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Stepwise regression

Method of statistical factor analysis

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Record originEnglish Wikipedia
Text licenseCC BY-SA 4.0
Source revisionMay 13, 2025
Entity authorityQ7611170 ↗
Source-derived summary

In statistics, stepwise regression is a method of fitting regression models in which the choice of predictive variables is carried out by an automatic procedure. In each step, a variable is considered for addition to or subtraction from the set of explanatory variables based on some prespecified criterion. Usually, this takes the form of a forward, backward, or combined sequence of F-tests or t-tests.

The frequent practice of fitting the final selected model followed by reporting estimates and confidence intervals without adjusting them to take the model building process into account has led to calls to stop using stepwise model building altogether or to at least make sure model uncertainty is correctly reflected by using prespecified, automatic criteria together with more complex standard error estimates that remain unbiased.

Main approaches

The main approaches for stepwise regression are:

Forward selection, which involves starting with no variables in the model, testing the addition of each variable using a chosen model fit criterion, adding the variable (if any) whose inclusion gives the most statistically significant improvement of the fit, and repeating this process until none improves the model to a statistically significant extent.

Backward elimination, which involves starting with all candidate variables, testing the deletion of each variable using a chosen model fit criterion, deleting the variable (if any) whose loss gives the most statistically insignificant deterioration of the model fit, and repeating this process until no further variables can be deleted without a statistically significant loss of fit.

Bidirectional elimination, a combination of the above, testing at each step for variables to be included or excluded.

Alternatives

A widely used algorithm was first proposed by Efroymson (1960). This is an automatic procedure for statistical model selection in cases where there is a large number of potential explanatory variables, and no underlying theory on which to base the model selection. The procedure is used primarily in regression analysis, though the basic approach is applicable in many forms of model selection.

Editorial summary

This brief starts where responsible research should: with the source description of “Stepwise regression” as method of statistical factor analysis. Everything that follows is an evidence route, not borrowed authority.

Editorial reviewA practical starting point whose main value is the path it opens into stronger specialist and primary sources. The current lead gives the account dated anchors—1960—that can be checked directly. The selected authority fields contribute no independent date. The account is most persuasive where Stepwise, regression and Method can be independently traced.
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This entry incorporates text from “Stepwise regression” on English Wikipedia. Contributors are listed in the page history. Text is available under the Creative Commons Attribution-ShareAlike 4.0 License. Selected authority identifiers and statements are retrieved from Wikidata under CC0; their references and qualifiers remain part of the verification path.