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 The following down below is the correlation matrix between absenteeism and potential independent variables. 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.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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
The following down below is the
- 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 |
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