Abstract：The measurement uncertainty of the least squares linear regression fitting results was evaluated by GUM method, and a general formula of standard uncertainty was proposed to estimate the influence of error of independent variable in coefficient matrix and dependent variable simultaneously. Firstly, the linear regression fitting model and least squares estimation results were described.Secondly, considering the influence of coefficient matrix, the general formulas for fitting parameters, fitting values, sensitivity coefficients on independent and dependent variables, and standard uncertainty were derived. At the same time, considering the correlation, a general formula for standard uncertainty after special treatment of variable correlation is given. Finally, the sensitivity of linear displacement sensor (without considering the correlation) and the additive multiplying constant of geodimeter (considering the correlation) were taken as examples to compare with the Monte Carlo method (MCM).The research results showed that the calculation results of the GUM method were basically consistent with the results of the MCM method.
Zhang F, Zeng Y H, Zhang W.Research on calibration of linear displacement transducer ［J］. Optical Instruments, 2016, 38 (1): 63-68.
Chen S L, Zhu H Y, Chen Y M, et al. Evaluation of uncertainty of addictive and multiplication constants in the EDMs calibration measurement ［J］. Bulletin of Surveying and Mapping, 2001(2): 6-8.
Gao J P, Jiang T, Zhang G L. An error compensation method on ABS gear parameters measurement system ［J］. Acta Metrologica Sinica, 2019, 40(2): 201-207.
Lou J Q, Li W, Fu Y H, et al. Study on flatness error evaluation method of discontinuous plane ［J］. Acta Metrologica Sinica, 2022, 43 (1): 14-20.
Xu J X, You Q. Uncertainty calculation for arbitrary order polynomial least－square fitting and analysis of the best fitting order ［J］. Acta Metrologica Sinica, 2020, 41 (3): 388-392.
［10］
JJF 1059.1—2012测量不确定度评定与表示［S］. 2012.
Liu Q, Shao Z X.Discussion of linear fitting uncertainty of regress analysis ［J］. China Measurement & Test, 2009, 35 (3): 41-44.
［13］
Willink R. Estimation and uncertainty in fitting straight lines to data: different techniques ［J］. Metrologia, 2008, 45 (2008): 290-298.
［15］
JCGM 101: 2008 Evaluation of measurement data-supplement 1 to the “guide to the expression of uncertainty in measurement”-propagation of distributions using a Monte Carlo method ［S］.
Ju Y F, Wang J B, Chang C Y, et al. Monte Carlo Method for the measurement uncertainty evaluation considering non-positive definite correlation ［J］. Acta Metrologica Sinica, 2022, 43 (6): 831-836.
2023, Vol. 44 
