Adjusted R-Squared

The R-Squared value always increases when a term is added to the model, irrespective of whether or not the new model is better than the previous one. With every additional term in the model, the residual Degrees of Freedom (DOF) are reduced by one. Therefore, unless the error Sum of Squares (SS) of the new model is reduced by an amount greater than the previous error Mean Squares (MS), the new model will have a larger error mean square and is therefore not a better model. To overcome this deficiency, the adjusted R-squared value is based on the ratio of model mean square to total mean square.

Values: The adjusted R-squared value is typically smaller than the R-squared value for a given regression model. When the R-squared value is very small, the adjusted R-squared can be a negative number.

Troubleshooting: If the R-squared value is fairly high but the adjusted R-squared value is low, it indicates that some of the terms in the model are not very useful. It also indicates that all the variability in the response data has not been explained by the model. You should examine the terms and make a decision about dropping some terms and adding some new ones. The decision about which terms to drop can be made by looking for terms with low T-values.