Independent component regression (ICR) is an efficient method for tackling non-Gaussian problems. In this work, the defects of the conventional ICR are analyzed, and a novel quality-relevant independent component regression (QR-ICR) method based on distance covariance and distance correlation is proposed. QR-ICR extracts independent components (ICs) using a quality-relevant independent component analysis (QR-ICA) algorithm, which simultaneously maximizes the non-Gaussianity of ICs and statistical dependency between ICs and quality variables. Meanwhile, two new types of statistical criteria, called cumulative percent relevance (CPR) and Max-Dependency (Max-Dep), are proposed to rank the order and determine the number of ICs according to their contributions to quality variables. The proposed QR-ICR ((CPR)) and QR-ICR(Max-Dep) methods were validated through a vinyl acetate monomer production process and a benchmark near-infrared spectral data. The results have demonstrated that the proposed QR-ICR(CPR) and QR-ICR ((Max-Dep)) provide simpler predictive models and give better prediction performances than PLS,ICR, ICR(CPR), and ICR ((Max-Dep)). (c) 2018 Elsevier Ltd. All rights reserved.