The core principle asserts that in valid statistical models for regression analysis, residuals (estimation errors) must be statistically uncorrelated across observations to satisfy the Gauss-Markov theorem assumptions. This condition ensures that Ordinary Least Squares estimators possess minimum variance among unbiased linear estimators and prevents efficiency losses inherent in autoregressive structures. The concept resides within econometrics and general statistical inference, specifically addressing the structural properties of stochastic error terms required for optimal parameter estimation.
Prerequisite chain context: requires Normal Distribution of Error Terms.