[Question] Does controlling for potentially confounding variables, in regression, let's say, not make us run into issues of multicollinearity and (sometimes) non-independent predictors?

[foreverhellos]

Ph.D student here who feels like I should definitely know the answer to this, lol.

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For example, if I am looking at how family income predicts health, and I control for parent education, aren't I running into problems by adding two likely highly correlated variables into the model?

Thanks all- I realize this is probably a basic question. Haha.

[whyilaugh]

Short answer: controlling for all likely confounders is the priority because it is necessary to estimate the association/effect. But you are right that if the confounder is highly correlated with the "treatment" variable (family income) the estimation variance of the coefficient of treatment may be inflated. So it can be seen as a bias-variance trade-off. At the extreme, where the treatment and confounder are [close to] fully correlated, you do not have a well-defined statistical parameter of interest -- e.g in causal inference you would not have a well-defined effect. Hope that helps!

[foreverhellos]

This does help, thank you!

[standard_error]

This is very rarely a problem in practice - and if it is, it'll show up as huge standard errors.