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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
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
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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