格鲁布斯检验法检验一元线性回归直线上的异常点研究  

Examine the outliers on unitary linear regression lines by Grubbs test method

作　　者：李建国[1] 张正红 雷用东[1,2] 段云浩 常恒瑞 王静[1] LI Jianguo;ZHANG Zhenghong;LEI Yongdong;DUAN Yunhao;CHANG Hengrui;WANG Jing(Center of Food Quality Supervision and Testing,Ministry of Agriculture,Xinjiang Agricultual and Reclamation Science,Shihezi 832000 China;College of Food Science,Shihezi University,Shihezi 832000,China;Tianjin Agricultural College,Tianjin 300384,China)

机构地区：[1]新疆农垦科学院农业农村部食品质量监督检验测试中心,新疆石河子832000 [2]石河子大学食品学院,新疆石河子832000 [3]天津农学院,天津300384

出　　处：《中国高新科技》2021年第2期125-129,共5页

基　　金：农业农村部农产品重点实验室开放课题(项目编号:201809)。

摘　　要：文章简述了格鲁布斯(Grubbs)检验法的检验原理、步骤以及判定异常值的依据。详细叙述了利用格鲁布斯检验法检验一元线性回归直线上异常点(或异常值)的理论依据和具体检验方法。通过对已达到显著性相关水平的一元线性回归直线的数学模型进行检验,验证了其可行性和科学性。同时,对这些数学模型剔除异常点前、后一元线性回归方程相关系数的变化比较,说明剔除异常值后,相关系数明显提高,证明该方法也是一种较为严谨地剔除一元线性回归直线上异常点的方法。最后,对其应用前景进行了预测。In this paper,the principle and procedure of Grubbs test,and the criteria for determining outliers are introduced.The theoretical basis and specific test method of Grubbs test to examine outliers on linear regression lines with one variable are described in detail.By testing the mathematical model of linear regression line with one variable which has reached the level of significance correlation,the feasibility and scientificity are verified.At the same time,before and after the removal of outliers,the comparison of the changes of the correlation coefficients of these mathematical models shows that the correlation coefficients are significantly increased after the removal of outliers,which proves that this method is also a relatively rigorous method for the removal of outliers on the line of unitary linear regression,and then its application prospect is forecasted.

关 键 词：格鲁布斯检验法 格鲁布斯检验法临界值 一元线性回归直线 一元线性回归方程 

分 类 号：O177[理学—数学]