Abstract We consider making predictions with a fitted regression model when one of the necessary covariates is expensive, either in terms of actual cost or in terms of the effort required to collect its value. We propose a two-stage procedure that either makes the prediction without using the expensive covariate, or decides to collect the covariate and then make the prediction. The criterion for deciding whether to collect the covariate is the probability that the prediction without using the covariate is satisfactorily close to the prediction that could be made if the covariate was collected. Three different approaches to making the prediction without using the covariate are considered. The proposed methodology is illustrated with two examples where the distributions of the covariates follow a multivariate normal distribution, and a bivariate conditional exponential distribution, respectively.

中文翻译：

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线性模型中的两阶段预测

摘要 当必要的协变量之一很昂贵时，我们考虑使用拟合回归模型进行预测，无论是在实际成本方面还是在收集其价值所需的努力方面。我们提出了一个两阶段程序，要么在不使用昂贵的协变量的情况下进行预测，要么决定收集协变量然后进行预测。决定是否收集协变量的标准是不使用协变量的预测与收集协变量可以做出的预测令人满意地接近的概率。考虑了在不使用协变量的情况下进行预测的三种不同方法。所提出的方法用两个例子来说明，其中协变量的分布遵循多元正态分布，