A Methodology for Determining Experimental Uncertainties in Regressions

Abstract

A methodology to determine the experimental uncertainties associated with regressions is presented. When a regression model is used to represent experimental information, the uncertainty associated with the model is affected by random, systematic, and correlated systematic uncertainties associated with the experimental data. The key to the proper estimation of the uncertainty associated with a regression is a careful, comprehensive accounting of systematic and correlated systematic uncertainties. The methodology presented in this article is developed by applying uncertainty propagation techniques to the linear regression analysis equations. The effectiveness of this approach was investigated and proven using Monte Carlo simulations. The application of that methodology to the calibration of a venturi flowmeter and its subsequent use to determine flowrate in a test is demonstrated. It is shown that the previously accepted way of accounting for the contribution of discharge coefficient uncertainty to the overall flowrate uncertainty does not correctly account for all uncertainty sources, and the appropriate approach is developed, discussed, and demonstrated.