This article presents a counterintuitive result regarding the estimation of a regression slope coefficient. Paradoxically, the precision of the slope estimator can deteriorate when additional information is used to estimate its value. In a randomized experiment, the distribution of baseline variables should be identical across treatments due to randomization. The motivation for this article came from noting that the precision of slope estimators deteriorated when pooling baseline predictors across treatment groups.

中文翻译：

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估计回归系数的矛盾结果

本文提出了一个关于回归斜率系数估计的违反直觉的结果。矛盾的是，当使用附加信息来估计斜率估计器的值时，斜率估计器的精度可能会下降。在随机实验中，由于随机化，基线变量的分布在不同治疗中应该是相同的。这篇文章的动机来自注意到斜率估计器的精度在跨治疗组合并基线预测器时会恶化。