Lab 11 – Multivariate Regression, Diagnostics and Regression in ArcGIS

Regression analysis can be used in ArcGIS to model a phenomenon which may vary spatially.  There are three main reasons for regression analysis: 1) to predict values in unknown or un-sampled areas, 2) to measure the influence of variables to a particular phenomenon, or 3) to test hypotheses about the influence of variables on a phenomenon.  It is very important to test the usability, performance, or predictive power of a model due to its potential in policy decisions.  There are several diagnostics to test the performance of a regression model that go past simply determining the R-squared value (which may be very misleading).  ArcMap contains an Ordinary Least Square regression tool, among others, which produces some of these diagnostics, however it is up to the user to evaluate these statistics in the context of the model.  The six step process outlined by ESRI to interpret these statistics provides a foundation for determining the "best" model.  One important thing to note is the frequency distribution of residuals in a histogram.  The residuals should be distributed standard normal.  A positive or negative skew may be the result of spatial auto-correlation.  This is perhaps the biggest use of regression analysis is GIS, as spatial analysis is central in ArcMap processing.