# Talk:Curve fitting

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## Problems

This article covers math skill that could be learned in a high school physics class but causes the reader to think about concepts one shouldn't even think about until calc II. There are better examples of these principles. Talking about osculation and using curvature to find the magnitude of a force vector are not really necessary. Here is a rule for education. The more simple, the better, if it gets the job done. —Preceding unsigned comment added by 67.213.3.6 (talk) 02:12, 17 February 2008 (UTC)

## Illustrations Needed

Some examples would be extremely useful here.--jazzle 12:02, 28 August 2006 (UTC)

Agreed. Do you have any in mind ? StuRat 07:05, 30 August 2006 (UTC)
ok, here's my 2 bits

here is a simple example using the free Pari-GP program (or can use calculator) and basic matrix ops:
given a data set (x,y) (2,5),(3,10) and (4,19)

to solve to a presumed quadratic fit,

a=[1,2,4;1,3,9;1,4,16]  : b=[5;10;19]

c=matsolve(a,b) returns [7 -5 2 ]

y=2x^2-5x+7

One can then evaluate this in a spreadsheet/plot for adequacy of fit

Now, say you change the presumed fit to the form Y=C2*EXP(x)+C1* x+ C0

we modify a to a=[1,2,7.39;1,3,20.01;1,4,54.6] (where for clarity 54.6=EXP(4))

for this limited dataset, we get an equally great fit  ::(C2,C1,C0)=(0.1821,2.702,-1.750)
The proper fit would be dictated by any data outside of the orig data set [as the data cannot be both quadratic and exponential]
The matrices must be square I believe ...--Billymac00 (talk) 00:12, 11 March 2008 (UTC)

I have written a TableCurve 3D user defined function (udf) for a rotated and shifted paraboloid. With this module, available upon request, one can obtain the shift and rotation of paraboidal data with a few clicks in TableCurve 3D by Systat Software, Inc. http://www.systat.com

There is some problem with the syntax of the second paragraph, I think. Charles Matthews 16:34, 23 Jun 2004 (UTC)

This article seems to overlap strongly with regression analysis and (to some degree) with supervised learning and function approximation. Should we merge this into regression analysis? -- hike395 04:44, 1 Feb 2005 (UTC)

## Restored article

This section has been restored to be an intro to both interpolation and regression analysis. It will be expanded, to hopefully include some illustrations. StuRat 05:36, 8 August 2005 (UTC)

I feel that the reference to a line in slope/intercept form, y = mx + b, has some value to explain the relationship with a first degree polynomial, and should be restored. The later modification also makes it unclear whether the 3 collinear points is a case where we "got lucky" or not. The rest of the mods look good to me. StuRat 05:36, 8 August 2005 (UTC)

Feel free to put that back. :) By the way, it is good to keep a formal style, rather than conversational style, if possible. Cheers, Oleg Alexandrov 15:31, 8 August 2005 (UTC)

I will keep that in mind, or should I say, "One will endeavor to utilize maximal formality, henceforth and hereafter, inasmuch as said formality is applicable." LOL
We should also add sections on other types of curves, like Bezier/NURBS curves, in the future. These could be added to the new "Fitting data points to other curves" section, if small, or a new section for each curve type could be added, if large. StuRat 23:30, 8 August 2005 (UTC)
Oleg, referring to your (apparently truncated) comment on my last revision: I still think that the sentence "as opposed to the usual slope m for a line is slope/intercept form, or y = mx + b" is reduntant, come on, if people must know slope
... I think we should write for people of all skill levels and backgrounds. While your students wouldn't need us to explain such basics, we might have high school or even middle school students looking up "curve fitting" here. While the detailed theory may well be beyond them, they could still benefit from learning the basics. StuRat 01:37, 9 August 2005 (UTC)

## Non-linear curve fitting

There exists a stub article on non-linear curve fitting. I think that rather than expanding that stub, we should do a merge and expand on the material that already exists on non-linear curves in this article. Jyotirmoyb 05:24, 15 February 2007 (UTC)

## Integrate with article nonlinear regression

In addition to nonlinear curve fitting, some coordination is needed with the regression articles, in particular with the article "nonlinear regression."

From a statistician's perspective, regression includes not only curve fitting but inference, for example computing a confidence interval for a regression prediction. Dfarrar 20:18, 20 February 2007 (UTC)

## Merge curve fitting with smoothing

• Oppose - I would like to object to merging curve fitting and smoothing together; I think they are different concepts. Curve fittings involves fitting a function and often calculating minimal error, while smoothing can be done without fitting a curve, implying a more "on the fly" algorithm that can process points one by one. Anoko moonlight (talk) 08:27, 14 May 2008 (UTC)
• Oppose - Smoothing and fitting are fundamentally different things - a smoothing function goes through all the given data points; a fitting curve often doesn't go through any data points at all. You might write one article covering both, since they are related, but I don't think that's a good idea.--Noe (talk) 09:38, 14 May 2008 (UTC)
• Oppose - Not a good idea. Curve fitting is often an analytic scientific tool, while smoothing is more for cosmetic choices, in my view. Hess88 (talk) 23:08, 19 May 2008 (UTC)

Given that the merger proposal has been cancelled, I have added a little to smoothing to attempt to distinguish smoothing from curve fitting and which can benefit from improvement if it doesn't cover all requirements. Melcombe (talk) 12:45, 20 May 2008 (UTC)