What are the Gauss-Markov assumptions for OLS?

medium

Answer

$E[Y\; \mid \;X]\; = \;X{\beta}$
$E[{\varepsilon}\; \mid \;X]\; = \;0$
$\operatorname{Var}({\varepsilon}\; \mid \;X)\; = \;{\sigma}^{2}$
$\operatorname{Cov}({\varepsilon}_{i}, \;{\varepsilon}_{j})\; = \;0$
$(5) No perfect multicollinearity.$
$Under (1)-(5), OLS is BLUE (Best Linear Unbiased Estimator).$
$Normality of ε is NOT required for BLUE, only for exact-sample t / F inference — CLT-robust for large n.$

Check yourself — multiple choice

Only normality
Linearity + exogeneity + homoscedasticity + no autocorr + no perfect collinearity → OLS is BLUE; normality only needed for exact-sample inference
Requires large n
Not real

Gauss-Markov: linearity + exogeneity + homoscedasticity + no autocorr + no collinearity → BLUE.

#regression#assumptions

215 interview questions in this topic.