Prove significant effect of third variable on a correlation

So I was measuring correlations in Boxscores of basketball players in the NBA.

3PA  DRB            -0.205499


I was trying to find some interesting correlations. This is a correlation between 3 point shots attempted (3PA) and defensive rebounds (DRB). It is something that is not correlated with the development of play. Players who take more 3 point shots are usually guards that rebound less. So I tried to account for this by stratifying. I divided the data into two groups (centers/forwards & guards).

0.09863996993231319 -0.15288533987772265


These are the correlations between the two attributes for the groups. The correlations are smaller, but is it significant?

What I want to know is how can you statistically prove this type of effect?

• Searching on "statistical significance correlation" should give you everything you need to know. Also, did you notice the minus sign on your first result? – rolando2 Jul 27 '18 at 14:59
• Of course I noticed the minus, it is a negative correlation. – Borut Flis Jul 27 '18 at 18:48
• I knew about statistical significance of the correlation before. But I was asking something else. Well I suppose I could test all the correlations and see if they are no longer significant after the introduction of the third variable. – Borut Flis Jul 28 '18 at 7:18
• Regression interaction will test the difference between two groups' correlations. But to test whether a change after introducing another variable will be statistically significant -- I don't see how any distribution under the null hypothesis would be known. Thus I don't see how one could perform such a test. – rolando2 Jul 28 '18 at 11:13
• I need to learn about Regression more. – Borut Flis Jul 28 '18 at 12:39