Regression (for HR) a Look

Regression (for HR)

A look at the problem

ABC Corp. (an alias) believes it has a problem with the way employees are using vacation time. It seems that employees are accruing large amounts of vacation time and then not using that time or losing it because of company rules regarding how much time an employee can carry. ABC wants to test, through regression analysis, whether this is a legitimate, company-wide problem or whether it is only occurring in isolated cases.

Before we can conduct a regression analysis, it is important to first understand how ABC employees accrue vacation time. When employees first begin their employment at ABC, they accrue vacation time at a rate of two weeks (10 days, or 80 hours) per year. Employees are paid 26 times a year (every two weeks), so they essentially are credited with 3.1 vacation hours per pay period.

Once an employee has been with ABC for five years, that employee will accrue three weeks of vacation time per year (15 days, or 120 hours). That results in an accrual rate of 4.6 hours per pay period. Finally, once employees have been with ABC for 10 years, they accrue vacation time at a rate of four weeks per year (20 days, or 160 hours), or 6.2 hours per pay period. This is the highest rate of vacation time accrual at ABC. Furthermore, although employees are allowed to carry vacation time over from one year to the next, they are not allowed to carry more than four weeks. Anything above four weeks, as of Jan.1 of a new year, is forfeited.

Methodology

ABC believes that its more senior employees, who accrue more vacation time, are not using the vacation time and are, in some cases, losing it. As a first step toward understanding whether this problem is anecdotal or quantifiable, ABC wants to perform a regression analysis that analyzes the length of time an employee has been with ABC vs. how much vacation time that employee takes per year. ABC has 36 employees, 22 of whom have been with the company at least two years. We are only going to consider those 22 employees, as they have had the opportunity to accrue, in theory, at least four weeks of vacation time - enough to lose time under ABC's vacation time policy.

Furthermore, new employees could provide skewed results. An employee who has only been with the company for six weeks will have fewer than 10 hours of vacation time and will likely have taken no time yet. If we took a random sample that was skewed toward new employees, we could get data of limited value. In short, it's the veteran employees, who seem to not be using their vacation time, that are creating the perceived problem.

By taking a regression that analyzes length of tenure vs. vacation time taken in the most recently completed calendar year (2005), we can see if employees are taking more time off as they accrue more vacation days. Our hypothesis is that they are not and that there will be no correlation between length of tenure and time off taken.

The main statistic we will analyze is the coefficient of determination. According to Aczel and Sounderpandian, the coefficient of determination measures the strength of the regression relationship on a scale of zero to 1; the closer the figure is to 1, the stronger the relationship (p.457). As Aczel and Sounderpandian indicate, it is difficult to state definitively how close to 1 our coefficient of determination must be before we declare a strong relationship, but we will use their general rule that a value higher than 0.9 is considered very good; more than 0.8 is good; and more than 0.7 is satisfactory (p.459).

Results

The regression results clearly demonstrate that there is very little correlation between the amount of time an employee has been with ABC and the amount of vacation time that employee takes. The regression yielded a coefficient of determination of 0.0364, which indicates a very weak relationship.