In the linear regression model, the true error vector $U=Y-X\beta$ is based upon the true value of the unknown coefficient vector $\beta$. Meanwhile, the OLS residual vector $U^\* =Y-X\beta^\*$ uses the OLS estimator $\beta'$ of $\beta$, where $U^\*$ and $\beta^\*$ are the estimators of $U$ and $\beta$.

Then is it true that $U'U\lt {U^\*}'U^\*$?