A Note on Geometric Interpretations of Regression Analysis

• Activity Number: 143
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Education
• Author(s): Bilin Zeng* and Kang Chen and Cong Wang
• Companies: California State University at Bakersfield and National University of Singapore and Chinese University of Hong Kong
• Keywords: Regression Analysis ; Geometric Interpretation ; Partial Correlation Coefficient ; Frisch-Waugh-Lovell Theorem

Abstract

Regression analysis is traditionally presented in algebraic forms. In fact, all concepts of regression analysis can be visualized by applying a few principles of geometry. This paper aims to systematically restate and interpret basic concepts and important properties of regression analysis under the geometric framework. We first propose a simple geometric proof for the Frisch-Waugh-Lovell Theorem which is then followed by developing geometric expressions of regression coefficients and partial correlation coefficients. In addition, we apply geometric approaches to prove and verify three formulas that display the relationship among simple, multiple and partial correlation coefficients. Moreover, by describing the geometric analogues of the regression concepts systematically, this article also illustrates that geometric approach can provide a better understanding of regression analysis. Although these formulas are well known in the basic statistics textbooks and have already been proved by algebraic methods, we are among the first who give the geometric proof.