# Comparing two pearson coefficents w/ r^2

I have three variables, x,y, z. My sample n is about 17,000.

My pearson coeficients & r^2:

for x -> z it is 0.187, 0.034

for y -> z it's 0.311, 0.096

testing for significance, I receive a z-score of 12.3 & p < 0.00

So, I know the difference is significant, but I want to say in (somewhat layman's terms) how strong it is. So, I have looked at coefficient of determination, r^2, to get the ratio: 0.096:0.034, or 2.8.

Is it then correct/accurate to say the correlation between y & z is 2.8 times as strong as the correlation between x & z?

## 1 Answer

It is accurate to say the explained variance between y & z is 2.8 times as strong as the explained variance between x & z.

Or, that z explains almost 10% of the variance of y, but only an estimated 3% of y.

More generally, you could highlight that the correlations you found are both positive and small to moderate. And that given the size of the sample the difference is significant (for a smaller n of, say 400, the difference would not have been significant).