Principal component regression (PCR) is a two-stage procedure: the first stage performs principal component analysis (PCA) and the second stage builds a regression model whose explanatory variables are the principal components obtained in the first stage. Since PCA is performed using only explanatory variables, the principal components have no information about the response variable. To address this problem, we present a one-stage procedure for PCR based on a singular value decomposition approach. Our approach is based upon two loss functions, which are a regression loss and a PCA loss from the singular value decomposition, with sparse regularization. The proposed method enables us to obtain principal component loadings that include information about both explanatory variables and a response variable. An estimation algorithm is developed by using the alternating direction method of multipliers. We conduct numerical studies to show the effectiveness of the proposed method.

主成分回归（PCR）分为两个阶段：第一阶段执行主成分分析（PCA），第二阶段建立回归模型，该模型的解释变量为在第一阶段获得的主要成分。由于仅使用解释变量执行PCA，因此主要组件没有有关响应变量的信息。为了解决这个问题，我们提出了一种基于奇异值分解方法的PCR第一步程序。我们的方法基于两个损失函数，分别是回归损失和奇异值分解带来的PCA损失，并具有稀疏正则化。所提出的方法使我们能够获得包含有关解释变量和响应变量的信息的主成分载荷。通过使用乘法器的交替方向方法，开发了一种估计算法。我们进行了数值研究，以显示该方法的有效性。