Lab 12 - Geographically Weighted Regression

This week's lab wrapped up a 3-week exploration into the use of regression; the focus for this week was specifically using geographically weighted regression. 

Geographically weighted regression (GWR) is different from using a regular regression method like ordinary least squares (OLS) in that it takes into account the spatial difference between the variables, as well as the variables themselves.  Each set of variables is then weighted according to its position near or away from the other variables (and, incidentally, the nearer something is the more likely it is to have a higher weight - because it's more likely to be related to the other variables).

For the final part of our lab we had to compare an OLS model with a GWR model - all using the same variable inputs, of course.  Using the rate of hit-and-run counts as my dependent variable I then compared four other neighborhood statistics (such as percentage of renter occupied units) against the hit-and-run crime rate.

Unfortunately in my case I did not observe much of a change between the two regression models, although I have a fairly good idea of why that may have been - I had two variables that probably were too similar to each other and so one should have been dropped (a variable for the percentage of renter occupied units and a separate variable for median home value).  Neither of these variables set off any colinearity alarms during the OLS stage (the VIF statistic provided with the ArcGIS OLS results would have shown me that), but something was clearly amiss.  When comparing my AIC, Adjusted R-square, and z-score results between the GWR and the OLS models it was clear that any changes between the two were not very significant.  Considering my overall low Adjusted R-square values between the two models (both were at 0.189) it's back to the drawing board in terms of choosing variables for my model.