基于加总和乘积的方差分解法及其应用

研究了加总式和乘积式的方差分解问题，证明了在因变量等于各自变量之和的条件下，因变量方差等于各自变量与因变量的协方差之和；在因变量等于各自变量之乘积的条件下，因变量对数值的方差等于各自变量对数值与因变量对数值的协方差之和．以中国31个省份2005－2012年的居民人均收入及其影响因素的统计数据资料为例，说明了加总式和乘积式的方差分解法的具体应用．

Decomposition of Variance Based on the Sum and the Product and its Application

This article studies on decomposition of variance the based on the sum and the product. It reveals that under the condition that the dependent variable is equal to the sum of the respective variables, the variance of the dependent variable is equal to the sum of covariance of respective variables and the dependent variable. Under conditions of the dependent variable is equal to the product of respective variables, the logarithm variance of the dependent variable is equal to the sum of the covariance of the value of each variable and dependent variable. Taking the statistics of residents＇ income of 31 provinces from 2005-2012 and its influencing factors, it indicates the application of decomposition of the variance the based on the sum and the product.