Ordinary Least Squares Spatial Statistics Esri

The feature class containing the dependent and independent variables for analysis. An integer field containing a different value for every feature in the Input Feature Class. The output feature class that will receive dependent variable estimates and residuals. The numeric field containing values for what you are trying to model. A list of fields representing explanatory variables in your regression model. Regression analysis may be the most commonly used statistic in the social sciences.

Regression is used to evaluate relationships between two or more feature attributes. Identifying and measuring relationships allows you to better understand what's going on in a place, predict where something is likely to occur, or examine causes of why things occur where they do. Ordinary Least Squares (OLS) is the best known of the regression techniques. It is also a starting point for all spatial regression analyses. It provides a global model of the variable or process you are trying to understand or predict; it creates a single regression equation to represent that process. There are a number of resources to help you learn more about both OLS regression and Geographically Weighted Regression.

Start with Regression analysis basics. Next, work through the Regression Analysis tutorial. This topic will cover the results of your analysis to help you understand the output and diagnostics of OLS. To run the OLS tool, provide an Input Feature Class with a Unique ID Field, the Dependent Variable you want to model, explain, or predict, and a list of Explanatory Variables. You will also need to provide a path for the Output Feature Class and, optionally, paths for the Output Report File, Coefficient Output Table, and Diagnostic Output Table. Output generated from the OLS tool includes an output feature class symbolized using the OLS residuals, statistical results, and diagnostics in the Messages window as well as several optional outputs such as a PDF...

Each of these outputs is described below as a series of checks when running OLS regression and interpreting OLS results. The Spatial Statistics toolbox provides effective tools for quantifying spatial patterns. Using the Hot Spot Analysis tool, for example, you can ask questions like these: Each of the questions above asks "where?" The next logical question for the types of analyses above involves "why?" Tools in the Modeling Spatial Relationships toolset help you answer this second set of why questions. These tools include Ordinary Least Squares (OLS) regression and Geographically Weighted Regression.

Regression analysis allows you to model, examine, and explore spatial relationships and can help explain the factors behind observed spatial patterns. You may want to understand why people are persistently dying young in certain regions of the country or what factors contribute to higher than expected rates of diabetes. By modeling spatial relationships, however, regression analysis can also be used for prediction. Modeling the factors that contribute to college graduation rates, for example, enables you to make predictions about upcoming workforce skills and resources. You might also use regression to predict rainfall or air quality in cases where interpolation is insufficient due to a scarcity of monitoring stations (for example, rain gauges are often lacking along mountain ridges... OLS is the best known of all regression techniques.

It is also the proper starting point for all spatial regression analyses. It provides a global model of the variable or process you are trying to understand or predict (early death/rainfall); it creates a single regression equation to represent that process. Geographically weighted regression (GWR) is one of several spatial regression techniques, increasingly used in geography and other disciplines. GWR provides a local model of the variable or process you are trying to understand/predict by fitting a regression equation to every feature in the dataset. When used properly, these methods provide powerful and reliable statistics for examining and estimating linear relationships. Output generated from the OLS Regression tool includes the following:

Each of these outputs is shown and described below as a series of steps for running OLS regression and interpreting OLS results. (A) To run the OLS tool, provide an Input Feature Class with a Unique ID Field, the Dependent Variable you want to model/explain/predict, and a list of Explanatory Variables. You will also need to provide a path for the Output Feature Class and, optionally, paths for the Output Report File, Coefficient Output Table, and Diagnostic Output Table. After OLS runs, the first thing you will want to check is the OLS summary report, which is written as messages during tool execution and written to a report file when you provide a... (B) Examine the summary report using the numbered steps described below: The feature class or feature layer containing the dependent and candidate explanatory variables to analyze.

The numeric field containing the observed values you want to model using OLS. A list of fields to try as OLS model explanatory variables. A file containing spatial weights that define the spatial relationships among your input features. This file is used to assess spatial autocorrelation among regression residuals. You can use the Generate Spatial Weights Matrix File tool to create this. When you do not provide a spatial weights matrix file, residuals are assessed for spatial autocorrelation based on each feature's 8 nearest neighbors.

Note: The spatial weights matrix file is only used to analyze spatial structure in model residuals; it is not used to build or to calibrate any of the OLS models.

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