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In econometrics, we are usually interested in estimating $E[y|x]$, rather than just $E[y]$. Why is that?
Once we estimate $E[y|x]$, it is easy to find $E[y]$ using the Law of Iterated Expectations.
We are interested in the relationship between $y$ and $x$, not just characterizing the typical value of $y$.
Conditioning on $x$ makes our analysis of $E[y]$ easier, since we have data on $x$.
$E[y|x]$ is always a linear function, so it is a good application for regression techniques.