Abstract
This work concerns on the estimation of the accuracy of function determined by the linear regression method for the description of noncorrelated measured data of Y. Recommendations of the international Guide to the Expression of Uncertainty in Measurement (GUM) are used. The impact of Type B measurement uncertainties is included, which is omitted in the statistical literature on the accuracy of regression method. The introduction presents the essence of the uncertainty calculations used in GUM. The case of random changes of variable Y and the criteria used in linear regression are discussed in detail. For known values of X variable, the parameters and uncertainty bands of regression line are determined for measurements of uncorrelated values of Y with Type A and Type B uncertainties. Considerations are illustrated with four numerical examples of the measurement points with the same coordinates, but different absolute and relative uncertainties.
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Notes
- 1.
This common term for metrology and the basics of measurement technique have been proposed in Acta IMEKO in the 1970-s by Ludvik Finkelstein, professor at City University in London, born in Lviv.
- 2.
Similar approach was applied in the early 1950-s, in the doctoral dissertation by Stanislaw Trzetrzewiński, later professor of the Gdansk University of Technology, i. e. over 40 years before the publication of the first version of the GUM guide.
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Warsza, Z.L., Puchalski, J. (2021). Uncertainty Bands of the Regression Line for Data with Type A and Type B Uncertainties of Dependent Variable Y. In: Szewczyk, R., Zieliński, C., Kaliczyńska, M. (eds) Automation 2021: Recent Achievements in Automation, Robotics and Measurement Techniques. AUTOMATION 2021. Advances in Intelligent Systems and Computing, vol 1390. Springer, Cham. https://doi.org/10.1007/978-3-030-74893-7_32
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