Uncertainty Bands of the Regression Line for Data with Type A and Type B Uncertainties of Dependent Variable Y

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.