Talk:Correlation

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This article has been mentioned by a media organization:

Heta, Marco (March 18, 2018). "Neymar and the magical influence of an enigmatic amulet". Football Paradise. Retrieved March 27, 2018. Wikipedia, the convenient data bank for journalists around the globe, defines correlation as follows: 'Correlation is any of a broad class of statistical relationships involving dependence, though in common usage it most often refers to how close two variables are to having a linear relationship with each other.'

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numerical instability

You need to be a little bit careful running around claiming algorithms are numerically unstable. Instability depends on the range of numbers used. The one pass algorithm is stable if the full calculation can be done using integer arithmetic without intermediate results overflowing. Charles Esson (talk) 08:11, 8 October 2009 (UTC)[reply]

I am most used to numerical instability in the case where there is an exponentially growing term that should, ideally, be zero. This often happens in numerical integration. The term ill-conditioned is, for example, used in matrix operations where cancelation and round-off cause numerical problems. Seems to me that the latter is appropriate here. Gah4 (talk) 23:20, 17 July 2018 (UTC)[reply]

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Relationship between mean values?

The third paragraph of the lead says

when used in a technical sense, correlation refers to any of several specific types of relationship between mean values.

I’m not sure what this means—e.g., in what sense does the Pearson correlation coefficient measure a relationship between mean values? Can we rewrite this more clearly? Loraof (talk) 19:29, 23 November 2017 (UTC)[reply]

I attempted to improve the language there. Since it's referring to a technical sense I took the liberty of dealing with ambiguity by being slightly more technical. Glenbarnett (talk) 03:45, 19 April 2024 (UTC)[reply]

External video

I find the external video "floating link", Lecture 21: Covariance and Correlation, Statistics 110, Harvard University, 49:25, April 29, 2013 slightly unwikipedian. I somewhat dislike external links within a wikipedia article in general (I think they should be relegated to the bottom of the page) but I feel this one crosses some line. 129.240.43.144 (talk) 11:31, 28 September 2018 (UTC)[reply]

Agree. Removed per Template:External media#When to use - readers will not expect this type of media in the article. (I watched the beginning and it's not like it was compelling viewing.) Thanks for posting this. Qwfp (talk) 19:34, 28 September 2018 (UTC)[reply]

Main photo incorrect?

Image here: https://wiki.riteme.site/wiki/Correlation_and_dependence#/media/File:Correlation_examples2.svg

The figure second from the left on the bottom row says correlation 0. For all the other figures in that row it makes sense to me, because they are symmetrical and that symmetry is either flat or vertical. However in that example, which is a square tilted upward at an angle, the data are correlated linearly are they not? — Preceding unsigned comment added by 192.195.81.229 (talk) 21:11, 19 March 2019 (UTC)[reply]

I believe the intent is that the square is rotated about its center. The correlation should be zero for any rotation angle. Glenbarnett (talk) 03:25, 19 April 2024 (UTC)[reply]

The image is slightly flattened (squished vertically relative to its width) which may be distorting the visual impression a bit (without actually changing the correlation). Note the "ring" looks elliptical when it was intended to be circular Glenbarnett (talk) 03:27, 19 April 2024 (UTC)[reply]

I would add that this article at one point in the past used to say something along the lines that the third row of plots in that image showed dependence with zero correlation. While it doesn't actually say that now, people will continue to gain that impression (because all but one of those plots does that). However the last plot (the four 'circular' point clouds arranged in a square) looks to actually be showing a pair of independent bimodal variables. More specifically I think that in that example each margin is a 50-50 mixture of two Gaussians with different mean but the same standard deviation (albeit the issue is much more general). If within each of the point four clouds the variables were independent, the plot as a whole is. The algebra is easy enough but if algebraic arguments are unconvincing, I was able to replicate the impression of the image by recentering four bivariate standard normals at the corners of a square in the x-y plane and sampling from each with equal probability. For such an example, the empirical bivariate copula is uniform over the unit square. Glenbarnett (talk) 03:58, 19 April 2024 (UTC)[reply]

Article title: discrepancy with the content

Hello. I wonder why the article is titled 'Correlation and dependence', but the definition states 'correlation or dependence is any statistical relationship ...'. How can this be correctly resolved? --TadejM ^{my talk} 10:56, 20 July 2021 (UTC)[reply]

I've moved the article to 'Correlation' in accordance with the principle of using one article for one concept. In addition, the article defines both terms as synonyms. --TadejM ^{my talk} 14:24, 20 July 2021 (UTC)[reply]