Talk:Least squares
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(this article needs work, more content, explanation of the Gauss method)
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[edit] Addition
I have moved some that information that belongs in least squares instead of in the article on linear regression. The article Least-squares estimation of linear regression coefficients should also be examined and merged with this.Woollymammoth 02:14, 24 February 2007 (UTC)
[edit] political science
A number of politics articles goes here, can this article be made more relevant to the political usage please? --Gregstephens 02:20, 25 Mar 2005 (UTC)
- I have no idea what the political usage is, and I am unable to find those political articles linking here (I clicked on "What links here"). Unless it's very much related to this topic, I think its inclusion would be inappropriate; it should be in a separate article titled least squares (politics) or the like. Michael Hardy 03:02, 25 Mar 2005 (UTC)
- It is linked to from proportional representation, it is a measurement ot figure out how disproportional an electoral system is. The formula used is:
- Lsq= square root of (half the sum of (Vi-Si)^2)
Is that similar to what is used here? Or is it different? If it is, I will start an article on measures of disproportionality, as that can cover more. --Gregstephens 04:52, 25 Mar 2005 (UTC)
I find the remarks above cryptic. What, in particular, are the quantities you are calling Vi and Si? Michael Hardy 30 June 2005 21:11 (UTC)
Firstly, the formula cited above seems to be basically the same as the usual definition, save for some proportionality constant. So there is no need to involve politics here. Secondly, there is no such formula in proportional representation at this date. It was removed on the 5th of June. --HelgeStenstrom 12:37, 21 November 2005 (UTC)
The Gallagher Index is sometimes refered to as the least squares method of calculating disproportionality. --LeftyG 07:24, 6 January 2006 (UTC)
[edit] Recursion
Could someone put in a short discussion of how to solve the problem using recursion? I filled a request for Recursive least squares algorithm by redirecting to this article, but perhaps someone whoever requested it wouldn't find all they're looking for here.--Joel 03:26, 25 Jun 2005 (UTC)
- I don't think that redirect is very helpful as the current article does not talk about solving the least squares problem recursively at all. Unfortunately, I can't add it to the article since I have no idea how the algorithm is supposed to work. -- Jitse Niesen (talk) 11:30, 25 Jun 2005 (UTC)
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- Isn't that at Solving linear recurrence relations in Recurrence relation? 212.102.225.147 30 June 2005 12:54 (UTC)
- I am sorry, but I don't see anything there about least squares problems. Could you please be more specific? -- Jitse Niesen (talk) 2 July 2005 23:52 (UTC)
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- No (sorry from my part), my response was more based on a hunch feeling then in-depth study of the article. 212.102.225.147 16:21, 11 July 2005 (UTC)
[edit] Ordinate
Ah, the residuals are measured along the ordinate (assuming no error in the x-values) now allows me to understand what you mean by ordinate. But it wasn't at all obvious. Doesn't between the fitted function and the data. make this clear anyway, and rather more clear? William M. Connolley 09:25:26, 2005-08-24 (UTC).
"Between the fitted function and the data" is certainly erroneous. When "distance" is measured between a point and a particular line (in this case the fitted function), the outcome will vary with the choosen direction along which you want to measure. In geometry "distance" would create no problem, because by definition the measurement is assumed to be in orthogonal direction. However, in OLS, this is certainly not the case. The objective in OLS (as well as the optimization of the underlying partial derivative problem) is to minimize the error in the Y dimension. As a consequence, in OLS the "distance" is measured along the direction of the Y-axis (= the ordinate).
A challenge: try to define a formula for Orthogonal Least Squares, and you'll understand immediately why Ordinary LS is such a popular method. User:Witger
You have any info about this Witger? I am using OR at the moment (or Total Least Squares regression to be more precise, isn't that the same?) Until now I haven't been able to find any 'basic' information about Orthogonal Regression except: SIAM Review 36 (2) 258-264 Jeroenemans 16:42, 5 December 2006 (UTC)
[edit] Nonrubustness of Least Squares and IRLS
I have noticed that outside certain fields (computer vision) there seems to be little discussion of robust statistics. Least squares is utterly crippled by any form of asymmetric outliers, and I believe that more of this article should be spent on discussing the limitations of the method and pointing to similar methods (Iterated Reweighted Least Squares, or Least Median Squares, or consensus based algorithms like RANSAC... interestingly wikipedia doesn't have any articles on IRLS or Least Median Squares, despite their importance in high noise environments... perhaps I'll write some). Anyone have any thoughts on this? - JustinWick 18:09, 5 December 2005 (UTC)
[edit] Merge
I support the merge of Least mean squares into this page. Possible with a section on adaptive filters. --Pfafrich 23:13, 10 January 2006 (UTC)
- I won't mind. But that text needs a good cleanup before that. Anybody willing to do the work? Oleg Alexandrov (talk) 00:13, 11 January 2006 (UTC)
- I oppose. The article Coefficient of determination will not be comprehensive, if this article disappears. A.L.
I support the merge of RSS with "Least Squares" (This article). Could we reference the definition as a sub-section titled "RSS"? Having a reference for the term would be helpful in other articles as well. What's required before a merge is allowed? Yoderj 19:19, 14 February 2007 (UTC)
[edit] History: Fact Checking
The submission by 81.173.155.84 (diff) reads, in part:
- On New Year's Day in 1801, the italien astronomer Giuseppe Piazzi discovered the asteroid Ceres. He was able to track its path for 40 days, until Ceres disappeared behind the sun.
I'm removing the wording "until Ceres disappeared behind the sun" on the grounds of error. Modern astronomy software confirms that on 10 Feb 1801 Ceres was still more than 90 degrees away from the sun, therefore not behind the Sun, and not even lost in the Sun's glare. (Jean Meeus, in Mathematical Astronomy Morsels, p. 300, agrees.) Conjunction with the Sun did not occur until July 1801. A much more likely guess is that Ceres, which had dimmed from magnitude 7.8 to 8.5 and was also progressively lower in the western sky each evening by the end of twilight, became too dim to be seen, but the date at which this happened depends on the aperture of Piazzi's telescope. Perhaps also Ceres became lost in the star fields between the Pleiades and Hyades. My own experience is that Ceres is difficult to track with 80mm binoculars in the best of conditions, so I favor the dimness explanation. I suggest someone find Piazzi's notebook and see what he said. - JEBrown87544 16:05, 22 July 2006 (UTC)
[edit] Robert Adrain
The Robert Adrain page states,
- He is chiefly remembered for his formulation of the method of least squares, published in 1808. Adrain certainly did not know of the work of C.F. Gauss on least squares (published 1809), although it is possible that he had read A.M. Legendre's article on the topic (published 1804).
anyone know anything about this? --Salix alba (talk) 20:54, 29 September 2006 (UTC)
[edit] Wording in intro
I don't like saying LS is "a mathematical optimization technique." I would prefer something like that it is a criterion of agreement between the data and the fitted curve. Once a criterion has been decided upon, LS or whatever, one needs a mathematical optimization technique such as Levenberg-Marquandt, Gauss-Newton, etc.
Dfarrar 00:25, 2 March 2007 (UTC)
