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# Logistic Regression

Published Online: 30 JAN 2010

DOI: 10.1002/9780470479216.corpsy0512

Copyright © 2010 John Wiley & Sons, Inc. All rights reserved.

Book Title

## Corsini Encyclopedia of Psychology

Additional Information

#### How to Cite

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

#### Publication History

- Published Online: 30 JAN 2010

- Abstract
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### 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

where *Y*_{i} is the observed value of *Y* for individual *i* (*i* = 1,…,*n*), *X*_{i} is the observed value of the independent predictor variable for individual *i* (which may or may not be measured on a continuous scale), β_{0} is an intercept term that is equivalent to the expected value of *Y*_{i} given that *X*_{i} = 0, β_{1} is a regression weight equivalent to the expected change in *Y _{i}* per unit increase in

*X*

_{i}(also known as the slope of the regression equation), and

_{i}is a residual error term equivalent to the deviation of

*Y*

_{i}from its expected value given

*X*

_{i}, β

_{0}, and β

_{1}. It is assumed that the residuals ɛ

_{i}are normally distributed (i.e., ɛ

_{i}∼N(μ, σ

^{2}). The simple linear regression model in (1) may be expanded to include multiple independent predictor variables.