What does it mean for two variables to be uncorrelated? How is it possible for two variables to be strongly related but still uncorrelated
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possible duplicate of Can somebody illustrate how there can be dependence and zero covariance?. Also this closely related question is relevant/overlapping. There are many others. This is almost a FAQ on this site at this point. I'm hoping that certain veteran users will stop answering questions that are obvious duplicates/FAQs, as this wastes their time and adds to clutter on this site. – Macro Mar 11 '13 at 13:31
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Correlation is a measure of linear relationship. A positive correlation between X and Y means that, as X goes up, Y tends to go up. A negative correlation means that as X goes up, Y tends to go down.
It is certainly possible to have 0 correlation and yet have a relationship, if the relationship is nonlinear. For example, if X ranges from -4 to 4 (say) and $Y = X^2$, then there is a relationship but correlation will be 0. If there is error, then the correlation will not be exactly 0 but will be close.
e.g
#Random error, corr close to 0
set.seed(129231)
x <- runif(100, -4,4)
y <- x^2
cor(x,y)
#No error, correlation = 0
x <- rep((-4:4),50)
y <- x^2
cor(x,y)
Peter Flom
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1Maybe what @marian really needs is Distance Correlation http://en.wikipedia.org/wiki/Distance_correlation – curious_cat Mar 11 '13 at 11:43