Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 218 / 3 / e / Solution

The ordinary least squares equations for model 2 areFor the Gamma generalized linear model, $V(\mu )={\mu }^2$ and $d\mu /d\eta =\mu$, so its score equation under the logarithmic link isWhen $T_i$ is close to ${\mu }_i$,by the first-order Taylor expansion of the exponential function. The Gamma score equations then become the model-2 normal equations, so their coefficient estimates are close.