Four input parameters and one output parameter, try to model or fit the input and output values

Hi, I am quite new to Matlab. I have this problem to develop a model to fit the data between multiple inputs and output. What I need to do is to find a suitable model y=f(x1,x2,x3,x4). I need to try different models, linear or non-linear, or using other tools like neural network. I can find the curve fitting to two parameters (y=f(x1,x2), but for four inputs, I have some problems. Does anyone has a clue? Thanks

Answer 1

[Star Strider]

Yes. If you have more than one independent variable, concatenate all of them in a matrix (I prefer they be column vectors), then refer to them by their columns within the model function you want to fit.

For instance, if you want to fit: y = a*x1^2 + b*exp(c*x2), create your ‘x1x2’ matrix (or whatever you want to call it) as:

x1x2 = [x1 x2];

then in the function you want to use to fit your data, using a single vector ‘b’ for your parameter vector:

% b(1) = a,  b(2) = b,  b(3) = c
f = @(b,x) b(1).*x1x2(:,1).^2 + b(2).*exp(b(3).*x1x2(:,2));

and the call to nlinfit (for example) would then be:

B = nlinfit(x1x2, y, f, B0);

That is how I do it, and it works. You would simply expand what I call ‘x1x2’ here to include your four independent variable value vectors.

(Note: all the code here is untested, but then it’s also all hypothetical.)

[Wu Ying]

I tried and there are outputs for the coefficients. does this method give you the error also?

[Star Strider]

It won’t give you the errors directly. If you use nlinfit, you can get the parameter confidence intervals with nlparci and the confidence intervals on the fit with nlpredci. You simply have to request the appropriate additional outputs from nlinfit and pass them to the other functions.

If by ‘errors’ you mean ‘residuals’, that is the second output of nlinfit. You simply have to ask nlinfit to return that vector in its output arguments.

There are links to all those functions at the end of the documentation page for nlinfit.

[Wu Ying]

Thank you.

[Star Strider]

My pleasure!

[Wu Ying]

Sorry to bother, I have more than 9 b, it says b is only allowed 9 numbers, b[1-9], how can I do it?

[Star Strider]

I do not understand. What function does not allow you more than 9 parameters?