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Contribution of individual variables to the regression sum of squares

机译：各个变量对平方和的回归贡献

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摘要

In applications of multiple regression, one of the most common goals is to measure the relative importance of each predictor variable. If the predictors are uncorrelated, quantification of relative importance is simple and unique. However, in practice, predictor variables are typically correlated and there is no unique measure of a predictor variable’s relative importance. Using a transformation to orthogonality, new measures are constructed for evaluating the contribution of individual variables to a regression sum of squares. The transformation yields an orthogonal approximation of the columns of the predictor scores matrix and it maximizes the sum of the covariances between the cross-product of individual regressors and the response variable and the cross-product of the transformed orthogonal regressors and the response variable. The new measures are compared with three previously proposed measures through examples and the properties of the measures are examined.
机译：在多元回归的应用中，最常见的目标之一是测量每个预测变量的相对重要性。如果预测变量不相关，则相对重要性的量化既简单又独特。但是，实际上，预测变量通常是相关的，并且没有唯一的度量变量相对重要性的度量。使用正交性变换，可以构造新的度量来评估各个变量对平方和的回归的贡献。该变换产生了预测因子分数矩阵的列的正交近似，并且它最大化了各个回归变量与响应变量的叉积和转换后的正交回归变量与响应变量的叉积之间的协方差之和。通过实例将新措施与之前提出的三项措施进行了比较，并检验了这些措施的性质。

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