Question

1. How might squaring a correlation coefficient be useful to understanding the relationship between two variables?
2. Why is it important to remember “association, not causation” when discussing correlations? Please provide an example.

Answer 1

Suppose the correlation coefficient between X and Y is -0.9 and that between X and Z is 0.3. It is difficult to compare the correlation between X, Y and X, Z. Now if we look into the square of correlation coefficient ie r². We see that for X and Y, r² = 0.81 and for X, Z, r² takes value 0.09. Now it is possible to see which relationship is much stronger.

Suppose we find that the correlation coefficient between "marks obtained by girls" and "marks obtained by boys" in a particular subject is 0.9. We can say that the association between two variable is high enough. But we cannot tell that the marks obtained by girls is highly affected by the marks obtained by boys because both boys and girls studied and had given exams independently of each other. So if we interpret the correlation coefficient as a causation then the interpretation becomes meaningless.