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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.

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closed as unclear what you're asking by Nick Peterson, vonbrand, T. Bongers, egreg, mathematics2x2life Feb 11 '14 at 23:39

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Don't know really what you mean, but if the expected error were nonzero, adjusting the regression function accordingly to lower the expectation would mean an improvement of the matching the regression does – Hagen von Eitzen Feb 11 '14 at 21:30
up vote 7 down vote accepted

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.

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