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Covariance and correlation coefficient

  1. Nov 4, 2015 #1
    How do you prove that the maximum value of 2*cov(x,y) can be is equal to var(x) + var(y).

    Moreover, how do you prove that the correlation coefficient, cov(x,y)/(sigma(x)*sigma(y), can only be between -1 and 1.
  2. jcsd
  3. Nov 4, 2015 #2
    Forget the first sentence the question is only the second sentence
  4. Nov 4, 2015 #3
    Try computing a bunch for random and real data sets and you will see that the rule is never violated.

    Of course, I'm an experimentalist.
  5. Nov 5, 2015 #4
    is there a proof?
  6. Nov 5, 2015 #5
    I bet there is for a statement for which no counter example exists. I think I recall even seeing one when I taught statistics.

    But you can probably Google it up as easily as I can.
  7. Nov 5, 2015 #6
    Google sucks, I want some pictures bro. Because I did some examples and I don't understand, I think it doesn't violate those rules because of like dot products or something but I don't see the correlation coefficient. Can someone please enlighten me with some insight.
  8. Nov 5, 2015 #7


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