Exploring the degree to which phenotypic variation, influenced by intrinsic nonlinear biological mechanisms, can be accurately captured using statistical methods is essential for advancing our comprehension of complex biological systems and predicting their functionality. Here, we examine this issue by combining a computational model of gene regulation networks with a linear additive prediction model, akin to polygenic scores utilized in genetic analyses. Inspired by the variational framework of quantitative genetics, we create a population of individual networks possessing identical topology yet showcasing diversity in regulatory strengths. By discerning which regulatory connections determine the prediction of phenotypes, we contextualize our findings within the framework of core and peripheral causal determinants, as proposed by the omnigenic model of complex traits. We establish connections between our results and concepts such as global sensitivity and local stability in dynamical systems, alongside the notion of sloppy parameters in biological models. Furthermore, we explore the implications of our investigation for the broader discourse surrounding the role of epistatic interactions in the prediction of complex phenotypes.