Simple Linear Regression Analysis
As stated earlier in the paper, American employers nowadays are rearranging their firms’ policies to meet the needs, wants, and expectations of their customers by satisfying employees. Since workers constitute the firms’ important and valuable resource, their performance and productivity directly relate to the quality of the products or services the company provides, or to the speed of delivery of these products or services. Some experts claim that freedom to choose days off, for whatever reason, has a positive effect on employees’ overall productivity in long term. In this simple linear regression analysis, our group will put all effort to determine whether there really is a correlation between paid-time-off and employee productivity. (All the calculations and the graph are presented in the Excel file.)
With the two small sets of data, both comprising 20 observations each, we are going to determine the correlation coefficient of these data sets, and measure the strength of this simple linear regression model. The first data set represents the quantity of paid days off in banks of ten groups of employees, starting from 11 days and up to 30 days. This is the predictor variable of this simple regression model. The dependent variable is the total productivity of each of the twenty groups of employees during three months measured in sales they generate (in thousands of dollars). So, the sales of the ten groups in thousands of dollars were 20.9, 22, 23.1, 22.7, 30.7, 33, 35.6, 35.3, 36.3, 38.2, 38.5, 40.4, 40.2, 41.8, 42.3, 42, 42.7, 43.6, 44.1, and 45.4. Since we want to test whether there is a relationship between the two sets of data, our null hypothesis is "no linear relationship exists between paid days off and productivity", and our alternative hypothesis is "the relationship between paid days off and productivity of employees does exist." That is, H0:ρ=0; and Hf:ρ≠0, where ρ is the correlation coefficient of the entire population. We are using standard significance level, α=0.5. The test statistic is t with n-2 degrees of freedom, which is equal to r/√[(1-r2)/(n-2)], where r is the correlation coefficient of the sample, and n is the sample size. The table value of t0.25; 18df equals 2.101. The computed value of t* is 6.31. Because the computed value is greater than the tabular value, we reject the null hypothesis.
The outcome of the test is, truly paid-time-off does influence employee productivity. Moreover, the more paid days off the organization offers to the group, the higher the separate group’s productivity (measured in thousands of dollars in sales). The correlation of the two data sets is very high, 0.83. Those who had 11 through 14 paid days off in their banks made approximately $26,000, while the groups that had 27 through 30 paid days off made $42,000 on average. Thus, if the workers have paid days off in their banks, and they can plan their leaves, this highly influences their productivity in a positive way. The more freedom they get, the more productive they become.
The significance level α was 0.5 in our test, which means that we could have made an error in our analysis with a 5% probability. In other words, there is a little probability that our analysis is erroneous and there really is no significant evidence to believe that paid-time-off directly influences employee productivity.
Another limitation of this simple linear regression analysis is that according to the model, the more paid days off employees have the higher will be the productivity. This is of course wrong, because with 365 paid days off workers simply would not work at all, while the model suggests that their productivity would skyrocket. With the help of this model we could predict the productivity of workers if they were given 35, 37, 40 and so on days off, but first, these values would only be approximate, and secondly, there is a single point somewhere between 30 days and 365 days after which actual productivity would begin to decrease.
The organization can utilize the inferences of our simple regression analysis, and provide all employees with 30 paid days off. Although there are some limitations in our analysis, and some disadvantages of paid-time-off, the system proved to be very effective in terms of long term employee productivity.
Bibliography
1. Pavur, R. and Kvanli, A. (1992). Correlation and Simple Linear Regression. Introduction to Business Statistics. St. Paul, West Publishing Company.
2. Reh, J. (2005). Sick Leave vs. Paid Time Off (PTO). Management. About.com. Web-site: http://management.about.com/ od/conflictres/a/SickLvPTO1104.htm