Multivariate Nonlinear Least Squares

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

Answer 1

[Star Strider]

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.

[jlt199]

Thank you very much! Your name is very apt because you are indeed a star!! :)

[Star Strider]

My pleasure! Thank you!

[Pedro Machado]

Simply the most useful info I have ever gotten. Thank you very much for the question, Jlt, and thank you so so much for the answer, Star.

[Star Strider]

@Pedro Machado —

My pleasure.

A vote for my Answer would be appreciated!

[LANDON THOMAS KAMPS]

Thanks for the nice curve-fitting module.

This is working great for me too.

Much appreciated

[Star Strider]

@Landon —

My pleasure!