Regression Analysis Used in Compensation Administration

Multiple Regression

Linear regression allows you to predict the value of y given x. One variable allows you to reach a conclusion about another because of correlation and an estimate of its size by an equation. Multiple regression represents the same concept using more than one variable x to predict y. Often, salary level depends on more than one factor. Multiple regression allows you to make predictions based on several factors. The figure below depicts multiple regression:

In the figure above, Sales, Profits, Assets, Employees, Sales Experience, Tenure are all x variables or predictors used in a regression formula to predict the y variable, Compensation.

Multiple Regression Model

Multiple regression can be expressed mathematically as:

y = β₀ + β₁X₁ + β₂X₂ + ... + β_kX_k + ε

In multiple regression:

• y is the predicted value of the dependent variable
• β₁X₁ where the value of the regression coefficient β₁ determines the contribution of the first independent variable x₁ to the regression line, given that the other x variables are held constant
• β₀ is the y-intercept
• ε is the model error

Using the above illustration, compensation can be written as:

Compensation = β₀ + β₁Sales + β₂Profits + β₃Assets + β₄Employees + β₅Sales Experience + β₆Tenure

Each of the coefficients in front of the independent variables determines how much that independent variable contributes (holding all other variables constant) to the overall regression equation in determining compensation.