Talk:Uncorrelated
From Wikipedia, the free encyclopedia
Someone needs to check this page. Covariance = 0 and correlation = 0 are NOT equivalent. The usual definition is E[XY] = 0 --> ORTHOGONAL cov(X,Y)=- --> UNCORRELATED
only with zero mean X and Y are the two equivalent.
- Sorry, you're wrong. The only time covariance = 0 is not exactly equivalent to correlation = 0 is when the variances are 0, in which case the correlation is undefined. Michael Hardy 19:58, 13 April 2006 (UTC)
Michael: I have to agree with the previous commenter. I will add that your comment is inconsistent with the wikipedia definition for covariance which defines cov[X,Y]=E[(X-E[X])(Y-E[Y])] which implies cov[X,Y]= E{XY]-E[X]E[Y]. This leads me to believe you are using the term correlation for cov[X,Y]/sqrt(var[X]var[Y]) which AFAIK is usually called the correlation coefficient. By the way, the wiki page for covariance has the correct definition for uncorrelated. Roy Yates, April 17 2006 (I'd register but I haven't figured out how to do that yet.)
I just tried to rewrite to clarify what I think is a confusion over two definitions of correlation. In my field and I suspect Michael's, we just take "correlation" to mean the Pearson correlation coefficient. This is also the primary definition on the correlation Wikipedia page. It seems to me that Roy and the previous commmenter are taking correlation to refer to E[XY] (please correct me if I am wrong... I'm not familiar with this definition, but it may be common in other fields?). Of course, uncorrelated does mean that the correlation coefficient is zero (except in the trivial case Michael mentioned). But uncorrelated does not mean that E[XY] is zero except in the zero mean case. I tried to express both points with the new page, but I did use the term correlation to refer to the Pearson correlation coefficient to be consistent with the main Wikipedia definition. Matt Atwood 19:01, 17 June 2006 (UTC)
