# How to test if the effect of one regressor entirely comes from other regressors?

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?

• 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. – Andrew M Nov 18 '19 at 2:36

## 1 Answer

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.

• How does this answer the question? How do you 'see' the multicollinearity problem from the correlation matrix? – Brennan Dec 22 '19 at 1:15
• 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. – Rumi Dec 27 '19 at 1:54
• 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. – Brennan Dec 27 '19 at 19:38
• 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. – Rumi Dec 27 '19 at 22:15
• Yeah, you should edit your answer and include it, it would make for a comprehensive answer to the more general question – Brennan Dec 28 '19 at 1:07