A study of MT systems applied to multivariate regression

Abstract

Taguchi’s T-method belong to the MT System, which is a representative method in quality engineering. Another relevant technique is multiple single regression (MSR), which incorporates the concept of the resistance line. These methods are used to make predictions when there is one output. In addition, multivariate multiple regression analysis is used as a prediction method when there are multivariate outputs.

This study proposes methods that apply the T-method and MSR to multiple outputs. The proposed methods are: "independent multivariate T-method" (iMvT), "multivariate T-method" (MvT), "simple multivariate T-method" (MvT+), "independent multivariate multiple single regression" (iMMSR), "multivariate multiple single regression" (MMSR), and "simple multivariate multiple single regression" (MMSR+). iMvT and iMMSR combine predictions simply, MvT and MMSR apply generalized least squares, and MvT+ and MMSR+ apply Moore–Penrose’s generalized inverse matrix. We compared the accuracy of the proposed methods with that of multivariate multiple regression analysis. Artificial data analysis was performed by changing the number of training data and correlation. We also performed analyses on the actual data. The results indicate that the proposed methods are more accurate than the existing methods.