fitting to a pure cubic and getting residuals

Hi. I want to perform a cubic fit (i.e. jsut a term in x^3 with no x^2 or x^1 so cannot use polyfit:

I need to do the fit of my data x and N(:,1). I also need the residuals.

This is my x:

x=[-0.625,-0.5,-0.4,-0.3,-0.2,0,0.2,0.3,0.4,0.5,0.625]'

ft=fittype('a*x^3')
    [fitobj,~,~,~]=fit(x,N(:,i),ft)
    coeff=fitobj.a
    y=N(:,1)
    yfit=coeff*x^3
    res=y-yfit

Answer 1

[John D'Errico]

Simple is to download polyfitn. But even easier is to just do this:

coeff = (x.^3)\y;
resid = y - coeff*x.^3;

[Image Analyst]

Nice solution John. Jason, you might also like this somewhat related discussion by the Mathworks support team and John: http://www.mathworks.com/matlabcentral/answers/94272-how-do-i-constrain-a-fitted-curve-through-specific-points-like-the-origin-in-matlab

[Jason]

Thanks both of you. It was the dot after the x I was missing. I've used polyfit before, but I don't want any other terms (i.e. x^2, x etc)

[John D'Errico]

Yes, what a difference a dot makes. But I meant that you can use polyfitn (a download from the file exchange) to do this. It is hardly worth the effort for such a simple model though, when backslash is so easy to use here.