How do I make a fitting function with the fitting coefficient for x-data?

Hi.

I am trying to fit the experimental data to the mastercurve we have.

I have set of "xdata".

Let's say I have [0,1,2,3,4,5].

Then, the master curve is the function of xdata.

Let's say master = (xdata)^2.

Here, I also have ydata that corresponds to the xdata from the experiment.

My whole set of data are

xdata = [0,1,2,3,4,5]
ydata = [0,1,2,3,4,5]

Here, I want to have a fitting coefficient multiplied on "xdata" to fit the ydata into mastercurve.

Which means, I will have new plot of ydata vs C*xdata and mastercurve as a function of C*xdata.

I tried to write out a fitting function but confused about the setting since the input parameter is changing for both raw data set and mastercurve. (I tried to use lsqcurvefit but xdata is changing so I am confused.)

Can anyone help me on this?

I also want to obtain a R-squared value out of it.

Thank you very much!

- Sean

[Joe Goddard]

I can provide a recently written Matlab program to estimate a master curve using fmincon. Joe Goddard [e-mail]

Answer 1

[Matt J]

For a single coefficient, it's as simple as,

 C=((xdata(:)).^2)\ydata(:);

[Joe Goddard]

I believe a derivation is in order. This does not seem to agree with a rigorously derived formula for finding shift factors for a master curve of y vs x.

[John D'Errico]

@Joe - actually, it does. This is the correct answer. There is no need to use fmincon either.

[Matt J]

@Joe- I'm not sure how I could "derive" it when my answer consists only of a function call. A\b is a Matlab command which invokes a least squares solver for linear equations A*x=b. I have simply applied it here with the substitutions,

A=xdata(:).^2 
b=ydata(:)
x=C

[Joe Goddard]

You have provided a numerical formula without a mathematical derivation to back it up. To obtain a "best fit" to the scale factors necessary to reduce a set of curves to a master curve is not a trivial matter. If this is not what you are trying to do, then we are talking past one another. JG

[Matt J]

My best interpretation of what the OP was trying to do is to find the scalar C that minimizes

   f(C) = norm( C*xdata(:).^2 -ydata(:) )^2

If that much is true, then the solution is trivially given by what I posted.