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Linear Regression

  1. Leona S. Aiken,
  2. Stefany Coxe

Published Online: 30 JAN 2010

DOI: 10.1002/9780470479216.corpsy0510

Corsini Encyclopedia of Psychology

Corsini Encyclopedia of Psychology

How to Cite

Aiken, L. S. and Coxe, S. 2010. Linear Regression. Corsini Encyclopedia of Psychology. 1–3.

Author Information

  1. Arizona State University

Publication History

  1. Published Online: 30 JAN 2010

Abstract

Linear regression characterizes the relationship of a set of independent variables or predictors X1, X2, …Xp to a single dependent variable or criterion Y. The goals of linear regression are (1) to characterize the overall strength of the relationship of the set of predictors to the criterion and (2) to identify those individual predictors or subsets of predictors that contribute to this overall relationship. Through a multiple regression analysis, all the predictors are combined into a composite predicted score Ŷ (“Y hat”) that has the highest possible linear correlation with the observed criterion Y. The square of this correlation, termed the squared multiple correlation inline image, is the overall effect size measure for a regression analysis and measures the proportion of variation in the criterion accounted for by the set of predictors. In general, regression analysis, of which linear regression analysis is one example, can be used for (1) description (i.e., to summarize the relationship of predictors to the criterion); (2) prediction (i.e., to make judgments about the future based on the predicted score of an individual); or (3) theory testing (i.e., to examine whether relationships predicted by theory are, in fact, supported).

Keywords:

  • correlation;
  • linear regression;
  • measurement;
  • regression;
  • statistics