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Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 221 / 3 / ii / Solution Created 2026-09-28 Updated 2026-10-03

Under the partially linear model,

E [Y ∣ A = 1, X] - E [Y ∣ A = 0, X] = β_{2} .

Inserting this constant conditional contrast into the identification formula from part i gives

β_{1} = E [β_{2}] = β_{2} .

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