Hi thanks everyone for your help in advance. Im working on a two-stage regression, in which a coefficient from the first regression is used as an independent variable for the second regression. Both regressions turn out significant, but I have no idea what that proves, since the hypothesis tests are mis-specified.

1st stage (simplified): y = a + bx (where a and b are normal regression coefficients)
2nd stage: y = c + dzb (where c and d are normal regression coefficients, z is new data, and b is the coefficient from the 1st stage.)

The null hypotheses, as specified, are b = 0 and d = 0. However, I strongly suspect the following regression is significant: y = c + dz which would lead to a tautological conclusion. It seems that the implicit hypothesis test is that b is actually adding any information to the regression. Perhaps the appropriate test would be b = k, where k is a constant or perhaps that would just be a precondition, Im not sure. If this were a more normal regression, an F test would be appropriate, but we cant separate b from z here under the assumptions of that test.

I need to be able to make my comments in the most concise way possible ideally with cites to back up my point. This isnt going to look good for my boss, and in any case he can point to peer-reviewed studies that take this same problematic approach. Such are the standards in financial statistics. I'm pretty sure I haven't oversimplified this in any significant way.