# Do two variables need to be independent in order to obtain a correlation?

I would like to find the correlation between two variables. It was suggested to me that two variables should be independent; otherwise it is not meaningful statistically to calculate a correlation. For example, variable is x and another is $y$ which won't be calculated from $x$, e.g., $y=ab/c+x$. $a$, $b$, and $c$ are some constant value that are the same for all $y$.

### Questions

1. Is what I understand correct?
2. The data set is $y = P+Q+x$. $P$ and $Q$ depends on each $x$, and the same $x$ value can have different value of $P$ and $Q$. Is it meaningful to find a correlation given this data?
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I tried to transform a question to the form that it is answerable. Please confirm that nothing is lost from the original form. –  mpiktas Mar 7 '11 at 12:53
@mpiktas Thank you for your valiant effort to rescue this question. However, the changes were so substantial that significant and potentially important parts of the original question disappeared or were altered beyond recognition. Therefore I have rolled this back to the original question. Let's try to make sense of it as it stands. –  whuber Mar 7 '11 at 15:35
We can try to fix the English--that shouldn't be a problem--but there are problems with the mathematical expressions in the questions. When $y = ab/c + x$, obviously $y$ is "calculated from" $x$. In this case the correlation of a set of $(x,y)$ would equal $1$. In the second question it is mysteriously redundant to write $y=P+Q+x$; you might just as well write $y=P(x)$. These solecisms suggest you might not have properly expressed the questions that you really want answered. Please clarify these points or we'll have to close the question as unanswerable. –  whuber Mar 7 '11 at 15:39
@whuber the OP says he had a suggestion that it would only be meaningful statistically if he attempted to calculate correlation on variables that are independent. Is this suggestion right? Doesnt 'Independence of X and Y mean they are uncorrelated'? –  garciaj Oct 31 at 11:42