The coefficient of determination, R², also called the explained variance, is often taken as a proportional measure of the relative determination of model on outcome. However, while R² has some attractive statistical properties, its reliance on squared variations (variances) may limit its use as an easily interpretable descriptive statistic of that determination. Here, the properties of this coefficient on the squared scale are discussed and generalized to three relative measures on the original scale. These generalizations can all be expressed as transformations of R², and alternatives can therefore also be calculated by plugging in related estimates, such as the adjusted R². The third coefficient, new for this article, and here termed the CoDSD (the coefficient of determination in terms of standard deviations), or Rπ (R-pi), equals R²/(R²+1-R²). It is argued that this coefficient most usefully captures the relative determination of the model. When the contribution of the error is c times that of the model, the CoDSD equals 1/(1 + c), while R² equals 1/(1 + c²). (PsycInfo Database Record (c) 2024 APA, all rights reserved).

中文翻译：

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以与结果相同的尺度测量的决定系数：使用标准差而不是解释方差的 R² 替代方案。


决定系数 R²，也称为解释方差，通常被视为模型对结果的相对决定的比例度量。然而，虽然 R² 具有一些有吸引力的统计特性，但它对平方变化（方差）的依赖可能会限制其作为该确定的易于解释的描述性统计的使用。在这里，讨论了该系数在平方尺度上的属性，并将其推广到原始尺度上的三个相对度量。这些概括都可以表示为 R² 的变换，因此也可以通过插入相关估计（例如调整后的 R²）来计算替代方案。第三个系数是本文的新系数，此处称为 CoDSD（标准差决定系数）或 Rπ (R-pi)，等于 R²/(R²+1-R²)。有人认为，该系数最能有效地捕捉模型的相对确定性。当误差贡献为 c 乘以模型贡献时，CoDSD 等于 1/(1 + c)，而 R² 等于 1/(1 + c²)。 （PsycInfo 数据库记录 (c) 2024 APA，保留所有权利）。