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?
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.