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I have 10 independent variables to include in an OLS regression model. I know how to interpret the results and that for comparing models, the AICc value can be used, where a smaller value indicates a better model (ArcGIS Help).

But to find the best OLS model I cannot try all different combinations of the independent variables myself. So if I start with all 10 independent variables for the first model, how should I define, which independent variables to keep/remove to get a better model? Removing those variables where the coefficient is small? Removing those variables that are not statistically significant?

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You should use "Exploratory Regression" tool which is a tool inside a complementary toolbox called "Supplementary Spatial Statistics". you can define many criteria for a passing model including R-square, VIF, p-values and ...

Download from: Supplementary Spatial Statistics Toolbox for ArcGIS 10

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