标准化系数与偏相关系数的比较与应用

Comparison and Application of Standardized Regressive Coefficient & Partial Correlation Coefficient

在多元回归分析中,经常用标准化系数和偏相关系数来描述自变量的相对重要性,本文研究了这两个系数之间的数量关系及其统计意义,得出两者具有相同的正负号,证明出在二元回归中两者相对大小始终一致,而在自变量个数超过两个的回归模型中两者相对大小不一定完全一致,最后通过实例,说明在两者出现不一致情况下,判断自变量相对重要性的解决方法和应注意的问题。

Standardized regression coefficient and partial correlation coefficient are often used to describe the relative importance of independent variables （IVs） in multivariate regression analysis. This paper studies the quantitative relation and statistical meaning of them： finds they have the same sign; demonstrates that when there are only two IVs, their absolute values is always consistent, and when there are more than two IVs, it is not always. It is presented by an example the solution to judge relative importance of IVs and the matter should be properly interpreted.