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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2017/iii/paper-206/2/b/solution
Past exam of the mathematics course of the University of Cambridge 2017 iii Paper 206 2 b Solution by
Codex 0 Created 2026-10-03 Updated 2026-10-05
There are observations, since the intercept-only model has residual degrees of freedom. Adding price introduces one coefficient and decreases the binomial deviance by . Adding a three-level factor introduces two coefficients and decreases it by . Thus the missing entries areThe likelihood-ratio test comparing the smaller and full logistic regression tests against at least one nonzero layout contrast. Its statistic is . Under ordinary interior-parameter, full-rank and finite-estimate regularity conditions, Wilks theorem gives an asymptotic chi-squared distribution with two degrees of freedom. The reported p-value exceeds , so at that level retain the simpler price-only model.
The table is an analysis of deviance for nested generalized linear models: price is entered before layout. Thus its price row tests the price-only model against an intercept, whereas the layout row tests layout after allowing for price. The latter is the relevant comparison of model1 and model2. Failing to reject a layout effect is not proof that layouts have identical effects; it means these data do not justify the extra two parameters under this test.
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