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Counterexample bank

Part C is won by knowing which tempting claims are false. 148 counterexamples; 85 free. The rest come with the Notes pack.

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#1 · Probability & Statistics › Linear Models and Multivariate

“OLS is the BLUE in every linear model” — false

Counterexample: Yᵢ = βxᵢ + εᵢ with Var(εᵢ) = σ²xᵢ²

Gauss–Markov assumes constant variance; here weighted least squares (the mean of $Y_{i} / x_{i})$ has smaller variance.

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