In the context of two Poisson regressions with varying exposures, which statement is true?

In two Poisson regressions that account for varying exposures, the statement that one model handles overdispersion better is accurate. Overdispersion occurs when the observed variance in the data is greater than what the Poisson model would predict. In such cases, traditional Poisson regression may not adequately capture the underlying structure of the data.

To address overdispersion, alternative modeling approaches such as the negative binomial regression can be employed. This approach adds an extra parameter to allow for greater flexibility in the variance structure of the model, effectively accommodating the observed data distribution better than standard Poisson regression.

Choosing a model that effectively deals with overdispersion is critical, especially for accurately estimating the coefficients and their significance levels, leading to more reliable inferences. Hence, the statement regarding one model's improved capacity to handle overdispersion directly points to a vital consideration in modeling practices in statistics.