GWR_Tutorial - Geographically Weighted Regression A...

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Geographically Weighted Regression A Tutorial on using GWR in ArcGIS 9.3 Martin Charlton A Stewart Fotheringham National Centre for Geocomputation National University of Ireland Maynooth Maynooth, County Kildare, Ireland http://ncg.nuim.ie
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2 The authors gratefully acknowledge support from a Strategic Research Cluster grant (07/SRC/I1168) by Science Foundation Ireland under the National Development Plan.
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1 Introduction Geographically Weighted Regression (GWR) is a powerful tool for exploring spatial heterogeneity. Spatial heterogeneity exists when the structure of the process being modelled varies across the study area. We term a simple linear model such as i i i x y ε β + + = 1 0 a global model – the relationship between y and x is assumed to be constant across the study area – at every possible location in the study area the values of 0 and 1 are the same. The residuals from this model ε i are assumed to be independent and normally distributed with a mean of zero (sometimes this is termed iid independent and identically distributed). This short tutorial is designed to introduce you to the operation of the Geographically Weighed Regression Tool in ArcGIS 9.3. It assumes that you understand both regression and Geographically Weighted Regression (GWR) techniques. A separate ESRI White Paper is available which outlines the theory underlying GWR. Modelling the Determinants of Educational Attainment in Georgia We use a simple example: modelling the determinants of educational attainment in the counties of of the State of Georgia. The dependent variable in this example is the proportion of residents with a Bachelor’s degree or higher in each county ( PctBach ). The four independent variables that we shall use are: Proportion of elderly residents in each county: PctEld Proportion of residents who are foreign born: PctFB Proportion of residents who are living below the poverty line: PctPov Proportion of residents who are ethnic black: PctBlack The spatial variation in each of the variables should be mapped by way of initial data exploration. There are some clear patterns in the educational attainment variable – high values around Atlanta and Athens. This is perhaps not surprising since the campuses of Georgia Institute of Technology, Georgia State University, Kennesaw State University, and Georgia Perimeter College are around Atlanta, and the University of Georgia (which has the largest enrolment of all the universities in Georgia) is located in Athens. Mapping the individual independent variables suggests that there might be some relationships with the variation in educational attainment, and some initial analysis also suggests that these variables are reasonable as predictors. The proportion of elderly is included because concentrations of educational attainment are usually associated with concentrations of the young rather than the old – we would expect there to be increased proportions of the elderly to have a negative influence on educational attainment. It is suspected that
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GWR_Tutorial - Geographically Weighted Regression A...

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