R Square

Definition

In multiple linear regression, R square indicates how well a particular combination of X variables (the model drivers or independent variables) explains the variation in Y (the dependent variable).

R square ranges in value from 0 to 1. A value of 0 means that the multiple linear regression model does nothing to explain the variation in Y. A value of 1 means that the model is a perfect fit. A value of 0.9 or more indicates an acceptable model.

R square is also known as the coefficient of determination or measure of goodness-of-fit.

It is defined as

where the total sum of squares is

When comparing two models with this measure, make sure you use the same dependent variable.

R square is a nondescending function of the number of explanatory variables present in the model; that is, as you add more historical data and as you add more explanatory variables (X's), R square almost always increases and never decreases. This is because the addition of explanatory variables to the model causes prediction errors to be small.