Poisson regression assumes that the mean equals the variance of the response variable.

Poisson regression assumes that the mean equals the variance of the response variable.

• A. True
• B. False
• C. Only approximately
• D. It depends on the link function

Answer: (A)

Poisson regression is built on the Poisson distribution for the response. For a given set of predictors, the Poisson model assumes Var(Y|X) = E(Y|X) = μ, meaning the variance equals the mean. The link function (often the log) ties the mean μ to the linear predictor, but it doesn’t change this variance relationship. Thus the standard Poisson model imposes equidispersion: the conditional variance equals the conditional mean. If data show overdispersion or underdispersion, that signals a deviation from the Poisson assumptions and may lead to using alternatives like quasi-Poisson or negative binomial models.

Poisson regression is built on the Poisson distribution for the response. For a given set of predictors, the Poisson model assumes Var(Y|X) = E(Y|X) = μ, meaning the variance equals the mean. The link function (often the log) ties the mean μ to the linear predictor, but it doesn’t change this variance relationship. Thus the standard Poisson model imposes equidispersion: the conditional variance equals the conditional mean. If data show overdispersion or underdispersion, that signals a deviation from the Poisson assumptions and may lead to using alternatives like quasi-Poisson or negative binomial models.