Regression Analysis

In statistics, regression analysis is a statistical technique 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. More specifically, regression analysis helps one understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed. 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, the estimation target is a function of the independent variables called the regression function. 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.

Regression analysis is widely used for prediction and forecasting, where its use has substantial overlap with the field of machine learning. Regression analysis is also used to understand which among the independent variables are related to the dependent variable, and to explore the forms of these relationships. In restricted circumstances, regression analysis can be used to infer causal relationships between the independent and dependent variables. However this can lead to illusions or false relationships, so caution is advisable: See correlation does not imply causation.

A large body of techniques for carrying out regression analysis has been developed. Familiar methods such as linear regression and ordinary least squares regression are parametric, in that the regression function is defined in terms of a finite number of unknown parameters that are estimated from the data. Nonparametric regression refers to techniques that allow the regression function to lie in a specified set of functions, which may be infinite-dimensional.

The performance of regression analysis methods in practice depends on the form of the data generating process, and how it relates to the regression approach being used. Since the true form of the data-generating process is generally not known, regression analysis often depends to some extent on making assumptions about this process. These assumptions are sometimes testable if a large amount of data is available. Regression models for prediction are often useful even when the assumptions are moderately violated, although they may not perform optimally. However, in many applications, especially with small effects or questions of causality based on observational data, regression methods give misleading results.

Read more about Regression AnalysisHistory, Regression Models, Underlying Assumptions, Linear Regression, Interpolation and Extrapolation, Nonlinear Regression, Power and Sample Size Calculations, Other Methods, Software

Other articles related to "regression analysis, regression":

Regression Estimation
... In statistics, regression analysis is a statistical technique for estimating the relationships among variables ... More specifically, regression analysis helps one understand how the typical value of the dependent variable changes when any one of the independent ... 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 ...
Sports Betting Systems - Two Types of Betting Systems - Regression Analysis
... Regression analysis is a type of statistical technique used to determine the important variables that affect the outcome of the event ... this is usually done with multivariate linear regression ... Also, regression analysis assigns a "weight" to each variable that identifies how much it affects the outcome of the event ...
Regression Analysis - Software
... software packages perform least squares regression analysis and inference ... Simple linear regression and multiple regression using least squares can be done in some spreadsheet applications and on some calculators ... statistical software packages can perform various types of nonparametric and robust regression, these methods are less standardized different software packages implement different ...
Logistic Regression - Model Fitting - Deviance and Likelihood Ratio Tests
... In linear regression analysis, one is concerned with partitioning variance via the sum of squares calculations – variance in the criterion is essentially divided into variance accounted for ... In logistic regression analysis, deviance is used in lieu of sum of squares calculations ... Deviance is analogous to the sum of squares calculations in linear regression and is a measure of the lack of fit to the data in a logistic regression model ...

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