I have a regression model that includes IQ test scores as the dependent variable; my own education, my father's education and my mother's education as independent variables. Suppose I want to know whether the only way parents'education increases my IQ test score is through my own education. How would I test that hypothesis?
1$\begingroup$ So if you think about this, then according to your hypothesis if we ran the regression of IQ test score on parents education then parents education should be significant. And if we regess IQ test score on own education then own education should be statistically significant. However, if we regress IQ test score on own education and parents education then parents education would be insignificant and own education would be significant since own education contains additional information than parents. This assumes that the model is correct and that there isn't something important that is missing. $\endgroup$– Andrew MNov 18, 2019 at 2:36
$\begingroup$ I can't give an answer, I don't know it well enough, but I suggest you read into mediation analysis. This is perhaps a good starting point: onlinelibrary.wiley.com/doi/full/10.1111/joes.12452 $\endgroup$– PapayapapDec 6, 2022 at 12:13
For Bivariate Regression
Your model would be :
IQ = B0 + B1(Your Education)
For Multiple Regression:
You would use a correlation matrix/plot to do this. Basically it would give you a matrix with correlation values of all variables to each other 0 being none and 1 being perfect. This will also allow you to see the multicollinearity problem which is when independent variables are related to each other.
You can do this in R or Stata. I can post the R script of a similar regression I have done if you would like.
1$\begingroup$ How does this answer the question? How do you 'see' the multicollinearity problem from the correlation matrix? $\endgroup$ Dec 22, 2019 at 1:15
$\begingroup$ The correlation will be near to unity if there is multicollinearity between two independent variables. This is usually the first form of detection used and is a solid indicator. $\endgroup$– RumiDec 27, 2019 at 1:54
1$\begingroup$ I would say its one way but by no means is it sufficient, whats the cutoff for ‘near unity’? What if it is 0.8? I think you should include your above comment in the answer as OP may not be familiar with what to look for, all you say is you can ‘see it’. I think there is too much ambiguity using this measure alone. I would include VIF’s in your answer. $\endgroup$ Dec 27, 2019 at 19:38
$\begingroup$ I certainly agree to some extent with what have you said. Obviously what I had stated is what you would look at initially. If you are not satisfied you would go about using the VIF way or Eigensystem Analysis. I guess I should have included that in my answer. $\endgroup$– RumiDec 27, 2019 at 22:15
$\begingroup$ Yeah, you should edit your answer and include it, it would make for a comprehensive answer to the more general question $\endgroup$ Dec 28, 2019 at 1:07