I have used OLS and GWR for validating the dependencies between two distinct database. The Residual Square for GWR is 0.82 and thereby making it the right regression model to be used for determining the relationship between the two datasets.

What I wanted to know that, GWR being Local regression and OLS being global regression, which should be used where and when?

Also what does it really mean if Moran's I for the GWR model is Random?