Author(s)

Zhaoyang Li¹, Bostjan Antoncic^2*

¹Shanghai University of International Business and Economics, Shanghai, China.
²School of Economics and Business, University of Ljubljana, Ljubljana, Slovenia.

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.

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

Li, Z. and Antoncic, B. (2021) A Geometric View on Inner Transformation between the Variables of a Linear Regression Model. Applied Mathematics, 12, 931-938. doi: 10.4236/am.2021.1210061.