Assignment: Correlation and Regression
A human resources (HR) manager wants to know if annual performance review scores can be predicted by the number of vacation days taken during the year and the number of dependents an employee claims. She randomly pulls the vacation, W-2, and performance review records of twenty employees. The data is presented below.
| Employee |
Number of Vacation Days Taken |
Number of Dependents |
Overall Performance Rating (from 1 [lowest] to 4 [highest]) |
| 1 |
10 |
2 |
2.9 |
| 2 |
12 |
3 |
2.4 |
| 3 |
10 |
4 |
2 |
| 4 |
15 |
2 |
2.3 |
| 5 |
14 |
3 |
3.2 |
| 6 |
12 |
5 |
1.9 |
| 7 |
13 |
1 |
3.4 |
| 8 |
15 |
3 |
2.1 |
| 9 |
16 |
2 |
2.9 |
| 10 |
14 |
3 |
2.4 |
| 11 |
13 |
4 |
2 |
| 12 |
12 |
2 |
2.3 |
| 13 |
11 |
3 |
3.2 |
| 14 |
10 |
5 |
1.9 |
| 15 |
13 |
1 |
3.4 |
| 16 |
13 |
3 |
2.1 |
| 17 |
14 |
2 |
2.9 |
| 18 |
18 |
3 |
3.4 |
| 19 |
17 |
4 |
3 |
| 20 |
14 |
0 |
3.3 |
Using the above data, run a correlation matrix and then run a regression analysis in Microsoft Excel that will answer the human resources (HR) manager's question. Examine the results and consider the implications. Write a 3- to 4-page paper based on the results and implications. Make sure to include your data printout and justify your responses. In your paper, address the following questions:
• Identify the R-squared value for this data set, along with the R-value. Explain what each means.
• Describe what the F-test and the p value tell us in general and name each for these data sets and analyses.
• Explain what can be learned from the multiple regression that may not be known from the correlation matrix.
• Justify whether performance review scores can be predicted by the number of days of vacation taken, dependents claimed, or vacation days taken in combination with the number of dependents. Support your position.
• Describe any potential ethical or legal concerns related to this research. Provide a rationale backed by authoritative references to support your position.