There are many data sets in the literature without uncertainty information. This paper introduces a novel approach to estimate data uncertainty where replicate experiments are not available. For a physical phenomenon, the dependent variable generally changes smoothly with small changes in each independent variable while other independent variables are kept constant. We hypothesize that if experimental data in this form is available, the relationship between the dependent variable and each independent variable may be approximated with the best fit regression model and that the residuals of these models can be aggregated to estimate the uncertainty of the dependent variable measurements. The statistical tests calculated using the computational experiments support the hypothesis. As a case study, erosion-rate measurement uncertainty is estimated using the approach. The results reveal that the uncertainty estimates of the erosion-rate measurements are in good agreement with expert opinions and with values reported in the literature. (C) 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.