2
892
34
2
924
32
1
968
26
1
864
Explanation / Answer
Score/40
Years
Wage ($ )
37
0
1,084
29
1
932
24
2
852
32
1
968
36
1
1,044
27
0
792
31
0
912
22
2
820
38
3
1,292
21
1
724
30
3
900
34
5
1,192
28
0
836
25
1
800
33
2
1,112
35
1
1,080
29
2
892
34
2
924
32
1
968
26
1
864
Wage represents the gross weekly wage ($) of trainees once they have found employment.
Score is the test score received.
Years represent the number of years of relevant job experience.
(a) Using Excel, perform three regression analyses to regress (1) Wages against Score, (2) then against Years, (3) then against both of them simultaneously. Paste your results into Word. State the cost equation from each. Analyse and comment on the results of each regression as you perform it and determine the best one to use as a basis for future use.
(b) If you had to settle for the results of a simple regression, which one would you use and why?
(c) How do you explain the difference between the simple regression results and the multiple regression results?
(d) If the multiple regression were adopted, what would be the predicted Wage for a trainee who had a test score of 30 and had 2 years relevant job experience?
Score/40
Years
Wage ($ )
37
0
1,084
29
1
932
24
2
852
32
1
968
36
1
1,044
27
0
792
31
0
912
22
2
820
38
3
1,292
21
1
724
30
3
900
34
5
1,192
28
0
836
25
1
800
33
2
1,112
35
1
1,080
29
2
892
34
2
924
32
1
968
26
1
864
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