We present a novel approach for the determination of the relationship between two random variables, which we call Regression by Integration. The resulting curve is a least absolute error estimate. Compared to other regression methods, it has the advantage that, instead of a sample of simultaneously taken pairs of the two random variables, only a separate sample of each of the random variables is required. We demonstrate the practicability of the method on Angstrom-Prescott-type relations and compare the results with those obtained by least square error fits. We present supporting theoretical background information based on copulas. We show that Regression by Integration leads to the strict interdependence of the two random variables; Spearman's rho is equal to one. (C) 2018 Elsevier Ltd. All rights reserved.