Non-linear Regression analysys with two input variables

I would like to obtain a regression parameters for the following case:

y=f(X1, X2)

Relationship between y and X1,X2 are non-linear. The equation might be as follows:

y=a1*X1+a2*X2+a3*X1^a4+X2^a5+a6

Could you please advise, how I can get the following information using matlab: 1. Optimum structure of regression equation 2. optimum regression parameters

入力変数(独立変数）2個で、従属変数1個のデータがあり、従属変数をこれら2個の独立変数の関数として表現したいのですが、そのやり方をご教示願います。 従属変数とこれら2個の独立変数の関係は、非線形です。

Answer 1

[Star Strider]

The nonlinear regression routines will only allow one input for the independent variable, but the independent variable can be a matrix.

For your hypothetical equation, you would evaluate it as:

Yfcn = @(a,X) a(1).*X(:,1) + a(2).*X(:,2) + a(3).*X(:,1).^a(4) + X(:,2).^a(5) + a(6);

with X being an (Nx2) matrix, Y being a (Nx1) vector, and a being a (6x1) vector.

The call to nlinfit would be:

aest = nlinfit(X, Y, Yfcn, a0)

and if you chose lsqcurvefit:

aest = lsqcurvefit(Yfcn, a0, X, Y)

with a0 being your initial parameter estimates, and aest being the vector of estimated parameters.