线性回归中多重共线性的几何解释  

Geometric Interpretation of Multicollinearity in Linear Regression

作　　者：肖霞[1] 伍兴国[1] Xiao Xia;Wu Xingguo(Dongguan Polytechnic,Dongguan Guangdong 523808,China)

机构地区：[1]东莞职业技术学院,广东东莞523808

出　　处：《统计与决策》2021年第21期46-51,共6页Statistics & Decision

基　　金：广东省教育厅普通高校特色创新类项目(2020WTSCX261);东莞市老年社会工作服务及评估项目(政201724);东莞职业教育产学研创研究与服务中心项目(CXTD202101)。

摘　　要：在多元线性回归模型中,分解定理的代数式解释了一元回归系数与偏回归系数的关系,文章用几何学描述分解定理,发现是将一元回归系数按照平行四边形法则进行分解得到各自的偏回归系数。并借助分解定理分析了多重共线性的现象,发现其产生原因可能在于因变量与自变量之间的总体结构,也可能是样本选择的结果。目前一些诊断多重共线性的方法仅仅单独考虑自变量的相关性,因此这些方法基本上是不可靠的,在未区分产生的原因之前,对多重共线性的处理都是盲目的。In the multiple linear regression model, the algebraic formula of the decomposition theorem explains the relationship between the univariate regression coefficient and the partial regression coefficient. This paper uses geometry to describe the decomposition theorem, discovering that the partial regression coefficients are obtained by decomposing the univariate regression coefficients according to the parallelogram law. The paper also analyzes the phenomenon of multicollinearity by means of decomposition theorem, finding that its cause may lie in the overall structure between dependent variables and independent variables, or may be the result of sample selection. At present, some diagnostic methods for multicollinearity only consider the correlation of independent variables, so these methods are basically unreliable, and the multicollinearity is treated blindly until the cause is distinguished.

关 键 词：多重共线性 分解定理 几何解释 变量结构 

分 类 号：F224.0[经济管理—国民经济]