Marquandt and Snee (Am Stat 29(1):3–20, 1975), Marquandt (J Am Stat Assoc 75(369):87–91, 1980) and Snee and Marquardt (Am Stat 38(2):83–87, 1984) refer to non-essential multicollinearity as that caused by the relation with the independent term. Although it is clear that the solution is to center the independent variables in the regression model, it is unclear when this kind of collinearity exists. The goal of this study is to diagnose the non-essential collinearity parting from a simple linear model. The collinearity indices \(k_{j}\), traditionally misinterpreted as variance inflation factors, are reinterpreted in this paper where they will be used to distinguish and quantify the essential and non-essential collinearity. The results can be immediately extended to the multiple linear model. The study also has some recommendations for statistical software such as SPSS, Stata, GRETL or R for improving the diagnosis of non-essential collinearity.

中文翻译：

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非必要共线性的诊断和量化

Marquandt和Snee（Am Stat 29（1）：3-20，1975），Marquandt（J Am Stat Assoc 75（369）：87-91，1980）和Snee and Marquardt（Am Stat 38（2）：83-87） ，1984）指非本质多重共线性，它是由与独立项的关系引起的。尽管很明显的解决方案是将自变量集中在回归模型中，但是尚不清楚何时存在这种共线性。这项研究的目的是从一个简单的线性模型中诊断出非必要的共线性。共线性指数\（k_ {j} \）传统上被误解为方差膨胀因子，在本文中将进行重新解释，将其用于区分和量化基本和非基本共线性。结果可以立即扩展到多重线性模型。该研究还对SPSS，Stata，GRETL或R等统计软件提出了一些建议，以改善对非共线性的诊断。