# Thread: Curve fitting of experimental data

1. ## Curve fitting of experimental data

Hi, everyone.

I need to fit a set of data with an approximating function. I have tried functions such as polynomial, exponential & power law, but without success.

Pls., could someone kindly help fit the set of data given below with a closely approximating curve, and give the approximating function.

I need to use the approximating function for further analysis.

Data:

i 1 2 3 4 5 6 7 8 9 10 11 12 13
x 0.161166 0.53935
 0.844731
 0.910587
 0.98339
 1.12121
 1.16512
 1.18679
 1.27404
 1.31795
 1.38353
 1.41993
 1.51468
y
 0.039954
 0.049806
 0.074614
 0.09902
 0.12425
 0.149126
 0.17226
 0.19807
 0.246139
 0.295268
 0.393406
 0.493437
 0.689996

Looking forward for the kind assistance.

Thanks a lot.

---
Sam

2. ## Re: Curve fitting of experimental data

Have you plottied the data to see what might be a good fit? It increases quickly so it looks like an exponential or a high order polynomial would fit well. I tried to fit these and you were right that an exponential fit does not work well but a quadratic or cubic relationship fits quite well.

3. ## Re: Curve fitting of experimental data

Did you try y = a + b exp(c x) ?

4. ## Re: Curve fitting of experimental data

The equation y = a + b exp(c x) generaly requires the use of a non-linear linear method of regression because the function is non-linear relatively to the parameter c.These methods are recursive and a guessed value of c is necessary to start the iterative process.
A different method (straightforward, i.e. not recursive) is published on Scribd, "Régressions et équations intégrales", p.16-17 (in French, but the equations are very simples and understandable in any language). Link to Scribd :
JJacquelin's Documents | Scribd
The result with this method is shown below :

5. ## Re: Curve fitting of experimental data

There is a typing mistake on the first figure (message #3, 10:17 AM) : it is not c=0.08628, but c=4.045969
Anyway, this preliminary result was less accurate than the result in message #4.