Estimation of Regression Lines through the Focal Point and Related Theories

Abstract

This paper discusses two kinds of regression models, namely the model of regression lines through the focal point (RLF) and the model of regression line through the origin (RLO). The focal point will change according to the conditions of the experiments or the measurement site, so it will be estimated together with regression coefficients. Considering the experimental conditions, four models are proposed and the best model among them is selected by AIC. The models are verified by numerical experiments, and are applied to the wind-blown sand data.
Especially, as RLO has the unique characteristics of not necessarily crossing a centroid, it is different to the ordinal regression line. For this reason, some related theories and relationship with RLF and RLO are discussed.