= Exogeneity
In <linear regression>, a common mean-exogeneity condition is $\mathbb E[\varepsilon\mid X]=0$: after conditioning on the <design matrix>, the <regression error> has zero <conditional expectation>. For a full-column-rank design, <ordinary least squares> satisfies $\widehat\beta=\beta+(X^\top X)^{-1}X^\top\varepsilon$, so this condition gives $\mathbb E[\widehat\beta\mid X]=\beta$ without requiring constant error <variance>.
A weaker condition, $\mathbb E[X_i\varepsilon_i]=0$, states an unconditional moment restriction and is not identical to zero conditional mean. If an omitted variable contributes to the <regression error> and is correlated with a predictor, either condition can fail. Exogeneity must therefore be stated relative to a specified model and information set; it does not by itself turn an associational regression into a <causal effect>.
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