Talk:Curve fitting

Confusing Text
I am not sure how to fix this, but the following text is a little confusing: "to infer values of a function where no data are available" At first look I thought "you can't just make up data". I am pretty sure what they mean there is interpolation between points where you have surrounding data but no data point for that particular independent variable value. However, it is a little clumsy (as is my explanation, hence not in the article :)) DeepNorth (talk) 02:36, 27 November 2020 (UTC)

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)

Wolfram Alpha
well, this site can quickly return fits. An example is box input: quadratic fit {{0,-1.5},{100, 1.4},{200,0},{300,-6.5},{400,-18.9},{500,-38.4}}  which shows one the plot as well as the least squares quadratic fit. Samples of various fit types (linear, cubic, etc) is at the site .--Billymac00 (talk) 05:23, 29 November 2009 (UTC)

I'll put on some images created with Mathematica 7 --Marco4math (talk) 21:39, 25 February 2010 (UTC)

This page now links to Wolfram Alpha, so this particular "talk page" discussion may no longer be needed. — Preceding unsigned comment added by 108.81.189.144 (talk) 00:43, 16 August 2014 (UTC)

Applications to 3d
Under this heading, it could be construed as ambiguous that the author used the word "net" when there is a mathematical construct that is named the same thing, without making a link of the word. I'm not an expert on Regression by any means, but it seems to be that the author is talking about net as in a "sum" instead of net as in a generalized sequence. I am not absolutely sure though, and we need absolute surety in mathematics, so I did not want to change the author's work if it was indeed what he/she meant, and I did not want to link to the Topology topic of nets in case that wasn't what he/she meant. I'd be glad if someone with enough expertise to properly read this in context could clarify it in the article. Thanks. :) 67.8.93.121 (talk) 03:22, 3 September 2010 (UTC)

Multiple issues with article
The first issue with the article is that it basically lacks any references, except to a research paper and an MSc thesis which probably does not meet Wikipedia's reliable source criteria. I've added some appropriate tags about references to the article. The second issue is the tone of the article, containing such phrasings as Now, you might wonder why we would ever want to get an approximate fit when we could just increase the degree of the polynomial equation and get an exact match. This isn't the appropriate tone for Wikipedia articles. I've added the "tone" tag to the article. The article seems to have been in this state for a long time. JoshuSasori (talk) 01:47, 6 October 2012 (UTC)

Fitting Other Curves to Data Points
Can someone improve this section by explaining methods or listing tools which can be used to discover what curve to fit to experimental data of unknown relationship? Power, exponential, logarithmic, etc.? 129.55.200.20 (talk) 22:33, 9 May 2013 (UTC)


 * I tried to do this, indirectly, by adding an external link to an online tool that demonstrates exactly this. But User:Billinghurst has repeatedly removed this link. The link is non-commercial, and spot-on topic.
 * Isn't this kind of action by an administrator subject to review? He's been hunting down any changes I make (some demonstrably correct error-fixes) and reversing them, repeatedly.
 * I'm new to this, so if someone can help, please do. Actions like what I see from Billinghurst really leave a bad taste for people who legitimately have something to contribute. I have no problem with a legitimate peer review, but one person vanadlizing, repeatedly, another person's good-intentioned changes is discouraging. — Preceding unsigned comment added by 24.130.168.37 (talk • contribs) 18:04, 23 February 2014

Fitting ellipses, circles, and lines by least squares
To my knowledge, the most complete reference to fitting circles is Nikolai Chernov's book, Circular and linear regression: Fitting circles and lines by least squares, Chapman & Hall/CRC, 2010, where he collected his 30 years of experience with this topic. A few chapters, a few dozen programs and his research papers are available from his web page at the University of Alabama in Birmingham, http://people.cas.uab.edu/~mosya/cl/ --Peterlin (talk) 21:40, 21 August 2015 (UTC)

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