MATLAB: Multivariate Nonlinear Least Squares

least squaresmultivariatenonlinear

Morning everyone,
I've tried talking to MathWorks and playing with the tools in the curve fitting toolbox, but I can't seem to find a solution to my problem.
I have a model Y(P,W,L) = P^a * W^b *L^c + d where a, b, c and d are unknown coefficients I need to find. I have vectors for Y, P, W and L.
Please can you help me find a solution to this problem. I was told that the curve fitting toolbox was the way to go, but so far I haven't had any success setting up the model using fittype.
I would really appreciate a quick response to this problem as I need to have found a solution and reported my findings by this Friday.
Many thanks

Best Answer

I don’t have the Curve Fitting Toolbox, so I’m using fminsearch here:
P = randi(9, 10, 1);                                    % Create Data



W = randi(9, 10, 1);                                    % Create Data
L = randi(9, 10, 1);                                    % Create Data
Y = randi(9, 10, 1);                                    % Create Data
PWL = [P(:) W(:) L(:)];                                 % Create Single Variable
% % MAPPING: b(1) = a,  b(2) =b,  b(3) = c,  b(4) = d
Y_fit = @(b,PWL) PWL(:,1).^b(1) + PWL(:,2).^b(2) + PWL(:,3).^b(3) + b(4);
SSECF = @(b) sum((Y(:) - Y_fit(b,PWL)).^2);             % Sum-Squared-Error Cost Function
B0 = [1; 1; 1; 1];                                      % Initial Parameter Estimates
[B, SSE] = fminsearch(SSECF,  B0);                      % Estimate Parameters
figure(1)
subplot(3,1,1)
plot(P, Y,'xr', P, Y_fit(B,PWL),'bp')
grid
subplot(3,1,2)
plot(W, Y,'xr', W, Y_fit(B,PWL),'bp')
grid
subplot(3,1,3)
plot(L, Y,'xr', L, Y_fit(B,PWL),'bp')
grid
I added the plots, since it usually helps me determine how good the fit is. If you want to plot your data and the regression, you will have to experiment with the plots, since they can be a bit difficult when you have three independent variables. The plotting I did here works, but it may not be the best for your data.
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