Assessment of the experimental uncertainty associated with regression

This dissertation presents a methodology to assess the experimental uncertainty associated with linear regressions based upon propagating uncertainties using accepted uncertainty analysis techniques. The regression methodology was developed to assess the uncertainty of regression coefficients and the uncertainty of predicted values using the regression model. The effectiveness of this methodology was investigated using Monte Carlo simulations, and it was demonstrated that the methodology provides the appropriate uncertainty intervals for first order regression coefficients and for predicted values from first order and higher order regression models. It is shown that the key to the proper estimation of the uncertainty associated with regressions is a careful, comprehensive accounting of precision, systematic and correlated systematic uncertainties. The regression uncertainty methodology presented shown to be superior to other published techniques, including classical statistical methods. The methodology does not account for uncertainty introduced by an improper choice of regression model to represent the experimental data.;The development of the regression uncertainty methodology required investigation of the proper method to account for correlated systematic uncertainties. A new approach, called the Sum of Products (SOP) approximation, was developed and evaluated using Monte Carlo simulations. The SOP approximation was demonstrated to be superior to previously used approximations, and has been incorporated into national uncertainty standards and guidelines published by international advisory groups.;The new correlated bias term approximation enabled the development of the regression uncertainty methodology so that it applied for data containing any type of systematic uncertainty. Regressions are often performed in which all data points are obtained from the same experimental setup, and thus the data points share systematic uncertainties from the same sources. When a linear least squares regression is performed with this data, the results will be affected by the correlated biases and proper accounting of the correlated systematic uncertainties is necessary to estimate the uncertainty associated with the regression.;Application of the regression uncertainty methodology is demonstrated for simulations of Space Shuttle Main Engine High Pressure Fuel Turbopump turbine efficiency maps and gas turbine engine compressor stage characteristic maps, and in experiments for lift slope determination for a NACA 0012 airfoil and a venturi flowmeter calibration. These applications demonstrate how the regression uncertainty methodology can be used to provide additional information about the experimental results which was not previously available.