MATLAB: Calculate goodness of fit

data fittinggoodness of fitlsqcurvefit

I have a data set which looks like this
I have around 7 equations like
y=atp*kcat*Et.*x ./ (kd_A*km_g + km_g*atp + km_a*x + atp*x.*(1+x./ksi));
y=atp*kcat*E.*x ./ (km_g*atp + km_a*x.*(1+x./ksi) + atp*x);
and more…
There are 4 – 5 parameters to fit for in each equation and there are 3 – 4 known variables.
One of these equations should be the best fit for the data and I want to find that. I tried using lsqcurvefit and got pretty good results. But similar values fpr the variables using all the equations and the resnorm is identical. Is there a way to find the goodness of fit? And am I doing it correct?

Best Answer

If you have the Statistics Toolbox, I suggest fitnlm. It produces a number of useful statistics. To the best of my knowledge, these aren’t available with lsqcurvefit and the Optimization Toolbox.
As a general rule, if all your functions produce similar residual errors, the model with the fewest parameters to estimate will have the best goodness-of-fit because it has the greatest degrees-of-freedom. The F-statistic may be the best measure, although the likelihood ratio may be best for for comparing two models with the same number of parameters.
That said, there are a number of other techniques to assess regression models. It is too broad a subject to go into here.
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