Lab 11 - Multivariate Regression, Diagnostics and Regression in ArcGIS

Lab 11, like 10, was about regression, and equally challenging to someone new to statistics, as I am. Through 4 different parts of the lab using Excel and ArcGIS we practiced making correlation coefficient matrixes, linear multivariate regression models, predictive modeling, model comparison, and carrying out regression using the OLS, Spatial Autocorrelation, and Exploratory Regression tools.

Focusing specifically on regression analysis in ArcGIS, I started with the OLS (Ordinary Least Squares) tool. This tool is used to create global linear regression models and includes an OLS summary report to review model statistics. After inputting a dependent variable and one or more explanatory (independent) variables into the OLS dialog, I can review the statistics to determine the performance of my model. This includes Adjusted R-squared values, p-values, regression coefficients, AIC values, and more. There are 6 basic checks to walk through to help with this process, each of which considers different aspects of the statistics, for example high R-squared or adjusted R-squared values denote a strong correlation, low p-values suggest variable significance, an asterisk by the Jarque-Bera value indicated bias in the residuals, etc. See ArcGis' Help guide for more detailed information on the 6 checks at http://resources.arcgis.com/en/help/main/10.2/index.html#/What_they_don_t_tell_you_about_regression_analysis/005p00000053000000/. Depending on what I find during these 6 checks, I may need to add or remove variables to improve my model.

One important part (and included in Check #5) in determining the performance of our model is to look at the spatial autocorrelation of the residuals using the Spatial Autocorrelation (Global Moran's I) tool. Clustering or non-random patterns in the residuals indicate I do not have key variables and need to change or add variables in my model. If I find my model does not perform well and I want to consider other variables, I can use the Exploratory Regression tool to more easily narrow down the variable combinations. This tool produces a report based on all input explanatory variables and the dependent variable that tells me which variable combinations create "passing" models. Again looking at the statistics such as Adjusted R-squared value (higher is best), AIC value (lower is best), and others I can determine which variable combinations might produce a better model for my dependent dataset.

Map of residuals used to identify spatial autocorrelation and potential lack of key variables in model. This map reflects no clustering and a good set of explanatory variables.

Part of the HMTL file produced by the Spatial Autocorrelation tool to identify potential clustering in the residuals of a model. This report reflects no clustering (low z-score) and a good set of explanatory variables.