Regression Analysis Used in Compensation Administration

Interpreting ANOVA (Analysis of Variance) Outputs

There are several available software products that will model a regression equation for you. When these software applications are used, the output often comes in a standard ANOVA format. Use this sample ANOVA output as a reference in this and the next few sections.

There are several components that a regression output will give you. Only a few are essential to your analysis. Those important components are in bold in the sample ANOVA output.

Writing the Regression Equation From the Output

Although the regression output does not give you the overall regression equation, it gives out all the information that you would need to write the regression equation yourself.

Remember the basic form of a regression equation:

y = β₀ + β₁x₁ + β₂x₂ + ... + β_kx_k + ε

y is the dependent variable, in this case, it is Compensation.

β₀ is the y-intercept, in this case, it is equal to 20,951.14 (from the first line of the third table labeled Intercept from the ANOVA output)

β₁, β₂, etc., are coefficients of their respective variable. In this case:

β₁ equals 0.0450, which is the coefficient of the Sales variable
β₂ equals -0.00034, which is the coefficient of the Profits variable
β₃ equals -7.2^-5, which is the coefficient of the Assets variable
β₄ equals -0.0303, which is the coefficient of the Employees variable
β₅ equals -65.8086, which is the coefficient of the Sales Experience variable
β₆ equals -22.3804, which is the coefficient of the Tenure variable

The overall regression equation is:

Note: This example appears to have random assignment of signs. For example, tenure, profits and assets are known to be good predictors of compensation; however, they all have negative signs in front of them, indicating that as compensation goes up, these factors go down. In fact, this equation shows the limitations of working with small samples. When analyzing data, be sure to use large samples from multiple sources.

In the above equation, these factors and the large standard error imply that collinearity might exist.

Collinearity

In multiple regression, because multiple variables are used, in most cases, there is inter-correlation between the variables. Collinearity occurs when independent variables are so highly correlated that their individual contribution to the dependent variable is hard to determine. Collinearity does not affect the ability of the overall regression equation to predict the dependent variable. Collinearity does affect your ability to estimate the individual coefficients. Collinearity may exist when the following are present from your ANOVA output:

• Regression coefficients change dramatically when certain variables are added or removed from the regression model.
• Large standard errors.
• Independent variables that are highly correlated and therefore are good predictors of the dependent variable may have coefficients that are insignificant.
• Collinear variables may have large coefficients with apparently randomly assigned signs.

If you suspect that collinearity exists, choose your predictors carefully when setting up your regression model. There are techniques to assess the level of collinearity present (such as variance inflation factors, VIFs); however, this can get highly technical.

Collinearity is addressed by trial-and-error testing of the different predictors.