The SURVEYREG Procedure

Multiple R-Square

PROC SURVEYREG computes a multiple R-square for the weighted regression as

\[ R^2=1-\frac{\mbox{SS}_\mathit {error}}{\mbox{SS}_\mathit {total}} \]

where $\mr{SS}_\mathit {error}$ is the error sum of squares in the ANOVA table

\[ \mbox{SS}_\mathit {error} = \mb{r'Wr} \]

and $\mr{SS}_\mathit {total}$ is the total sum of squares

\[ \mbox{SS}_{\mathit{total}} = \left\{ {\begin{array}{ll} \mb{y'Wy} & \mbox{if no intercept}\\ \mb{y'Wy}- \displaystyle {\left(\sum _{h=1}^ H \sum _{i=1}^{n_ h} \sum _{j=1}^{m_{hi}}w_{hij}y_{hij}\right)^2 / ~ w_{\cdot \cdot \cdot } } & \mbox{otherwise} \end{array} } \right. \]

where $w_{\cdot \cdot \cdot }$ is the sum of the sampling weights over all observations.