Question

What can a Poisson regression be used to estimate?

Answer 1

Pretty much anything countable that could be any value from 0 to infinity.

Explanation:

The Poisson distribution is used for modelling things that must be countable, potentially 0, but also potentially quite large/infinite. As a reminder, here's a picture of the probability mass function of a Poisson distribution:

Common examples of situations best modelled with Poisson are:

• length of a phone call to a help desk (in minutes),
• number of cars passing through an intersection during a single green light,
• number of customers rung through a checkout in 5 minutes,
• number of children in a family,
• number of people waiting at a bus stop,
• etc.

All of these examples are for things that are discrete (a.k.a. countable), non-negative, and potentially quite large. If the range of possible values needs to be positive and continuous (rather than discrete), a Gamma distribution may be best. If the data range is far enough from zero (or could potentially include negative values), a Normal distribution is usually preferred.