I am looking for both a 1) mechanical and 2) intuitive explanation for how the effects of individual variables are determined holding other variables constant.
In an example using survey data, what exactly does it mean to say:
"holding constant age, sex, and income, the effect of education is ___"
My understanding is that with regression we are attempting to recreate the experimental setting, and in the example above are trying to compare sub-populations with equal age, sex, income, etc., but with differing levels of education, and estimating the difference in mean of those subpopulations. Questions:
- Is this intuition correct?
- Do these subpopulations necessarily exist? What if the survey does not contain respondents with exactly the same values on the controls?
- How is uncertainty about the estimates of these subpopulations determined?