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Jun 11, 2020 at 14:32 history edited CommunityBot
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Jan 23, 2018 at 17:16 comment added Haitao Du I love this answer because it gives much more intuition than algebra. BTW, not sure if you checked this guy's youtube channel. I enjoyed it a lot
Apr 13, 2017 at 12:44 history edited CommunityBot
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Sep 19, 2014 at 15:20 history post merged (destination)
Aug 26, 2014 at 13:12 comment added whuber @Caracal Thank you for the references. I originally envisioned an answer that uses diagrams like those in your answer--which make a wonderful supplement to my answer here--but after creating them felt that pseudo-3D figures might be too complex and ambiguous to be entirely suitable. I was pleased to find that the argument could be reduced entirely to the simplest vector operations in the plane. It may also be worth pointing out that a preliminary centering of the data is unnecessary, because that is handled by including a nonzero constant vector among the $x_i$.
Aug 26, 2014 at 7:39 comment added caracal More illustrations along these lines can be found in Wicken's book "The Geometry of Multivariate Statistics" (1994). Some examples are in this answer.
Aug 25, 2014 at 20:40 history answered whuber CC BY-SA 3.0