A geometric view on inner transformation between the variables of a linear regression model

Li, Zhaoyang (author), Antončič, Boštjan (author)

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.

• Language: English
• Keywords: econometrics, regression analysis, matrix singular value decomposition, Moore-Penrose generalized inverse, matrix inner transformation
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: EF - School of Economics and Business
• Publication status: Published
• Publication version: Version of Record
• Year: 2021
• Number of pages: Str. 931-938
• Numbering: Vol. 12, no. 10
• PID: 20.500.12556/RUL-134026
• UDC: 51-7
• ISSN on article: 2152-7385
• DOI: 10.4236/am.2021.1210061
• COBISS.SI-ID: 83841027
• Publication date in RUL: 22.12.2021

Record is a part of a journal

• Title: Applied mathematics
• Shortened title: Appl. math.
• Publisher: Scientific Research Publishing, Inc.
• ISSN: 2152-7385
• COBISS.SI-ID: 1462364

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.
• Licensing start date: 29.10.2021

Secondary language

• Language: Slovenian
• Keywords: ekonometrija, regresijske analize