Why can we assume that the expected value of the error term in a linear regression model is zero?
This is with regard to a simple linear regression.
2026-04-01 22:36:23.1775082983
Why can we assume that the expected value of the error term is zero?
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Because you estimate a constant term $\alpha$ in simple linear regression $$y_i=\alpha+\beta x_i+\varepsilon_i,$$ so that $E[\varepsilon_i]\neq 0$ just means $\alpha$ is replaced by $\hat{\alpha}=\alpha-E[\varepsilon_i]$. Hence, you might as well assume the error term has mean zero.