From what you are saying, the rank is an external piece of information, and apparently, you already have the formula. So I don't see the problem. The linear regression doesn't use F at all. If you find the parameters 1, 2, 3, and 4:

D = ( 1 + 2*A + 3*B + 4*C)

Then

D = ( 1/F + 2/F * A + 3/F * B + 4/F * C ) * F

Just like I divided all number by five above. Does that help?

(°v°)