The purpose of this study is to compare the Partial Least Squares (PLS), Ridge Regression (RR) and Principal Components Regression (PCR) methods, used to fit regressors with severe multicollinearity against a dependent variable. To realize this, a great number of varying groups of datasets are generated from standard normal distribution allowing for the inclusion of different degrees of collinearities for 10000 replications. The design of the study is based on a simulation work that has been performed for six different degrees of multicollinearity levels and sample sizes. From the generated data, a comparison is made using the value of mean squares error of the regression parameters. The findings show that each prediction method is affected by the sample size, number of regressors or multicollinearity level. However, in contrast to literature (say ), whatever the number of regressors is, PCR had significantly better results compared to the other two.

中文翻译：

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通过生成的数据比较偏最小二乘法与其他预测方法

本研究的目的是比较偏最小二乘法 (PLS)、岭回归 (RR) 和主成分回归 (PCR) 方法，用于将具有严重多重共线性的回归量与因变量进行拟合。为了实现这一点，从标准正态分布生成了大量不同的数据集组，允许包含 10000 次重复的不同程度的共线性。该研究的设计基于对六种不同程度的多重共线性和样本大小进行的模拟工作。从生成的数据中，使用回归参数的均方误差值进行比较。研究结果表明，每种预测方法都受到样本大小、回归量或多重共线性水平的影响。然而，