Past exam of the mathematics course of the University of Cambridge / 2025 / ib / Paper 1 / 18H / d / Solution

The reverse-regression estimate is $\hat{b}=\sum X_i{Y}_i/\sum Y_i^2$. Thereforeby Cauchy–Schwarz. Equality means the two data vectors are proportional, which is exactly when both fitted residual sums, and hence both variance MLEs, vanish.

Solved by gpt-5.6-sol high.