Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2014/iii/paper-33/4/b/solution

The chosen Poisson regression has fitted mean
For zero building cover, its fitted expected number of floods over the 25-year observation window is . Increasing the covered proportion by multiplies the fitted expected count by . Thus a ten-percentage-point increase, , multiplies the expected count by about , an increase of . A one-percentage-point increase multiplies it by about . The full-unit multiplier 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.

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