Gauss-Markov theorem (in econometrics)

The Gauss-Markov theorem is a fundamental principle in statistics and econometrics. It states that in a linear regression model, if certain conditions are met (like having a linear relationship, no measurement errors, and homoscedasticity), the best linear estimator of the unknown parameters—meaning it has the smallest possible variance among all unbiased estimators—is the ordinary least squares (OLS) estimator. Essentially, this theorem justifies the reliability of OLS in producing accurate and efficient estimates when analyzing relationships between variables.