I know it is straightforward enough to test for a statistically significant difference between two coefficients... but I have kind of a funny case that has gotten me rather confused (and a push in the right direction would be great). I am running 4 regressions. Let's say they are
y = a1 + a2x1 + additional things
y = b1 + b2x1 + additional things
y = c1 + c2x1 + additional things
y = d1 + d2x1 + additional things
Where "additional things" is different between each regression. I am interested in the value F1 = exp(a2)/exp(b2) and F2 = exp(c2)/exp(d2). I want to test whether or not there is a statistically significant difference between F1 and F2, but this has thrown me for quite a loop because I am using both ratios and exponentials. Can anybody give me any insight in this respect? I would really appreciate it!