Anova: Adjusted R-Squared

R-squared adjusted for the number of parameters in the model relative to the number of points in the design. A measure of the amount of variation about the mean explained by the model.

\(Adj.\,R^2=1-\left [\left (\frac{SS_{residual}}{df_{residual}} \right)/\left ( \frac{SS_{residual}+SS_{model}}{df_{residual}+df_{model}} \right ) \right ]=1-\left [ \left (\frac{SS_{residual}}{df_{residual}} \right)/\left ( \frac{SS_{total}-SS_{curvature}-SS_{block}}{df_{total}-df_{curvature}-df_{block}} \right ) \right ]\)

The Adjusted R-squared and Predicted R-squared should be within approximately 0.20 of each other to be in “reasonable agreement.” If they are not, there may be a problem with either the data or the model.