Logistic Regression:Defintion


	Logistic Regression:Defintion from Wikipedia [For a Collection of Articles on Logistic Regression, and Related Issues, click here.] Logistic regression is a statistical regression model for binary dependent variables. It can be considered as a generalized linear model that utilizes the logit as its link function, and has binomially distributed errors. The model takes the form $\operatorname{logit}(p)=\ln\left(\frac{p}{1-p}\right) = \alpha + \beta_1 x_{1,i} + \cdots + \beta_k x_{k,i},$ $i = 1, \dots, n,\,$ where $p = \Pr(Y_i = 1).\,$ The logarithm of the odds (probability divided by one minus the probability) of the outcome is modelled as a linear function of the explanatory variables, X1 to Xk. This can be written equivalently as $p = \Pr(Y_i = 1\|X) = \frac{e^{\alpha + \beta_1 x_{1,i} + \cdots + \beta_k x_{k,i}}}{1+e^{\alpha + \beta_1 x_{1,i} + \cdots + \beta_k x_{k,i}}}.$ The interpretation of the β parameter estimates is as a multiplicative effect on the odds ratio. In the case of a dichotomous explanatory variable, for instance sex, eβ (the antilog of β) is the estimate of the odds-ratio of having the outcome for, say, males compared with females. The parameters α,β1,...,βk are usually estimated by maximum likelihood. Extensions of the model exist to cope with multi-category dependent variables and ordinal dependent variables. Go Back to Article Direct Response Marketing For more information about this article, call Bruce Ratner at 516.791.3544, 1 800 DM STAT-1, or e-mail at br@dmstat1.com. DM STAT-1 CONSULTING / br@dmstat1.com 574 Flanders Drive / North Woodmere, NY 11581 / U S A Voice 1-516-791-3544 / Fax 1-516-791-5075 Toll Free 1 800 DM STAT-1