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 Huge errors for the fitting parameters		  New Topic  Reply to Topic
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twelvetang

Canada
Posts
Posted - 12/14/2006 :  2:44:52 PM  Show Profile  Edit Topic  Reply with Quote  View user's IP address  Delete Topic
Origin Version (Select Help-->About Origin): 7.5
Operating System: XP

I rescently use exponatial equation to fit a set of data. the fitting curve is quite well but the errors for the parameter X0 and A1 are too huge to accept.


Does it mean this function don't work? Do I just ignore it or try other parameters/functions?


Edited by - twelvetang on 12/14/2006 3:56:36 PM

easwar

USA
1964 Posts
Posted - 12/14/2006 :  4:27:40 PM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
Hi,

This is because your data basically has zero offset in x and you are fitting with a function that has an offset parameter x0 which is not really required to fit this data. The minimization algorithm thus cannot find a unique value for all the parameters. There are many possible parameter values that give the same quality of fit - note that your final parameter value for x0 is 69.6 which is way off the zero x offset in your data, but that set of parameters still describes the data well - thus the function is essentially over-parameterized for your data. This is why, due to lack of a unique value/minimum for some of the parameters, the error on the parameter is too large.

You could try one of the following:
1> fixing your x0 parameter to a value such as zero (or close to zero if there is a physical reason to even have an x0 parameter in your equation)
2> place upper and lower bounds on your x0 parameter to restrict it to some physically acceptable/expected values
3> fit with another function such as expgro1 which is
y=y0+A*exp(x/t1)

Easwar
OriginLab
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twelvetang

Canada
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Posted - 12/15/2006 :  10:14:43 AM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
Thank you very much, Easwar!
Now I used the expgro1 and get rid of the "huge error" problem.

In terms of the fitting accuracy, which factor (Dependency or R^2) whould describe better. For Dependency (comes with the error), is it the closer to 1, the better?
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Mike Buess

USA
3037 Posts
Posted - 12/15/2006 :  12:19:55 PM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
R^2 = 1 and chi^2/DOF = 0 describe a perfect fit. A dependancy close to 1 signifies overparameterization... that parameter is not necessary. (You probably saw that when fitting to ExpGrow1.)

http://www.originlab.com/www/helponline/origin/The_Fitting_Session_Concept.htm


Mike Buess
Origin WebRing Member
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