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In statistics, binomial regression is a regression analysis technique in which the response has a binomial distribution: it is the number of successes in a series of n {\displaystyle n} independent Bernoulli trials, where each trial has probability of success p {\displaystyle p} . In binomial regression, the probability of a success is related to explanatory variables: the corresponding concept in ordinary regression is to relate the mean value of the unobserved response to explanatory variables.
Binomial regression is closely related to binary regression: a binary regression can be considered a binomial regression with n = 1 {\displaystyle n=1} , or a regression on ungrouped binary data, while a binomial regression can be considered a regression on grouped binary data. Binomial regression models are essentially the same as binary choice models, one type of discrete choice model: the primary difference is in the theoretical motivation. In machine learning, binomial regression is considered a special case of probabilistic classification, and thus a generalization of binary classification.