Normalize option in curve fitting toolbox. How does it work?

Hello everybody,

I would like to regress a curve to the model:

F(t) = k * E(t) + r * E'(t) + u*E''(t) + c

Where the target function F(t) and the input function E(t) are experimental data.

To work with E(t) I fit a sigmoidal function to E(t):

E(t) = b(1) + b(2)./ (1 + exp( -(x - b(3)) ./ b(4)))

Here comes the problem: The fit to E(t) only works, if I set the fitoption 'normalize' to 'on' and the results are very good (r-square > 0.99). But now I want to use the coefficients in b as input to the model for the regression. Because b is from a normalized fit, I receive a different result for the individual terms by using b in the model.

Here is the code to determine b:

[xdata, ydata] = prepareCurveData( x, sig );

expr = @(b(1), b(2), b(3), b(4), x) b(1)+b(2)./(1+exp(-(x-b(3))./b(4)));

ft = fittype(expr, 'independent', 'x', 'dependent', 'y');

opts = fitoptions( ft );

opts.Normalize = 'on';

[fitresult, gof] = fit( xdata, ydata, ft, opts );

In other words: How can I reconstruct E(t) with the coefficients from a normalized E(t) in b?

I hope this is understandable and someone can point me in the right direction. If necessary I can also post the code for the regression on F(t).

Thanks in advance, Kai

Answer 1

[MattH]

I have a similar question.

From the fitresult "where x is normalized by mean 590.4 and std 151.7" it is possible to get X=(x-590.4)/151.7 and use the coefficients of the regression model(thus answering the question above)

The problem is how to do that programmatically ? It is possible to get the coefficient with coeffvalues(equation) but how can I retrieve mean and std ?

Any idea, anyone ?

Thanks

[MattH]

Found a workaround: recalculate mean and std from xData

[JOHN GONZALEZ]

It works

Answer 2

[JOHN GONZALEZ]

Hello, good afternoon

I had the same problem. I can't take the mean and std of the normalized x from the fit results to make the correct calculations of the regression. Usign the advice of MattH I calculate xmean and xsigma variables appart.