Regression Analysis Used in Compensation Administration

Multiple R Square

R² is the same measure that was talked about in the Correlation section (page 7) with the exception that it involves multiple independent variables. It is also called the coefficient of determination. R² tells you how successful the predictors were at explaining the variation in the dependent variable. From the Summary Output, you can see that R² is approximately 0.21. This means that Sales, Profits, Assets, Employees, Sales Experience, and Tenure explained approximately 21% of the variability in Compensation.

Depending on your objective using the regression equation, different levels of R² are sufficient to determine the effectiveness of your regression model. If the purpose of your regression model is to predict, you would want a higher R², in the order of 0.8. If the purpose of your regression model is to examine relationships between the dependent and independent variables, an R² in the order of 0.2 would be sufficient.

F statistic

The F statistic measures the fitness of the entire regression equation.

In order to test this null hypothesis, you look at the F statistic and its associated probability in the second table from the ANOVA output. In this case, the F statistic is 0.7848 with a probability (significance) of 0.593. Generally speaking, you are looking for significance values less than .05 in order to reject the null hypothesis. You can also compare the F statistic to a critical F value obtained from F tables in a textbook or online. For this situation 8 as is the critical F value. If the F statistic from the regression output is larger than the critical F value of 8, we reject the null hypothesis. We can then conclude at least one of our predictors is significant.

In this case, we cannot reject the null hypothesis because the significance of the F statistic is not less than .05 (or the F value is less than the critical F value of 8). That means our model as a whole is not a good predictor of compensation.