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Apparently, there is a GWR function in R. I have not applied it myself, so I have no idea if it can be applied to rasters, but I did find this document for the command in R: http://cran.r-project.org/web/packages/spgwr/vignettes/GWR.pdf and this GWR python library: https://github.com/mkordi/pygwr


You might find CrimeStat useful for this: http://www.icpsr.umich.edu/CrimeStat/


As the comments (mainly by @Wes and @Michelle) ultimately conflate to answer the question, here is a summary: The ArcGIS Manual notes that the Geographically Weighted Regression (GWR) is not suitable for categorial/binary variables: Dependent and Explanatory variables should be numeric fields containing a variety of values. Linear regression methods, ...


You should look into variograms (look in the documentation under kriging). The variogram indicates the level of cross-correlation between observed features. If you plot the variogram you see it rising rapidly, then tapering off to level (the so-called sill). That would give you a quantitative indication of your "optimal distance". Quite possibly, though, you ...

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