社會科學研究中使用迴歸分析的五個重要觀念

Five Important Concepts of Using Regression Analysis in Social Science Studies

多元迴歸是統計分析中最重要也是最基本的分析方法與技術，本文討論在社會科學研究中使用迴歸分析的五個重要統計概念，透過實際範例一步一步的示範與圖形的講解，重新檢視與詮釋這五個重要概念與其數理原理背後的涵義。這五個概念依序為（一）、淨迴歸係數的意義與控制的概念、（二）、殘差項獨立性診斷的自我相關Durbin-Watson 統計量的意義與使用時機、（三）、多元共線性的意義與診斷統計量：變異數膨脹因子與條件數的解釋、（四）、具有交互作用項的調節迴歸分析、淨迴歸係數的解釋與標準化淨迴歸係數的意義、以及（五）、從決定係數的拆解決定解釋變項的相對重要性。最後，本文提出使用這五個概念的建議。

Multiple regression analysis is a fundamental and useful statistical method for data analysis. In this paper, we discuss five important statistical concepts of using regression analysis in social science research. We examine and explain these concepts using numerical examples with graphic illustration. The five concepts are partial regression coefficient, the Durbin-Watson statistic, multicollinearity and its diagnostic statistics: variance inflation factor and condition index, partial regression coefficient of moderated multiple regression and its standardized coefficient, decompositions of the coefficient of determination. We conclude the paper by giving general guidelines for applying these concepts in analyzing data in social science studies.