Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 4 / 17H / e / Solution

{c}

In a two-parameter Gaussian simple linear regression centered at $\bar x$, the intercept estimator is $\bar Y$. With residual standard deviation $s$,
$$
\frac{\bar Y-\alpha'}{s/\sqrt n}\sim t_{n-2},
$$
which gives the usual two-sided interval from the corresponding quantiles.


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 Incoming links: Student t confidence interval for a centered regression intercept