In statistics,<unk>  is a regression model for binomially distributed response/dependent variables. It is useful for modeling the probability of an event occurring as a function of other factors.   It is a generalized linear model that uses the logit as its link function.<unk>  is used extensively in the medical and social sciences.  Other names for<unk>  used in various other application areas include<unk>  model, logit model, and maximum-entropy classifier.<unk>  analyzes binomially distributed data of the form
where the numbers of Bernoulli trials ni are known and the probabilities of success pi are unknown. An example of this distribution is the fraction of seeds (pi) that germinate after ni are planted.
The model is then that for each trial (value of i) there is a set of explanatory/independent variables that might inform the final probability. These explanatory variables can be thought of as being in a k vector Xi and the model then takes the form
The logits of the unknown binomial probabilities (i.e., the logarithms of the odds) are modelled as a linear function of the Xi.
Note that a particular element of Xi can be set to 1 for all i to yield an intercept in the model.  The unknown parameters βj are usually estimated by maximum likelihood.
The interpretation of the βj parameter estimates is as the additive effect on the log odds ratio for a unit change in the jth explanatory variable.  In the case of a dichotomous explanatory variable, for instance gender, 
e
β
{\displaystyle e^{\beta }}
 is the estimate of the odds ratio of having the outcome for, say, males compared with females.
The model has an equivalent formulation as
This functional form is commonly identified as a single-layer "perceptron" or single-layer artificial neural network. A single-layer neural network computes a continuous output instead of a step function. The derivative of pi with respect to  X = x1...xk is computed from the general form:
where f(X) is an analytic function in X. With this choice, the single-layer network is identical to the<unk>  model. This function has a continuous derivative, which allows it to be used in backpropagation. This function is also preferred because its derivative is easily calculated:
Logistic regression
Linear regression
Multivariate analysis
Analysis of covariance
Analysis of variance
Proportional hazards models
Chi-square test
Likelihood-ratio test