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I ran three separate linear regressions.

lm(Y~X1) -> X1 statistically significant

lm(Y~X2)-> X2 statistically significant

lm(Y~X1+X2)-> X1 statistically significant and X2 not statistically significant.

I suppose this makes sense. X1 is clearly confounds the relation between X2 and Y since X1 is causally related to X2 and to Y. But I'm not so clear as to what is mathematically going on. How do the algorithms detect this? Does it have something to do with holding X1 constant while interpreting X2?