Covariance and correlation coefficient

  • #1

Main Question or Discussion Point

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.
 

Answers and Replies

  • #2
Forget the first sentence the question is only the second sentence
 
  • #3
Dr. Courtney
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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
Dr. Courtney
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is there a proof?
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.
 
  • #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.
 
  • #7
mathman
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