1. What is Poisson Regression?

Poisson regression is used to model count data and contingency tables where the outcome variable is a count (0, 1, 2, ...). It assumes the response variable has a Poisson distribution and the logarithm of its expected value can be modeled by a linear combination of parameters.

2. How Does the Calculator Work?

The calculator uses the Poisson regression equation:

Where:

• \( \mu \) — Predicted mean count
• \( \beta_0 \) — Intercept coefficient
• \( \beta_1 \) — Slope coefficient
• \( x \) — Predictor variable value

Explanation: The natural log of the expected count is modeled as a linear function of the predictor variables. The expected count is then calculated by exponentiating the linear combination.

3. When to Use Poisson Regression

Details: Poisson regression is appropriate when:

• Your outcome is a count of events
• The events are independent
• The mean and variance are approximately equal (no overdispersion)
• Examples: number of hospital visits, number of accidents, count of cells

4. Using the Calculator

Tips: Enter the intercept (β₀), coefficient (β₁), and predictor value (x). The calculator will compute the predicted mean count (μ) by exponentiating the linear predictor.

5. Frequently Asked Questions (FAQ)

Q1: What if my data shows overdispersion?
A: If the variance exceeds the mean, consider negative binomial regression or quasi-Poisson models.

Q2: Can I have multiple predictors?
A: Yes, but this calculator demonstrates the simple case with one predictor. The equation extends to: log(μ) = β₀ + β₁x₁ + β₂x₂ + ...

Q3: How do I interpret the coefficients?
A: A one-unit increase in x is associated with a multiplicative change of exp(β₁) in the expected count, holding other variables constant.

Q4: What's the difference from logistic regression?
A: Logistic regression models binary outcomes (0/1), while Poisson models count outcomes (0,1,2,...).

Q5: When should I use an offset?
A: Use an offset when you need to model rates (counts per unit time/space) rather than counts.