Goodness of fit coefficient 2

[QuentinNZ]

Hi,

I am trying to fit one experimental data curve using a power law fitting. To make my fit ting curve closer to the experimental one I have taken three overlapping interval on wich I fit a power law. My calculated curve is so made of three parts and I am trying to optimise the transition between the three parts of my curve (reducing the difference of gradient between the curves) while keeping the calculated data close enough to the experimental curve.

To keep the fitting tight I am looking at a coefficient that will tell me how good is my fit. I first thought using the R_squarred value, but it is penalising harshly the fit on a part of the graph where there is very little change.

What ohter coefficient could I use to assess the goodness of fit?

Cheers

 

[GregLocock]

R squared is pretty gentle, I often use R^4.

However, I think your problem is more fundamental. Have you tried transforming your data into a less aggressive domain, before curve fitting?

eg plot y vs log(x)?



Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[IRstuff]

Additionally, transforming the data might make it pretty obvious that the model is, or is not, correct, i.e., if the transformed data don't fall on a line, you know that the model is incorrect.

TTFN

FAQ731-376

 

[MortenA]

If you really wish to evaluate your fit you have to know some basic statistics:

You can perform a analysis of variance where you test you residual in a F test.

This is not something that you just read in a book. I had a lot of statistics in univercity (4 full semester course + propability). Douglas C. Montgomery "Design and analysis of Experiments" was my "high level" text book. But its been 15 years since i had the classes - and about 8 years since i actually used it for real - so now its rather rusty and i would dare do it myself without some reading up.

Best regards

Morten

 

[GregLocock]

Incidentally, does R^2 really mean anything for anything other than a linear correlation?

Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[btrueblood]

Far as I know, Greg, no. For linear fits, it correlates to (or is equal to?) the standard deviation of the error between fit and data.

I use procedures similar to Morten's. For me, usually, I look at the maximum error of the fit (relative to the data), and at the overall distributions of the errors (e.g. plot error vs. independent variables), and the standard deviation of errors, and kurtosis, ... as Morten states, there is an entire field of mathematics regarding curve fits.

Typically, I also try to show from 1st principles why the equation I'm using (fitting) is a reasonably valid model for the physical problem.

All of it depends on how accurate your fit needs to be. We once had a really fancy curve fit for a rocket engine's thrust rejected by a customer because their spacecraft's onboard controller only had room (time?) for a linear regression, and the error for that linear fit was "good enough".

NIST has some articles buried in their website regarding fitting of data.

 

[MortenA]

But linear regression is not the same as a n=1

Best regards

Morten

 

[MortenA]

ops: should have said

But linear regression is not the same as a n=1 polynominal (hope i spelled that right)

I learned how to test if increasing "n" would improve your model significantly or not. It was something with F tests but as i said before: I would have to crack that old textbook in order to be really sure

Best regards

Morten