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https://doi.org/10.1137/S0895479897329692

has been cited by the following article:

• TITLE: A Geometric View on Inner Transformation between the Variables of a Linear Regression Model

  AUTHORS: Zhaoyang Li, Bostjan Antoncic

  KEYWORDS: Matrix Singular Value Decomposition, Moore-Penrose Generalized Inverse, Matrix Inner Transformation, Regression Analysis

  JOURNAL NAME: Applied Mathematics, Vol.12 No.10, October 29, 2021

  ABSTRACT: In the teaching and researching of linear regression analysis, it is interesting and enlightening to explore how the dependent variable vector can be inner-transformed into regression coefficient estimator vector from a visible geometrical view. As an example, the roadmap of such inner transformation is presented based on a simple multiple linear regression model in this work. By applying the matrix algorithms like singular value decomposition (SVD) and Moore-Penrose generalized matrix inverse, the dependent variable vector lands into the right space of the independent variable matrix and is metamorphosed into regression coefficient estimator vector through the three-step of inner transformation. This work explores the geometrical relationship between the dependent variable vector and regression coefficient estimator vector as well as presents a new approach for vector rotating.