Regression analysis

Regression analysis is a set of statistical processes for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables (or 'predictors'). More specifically, regression analysis helps one understand how the typical value of the dependent variable (or 'criterion variable') changes when any one of the independent variables is varied, while the other independent variables are held fixed.

Overview

Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables – that is, the average value of the dependent variable when the independent variables are fixed. Less commonly, the focus is on a quantile, or other location parameter of the conditional distribution of the dependent variable given the independent variables. In all cases, a function of the independent variables called the regression function is to be estimated. In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function which can be described by a probability distribution.

Types of regression analysis

There are several types of regression analysis. Simple regression analysis uses a single independent variable to predict the value of a dependent variable. Multiple regression analysis uses more than one independent variable to predict the value of a dependent variable by fitting a best linear equation.

Uses of regression analysis

Regression analysis is primarily used for two conceptually distinct purposes. First, regression analysis is widely used for prediction and forecasting, where its use has substantial overlap with the field of machine learning. Second, in some situations regression analysis can be used to infer causal relationships between the independent and dependent variables.

See also

• Correlation and dependence
• Curve fitting
• Empirical statistical laws
• Errors and residuals in statistics
• Estimation theory
• Forecasting
• Linear regression
• Nonlinear regression
• Robust regression

References

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