Thread Subject: Least squares fitting

I need to find the coefficients k1-k6 of the following equation:

P = G*(k1 + k2*T + k3*log(G) + k4*(log(G)).^2 + k5*T*log(G)+
k6*T*(log(G)).^2+k7*T.^2);

The experimental data I have are P, G and T.

Is there any MATLAB function in order to obtain the
coefficients using least-squares fitting?
Do I need the Curve Fitting Toolbox?

Thank you very much,
Zaira

"Zaira " <Zaira.Girbau-Garcia@jrc.it> wrote in message
<g0ccfp$jd9$1@fred.mathworks.com>...
> I need to find the coefficients k1-k6 of the following equation:
>
> P = G*(k1 + k2*T + k3*log(G) + k4*(log(G)).^2 + k5*T*log(G)+
> k6*T*(log(G)).^2+k7*T.^2);
>
> The experimental data I have are P, G and T.
>
> Is there any MATLAB function in order to obtain the
> coefficients using least-squares fitting?
> Do I need the Curve Fitting Toolbox?

This is a linear least squares problem. You can
use my polyfitn to do the fitting. Find it on the
file exchange.

http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?
objectId=10065&objectType=FILE

Assuming that P,G,T are all column vectors,

LG = log(G);
model = polyfitn([G,LG,T],P,'G, G*T, G*LG, G*LG^2, G*LG*T, G*T*LG^2,
G*T^2');

HTH,
John

"Zaira " <Zaira.Girbau-Garcia@jrc.it> wrote in message <g0ccfp$jd9
$1@fred.mathworks.com>...
> I need to find the coefficients k1-k6 of the following equation:
>
> P = G*(k1 + k2*T + k3*log(G) + k4*(log(G)).^2 + k5*T*log(G)+
> k6*T*(log(G)).^2+k7*T.^2);
>
> The experimental data I have are P, G and T.
>
> Is there any MATLAB function in order to obtain the
> coefficients using least-squares fitting?
> Do I need the Curve Fitting Toolbox?
>
> Thank you very much,
> Zaira
-----------
  The undetermined k coefficients appear linearly in your expression, so this
is an ordinary problem in linear regression for which you can use the matlab
backslash operator. If P, G, and T are column vectors of the same length, do
this:

 A = G.*[ones(size(G)),T,log(G),log(G).^2, ...
        T.*log(G),T.*log(G).^2,T.^2];
 k = A\P;

Roger Stafford