I am on the learning curve with Grass7. I managed to make r.regression.multi work, but there is one thing that would be of high interest for me: it is possible to create a new raster showing the results (residuals) of the analysis in a new raster? This would enable me to nicely locate the areas with high residuals.
The command delivers overall statistics including AIC etc. (results are identical to R) as well as a "residuals" map. I have added this in the manual page.