We introduce a simple diagnostic test for assessing the goodness of fit of linear regression, and in particular for detecting hidden confounding. We propose to evaluate the sensitivity of the regression coefficient with respect to changes of the marginal distribution of covariates by comparing the so-called higher-order least squares with the usual least squares estimates. In spite of its simplicity, this strategy is extremely general and powerful. Specifically, we show that it allows to distinguish between confounded and unconfounded predictor variables as well as determining ancestor variables in structural equation models.

翻译：我们提出一个简单的诊断测试,评估线性回归的适宜性,特别是发现隐蔽的混乱。我们提议通过比较所谓的高阶最低方位和通常最低方位估计数,评估共差边际分布变化的回归系数的敏感性。尽管这一战略非常简单,但非常笼统和有力。具体地说,我们表明它能够区分有根据和无根据的预测变量,以及确定结构方程模型中的祖先变量。