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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.

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 Binary Response Models




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