Poisson regression is a generalized linear model for count data.

To model a dataset that is generated from a , we only need to model the mean $\mu$ as it is the only parameters. The simplest model we can have for some given features $X$ is a linear model. However, for count data, the effects of the predictors are often multiplicative. The next simplest model we can have is

$$\mu = \exp\left(\beta X\right).$$

The $\exp$ makes sure that the mean is positive as this is required for count data.

Planted: by ;