One has a simple dataset of 3 independent variables, e.g., x, y, z.
y and z are logically connected (this is known a priori) and indeed a nice & tight correlation (small scatter) between them is established;
two correlations are measured between x and y and between x and z, with some scatter in both of them. Characterising those correlations would be great because they're not expected a priori, and would add something new to a theory.
I wonder: is x correlated to y (or z) only because of the underlying correlation between y and z? In other words, what is the "more fundamental" correlation? x-y or x-z? (with the other being only a byproduct of the underlying y-z relation)
What is the best statistical tool to face this problem?