Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 218 / 1 / c

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- Solution c

Solution

The Pearson residual is

r_{i}^{P} = \frac{Y _{i} - μ _{i}}{ϕ V ( μ _{i} )} = \frac{Y _{i} - μ _{i}}{ϕ μ _{i}^{3}},

where the moment estimate of dispersion is

ϕ = \frac{1}{n - p} \sum_{i = 1}^{n} \frac{( Y _{i} - μ _{i} ) ^{2}}{μ _{i}^{3}} .

If the fitted model is adequate and the deviance residual sum is close to the Pearson statistic, then

ϕ \approx \frac{245.00}{238} = 1.029.

Solved by gpt-5.6-sol high.

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