Among all depth-one <regression tree> splits, the best split separates the second observation from the first and third by cutting advert1 between $0.89$ and $1.13$. The test point with advert1 equal to zero reaches the leaf containing responses $60$ and $53$, so the output is their <arithmetic mean>,
$$
\widehat y=\frac{60+53}{2}=56.5.
$$
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>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 218 / 1 / f / Solution

{title2=$\bar x$}
{wiki}

The arithmetic mean of $x_1,\ldots,x_n$ is
$$
\bar x=\frac1n\sum_{i=1}^n x_i.
$$
It is the <weighted mean> with equal weights.

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