[syntaxfree]

There's this other thing called the FWL theorem.

As long as the unexplained term is uncorrelated (in the probabilistic model; linear regression will force this to be the case computationally) with the included variables, your coefficients will remain unchanged. So adding/removing variables shouldn't change results at all -- unless the model is mis-specified and you're including variables that correlate with unobserved factors in unexpected ways.

So for example a regression of children's IQ on the income of their parents provides a plausible mechanism; but if you add the arm length of the kids you will have problems, since arm length is correlated to an omitted variable (kids with longer arms are older and perform better on IQ tests).

That's most of the "in context" story. Nothing to do with multicollinearity.

[SubiculumCode]

Thanks for the thoughtful comment and reference.

The 'in context' was not so much about multicollinearity but about shared and unique variance.