Poisson Regression calculator
Model count data or rates online. Fit a Poisson regression and calculate incident rate ratios (IRR) and log-likelihood.
What it does
Models how predictors relate to the rate of a count outcome (0, 1, 2, …), on the log scale.
When to use it
Your outcome is a count of events and you want how predictors multiply the event rate — optionally per unit of exposure (time or population).
Worked example
You want to know what drives how many support calls a customer makes. The outcome is a count — calls in a month — and the predictors might be the plan they are on, how long they have been a customer and whether they were onboarded by a person or a link. Use this when the counts are mostly small and not too spread out.
Alternatives
- Negative Binomial — the counts are overdispersed (variance exceeds the mean) — the usual case
- a zero-inflated / hurdle model — there are far more zeros than the model predicts
- Logistic — the outcome is really binary (event / no event), not a count
How to read the output
- Coefficient (Estimate) — log-rate scale
- On the log scale. Exponentiate it, exp(b), to get the incidence rate ratio (IRR): the multiplicative change in the event rate per 1-unit increase. The app does not exponentiate it for you. 'X changes the count by b' is wrong until you exponentiate — b is the log-rate coefficient.
- Dispersion
- Checks the Poisson assumption that the variance equals the mean; around 1 is fine. Well above 1 (overdispersion) means the Poisson standard errors are too small and p-values too optimistic — switch to Negative Binomial (the app flags this).
- z-statistic
- The Wald statistic (asymptotic, no degrees of freedom), as for other GLMs. It's z, not t — don't read it as a t-test.
- 95% CI
- The range compatible with your data; on the IRR scale, excluding 1 means the direction is determined. A CI spanning 1 (IRR) / 0 (log-rate) is undetermined, not null.
How this calculator is validated · Which statistical test should I use?