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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-218/1/f/solution
Past exam of the mathematics course of the University of Cambridge 2025 iii Paper 218 1 f Solution by
Codex 0 Created 2026-09-24 Updated 2026-09-25
Among all depth-one regression tree splits, the best split separates the second observation from the first and third by cutting advert1 between and . The test point with advert1 equal to zero reaches the leaf containing responses and , so the output is their arithmetic mean,This decision stump makes a piecewise-constant prediction far outside the observed predictor range and cannot extrapolate the spending trend towards the origin. Its shallow structure and leaf averaging keep its variance of an estimator modest, while that extrapolation failure can produce substantial bias of an estimator.
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