The Modeling Spatial Relationships toolset

The Modeling Spatial Relationships toolset contains a number of regression analysis tools that help you examine and/or quantify the relationships between features. They help measure how features in a dataset relate to each other in space.

The regression tools provided in the Spatial Statistics Tools toolbox model relationships among data variables associated with geographic features, allowing you to make predictions for unknown values or to better understand key factors influencing a variable you are trying to model. Regression methods allow you to verify relationships and to measure how strong those relationships are. The Exploratory Regression tool allows you to examine a large number of Ordinary Least Squares models quickly, summarize variable relationships, and determine whether any combination of candidate explanatory variables satisfy all of the requirements of the OLS method.

There are two regression analysis tools in ArcGIS which are as follows:

• Ordinary Least Squares: This tool is a linear regression tool used to generate predictions or model a dependent variable in terms of its relationships to a set of explanatory variables. OLS is the best-known regression technique and provides a good starting point for spatial regression analysis. This tool provides a global model of a variable or process you are trying to understand or predict. The result is a single regression equation that depicts a positive or negative linear relationship. The following screenshot depicts partial output from the OLS tool:

• Geographically Weighted Regression: Geographically Weighted Regression or GWR is a local form of linear regression for modeling spatially varying relationships. Note that this tool does require an Advanced ArcGIS license. GWR constructs a separate equation for each feature and is most appropriate when you have several hundred features. GWR creates an output feature class (shown in the following screenshot) and table. The output table contains a summary of the tool execution. When running GWR, you should use the same explanatory variables that you specified in your OLS model:

The Modeling Spatial Relationships toolset also includes the Exploratory Regression tool.

• Exploratory Regression: This tool can be used to evaluate combinations of exploratory variables for OLS models that best explain the dependent variable. This data-mining tool does a lot of the work for you for finding variables that are well suited and can save you a lot of time finding the right combination of variables. The results of this tool are written to the progress dialog, result window, and an optional report file. An example of the output from the Exploratory Regression tool can been seen in the following screenshot: