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I am sorry if this sounds redundant but I couldn't find a good explanation on this anywhere else yet. I understand that controlling for a variable in a regression can be imagined by drawing separate regression lines through different values of that variable as illustrated here:Is there a difference between 'controlling for' and 'ignoring' other variables in multiple regression? (first figure).

My question is, when we have several regression lines, how do we end up with a single regression coefficient? Is it an average of the slopes of all the separate lines or something?

Let's say I regress wage on years of experience and education. I am interested in the effect of experience holding education fixed. So I run:

$wage = \beta_0 + \beta_1 experience + \beta_2 education + u$

And let's say $\beta_1$ turns out to be 2.3. So is 2.3 an average of all slopes across all education levels (average of all regression lines)?

Thanks for your help!

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    $\begingroup$ See stats.stackexchange.com/…. Sorting those hits by score gives a nice selection of popular, informative threads on this topic. $\endgroup$
    – whuber ♦
    Commented Apr 22, 2021 at 16:11
  • $\begingroup$ I have voted to leave this closed for now, but I can see this question being reopened with a little bit more editing to make clearer the distinction between what's now being asked, and the duplicate stuff that's been asked already. If your focus now is on how the coefficient is calculated in a multiple regression, and whether it represents a kind of average, I think you might want to change a few other bits of the question around to reflect this (including the title) $\endgroup$
    – Silverfish
    Commented Apr 24, 2021 at 16:09

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