where Y is a vector n × 1 that contains the observations of the dependent variable, X is a matrix n×m whose columns contain the observations of the independent variables, and ε represents the random disturbance with E(ε) = 0 and cov(ε) = σ 2I and the first column of matrix X is a vector of ones, that is, X = [1 X2 . . . Xm], where 1 = (1 1 . . . 1)′n×1, several authors have contributed to the controversy surrounding the standardization of data when the model (1) presents a worrying degree of collinearity (Marquardt and Snee 1975; Smith and Campbell 1980; Marquardt 1980a; Belsley, Kuh, and Welsch 1980; Belsley 1982; Vinod and Ullah 1981). Gunst (1984) noted that “one of the problems of centering data is to carefully consider whether it is important to detect collinearity with the constant term.” In Marquardt’s comment to the article presented by Stewart (1987), he stated: “I fully agree with Stewart that when there is a constant term in the model, the model should be centered before the importance of the remaining variables is assessed and the centering simply shows the variable for what it is.” This discussion is extended to study how these transformations affect the traditionally applied measures to diagnose collinearity such as the variance inflation factor (VIF) and the condition number (CN) that are obtained from the following expressions, respectively

中文翻译：

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评论 Velilla 的“关于共线性诊断和居中的注释”（2018 年）

其中 Y 是包含因变量观测值的向量 n × 1，X 是矩阵 n×m，其列包含自变量的观测值，ε 表示 E(ε) = 0 和 cov( ε) = σ 2I 且矩阵 X 的第一列是 1 的向量，即 X = [1 X2 。. . Xm]，其中 1 = (1 1 . . . 1)'n×1，当模型 (1) 呈现令人担忧的共线性程度时，几位作者对围绕数据标准化的争议做出了贡献（Marquardt 和 Snee 1975；Smith和 Campbell 1980；Marquardt 1980a；Belsley、Kuh 和 Welsch 1980；Belsley 1982；Vinod 和 Ullah 1981）。Gunst (1984) 指出，“数据中心化的问题之一是仔细考虑检测与常数项的共线性是否重要。” 在 Marquardt 对 Stewart (1987) 发表的文章的评论中，他表示：“我完全同意 Stewart 的观点，即当模型中存在常数项时，在评估剩余变量的重要性和居中只是显示变量是什么。” 该讨论扩展到研究这些转换如何影响传统应用的共线性诊断措施，例如分别从以下表达式获得的方差膨胀因子 (VIF) 和条件数 (CN)