Geographically Weighted Regression (GWR) vs. Ordinary Least Squares (OLS)

If one is attempting to find any kind of statistically significant relationship between spatial variables, one might use a local Geographically Weighted Regression (GWR) model, which would attempt to demonstrate that change in one variable promotes a significant amount of change in another.  Alternatively, if one were looking to see if two or more variables were correlated, or just related to one another, it might be appropriate to use a global Ordinary Least Squares (OLS) model.  Both of these statistical models are specific to spatial analysis, as this type of modelling requires a slightly different perspective on the phenomena being modelled- illustrated conveniently with the spatial autocorrelation assumption inherent in Waldo Tobler's famous quote "Everything is related to everything else, but near things are more related than distant things."

GWR, by definition, involves regression- the modelling of the relationship between dependent and independent variables.  Regular statistical regression needn't take into account variables like spatial distribution and physical proximity, though, and thus the addition of "geographically weighted." OLS, on the other hand, involves simpler methods of correlation.  When two variables have a statistically significant relationship, that correlation found from running the OLS model can be used to justify performing further GWR analysis.  The appropriate model to use for spatial variables depends upon the context and the variables being examined- no one model is superior to another, and there is some amount of subjective measure required in the decision of which one to use in any given situation.