Justifying ridge regression from a geometrical perspective is one of the main contributions of this paper. To the best of our knowledge, this question has not been treated previously. This paper shows that ridge regression is a particular case of raising procedures that provide greater flexibility by transforming the matrix X associated with the model. Thus, raising procedures, based on a geometrical idea of the vectorial space associated with the columns of matrix X, lead naturally to ridge regression and justify the presence of the well‐known constant k on the main diagonal of matrix X^′X. This paper also analyses and compares different alternatives to raising with respect to collinearity mitigation. The results are illustrated with an empirical application.

中文翻译：

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共线性的几何解释：证明岭回归及其异常的自然方法

从几何学角度证明岭回归是本文的主要贡献之一。据我们所知，这个问题以前没有得到处理。本文表明，岭回归是引发过程的特殊情况，该过程通过转换与模型关联的矩阵X来提供更大的灵活性。因此，提高程序，基于与矩阵的列相关联的矢量空间的几何想法X，自然会导致岭回归和证明众所周知的常数的存在ķ上的矩阵的主对角线X ^' X。本文还就共线性缓解问题分析并比较了提高筹码的其他方法。结果以经验应用说明。