Uncertainty Evaluation of the Predicted Value in Regression Analysis Based on Repeated Observations

Abstract

Regression analysis is a practical statistical technique. It is mainly used to estimate the relationship among variables and then predict the unknown observations. In metrology, the calibration curve is an application of regression analysis, which describes the relationship between standard values and indications, or nominal values and standard values. According to ISO/IEC 17025:2005, the calibration certificates shall include the measurement uncertainty. Thus, when the standard value is obtained by a calibration curve, the uncertainty of the predicted value should be considered as an additional uncertainty component. The regression line can be fitted by estimating the regression coefficients from the observed data set. However, the observed data set may have different forms, such as one value of the independent variable against one observation of the dependent variable, and one value of the independent variable against repeated observations of the dependent variable. The latter form always confuses the laboratory staffs about calculation of the fitted regression line and evaluation of the measurement uncertainty. For this reason, this paper will focus on how to evaluate the measurement uncertainty of the predicted value in a simple linear regression line based on repeated observations. In addition, the analysis of variance (ANOVA) technique will be used to determine which uncertainty evaluation method is selected to avoid underestimating the measurement uncertainty.