 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ib/paper-1/18h/b/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

With

s^{2} = \sum (Y_{i} - X_{i} \hat{β})^{2} / (n - 1)

\frac{β ^ - β}{s / S _{xx}} \sim t_{n - 1} .

Thus the interval is

\hat{β} \pm t_{n - 1, 1 - α /2} \frac{s}{S _{xx}} .

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