# 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.

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by L Ma;

References:

- Fox J. Applied Regression Analysis and Generalized Linear Models. SAGE Publications; 2015. Available: https://play.google.com/store/books/details?id=cjB3BwAAQBAJ
- Rodríguez G, editor. Poisson Models for CountData. Generalized Linear Models. Available: https://data.princeton.edu/wws509/notes
- Chapter 19: Logistic and Poisson Regression by Marie Chesaniuk
- Poisson regression and non-normal loss (sklearn documentation)
- Beyond Multiple Linear Regression, Chapter 4 Poisson Regression

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