I am trying to calculate the covariance matrix from the residuals vector and the Jacobian matrix, which are optional outputs of the lsqcurvefit function. I keep getting negative values for the diagonal (variance) values, but they should be strictly positive. Does this have something to do with the method that lsqcurvefit uses? I have attached sample data and a sample extPar structure (this usually gets generated other peices of code that call this function). The part of the code that I think is germane is here:
[par,resnorm,R,~,~,~,J] = lsqcurvefit(FID,par0,fitTime,fitData);
pCov = inv(J'*J)*((R'*R)./(numel(fitData) - numel(par)));
The fit function converges to a nice looking solution, am I doing something drastically wrong here?
I am fully aware that the statistics toolbox solves this easily, but unless you give my prof the cash to buy it for me, I'm stuck with this.