Undergrad Correlation Coefficient Clarification

[Tchao]

Let's say that the correlation coefficient between X and Y were swapped so that the correlation coefficient between Y and X. If we were to compared the correlation coefficient between X and Y and Y and X. Based on my understanding of correlation coefficient, it doesn't matter if f X and Y were swapped. The correlation coefficient for both X and Y and Y and X would be the same.

 

[andrewkirk]

That is correct. Correlation coefficient between the two is defined as
$$\frac{E[\ (X-E[X])(Y-E[Y])]\ }{\sqrt{E[(X-E(X))^2]E[(Y-E[Y])^2]}}$$
As you can see, this formula is symmetric between X and Y.