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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.
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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
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Knowledge, 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
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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
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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.
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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
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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.
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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
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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? --
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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. --
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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?
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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.
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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.
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When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
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I believe the intent is that the square is rotated about its center. The correlation should be zero for any rotation angle.
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when used in a technical sense, correlation refers to any of several specific types of relationship between mean values.
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to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
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for additional information. I made the following changes:
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