A theorem stating that under certain assumptions the ordinary least squares estimator is the best linear unbiased estimator (BLUE) of the linear regression coefficients, where the best is defined in terms of minimum variance. The assumptions for a regression with fixed (non-stochastic) explanatory variables include the linear regression function being correct and errors being homoscedastic and serially uncorrelated. For stochastic explanatory variables the theorem and its assumptions are formulated in terms of conditional means and variances.