Nonlinear regression with two variables

Hello all, I want to fit a nonlinear model to a set of experimental data. It has 1 dependent variable, Y, and 2 indepenent variables, X1 and X2.

I have this equation. Y = C * ((X1)^1/2 * (X2)^a. I'd like to determine the values of the parameters, C and a.

X1 = QG_Lmin.*1.67*10^-5;

X2 = QG_Lmin ./ QL;

% Define the model function

model = @(coefficients, x) coefficients(1) * sqrt(x(:, 1)) .* x(:, 2).^coefficients(2);

% Define the initial parameter values

initialCoefficients = [1, 1];

% Perform nonlinear regression using lsqcurvefit

estimatedCoefficients = lsqcurvefit(model, initialCoefficients, [X1, X2], Y);

% Extract C and a from the estimated coefficients

C = estimatedCoefficients(1);

a = estimatedCoefficients(2);

But I got an error:

Initial point is a local minimum.

Optimization completed because the size of the gradient at the initial point

is less than the value of the optimality tolerance.

<stopping criteria details>

Could anyone help me out?

Answer 1

[Torsten]

I don't know your inputs, but theoretically, it works:

X = rand(50,2);
Y = rand(50,1);
% Define the model function
model = @(coefficients, x) coefficients(1) * sqrt(x(:, 1)) .* x(:, 2).^coefficients(2);
% Define the initial parameter values
initialCoefficients = [1, 1];
% Perform nonlinear regression using lsqcurvefit
estimatedCoefficients = lsqcurvefit(model, initialCoefficients, X, Y);

Local minimum possible.

lsqcurvefit stopped because the final change in the sum of squares relative to 
its initial value is less than the value of the function tolerance.

% Extract C and a from the estimated coefficients
C = estimatedCoefficients(1)

C = 0.8608

a = estimatedCoefficients(2)

a = 0.2220

Maybe your arrays X1 and X2 contain NaN or Inf values.