Spatial distribution of the houses used to develop the GWR model. The map displays satellite imagery from the Michigan Center for Geographic Data. Applying Geographically Weighted Regression to a Real Estate Problem An example from Marquette, Michigan By Robert Legg and Tia Bowe, Northern Michigan University Underpinning geographic thinking is the assumption that spatial phenomena will vary across a landscape. Regression-based models largely ignore this assumption, much to the detriment of spatially varying relationships. However, ArcGIS 9.3 provides an exciting tool that generates spatially calibrated regression models. Known as Geographically Weighted Regression (GWR), this tool generates a separate regression equation for every feature analyzed in a sample dataset as a means to address spatial variation. (The GWR tool requires an ArcInfo, ArcGIS Spatial Analyst, or ArcGIS Geostatistical Analyst license.) To illustrate these concepts, students in a spatial analysis class at Northern Michigan University (NMU) analyzed the listed sales price for single family houses in Marquette, Michigan, based on location and several other related variables. Prior to the availability of the GWR tool, linear regression was applied to generate these models. Frequently, students found linear models to be limited because they would often overestimate the asking prices in some neighborhoods while underestimating prices in other neighborhoods. Applying the GWR tool was a way to improve modeling accuracy and ameliorate some of these residual errors. 44 ArcUser Spring 2009 Application To calibrate this study, a sample of 93 homes listed on www.uprealestate.com in March 2008 was used. The coordinates for these houses were recorded in Universal Transverse Mercator (UTM) in North American Datum of 1983 (NAD83) Zone 16N. The listing price parameters included number of bedrooms and bathrooms, house square footage, and lot size. Because the number of bedrooms is closely linked with the square footage of the house, the number of bedrooms was excluded from further analysis. Initial linear regression analysis (entry method) was used for generating a global model predicting the listing price of homes in Marquette, Michigan. Using the GWR tool [found in the Modeling Spatial Relationships toolset in the Spatial Statistics tools in ArcToolbox], a spatially calibrated model was generated using the same dataset. The GWR tool gave separate regression coefficients for each of the 93 houses in the sample. These coefficients were mapped as raster surfaces, and the listing price of a common home (1,500-square-foot floor area with 1.5 bathrooms on a 38,400-square-foot lot) according to spatially varying regression coefficients was generated using the GWR tool in ArcGIS. www.esri.com