Regression Analysis Used in Compensation Administration

Formulating a multiple regression model

In linear regression, the y and x variables can be visualized in a two-dimensional scatter plot. In multiple regression where multiple x variables are present, the regression line cannot be visualized in two-dimensional space. However, the various coefficients in the above equation can be easily computed using multiple regression. In multiple regression y is a linear combination of the x variables and you can compute an equation for predicting Compensation from the variables listed above. The table below shows the standardized coefficients of these independent variables obtained through linear multiple regression:

It should be noted that in a simple linear regression (one x variable) the coefficient (slope) is the same as the correlation between x and y while in multiple regression the coefficients will not be the same as the respective correlations between the xs and y. The full equation is then:

Compensation = β₀ + 0.3 x Sales + 0.1 x Profits + 0.05 x Assets + 0.1 x Employees + 0.05 x Sales Experience + 0.05 x Tenure

Unless the coefficients have been standardized, their magnitude should not be viewed as an indicator of how good a predictor is. Dependent and independent variables are often on different scales, which impact the magnitude of the coefficients. Standardizing removes the potential impact of scale differences on coefficient magnitude, allowing for direct comparisons of coefficients. In the above equation, Sales is the best predictor of Compensation because it has the largest standardized coefficient of 0.3.