Recent work on Geographically Weighted Regression (GWR) (Bruns- don, Fotheringham, and Charlton 1996) has provided a means of inves- tigating spatial non-stationarity in linear regression models. However, the emphasis of much of this work has been exploratory. Despite this, GWR borrows from a well founded statistical methodology (Tibshi- rani and Hastie 1987; Staniswalis 1987a; Hastie and Tibshirani 1993) and may be used in a more formal modelling context. In particular, one may compare GWR models against other models using modern statistical inferential theories. Here, we demonstatrate how Akaike’s Information Criterion (AIC) (Akaike 1973) may be used to decide whether GWR or ordinary regression provide the best model for a given geographical data set. We also demonstrate how the AIC may be used to choose the degree of smoothing used in GWR, and how ba- sic GWR models may be compared to ‘mixed’ models in which some regression coefficients are fixed and others are non-stationary.