Talk:Linear least squares/Archive 4

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Archive 4

Parameter errors

Question on the second equation under "Parameter errors and correlation": shouldn't the weights "W" in the second inverse term have a transpose on it? I see under the comments that since "W" is a diagonal matrix, its transpose is equal to its non-transposed form, but I think the transpose should be explicit in the equation. It would be easier to follow the progression this way. — Preceding unsigned comment added by Sguimond (talk • contribs) 16:06, 21 March 2013 (UTC)

Inaccurate section?

The "Derivation of the normal equations" section reads:

"S is minimized when its gradient vector is zero. (This follows by definition: if the gradient vector is not zero, there is a direction in which we can move to minimize it further - see maxima and minima.)"

It is my understanding that the gradient vector being zero is a necessary but not sufficient condition for S to be minimized: The gradient is zero at any stationary point, minima or otherwise. So it does not follow by definition, and an explanation/proof is missing. — Preceding unsigned comment added by Saturnalia0 (talk • contribs) 18:37, 20 April 2016 (UTC)

In general multivariate optimization, you are right that grad == 0 is a necessary but not sufficient condition (on the interior of the domain of a smooth function). But linear least squares is not a general multivariate optimization. It is about optimizing a quadratic function, which is a fairly simple special case. The optima occur exactly where grad == 0. I agree that this should be explained better. Mgnbar (talk) 19:36, 20 April 2016 (UTC)

I see, because it's convex. I added an observation in the section, hopefully it's satisfactory. — Preceding unsigned comment added by Saturnalia0 (talk • contribs) 21:01, 20 April 2016 (UTC)

Rename

Linear least squares (mathematics) should be renamed to Numerical methods for linear least squares or Linear least squares (numerical analysis) because "mathematics" is too broad and vague -- "mathematical" is not synonymous with "numerical"; furthermore, the article about ordinary least squares, also called linear least squares in its lead, has a very mathematical treatment, too.fgnievinski (talk) 15:23, 1 August 2016 (UTC)

Do not rename. Linear least squares (mathematics) is succinct and correct. All the other suggestions are circumlocutions.Mollwollfumble (talk) 22:57, 7 April 2017 (UTC)

Scope of the article - remove code examples and proofs

The article goes way beyond the scope of an encyclopedia.

Both the code examples and the derivation (proofs!) should be removed (moved into more appropriate media, e.g. Wiki book Algorithm Implementations, Statistics).

HelpUsStopSpam (talk) 14:45, 1 November 2016 (UTC)

Split apart

The scope of the present article is ill defined and overlaps substantially with other articles. Therefore, I propose reverting the merge of Numerical methods for linear least squares here. Then split apart the rest. fgnievinski (talk) 00:50, 13 July 2018 (UTC)

We have many articles on this and closely related topics. Reorganizing these articles has been proposed many times. I don't understand what your specific proposal is, and I don't understand how splitting off multiple articles would help. Mgnbar (talk) 01:24, 13 July 2018 (UTC)

My proposal is to empty the present article until in can be deleted. fgnievinski (talk) 02:11, 13 July 2018 (UTC)

I've split weighted least squares, constrained least squares, and numerical methods for least squares. I believe the rest can be go into Linear regression and/or Ordinary least squares. fgnievinski (talk) 02:54, 13 July 2018 (UTC)

I've updated Linear least squares to become a WP:broad-concept article instead of a WP:DAB. fgnievinski (talk) 03:28, 16 July 2018 (UTC)

One of the main problems with the present article is that it only applies to ordinary least squares and not to the other types of linear least squares (weighted and generalized), so I've split accordingly. fgnievinski (talk) 03:28, 16 July 2018 (UTC)

Done. fgnievinski (talk) 04:44, 16 July 2018 (UTC)