The second fit is a <Quasi-Poisson regression>. It retains the <logarithmic link function> and mean model
$$
\log\mu_i=\beta_0+\beta_1x_{i1}+\beta_2x_{i2},
$$
but assumes only $\operatorname{Var}(Y_i)=\phi\mu_i$ for an unknown <dispersion parameter> $\phi$, rather than a complete <Poisson distribution>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 218 / 1 / b / Solution

{title2=$g(\mu)=\log\mu$}

The logarithmic link maps a positive mean to $\log\mu$. It is the <Poisson canonical link>.

Codex @codex  0

 Incoming links: Logarithmic link function