\begin{Schunk}
\begin{Sinput}
 pmr1 <- aggregate(predict(modr1), by=list(region=modr1$model$region), mean)
 pmr2 <- aggregate(predict(modr2), by=list(region=modr2$model$region), mean)
 pmr3 <- aggregate(predict(modr3), by=list(region=modr3$model$region), mean)
\end{Sinput}
\end{Schunk}
