A development of geographically weighted regression (GWR) model has been build, namely geographically weighted polynomial regression (GWPolR) model. Because it has more parameters, it has goodness of fit measures better than the GWR model does. However, it is urgent to test statistically whether the GWPolR model is significantly better than the GWR model in describing a given data set. There has not been a research to solve this problem. The purpose of this research is to discover a goodness of fit test procedure and its performance]. Based on the residual sum of squares (RSS) of GWR and GWPolR models and the distribution theory of quadratic forms, a statistical test approach was derived here. Furthermore, performance of the goodness of fit test procedure was investigated using some simulation studies. The results showed that the test procedure works well and can select an appropriate model for a given data set.