Link between Orthogonal and Standard Multiple Linear Regression Models
Link between Orthogonal and Standard Multiple Linear Regression Models
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DOI：
10.1021/ci950183m
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
M. Soskic;D. Plavsic;N. Trinajstic
中科院分区：
文献类型：
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作者：
M. Soskic;D. Plavsic;N. Trinajstic
与最近提出的预测变量的正交化方法(优势成分分析)有关的几个主题也被考虑。应用序贯回归方法，证明了主成分分析与标准多元线性回归方法之间存在着直接的相关性。此外，还证明了用一步回归可以有效地代替先前提出的相关变量正交化的迭代过程。文中还证明了正交描述子的决定系数与相应的平方半偏相关系数一致。最后，讨论了正交化预测变量中额外信息的来源。
Several topics in connection with a recently proposed method for the orthogonalization of predictor variables (dominant component analysis) are considered. Applying the sequential regression procedure, it is shown that dominant component analysis and the standard multiple linear regression method are directly related to each other. In addition, it is demonstrated that an earlier proposed iterative procedure for the orthogonalization of a correlated variable can be efficiently replaced by one step regression. It is also shown that the coefficient of determination for an orthogonal descriptor coincides with the corresponding squared semipartial correlation coefficient. Finally, the origin of extra information in an orthogonalized predictor variable is discussed.