The correlation coefficient between X and Y is the same as the correlation coefficient between Y and X: True or False
- I believe it is True because calculating the correlation coefficient for X and Y and Y and X will give you the same answer.
Yes, you are correct. The statement is true. The correlation coefficient measures the strength and direction of the relationship between two variables. Since the correlation coefficient only quantifies the strength and direction of the relationship, it does not matter which variable is designated as X or Y. Swapping the variables will not change the correlation between them.
To calculate the correlation coefficient between X and Y, you typically use a formula such as Pearson's correlation coefficient. This formula computes the covariance between X and Y, divided by the product of their respective standard deviations. However, this formula is symmetric, which means it produces the same result regardless of the order of the variables. So, whether you calculate the correlation coefficient for X and Y or Y and X, the answer should be the same.