= Solution
The <residual deviance> is $290.93$ on $98$ <residual degrees of freedom>. Under a suitable Poisson <deviance goodness-of-fit test> approximation it is compared with $\chi^2_{98}$, whose supplied 95th percentile is $122.1$. Since $290.93$ is much larger, \b[the chosen Poisson model does not provide a satisfactory absolute fit], despite being preferred among the three candidates.
The ratio $290.93/98\approx2.97$ suggests substantial <overdispersion> or mean-model misspecification. It is a deviance ratio, not the exact <Pearson dispersion estimator>, which cannot be computed from the excerpt. Check residual patterns, nonlinear effects, unusual rivers and dependence. A <Quasi-Poisson regression> could adjust uncertainty under an estimated dispersion, and a <negative binomial regression> could model extra count variation; a more adequate mean model may also be needed. The nominal Poisson tests in part (a) should be interpreted in light of this failure, rather than treated as a validated final analysis.
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