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Let's suppose you are estimating the following model, where monthly saving depends upon income:

$$savings = \beta_{0} + \beta_{1} income + u$$

The assumption $E(u|x) = 0$ implies:

$E(savings|income) = \beta_{0} income$

$E(savings|income) = \beta_{1} income$

$E(savings|income) = \beta_{0} + \beta_{1} income + u$

$E(savings|income) = \beta_{0} + \beta_{1} income$