FTP, name this doubly-eponymous theorem from statistics which defines the validity of Ordinary Least Squares Linear Regressions.
In order to formally test one assumption of this theorem one can use the coefficients of determination in order to compute the variance inflation factor or the tolerance. Another important assumption of this theorem can be tested via the Breusch-Pagan or White tests, and ARCH modeling can be used to resolve that issue for time-series data. That issue, which violates one of the conditions of this theorem occurs when the variances differ among supposedly random variables and is known as heteroscedasticity. This theorem states that for homoscedastic and uncorrelated errors the mean squared error of the estimate will be lowest possible and the estimated coefficients will be described as BLUE. FTP, name this doubly-eponymous theorem from statistics which defines the validity of Ordinary Least Squares Linear Regressions.
In order to formally test one assumption of this theorem one can use the coefficients of determination in order to compute the variance inflation factor or the tolerance.
{Gauss-Markov} Theorem