Several Type Ia supernova analyses make use of non-simultaneous regressions between observed supernova and host galaxy properties and supernova luminosity: first the supernova magnitudes are corrected for their light curve shape and color, and then they are separately corrected for their host galaxy masses. This two-step regression methodology does not introduce any biases when there are no correlations between the variables regressed in each correction step. However, correlations between these covariates will bias estimates of the size of the corrections, as well as estimates of the variance of the final residuals. In this work, we analyze the general case of non-simultaneous regression with correlated covariates to derive the functional forms of these biases. We also simulate this effect on data from the literature to provide corrections to remove these biases from the data sets studied. The biases examined here can be entirely avoided by using simultaneous regression techniques.

几项 Ia 型超新星分析利用了观测到的超新星和宿主星系特性以及超新星光度之间的非同时回归：首先，超新星星等根据其光变曲线形状和颜色进行校正，然后它们分别根据宿主星系质量进行校正。当在每个校正步骤中回归的变量之间没有相关性时，这种两步回归方法不会引入任何偏差。然而，这些协变量之间的相关性将使修正大小的估计以及最终残差的方差估计产生偏差。在这项工作中，我们分析了具有相关协变量的非同时回归的一般情况，以推导出这些偏差的函数形式。我们还模拟了对文献数据的这种影响，以提供更正以从研究的数据集中消除这些偏差。通过使用同步回归技术可以完全避免这里检查的偏差。