Regression analysis can help you dive deeper into the spatial relationships and the factors behind spatial patterns. At a slightly more advanced level, regression analysis can help you make predictions based on your data. The ArcGIS Resource Center has a very nice page called “Regression Analysis Basics” and gives users an introduction to both regression and the related tools available. It notes the different components of models such as dependent and independent variables and regression coefficients. One of my favorite components of the page is the table “Common regression problems, consequences, and solutions”.  This lists problems and links to solutions that could potentially help you make your regression model stronger. Even if your skill set is beyond the basics of regression analysis, this page is a good refresher and introduction to how Arc can aid in telling a story.

Another helpful page is titled “What they don’t tell you about regression analysis”. Whatever you are trying to model is likely a complex phenomenon (especially in this class) and may not have a simple set of answers. Models often need revision and Arc has created a step-by-step protocol for increasing the validity of your analysis and model; this page guides you through six questions/check-marks that you’ll want to pass before you can have confidence in your model.

In my data, for example, I have several layers that could potentially help me identify where wetlands lie within the valley; examples include elevation, hydrology (stream and flood inundation), vegetation, and soils. Often, GIS users simply stack these layers together and create polygons based on areas that contain all, or a majority of layers. This technique may be based in ecologically sound logic, but does not address the strength between layers or the degree to which one or more layers may influence (both positively and negatively) others.
A regression analysis using known areas of wetland as the dependent variable and a variety of GIS layers as explanatory variables could help me predict places where wetlands are located but may not have been mapped.  Or, even better, it could help me predict where wetlands were in the past. The two pages listed above are useful in guiding me through making a model through the individual decisions I need to make. For example, using Ordinary Least Squares versus Geographically Weighted Regression.

Take a look at the two introduction pages and consider if your data could be used in a regression analysis and if the tools available in the Spatial Statistics toolbox could be useful. You could even just bring three different variables (ex: hydro, soils, and elevation) to try out.
There are three resources to explore further if you’re interested in using your data to perform regression analysis:

1. Lauren Scott’s presentation on regression analysis
2. The seminar on regression analysis titled “Beyond Where: Using Regression Analysis to Explore Why“
3. The regression analysis tutorial (the same used in Scott et al.’s presentation) where you can “Learn how to build a properly specified OLS model and improve that model using GWR, interpret regression results and diagnostics, and potentially use the results of regression analysis to design targeted interventions”