Special Section The listing price of a typical house modeled based on spatially varying regression coefficients generated using the GWR tools in ArcGIS. Results While the linear regression model was found to be significant and had a strong R-squared value of 0.782 (p = 0.000), the GWR model improved on these statistics and increased the model's accuracy to an R-squared value of 0.865 (p = 0.000). [R-squared is a measure of goodness of fit. Its value varies from 0.0 to 1.0. Higher values are preferable. See the accompanying article, "Regression Analysis Components--Terms and basic concepts" for more information on these terms.] In addition, the range in residual value error decreased by $160,000 when using the GWR model instead of the linear model. The coefficient surfaces generated using the GWR tool were also helpful for identifying the spatial patterns apparent in the study area. For example, the lot value coefficients indicate that as lots are located nearer the urban core and farther from the rural townships, lot square footage price increases. In contrast, coefficients suggest that the larger the house, the less it contributes to the listing price (again, as properties are located nearer the urban core and farther from the rural townships). This pattern may be indicative of the age of houses in rural areas. Sprawling rural subdivisions tend to have newer houses than neighborhoods in the urban core, yet land values are lower. These newer houses command a higher listing price per square foot according to the data analyzed. This pattern may also indicate a response to differences in millage rates between the townships and urban core. [Millage is the tax rate on property expressed in mills per dollar of value of the property.] Taxation rates in the urban core are typically twice as high as rates in rural townships in the state of Michigan (according to the Michigan Department of the Treasury in 2008). Higher millage rates may discourage the construction of newer developments in the urban core. In conclusion, the user-friendly GWR tool offers a sophisticated basis to quantify and dissect spatial patterns across a study area. Application of www.esri.com GWR offers a noticeable improvement over linear regression and helps to promote spatial thinking in students enrolled in courses at NMU. For more information, contact Robert Legg in the Department of Geography at Northern Michigan University (rlegg@nmu.edu). About the Authors Robert Legg (rlegg@nmu.edu) is an assistant professor at Northern Michigan University. He specializes in spatial data modeling, remote sensing, and cartography. Legg received his master's degree in remote sensing from the University of Aberdeen, Scotland and doctorate in geography from Trinity College in Dublin, Ireland. Tia Bowe (tbowe@nmu.edu) is a professional cartographer majoring in GIS at Northern Michigan University. Currently, she holds an associate's degree in geographic information systems from Hocking College in Nelsonville, Ohio. Bibliography Fotheringham, A. Stewart, Chris Brunsdon, and Martin Charlton. Geographically Weighted Regression: The Analysis of Spatially Varying Relationships, Wiley. Chichester, United Kingdom, 2002. Michigan Center for Geographic Data. Spatial data retrieved March 2008. Michigan Department of the Treasury, https://treassecure.state.mi.us/, (data collected October 2008). Mitchell, Andrew. The Esri Guide to GIS Analysis, Volume 2: Spatial Measurements and Statistics, Esri Press. Redlands, California, 2008. Rogerson, Peter A. Statistical Methods for Geographers: A Student's Guide, SAGE Publications. Los Angeles, California, 2006. ArcUser Spring 2009 45