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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.
The...
This means that ABC is right to be concerned about employees accruing large amounts of vacation days and then not using them. The regression analysis clearly shows that long-tenured employees have no greater tendency to use large quantities of vacation time than employees with a shorter tenure at ABC. Put simply, the problem ABC perceived is quantifiable and not just anecdotal.
Naturally, these results present a new series of challenges for ABC. Extra vacation days, which ABC is using to reward longer-term employees, are perhaps not functioning well as a benefit. Also, perhaps long-term employees tend to be managers and feel uncomfortable taking large amounts of vacation time. Further analysis is needed to determine whether ABC needs to make changes to its vacation policy or take a look at its management culture.
Table 1: Coefficient of determination and raw data r2
Coefficient of Determination
Coefficient of Correlation
Years
Days
Error
Table 2: Scatter plot
Scatter Plot, Regression Line and Regression Equation
Works Cited
Aczel, Amir D. And Sounderpandian, Jayavel. Complete Business Statistics, 6th ed. New…
Works Cited
Aczel, Amir D. And Sounderpandian, Jayavel. Complete Business Statistics, 6th ed. New York: McGraw-Hill/Irwin, 2006.
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