Abstract: In this paper, we discuss all kinds of influence functions used to determine influential cases in regression diagnostics and their relation between each other, and propose the distribution for data set to influence fitted values of each point, which can be used as another measure to determine influential cases.We establish the relation between influence distributions and the complex correlation coefficient to finish up with, and generalize these results in regression diagnostics of multivariate linear models.

Key words: regression diagnostics, influence function, statistic, fitted value, complex correlation coefficient, influential case, multivariate linear model, residual

摘要： 本文讨论了回归诊断中用于判别强影响点的各种影响函数以及它们相互之间的关系,给出了数据集对各点拟合值的影响分布,它可以作为判别强影响点的又一度量工具。最后建立了影响分布与复相关系数的联系并在多元线性模型的回归诊断中推广了这些结果。

关键词: 回归诊断, 影响函数, 统计量, 拟合值, 复相关系数, 强影响点, 多元线性模型, 残差