= Solution
The <normal linear model> is $Y=X\beta+\varepsilon$ with $\varepsilon\sim N(0,\sigma^2I_n)$. Full column rank gives
$$
\widehat\beta=(X^TX)^{-1}X^TY.
$$
With hat <matrix> $H=X(X^TX)^{-1}X^T$, the $i$th <regression leverage> is $h_{ii}$. Since $e=(I-H)Y=(I-H)\varepsilon$ and $I-H$ is an orthogonal projection,
$$
\operatorname{Var}(e_i)=\sigma^2(1-h_{ii}).
$$
High-leverage observations can move their own fitted values strongly and may exert disproportionate influence; residual size alone can therefore conceal them.
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