6 - Modeling Relationships

Summary

This chapter deals with

• Linear regression notions and mathematical formations

• The assumptions that a linear regression model is based on

• Identifying linear relationships between a dependent variable and independent variables

• Residual plots, leverage and influential points

• Evaluate the degree (effect) to which one variable influences the positive or negative change of another variable

• The geometrical interpretation of the intercept and the slope, and various metrics and tests used to assess the quality of the results

• The interpretation of coefficients

• Studying casual relationships (under specific conditions)

• Building a predictive model by fitting a regression line to the data

• Evaluating the correctness of the model

• Model overfitting

• Ordinary least squares (OLS)

• Exploratory OLS

• Geographically weighted regression (GWR)

After a thorough study of the theory and lab sections, you will be able to

• Distinguish which regression method is more appropriate for the problem at hand and the data available

• Interpret statistics and diagnostics used to evaluate a regression model

• Interpret the outcomes of a regression model such as the coefficient estimates, the scatter plots, the statistics and the maps created

• Identify if relationships, associations or linkages among dependent and independent variables exist

• Analyze data through regression analysis in Matlab

• Conduct exploratory regression analysis in ArcGIS

• Conduct geographically weighted regression in ArcGIS