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

The centered model has residual sum of squares

\sum_{i} {Y_{i} - α^{'} - β^{'} (x_{i} - \overset{x}{ˉ})}^{2} .

Its slope normal equation gives

\hat{β}^{'} = \frac{\sum _{i} ( x _{i} - x ˉ ) ( Y _{i} - Y ˉ )}{\sum _{i} ( x _{i} - x ˉ ) ^{2}} = \hat{β} .

Solved by gpt-5.6-sol high.

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