Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 33 / 4 / b / Solution

The chosen Poisson regression has fitted meanFor zero building cover, its fitted expected number of floods over the 25-year observation window is $e^{0.96657}\approx 2.629$. Increasing the covered proportion by $\Delta$ multiplies the fitted expected count by $e^{3.02055\Delta }$. Thus a ten-percentage-point increase, $\Delta =0.1$, multiplies the expected count by about $1.353$, an increase of $35.3\%$. A one-percentage-point increase multiplies it by about $1.0307$. The full-unit multiplier $e^{3.02055}\approx 20.50$ compares proportions differing by one, not percentages differing by one.

These are associations in the conditional expectation with the recorded final-year building cover. The regression coefficient is not automatically a causal effect of changing development, especially since the count covers 25 years while cover was measured at the end.