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Linear Model with curve fitting parameter?

I suspect this is confusion about what Q is.  I was presuming that
the Q in this following formula was log(Q) with Q from the original data.
If the model is 
  
   Q=K*A*(R^r)*(S^s)

then

   log(Q) = log(K) + log(A) + r*log(R) + s*log(S)

Rearranging yields

   log(Q) - log(A) = log(K) + r*log(R) + s*log(S)

so what I labeled 'Z' below is

   Z = log(Q) - log(A) = log(Q/A)

so

   Z = log(K) + r*log(R) + s*log(S)

and a linear model fit of
   
   Z ~ log(R) + log(S)

will yield parameter estimates for the linear equation

   E(Z) = B0 + B1*log(R) + B2*log(S)

(E(Z) = expected value of Z)

so B0 estimate is an estimate of log(K)
   B1 estimate is an estimate of r
   B2 estimate is an estimate of s

More details and careful notation will eventually lead
to a reasonable description and analysis strategy.


Best

Steve McKinney