Department of Chemistry, Faculty of Sciences, University of Girona, Girona, Spain.
J Sep Sci. 2021 Dec;44(24):4431-4441. doi: 10.1002/jssc.202100555. Epub 2021 Oct 29.
Simple linear regression using ordinary least-squares is the most common function applied in laboratories for analytical calibrations. The determination and/or the correlation coefficients are usually the parameters applied for assessing the goodness-of-fit of a simple linear calibration. However, these parameters are unable to detect the highly biased results at low calibration levels that are obtained with ordinary least-squares. In this study, the use of other parameters based on the relative standard errors of the calculated contents is evaluated. It has been found that these alternative parameters can detect the biased results obtained at low calibration levels with ordinary least-squares, being the relative standard error the one that seems to provide the most adequate results. Ordinary least-squares should only be applied if the lower limit of quantification is set to at least five times above the conventional limit of quantification. For trace analysis, where the lowest possible limit of quantification is required, weighted least-squares should be applied to obtain accurate estimates, especially at low concentrations. One of the greatest advantages of the relative standard error is that this parameter can be determined for all types of regression functions and is not limited to calibrations with linear relationships between the variables.
简单线性回归使用普通最小二乘法是实验室中用于分析校准的最常用的函数。通常，决定系数和/或相关系数是用于评估简单线性校准拟合优度的参数。然而，这些参数无法检测到在低校准水平下使用普通最小二乘法得到的高度有偏结果。在这项研究中，评估了基于计算含量的相对标准误差的其他参数的使用。结果发现，这些替代参数可以检测到在低校准水平下使用普通最小二乘法得到的有偏结果，其中相对标准误差似乎提供了最适当的结果。只有在定量下限设置至少为常规定量下限的五倍以上时，才应应用普通最小二乘法。对于痕量分析，需要尽可能低的定量下限，应应用加权最小二乘法以获得准确的估计值，特别是在低浓度下。相对标准误差的最大优点之一是，该参数可以应用于所有类型的回归函数，并且不限于变量之间具有线性关系的校准。
