= Omitted-variable bias
{wiki}
If the true conditional mean is $\beta_0+\beta_1X+\beta_2Z$, the population slope from regressing on $X$ alone is $\beta_1+\beta_2\operatorname{Cov}(X,Z)/\operatorname{Var}(X)$, assuming a mean-zero error uncorrelated with the predictors. The omitted predictor can steepen, flatten, or reverse the pooled association. The same identity holds for fitted coefficients and empirical <covariances> when comparing nested ordinary least-squares fits. Adjustment changes the comparison being described; a causal interpretation requires additional assumptions.
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