I am requesting some insight into how multivariate regression analyses are implemented in CONN.

Looking at the z-score matrices of a bivariate correlation analysis and a multivariate regression analysis on the same subjects results in asymmetrical between-network z-scores for multivariate regression, and symmetrical z-scores for bivariate correlation. For clarification, I am looking at the functional connectivity between the DMN and visual network, and within both networks. Looking at the z-score matrix from the multivariate regression analysis, the scores between and within networks are asymmetrical (so the z-score from DMN-VN is not equivalent to the z-score from VN-DMN).

I was under the impression that the correlations would be bi-directional no matter the analysis run, so I am concerned that the asymmetries in the z-scores that appear when running a multivariate regression are the result of an error. I found elsewhere that uni-directional (asymmetrical) correlations have their perks (Asymmetric high-order anatomical brain connectivity sculpts effective connectivity - PMC), but I cannot figure out if CONN is actually computing uni-directional correlations for the multivariate regression analysis, since I cannot find any information about this in the documentation.

Are these asymmetries to be expected or are they the result of an error in the analysis?