What is true about a Poisson regression?

In the context of Poisson regression, when the model is adequate, the deviance, which measures the goodness of fit of the model compared to a saturated model, follows a chi-square distribution. This is important because it allows for the assessment of model fit through hypothesis tests, where the deviance can be compared to a chi-square distribution with degrees of freedom equal to the difference in the number of parameters between the two models being compared.

A proper understanding of this concept is crucial when checking whether the model you have created accurately represents the data. If the deviance value is significantly high relative to the chi-square distribution, it suggests that the model may not be an adequate fit. Hence, recognizing the relationship between deviance and the chi-square distribution is pivotal in validating the assumptions of Poisson regression.

The other options present alternatives that do not correctly reflect the properties of Poisson regression. For instance, the first choice implies that there is a preferred link function that is universally applicable, which is not the case as the log link is commonly used for Poisson regression. The second option suggests a specific distribution for deviance that is contingent on the model's assumptions rather than being inherently true. The third option misinterprets the relationship between the chi-square statistic and