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I Correlation Coefficient Clarification

  1. Apr 23, 2017 #1
    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.
     
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  3. Apr 23, 2017 #2

    andrewkirk

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    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.
     
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