Linear regression is one of the widest used data analytics techniques in support of human decision-making. In this paper we discuss some theoretical foundations of confounder detection used in our web-based decision making platform GrandReport. In the context of linear regression, controlling confounding effects means to add further influencing, potentially confounding factors to the analysis. This paper exactly explains confounding effects in terms of the various involved coefficients by utilizing a conjecture on the noise-independent relationship between crude, adjusted, confounder and latent coefficients. We discuss, in how far our findings can improve the explainability of linear regression models as well as the maturity of their application in various contexts.