Quantitative Analysis for Management, 13/e

4.9 Model Building

In developing a good regression model, possible independent variables are identified and the best ones are selected to be used in the model. The best model is a statistically significant model with a high $r^2$ and few variables.

The value of r² can never decrease when more variables are added to the model.

The adjusted r² may decrease when more variables are added to the model.

As more variables are added to a regression model, $r^2$ will usually increase, and it cannot decrease. It is tempting to keep adding variables to a model to try to increase $r^2.$ However, if too many independent variables are included in the model, problems can arise. For this reason, the adjusted $r^2$ value is often used (rather than $r^2$) to determine if ...