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Linear Model with curve fitting parameter?

Steven McKinney 
Doesn't look right to me based on the information you've provided.
I don't see anything labeled "y" in your previous emails, so I'm
not clear on what y is and how it relates to the original model 
you described

   > >> I have a model Q=K*A*(R^r)*(S^s)
   > >>
   > >> A, R, and S are data I have and K is a curve fitting parameter. 

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)

Let  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

and these are the only parameters you described in the original model.
K has disappeared from these equations so these model fits do
not correspond to the model originally described.  Now a b0
appears, and is used in models below.  I think changing notation
is also adding confusion.  What are "y" and "intercept" you
discuss above, in relation to your original notation?
You will be able to fit models appropriately once you have a
clearly defined system of notation that allows you to map between
the proposed data model, the parameters in that model, and the
corresponding regression equations.  

Once you have consistent notation, you will be able to see
if you can express your model as a linear regression, or
if not, what kind of non-linear regression you will need to
do to get estimates for the parameters in your model.

Best

Steve McKinney

Thread (5 messages)

stephen sefick Linear Model with curve fitting parameter? Apr 1 Peter Ehlers Linear Model with curve fitting parameter? Apr 1 Steven McKinney Linear Model with curve fitting parameter? Apr 1 stephen sefick Linear Model with curve fitting parameter? Apr 3 Steven McKinney Linear Model with curve fitting parameter? Apr 4