If someone has a "geekier" career path or educational background, they're almost certainly more likely to have geekier children.
If someone has a "geekier" career path or educational background, they're almost certainly more likely to have geekier children.
I think that controlling for variables means that you've tried to reduce the impact of other variables on the two that you're interested in. From Wikipedia: "In statistics, controlling for a variable is the attempt to reduce the effect of confounding variables on an observational study. It means that when looking at the effect of one variable, all other variable predictors are held constant." [1]
If you could control for all other variables then you'd know how much of a connection between the two variables that you're looking at.
I think this doesn't guarantee causation, though - you'd need to do experiments where you adjust the independent variable and then verify that the dependent variable changes the way you're proposing it should.
At least, I think that's how it works. Anyone else want to chime in?
[1] https://en.wikipedia.org/wiki/Controlling_for_a_variable
You also have to assume that it's possible for every person/unit of study to have a non-zero probability of receiving either treatment for all levels of the variables you are controlling for in order for the effect you're estimating to be defined. That is more likely to be violated the more things you have to control for.
Controlling for variables can rule out alternative causal relationships (shared causes between A and B rather than A causes B) as explanation for correlation, but can't rule out coincidence. They strengthen the case for these plausibility of a causal explanation.