# Question about regression and deriving omitted variables

usually when I see derivations of ommited variable bias, I see something of the sort: from y=xb + $$\eta$$, and looking at the for formula for the slope estimate:

1. $$cov(x,y)/var(x)$$
2. $$cov(x,xb+\eta )/var(x)$$=
3. b + $$cov(x,\eta)/var(x)$$

my question is, how does intuitively step 2 make sense? plugging in y in to the covariance formula? Is it that we are taking y=xb + $$\eta$$ literally of how Y is being generated, and so any y we see in the population is theoretically equivalent to xb + $$\eta$$?

• I don't get your question, because the gist of it reads, "assuming $y=xb+\eta,$ why is it valid to substitute $xb+\eta$ for $y$ in a covariance calculation?" There seems to be nothing to say. What am I missing?
– whuber
Jul 30, 2020 at 15:34
• I think I should have worded 'assuming' as part of the question- just meant its usually stated in that way, so is that saying that y literally equal to xb +$\eta$? Jul 30, 2020 at 17:19
• Equations are meant pretty literally, so yes.
– whuber
Jul 30, 2020 at 17:23