Absenteeism: Absenteeism can be a serious employment problem. It is estimated that absenteeism reduces potential output by more than 10%. Two economists launched a research project to learn more about the problem. They randomly selected 100 organizations to participate in a 1-year study. For each organization, they recorded the average number of days absent per employee and several variables thought to affect absenteeism. Management’s goal here is to analyze the data and determine which factors may be helpful in predicting absenteeism. Now let us build a model to predict absenteeism based on key independent variables available in this dataset; wage, PctPT, PctU, Av Shift and U/MRel. Correlation matrix is provided below. Why are the variables AvShift and U/MRel excluded from this correlation matrix? Which variable in the matrix is likely to provide the best simple linear regression model and why? Does the correlation matrix show any evidence of collinearity? Explain. Data: Wage Pct PT Pct U Av Shift U/M Rel Absent 22477 8.5 57.1 1 1 5.4 29939 1.9 41.5 0 1 4.1 22957 12.2 52.6 1 0 11.5 18888 30.8 65.1 0 1 2.1 15078 6.8 68.8 0 1 5.9 15481 5.1 46.4 0 0 12.9 21481 25.3 38.9 0 1 3.5 29687 9.2 17.2 0 0 2.6 13603 8.4 12.9 0 0 8.6 18303 4.9 18.1 0 1 2.7 20832 23.8 64.4 1 1 6.6 22325 24.1 63.7 1 1 2.1 19964 8.6 12.2 0 1 3.8 32496 5.9 11.8 1 0 4.3 15795 2.9 25.8 0 1 4.3 21138 24.3 53.2 0 0 2.2 18859 20.6 22.8 1 1 8.6 12023 9 49.8 1 1 10.8 33272 24 39.1 1 0 2.9 22325 11.9 32.6 1 0 5.3 26147 0 67.7 1 0 8.2 33229 11.7 10.8 0 0 2.8 37970 14.6 25.5 1 1 2.4 15281 27.2 31.8 0 0 2.8 19423 17.2 35 1 1 5 26587 13.9 41.9 1 1 9.5 22963 2.6 52.9 0 1 4.3 26404 6.4 64.4 0 1 8.9 16315 4.9 69.7 0 1 7.2 26759 23.2 61.8 1 1 5.6 30824 13.2 52.1 0 1 2.4 31979 27.7 57.4 1 1 2.7 23135 7 15.2 0 0 13.4 18014 0 38.7 1 0 14.8 18541 13.8 69.4 1 1 10.7 16747 9.9 67.2 1 0 10.3 13473 6.3 47.8 0 1 4.6 42986 13.4 24.5 1 0 3.9 23964 8.8 79.4 1 0 13.3 30794 0.4 12.1 1 0 2.2 21104 14.7 71 0 1 5.7 19137 7.7 28 1 0 11.8 26058 7.3 45.6 0 1 2.5 22085 6.8 25.4 0 1 2.1 29044 8.6 40.6 0 0 4.1 24205 19.6 25.1 1 1 4.9 17698 10.8 42.3 1 1 7.7 26399 4.5 63.3 1 1 6.3 40590 15.9 69.4 1 1 2.9 24805 5.7 17.7 1 1 2.6 18899 13.1 54.8 1 1 6.1 26802 15.5 46.5 0 1 6 30034 11.8 53.2 1 0 6.7 15713 16.6 41.2 1 0 11.9 18280 6.4 65 1 1 9.3 41009 6.7 54.9 0 1 3.6 24021 14 20.6 1 1 2.6 21836 27.6 29 0 1 2.1 21157 5.5 50.2 1 1 9 19529 14.5 56.6 1 0 11 31240 26.3 36.4 1 1 2.9 20963 0 0 1 1 2.2 33826 8.2 87.9 0 1 3.3
Absenteeism: Absenteeism can be a serious employment problem. It is estimated that absenteeism reduces potential output by more than 10%. Two economists launched a research project to learn more about the problem. They randomly selected 100 organizations to participate in a 1-year study. For each organization, they recorded the average number of days absent per employee and several variables thought to affect absenteeism. Management’s goal here is to analyze the data and determine which factors may be helpful in predicting absenteeism. Now let us build a model to predict absenteeism based on key independent variables available in this dataset; wage, PctPT, PctU, Av Shift and U/MRel. Correlation matrix is provided below. Why are the variables AvShift and U/MRel excluded from this correlation matrix? Which variable in the matrix is likely to provide the best simple linear regression model and why? Does the correlation matrix show any evidence of collinearity? Explain. Data: Wage Pct PT Pct U Av Shift U/M Rel Absent 22477 8.5 57.1 1 1 5.4 29939 1.9 41.5 0 1 4.1 22957 12.2 52.6 1 0 11.5 18888 30.8 65.1 0 1 2.1 15078 6.8 68.8 0 1 5.9 15481 5.1 46.4 0 0 12.9 21481 25.3 38.9 0 1 3.5 29687 9.2 17.2 0 0 2.6 13603 8.4 12.9 0 0 8.6 18303 4.9 18.1 0 1 2.7 20832 23.8 64.4 1 1 6.6 22325 24.1 63.7 1 1 2.1 19964 8.6 12.2 0 1 3.8 32496 5.9 11.8 1 0 4.3 15795 2.9 25.8 0 1 4.3 21138 24.3 53.2 0 0 2.2 18859 20.6 22.8 1 1 8.6 12023 9 49.8 1 1 10.8 33272 24 39.1 1 0 2.9 22325 11.9 32.6 1 0 5.3 26147 0 67.7 1 0 8.2 33229 11.7 10.8 0 0 2.8 37970 14.6 25.5 1 1 2.4 15281 27.2 31.8 0 0 2.8 19423 17.2 35 1 1 5 26587 13.9 41.9 1 1 9.5 22963 2.6 52.9 0 1 4.3 26404 6.4 64.4 0 1 8.9 16315 4.9 69.7 0 1 7.2 26759 23.2 61.8 1 1 5.6 30824 13.2 52.1 0 1 2.4 31979 27.7 57.4 1 1 2.7 23135 7 15.2 0 0 13.4 18014 0 38.7 1 0 14.8 18541 13.8 69.4 1 1 10.7 16747 9.9 67.2 1 0 10.3 13473 6.3 47.8 0 1 4.6 42986 13.4 24.5 1 0 3.9 23964 8.8 79.4 1 0 13.3 30794 0.4 12.1 1 0 2.2 21104 14.7 71 0 1 5.7 19137 7.7 28 1 0 11.8 26058 7.3 45.6 0 1 2.5 22085 6.8 25.4 0 1 2.1 29044 8.6 40.6 0 0 4.1 24205 19.6 25.1 1 1 4.9 17698 10.8 42.3 1 1 7.7 26399 4.5 63.3 1 1 6.3 40590 15.9 69.4 1 1 2.9 24805 5.7 17.7 1 1 2.6 18899 13.1 54.8 1 1 6.1 26802 15.5 46.5 0 1 6 30034 11.8 53.2 1 0 6.7 15713 16.6 41.2 1 0 11.9 18280 6.4 65 1 1 9.3 41009 6.7 54.9 0 1 3.6 24021 14 20.6 1 1 2.6 21836 27.6 29 0 1 2.1 21157 5.5 50.2 1 1 9 19529 14.5 56.6 1 0 11 31240 26.3 36.4 1 1 2.9 20963 0 0 1 1 2.2 33826 8.2 87.9 0 1 3.3
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 93E
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Absenteeism: Absenteeism can be a serious employment problem. It is estimated that absenteeism reduces potential output by more than 10%. Two economists launched a research project to learn more about the problem. They randomly selected 100 organizations to participate in a 1-year study. For each organization, they recorded the average number of days absent per employee and several variables thought to affect absenteeism. Management’s goal here is to analyze the data and determine which factors may be helpful in predicting absenteeism.
Now let us build a model to predict absenteeism based on key independent variables available in this dataset; wage, PctPT, PctU, Av Shift and U/MRel.
Why are the variables AvShift and U/MRel excluded from this correlation matrix?
Which variable in the matrix is likely to provide the best simple linear regression model and why?
Does the correlation matrix show any evidence of collinearity? Explain.
Data:
| Wage | Pct PT | Pct U | Av Shift | U/M Rel | Absent |
| 22477 | 8.5 | 57.1 | 1 | 1 | 5.4 |
| 29939 | 1.9 | 41.5 | 0 | 1 | 4.1 |
| 22957 | 12.2 | 52.6 | 1 | 0 | 11.5 |
| 18888 | 30.8 | 65.1 | 0 | 1 | 2.1 |
| 15078 | 6.8 | 68.8 | 0 | 1 | 5.9 |
| 15481 | 5.1 | 46.4 | 0 | 0 | 12.9 |
| 21481 | 25.3 | 38.9 | 0 | 1 | 3.5 |
| 29687 | 9.2 | 17.2 | 0 | 0 | 2.6 |
| 13603 | 8.4 | 12.9 | 0 | 0 | 8.6 |
| 18303 | 4.9 | 18.1 | 0 | 1 | 2.7 |
| 20832 | 23.8 | 64.4 | 1 | 1 | 6.6 |
| 22325 | 24.1 | 63.7 | 1 | 1 | 2.1 |
| 19964 | 8.6 | 12.2 | 0 | 1 | 3.8 |
| 32496 | 5.9 | 11.8 | 1 | 0 | 4.3 |
| 15795 | 2.9 | 25.8 | 0 | 1 | 4.3 |
| 21138 | 24.3 | 53.2 | 0 | 0 | 2.2 |
| 18859 | 20.6 | 22.8 | 1 | 1 | 8.6 |
| 12023 | 9 | 49.8 | 1 | 1 | 10.8 |
| 33272 | 24 | 39.1 | 1 | 0 | 2.9 |
| 22325 | 11.9 | 32.6 | 1 | 0 | 5.3 |
| 26147 | 0 | 67.7 | 1 | 0 | 8.2 |
| 33229 | 11.7 | 10.8 | 0 | 0 | 2.8 |
| 37970 | 14.6 | 25.5 | 1 | 1 | 2.4 |
| 15281 | 27.2 | 31.8 | 0 | 0 | 2.8 |
| 19423 | 17.2 | 35 | 1 | 1 | 5 |
| 26587 | 13.9 | 41.9 | 1 | 1 | 9.5 |
| 22963 | 2.6 | 52.9 | 0 | 1 | 4.3 |
| 26404 | 6.4 | 64.4 | 0 | 1 | 8.9 |
| 16315 | 4.9 | 69.7 | 0 | 1 | 7.2 |
| 26759 | 23.2 | 61.8 | 1 | 1 | 5.6 |
| 30824 | 13.2 | 52.1 | 0 | 1 | 2.4 |
| 31979 | 27.7 | 57.4 | 1 | 1 | 2.7 |
| 23135 | 7 | 15.2 | 0 | 0 | 13.4 |
| 18014 | 0 | 38.7 | 1 | 0 | 14.8 |
| 18541 | 13.8 | 69.4 | 1 | 1 | 10.7 |
| 16747 | 9.9 | 67.2 | 1 | 0 | 10.3 |
| 13473 | 6.3 | 47.8 | 0 | 1 | 4.6 |
| 42986 | 13.4 | 24.5 | 1 | 0 | 3.9 |
| 23964 | 8.8 | 79.4 | 1 | 0 | 13.3 |
| 30794 | 0.4 | 12.1 | 1 | 0 | 2.2 |
| 21104 | 14.7 | 71 | 0 | 1 | 5.7 |
| 19137 | 7.7 | 28 | 1 | 0 | 11.8 |
| 26058 | 7.3 | 45.6 | 0 | 1 | 2.5 |
| 22085 | 6.8 | 25.4 | 0 | 1 | 2.1 |
| 29044 | 8.6 | 40.6 | 0 | 0 | 4.1 |
| 24205 | 19.6 | 25.1 | 1 | 1 | 4.9 |
| 17698 | 10.8 | 42.3 | 1 | 1 | 7.7 |
| 26399 | 4.5 | 63.3 | 1 | 1 | 6.3 |
| 40590 | 15.9 | 69.4 | 1 | 1 | 2.9 |
| 24805 | 5.7 | 17.7 | 1 | 1 | 2.6 |
| 18899 | 13.1 | 54.8 | 1 | 1 | 6.1 |
| 26802 | 15.5 | 46.5 | 0 | 1 | 6 |
| 30034 | 11.8 | 53.2 | 1 | 0 | 6.7 |
| 15713 | 16.6 | 41.2 | 1 | 0 | 11.9 |
| 18280 | 6.4 | 65 | 1 | 1 | 9.3 |
| 41009 | 6.7 | 54.9 | 0 | 1 | 3.6 |
| 24021 | 14 | 20.6 | 1 | 1 | 2.6 |
| 21836 | 27.6 | 29 | 0 | 1 | 2.1 |
| 21157 | 5.5 | 50.2 | 1 | 1 | 9 |
| 19529 | 14.5 | 56.6 | 1 | 0 | 11 |
| 31240 | 26.3 | 36.4 | 1 | 1 | 2.9 |
| 20963 | 0 | 0 | 1 | 1 | 2.2 |
| 33826 | 8.2 | 87.9 | 0 | 1 | 3.3 |
| 23349 | 0 | 38.5 | 1 | 1 | 5.9 |
| 22695 | 25.4 | 47 | 1 | 1 | 4 |
| 30475 | 0 | 69.3 | 1 | 0 | 10.8 |
| 16631 | 5.9 | 48.2 | 1 | 1 | 7.1 |
| 28996 | 18.6 | 29.3 | 1 | 1 | 2.9 |
| 15807 | 16.9 | 42.9 | 1 | 1 | 6.2 |
| 15585 | 0 | 59.4 | 1 | 0 | 10.3 |
| 18466 | 9 | 69.4 | 1 | 0 | 13.5 |
| 35140 | 21.1 | 37.1 | 1 | 1 | 6.7 |
| 33459 | 14.1 | 19.5 | 1 | 1 | 2.6 |
| 24357 | 0 | 21.5 | 1 | 1 | 5.2 |
| 19370 | 3.7 | 35 | 1 | 1 | 7.2 |
| 21820 | 6.3 | 0 | 1 | 1 | 3.5 |
| 23351 | 12.3 | 27.1 | 1 | 1 | 5.4 |
| 22938 | 6.8 | 68.5 | 1 | 1 | 5.8 |
| 16477 | 10 | 61.5 | 1 | 1 | 11.7 |
| 20790 | 28.5 | 59.9 | 1 | 0 | 5.6 |
| 20352 | 19.4 | 34.6 | 1 | 0 | 4.6 |
| 19743 | 14.3 | 39.7 | 1 | 0 | 8.6 |
| 22775 | 10.3 | 35.7 | 1 | 1 | 2.1 |
| 24229 | 0.9 | 26.7 | 1 | 0 | 9.6 |
| 41195 | 8.6 | 66.7 | 1 | 0 | 4 |
| 23143 | 4.2 | 63.1 | 0 | 1 | 10.6 |
| 13400 | 28.1 | 46.7 | 0 | 0 | 5.8 |
| 21371 | 14.9 | 78.9 | 1 | 0 | 7.4 |
| 28675 | 7.7 | 63.4 | 0 | 0 | 10.3 |
| 18171 | 6.9 | 47.9 | 0 | 1 | 6.3 |
| 23670 | 20.5 | 46.3 | 1 | 1 | 6.7 |
| 29745 | 6.1 | 53.9 | 1 | 0 | 6.7 |
| 14672 | 13.9 | 46 | 1 | 0 | 13.3 |
| 20382 | 0 | 38.6 | 1 | 1 | 4.1 |
| 24952 | 14.6 | 53.8 | 0 | 1 | 4.6 |
| 28878 | 7.4 | 12.2 | 1 | 1 | 2.7 |
| 24558 | 24.5 | 37 | 1 | 1 | 8 |
| 20447 | 0.9 | 27.4 | 1 | 1 | 4.2 |
| 27714 | 8.7 | 58.1 | 0 | 0 | 9 |
| 18116 | 3.5 | 47.5 | 1 | 1 | 7.7 |
Transcribed Image Text:Wage
Pct PT
Pct U
Absent
Wage
Pct PT
0.0375
1
Pct U
-0.0416
0.0913
1
Absent
-0.3989
-0.2527
0.3379
1
Transcribed Image Text:Column 1, Wage:
Average employee wage
Column 2, Pct PT:
Percentage of part-time employees
Column 3, Pct U :
Percentage of unionized employees
Column 4: Av Shift : Availability of shiftwork
1= Yes
0 = No
Column 5: U/M Rel : Union-management relationship
1= good 0 = Not good
Column 6: Absent: Average number of days absent per employee
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