偏最小二乘回归分析是从应用领域中提出的一种新型多元数据分析方法。近十几年来， 它在理论和应用方面都已得到迅速的发展。偏最小二乘回归分析主要适用于多因变量对 多自变量的线性回归建模，并可以有效地解决许多用普通多元回归无法解决的问题， 诸如：克服变量多重相关性在系统建模中的不良作用以及在样本容量小于变量个数的情况下进行 回归建模等。而且它还可以将回归建模，主成分分析及典型相关分析的基本功能有机地结合起来。 文章通过一个化工案例揭示普通多元回归的缺陷，从而提出偏最小二乘回归的理论方法。 在此基础上，本文还专门讨论了在变量多重相关条件下，偏最小二乘回归对各类数据信息的 综合与筛选作用。 偏最小二乘回归继承了主成分中成分提取的思想，思路也有很大扩展。它在对自变量进行信息综合时，不但考虑了要最好地概括自变量系统中的信息，而且注重要求提取的成分必须对因变量有最强的解释性。 所以，偏最小二乘回归更具有先进性，其计算结果更为可靠，它的模型在实际系统中的解释性也更强。

Partial least-squares (PLS) regression is a new type of multivariate statistical method . In the recent twenty years , it has developed quickly in its theories and applications . PLS regression applies to regression modeling of multiple responses to variables . It can solve problems that cannot be adequately solved in the ordinary multivariate regression , such as collinearity in models and a sample size smaller than number of variables . Moreover , it has integrated the merits of ordinary regression modeling , principle component analysis and canonical correlation analysis . This essay first shows the deficiency of ordinary multivariate regression with a example in chemical engineering , before establishing the theoretical foundations of PLS regression . This essay also discusses the way of PLS regression synthesizing the data information on condition of collinearity . PLS regression has incorporated and extended the thoughts of principle component analysis . It not only synthesizes the information of independent variables , but also excludes the explanatory about dependent variables . Thus , it would be more reliable to use PLS regression . The explanatory in modeling is much stronger , with more apparent practical meanings .