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.