| 多重线性回归中数据联合影响的分解及数据的交叉影响 |
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| 引用本文： | 岳珠.多重线性回归中数据联合影响的分解及数据的交叉影响[J].系统科学与数学,1993,14(3):229-232. |
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| 作者姓名： | 岳珠 |
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| 作者单位： | 山西师范大学数学系 临汾041004
(岳珠)，山西师范大学数学系 临汾041004(吴诗詠) |
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| 基金项目： | 山西省自然科学基金资助课题 |
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| 摘 要： | 一、引言考虑多重线性回归模型Y=Xβ ε,(1)其中,Y=(y_1,…y_n_)′为 n×p 观察矩阵,X=(x_1,…,x_n)′为 n×(k 1)列满秩设计矩阵,β=(β_0,β_1,…β_k)′为(k 1)×p 未知参数矩阵,ε=(ε_1,…ε_n)′为 n×p 随机误差矩阵,ε_1…,ε_n 相互独立.
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FACTORIZATION OF COLLECTIVE INFLUENCES OF DATA AND CROSS INFLUENCE OF DATA IN MULTIVARIATE LINEAR REGRESSION |
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| YUE ZHU,WU SHI-YONG.FACTORIZATION OF COLLECTIVE INFLUENCES OF DATA AND CROSS INFLUENCE OF DATA IN MULTIVARIATE LINEAR REGRESSION[J].Journal of Systems Science and Mathematical Sciences,1993,14(3):229-232. |
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| Authors: | YUE ZHU WU SHI-YONG |
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| Institution: | (1)Shanxi Normal University,Linfen 041004;(2)Shanxi Normal University,Linfen 041004 |
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| Abstract: | In this paper,we discuss the relationship between the collective influences of multiplecases and the influence of each case on regression analysis in multivariate linear regression,that is,the factorization of the collective influences of cases.We also discuss the magnitudeof influence of case i on the fitted value at case j,that is,the cross influence of data;and theupper bound of the cross influence is obtained.Furthermore,we reveal the role of off-diago-nal elements of the hat matrix in the factorization and the cross influence of data. |
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