Poisson regression

In statistics, the Poisson regression model attributes to a response variable Y a Poisson distribution whose expected value depends on a predictor variable x (written in lower case because the model treats x as non-random, in the following way:

$\log \operatorname {E} (Y)=a+bx\,$

(where "log" means natural logarithm).

If Y_i are independent observations with corresponding values x_i of the predictor variable, then a and b can be estimated by maximum likelihood if i ≥ 2. The maximum-likelihood estimates lack a closed-form expression and must be found by numerical methods.