1

I have seen this said multiple times where (1) the cosine of the angle between the random variables (on a vector space) is equal to the correlation coefficient, and (2) the claim if random variables are orthogonal then their correlation coefficient is zero.

I don't think (1) is true unless the random variables are centered? Is (2) true even without centering?

kjetil b halvorsen
  • 63,378
  • 26
  • 142
  • 467
student010101
  • 334
  • 2
  • 10
  • https://stats.stackexchange.com/questions/97051/building-the-connection-between-cosine-similarity-and-correlation-in-r – kjetil b halvorsen Jul 12 '20 at 15:59
  • 2
    @kjetilbhalvorsen I don't think that post answers my specific questions. It states that correlation is a centered dot product, but that doesn't necessarily answer these questions. – student010101 Jul 12 '20 at 17:35
  • I didn't close it, ask whuber who did, or ask at meta ... – kjetil b halvorsen Jul 12 '20 at 17:37
  • @whuber Hello Whuber. I don't think the the post you linked necessarily answers my questions enumerated in the OP. It states that correlation is a centered dot product (which I do know as my OP states), but that doesn't necessarily answer these questions. In particular my question 2 asks if random variables are orthogonal, if that means their correlation coefficient is zero, even if the random variables are not centered? – student010101 Jul 12 '20 at 19:17

0 Answers0