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High Quality Content by WIKIPEDIA articles! In statistics, Poisson regression is a form of regression analysis used to model count data and contingency tables. Poisson regression assumes the response variable Y has a Poisson distribution, and assumes the logarithm of its expected value can be modelled by a linear combination of unknown parameters. A Poisson regression model is sometimes known as a log-linear model, especially when used to model contingency tables. In the simplest case with a single independent variable x. Y are independent observations with corresponding values x of the predictor variable, then a and b can be estimated by maximum likelihood if the number of distinct x values is at least 2. The maximum-likelihood estimates lack a closed-form expression and must be found by numerical methods. Poisson regression models are generalized linear models with the logarithm as the link function, and the Poisson distribution function.