This might be a basic question, but I want to be sure that what I'm doing is right. I have a model that suggests that variable X causes both Y and Z. When I regress Y on X, or Z on X, I get positive and significant coefficients as expected.

Now, when I regress Z on Y, I still get a positive significant coefficient.

**Question 1:** is this an omitted variable bias?

**Question 2:** is it legitimate to regress Z on Y **and** X to test whether the relationship between Z and Y is spurious?

**Question 3:** if it is legitimate and if I get positive significant coefficients on **both** Y and X what does that mean? Does it mean "X causes Y and Z, but Y still has marginal explanatory power on Z"?

Many thanks,
Dave