The technique of geographically weighted regression (GWR) is used to model spatial ‘drift’ in linear model coefficients. In this paper we extend the ideas of GWR in a number of ways. First, we introduce a set of analytically derived significance tests allowing a null hypothesis of no spatial parameter drift to be investigated. Second, we discuss ‘mixed’ GWR models where some parameters are fixed globally but others vary geographically. Again,models of this type may be assessed using significance tests.Finally, we consider a means of deciding the degree of parameter smoothing used in GWR based on the Mallows C p statistic. To complete the paper, we analyze an example data set based on house prices in Kent in the U.K. using the techniques introduced.