the Gauss-Markov theorem

The Gauss-Markov theorem states that, among all linear models estimating a relationship between variables, the ordinary least squares (OLS) method produces the most reliable estimates when certain conditions are met. Specifically, these estimates have the smallest possible variance, meaning they are the most precise or consistent, compared to other unbiased estimators. This theorem ensures that, under these conditions, OLS provides the best linear approximation of the true relationship, making it a preferred method in statistical modeling for its efficiency and reliability.