Hey Bethany and elsetton,
This is a really good question!! The answer is actually pretty simple. The overall R2 value for GWR is calculated the exact same way that it is calculated in OLS...essentially it's the proportion of the variability explained by the model. For both it is 1 - (Σ(predicted-observed)²/Σ(observed-mean of all observed)²). In other words, its 1 minus the variance of the residuals divided by the variance of the input data. In both OLS and GWR, the residuals are the predicted minus the observed, so it follows that you would expect OLS and GWR to have different R-squared values because those predicted values are calculated using different methods. So, its the same as OLS, the only difference is what values are being used for the predictions.
This is probably way more than you wanted to know, but hopefully it helps! Let me know if you need any more details. 🙂
Lauren Rosenshein
Geoprocessing Product Engineer