Multivariate Multiple Orthogonal Linear Regression

Abstract

We propose a multivariate multiple orthogonal linear regression (MMOLR) model. The MMOLR model expresses the relationship between two sets of dependent variables and independent variables. It is possible to use the MMOLR as a step to be followed by multivariate linear regression to compare and investigate the relationships between dependent variables, which are still limited in the multivariate linear regression model. The MMOLR takes into account the advantages of the errors-in-variables model, that is, total least squares, and thereby, examines the errors of all independent and dependent variables. Consequently, the assumptions of the model are easy to satisfy in practice. Moreover, in the context of total least squares, we reveal the relationship between the MMOLR and the canonical regression model.