Matlab's curve fitting toolbox results make no sense

So, this is driving me crazy and I don't understand why the results I get from the curve fitting toolbox is so unreasonable.

All I wanted to do is to fit a polynomial to my x and y (attached as a mat file).

I could get a good fit by using a polynomial of degree 6.

Now, as I tried to reproduce the nice figure cftool created using the coefficients it got me, it was very very far.

versus

, which is what I plotted with the provided coefficients. I used different ways to get the coefficients, too. From copying them from cftool to saving it to workspace and using a function or generating a code. All gave me something so off.

The results are so unreasoanable that when I tried a polynomial of degree 1 to fit this (p1(x) + p2) it gave me both p1 and p2 to be negative!! It is clear that whatever the fit is, p2 has to be positive.

I don't understand what I'm doing wrong. Will be very thankful if someone could help.

Answer 1

[Walter Roberson]

You are not getting a good fit. You should be normalizing your data:

[p, ~, mu] = polyfit(x, y, 6);
plot(x, polyval(p, x, mu))

Anyhow. If you tell cftool to save your fit to the default variable name fittedmodel then,

plot(x,polyval(coeffvalues(fittedmodel),x))

[Siavash]

Thank you for your quick answer. I didn't expect such a fast reply.

x is already normalized. However, normalizing y should not (and as I gave it a try, does not) resolve this problem I have. I believe this is a more fundamental issue as for example, in the case of a linear fit, the second parameter (y-intercept) is negative! It is not even about the accuracy of the fit, but what Matlab is providing as a fit seems to be totally randomly generated number.

Regarding the fit, from the plotted curve in the curve fitting toolbox, it actually seems to be a very good fit. However, the parameters (or coefficients in this case for a polynomial) do not seem to match the blue fitted curve Matlab has found.

[Walter Roberson]

cftool, choose x, choose y, choose polynomial, degree 6.

fit -> save to workspace. Leave variable names the same as default; in particular, fittedmodel as the name of the fit object.

Then

plot(x,polyval(coeffvalues(fittedmodel),x), 'b', x, y, '.k')

Looks pretty good to me.

If I use polynomial degree 1, then I get the same plot you post (except the legend), and p2 shows up as positive. I save to workspace as fittedmodel1 and then,

>> coeffvalues(fittedmodel1)

ans =

         -11037758.4418226          10305509.0653276

which is positive intercept.

[Siavash]

I guess now I understood what I was doing wrong.

I was basically using the coefficients that cftool was showing. What I had to do was to use the variables that I saved into workspace. Since the order of my data was in 10^6 and based on the domain I was doing the fit in, the coefficients were in 10^12 to 10^10 and the difference between what I copied and what I had to use was in 10^7 - causing so much issues (wow!)

It's funny that I made the same mistake with Excel, too.

Thank you very much Walter, both for helping me out and also for being so quick in that.