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Logistic Regression

  1. Timothy J. Ozechowski

Published Online: 30 JAN 2010

DOI: 10.1002/9780470479216.corpsy0512

Corsini Encyclopedia of Psychology

Corsini Encyclopedia of Psychology

How to Cite

Ozechowski, T. J. 2010. Logistic Regression. Corsini Encyclopedia of Psychology. 1–2.

Author Information

  1. Oregon Research Institute

Publication History

  1. Published Online: 30 JAN 2010

Abstract

In general, regression modeling is a foundational statistical procedure for studying the functional relationship between two or more variables. The most basic of all cases is the simple linear regression model in which the value of some dependent or outcome variable Y is expressed mathematically as a linear function of a single independent or predictor variable X. Given that values of Y are measured on a continuous scale (interval or ratio), the simple linear relationship between Y and X may be expressed by the following regression model

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where Yi is the observed value of Y for individual i (i = 1,…,n), Xi is the observed value of the independent predictor variable for individual i (which may or may not be measured on a continuous scale), β0 is an intercept term that is equivalent to the expected value of Yi given that Xi = 0, β1 is a regression weight equivalent to the expected change in Yi per unit increase in Xi (also known as the slope of the regression equation), and i is a residual error term equivalent to the deviation of Yi from its expected value given Xi , β0, and β1. It is assumed that the residuals ɛi are normally distributed (i.e., ɛi ∼N(μ, σ2). The simple linear regression model in (1) may be expanded to include multiple independent predictor variables.