13.5 POISSON REGRESSION
There are many other kinds of regression models that fall under the umbrella of GLM. We will examine one other: Poisson regression. Poisson regression is used when you want to predict a count of events, such as how many times a customer will contact customer service. The distribution of the response variable will be a count of occurrences, with a minimum value of zero.
The link function for a count response variable is g(μ) = ln(μ). We set the link function equal to our linear predictor to obtain
![equation](https://static.packt-cdn.com/products/9781119526810/graphics/images/c13-disp-0011.png)
After isolating μ, we have
![equation](https://static.packt-cdn.com/products/9781119526810/graphics/images/c13-disp-0012.png)
Working backwards from our abbreviated notation, we find the parametric version of the Poisson regression equation
![equation](https://static.packt-cdn.com/products/9781119526810/graphics/images/c13-disp-0013.png)
from which we can write the descriptive form
![equation](https://static.packt-cdn.com/products/9781119526810/graphics/images/c13-disp-0014.png)