We introduce a statistical regression model to investigate the impact of dyadic relations on complex networks generated from observed repeated interactions. It is based on generalised hypergeometric ensembles (gHypEG), a class of statistical network ensembles developed recently to deal with multi-edge graph and count data. We represent different types of known relations between system elements by weighted graphs, separated in the different layers of a multiplex network. With our method, we can regress the influence of each relational layer, the explanatory variables, on the interaction counts, the dependent variables. Moreover, we can quantify the statistical significance of the relations as explanatory variables for the observed interactions. To demonstrate the power of our approach, we investigate an example based on empirical data.