Beyond analyzing spatial patterns, GIS analysis can be used to examine or quantify relationships among features. The Modeling Spatial Relationships tools construct spatial weights matrices or model spatial relationships using regression analyses.
Tools that construct spatial weights matrix files measure how features in a dataset relate to each other in space. A spatial weights matrix is a representation of the spatial structure of your data: the spatial relationships that exist among the features in your dataset.
True spatial statistics integrate information about space and spatial relationships into their mathematics. Some of the tools in the Spatial Statistics toolbox that accept a spatial weights matrix file are Spatial Autocorrelation (Global Moran's I), Cluster and Outlier Analysis (Anselin Local Moran's I), and Hot Spot Analysis (Getis-Ord Gi*).
The regression tools provided in the Spatial Statistics 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. Exploratory Regression allows you to examine a large number of Ordinary Least Squares (OLS) models quickly, summarizing variable relationships, and determining if any combination of candidate explanatory variables satisfy all of the requirements of the OLS method.
The Exploratory Regression tool evaluates all possible combinations of the input candidate explanatory variables, looking for OLS models that best explain the dependent variable within the context of user-specified criteria.
Constructs a spatial weights matrix file (.swm) using a Network dataset, defining feature spatial relationships in terms of the underlying network structure.
Constructs a spatial weights matrix (.swm) file to represent the spatial relationships among features in a dataset.
Performs Geographically Weighted Regression (GWR), a local form of linear regression used to model spatially varying relationships.
Performs global Ordinary Least Squares (OLS) linear regression to generate predictions or to model a dependent variable in terms of its relationships to a set of explanatory variables.