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 Big Problem with Polynomial Curve Fitting		  New Topic  Reply to Topic
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VolkerPresser

Germany
Posts
Posted - 10/10/2006 :  10:51:52 AM  Show Profile  Edit Topic  Reply with Quote  View user's IP address  Delete Topic
Origin Version (Select Help-->About Origin): 7.5
Operating System: WinXP

Hello,

I do have the following problem: When fitting a polynomial function (2. order; type: A0 + A1*x + A2*x^2 = y) I get a very good fit (R 0.99887). However I CANNOT recalcuate the values obtained from non linear curve fitting, i.e. when calculating with the refined parameters the outcome is different to those provided in the NLSF sheet (and more than differing from those values as seen in the diagram).

example:

650 = x --> y (NLSF) = -17 / Y (calculated) = -14 !!

Funny... Excel comes up the the very same result for a polynomial function - but the outcome is also wrong when recalculating it! I honestly do have not a hint of a clue what went wrong....

Does someone has any idea about this problem? It's really creeping me out...

Thanks in advance :)

Volker

P.S. my data points are:

650 -17
700 -15.7
750 -14.5
800 -13.48
850 -12.5

Mike Buess

USA
3037 Posts
Posted - 10/10/2006 :  5:43:10 PM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
Hi Volker,

It's probably just a matter of precision. When I fit your data to the Poly function the results log and parameter worksheet tell me that a2 = -0.00002, but if I ask for a2 in the script window I get A2 = -2.342857E-5. A small difference in a high order coefficient can make a large difference when you try to reproduce the fit curve so you should use the nlsf parameter expressions (nlsf.p1, nlsf.p2, nlsf.p3 or a0, a1, a2) rather than copying/pasting from results log or worksheet. If your data are in cols A(X) and B(Y) then create col C(Y) and enter the following expression in the script window.

col(C) = a0 + a1*col(A) + a2*col(A)^2

If you've started another fit or closed and reopened the project then a0, a1 and a2 will have the wrong values. In that case you can redefine them from the parameter worksheet...

a0 = Parameters1_Value[1];
a1 = Parameters1_Value[2];
a2 = Parameters1_Value[3];

Although the worksheet cells are displayed with reduced precision their internal data are full precision.

For more discussion on this issue see this forum topic:
http://www.originlab.com/forum/topic.asp?TOPIC_ID=3663

Mike Buess
Origin WebRing Member
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