Is the following statement true? OLS is the BLUE in every linear model

Counterexample

Is this true?

OLS is the BLUE in every linear model

No — it is false.

The counterexample

$Y_{i} = \beta{}x_{i} + \varepsilon_{i}$ with $Var(\varepsilon_{i}) = \sigma^{2}x_{i}^{2}$

Why it fails

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

Keep practicing

Invariants don't determine

Two objects sharing an invariant were treated as the same object.

Published 23 Aug 2026. Found a mistake? Tell us — corrections are the fastest thing we act on.