# How do I interpret a partial correlation?

I'm working on a project that has three variables: X, Y, and Z. I suspect, based on my literature review, that X and Y are correlated. However, there is a possibility Z is related to Y as well.

I calculated the Person correlation coefficients:
$$r_{xy}= 0.318, (p<0.05)$$
$$r_{xz}= 0.141, (p>0.05)$$
$$r_{yz}= 0.33, (p<0.05)$$

This seems to match my suspicions - so I calculated the partial correlations between them:

$$r_{xy.z}= 0.29 (p<0.05)$$
$$r_{xz.y}= 0.04 (p>0.05)$$
$$r_{yz.x}= 0.30 (p<0.05)$$

What I am struggling with is how to understand what the partial correlation is telling me. Based on my results, can I say there is a significant relationship between x and y (controlling for z) as I had suspected? Or does the significant relationship between y and z (controlling for x) mean my hypothesized relationship between x and y only exists because of influence of z, as thus is of limited utility?

I suppose my fundamental question - is what exactly do partial correlations tell me about a proposed relationship between my primary two variables?

• Your first suggestion looks fine to me. – mdewey Feb 5 at 16:27