Poisson Regression

Poisson regression is a generalized linear model for count data.

To model a dataset that is generated from a [[Poisson distribution]] Poisson Process , 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 ;

L Ma (2021). 'Poisson Regression', Datumorphism, 05 April. Available at: https://datumorphism.leima.is/wiki/machine-learning/linear/poisson-regression/.