= Poisson mean saturation at three distinct times
For three distinct times, the columns $1,t,t^2$ are linearly independent by the <Vandermonde determinant>. Thus a quadratic <Poisson regression> for the log mean can reproduce any three positive time-group means. A grouped goodness-of-fit test of that mean form has zero residual degrees of freedom. Replicated observations still allow checks of the <Poisson distribution> and <overdispersion> within each time group; saturation of the mean does not establish the response distribution.
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