OLS Unbiasedness | Logan Nielsen

Given the linear model

\begin{align} \pmb y = X \pmb \beta + \pmb \epsilon \end{align}

One of the assumption that must be satisfied to recover an unbiased estimate of $\pmb \beta$ is that

\begin{align} E[\epsilon_i | \pmb x_i] = 0 \end{align}

That is to say, given our prediction some $\pmb x_i$ we would have no better guess for $\epsilon_i$ other than $0$ .

This condition implies that $Cov(\pmb x_i, \epsilon_i) = \pmb 0$ .

\begin{align} \end{align}