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本文以双变量回归模型为基础,讨论了在多元线性回归中完全多重共线性和不完全但高度多重共线性情况下参数及方差的估计问题。结果表明:在完全多重共线性情况下,偏回归系数不能估计,方差为无穷大;在不完全但高度共线性情况下,其偏回归系数的估计是可能的,但其方差和标准误随着变量间的共线性程度增加而变大,从而使得总体有关参数的置信区间变得更大,因而增加接受错误假设的概率。本文还对一个医学研究实例进行了分析,说明在高度多重共线性情况下对参数估计值可能造成的影响。
Based on the bivariate regression model, this paper discusses the estimation of parameters and variances in the case of complete multicollinearity and incomplete but highly multicollinearity in multiple linear regression. The results show that in the case of complete multicollinearity, partial regression coefficients cannot be estimated and the variance is infinite; in the case of incomplete but highly collinearity, the estimation of partial regression coefficients is possible, but its variance and standard error follow the variables. The degree of co-linearity between increases and increases, so that the confidence interval for the overall relevant parameters becomes larger, thus increasing the probability of accepting false assumptions. This article also analyzes a medical research example to illustrate the possible impact on parameter estimates in the case of highly multicollinearity.