This thesis deals with regression analysis of experimentally measured data of processed cheese. There is a polynomial regression used. The choice of regressors is based on Stepwise Regression and Mallows's Statistics. The estimation of the mean value is used to find the best mixture of the emulsifying salts with regards to the observed characteristic of the processed cheese. Analysis of the experiment and its results are well documented graphically.

The ability to predict accurately the critical quality characteristics of aircraft engines is essential for modeling the degradation of engine performance over time. The acceptable margins for error grow smaller with each new generation of engines. This paper focuses on turbine gas temperature (TGT). The goal is to improve the first principles predictions through the incorporation of the pure thermodynamics, as well as available information from the engine health monitoring (EHM) data and appropriate maintenance records. The first step in the approach is to develop the proper thermodynamics model to explain and to predict the observed TGTs. The resulting residuals provide the fundamental information on degradation. The current engineering models are ad hoc adaptations of the underlying thermodynamics not properly tuned by actual data. Interestingly, pure thermodynamics model uses only two variables: atmospheric temperature and a critical pressure ratio. The resulting predictions of TGT are at least similar, and sometimes superior to these ad hoc models. The next steps recognize that there are multiple sources of variability, some nested within others. Examples include version to version of the engine, engine to engine within version, route to route across versions and engines, maintenance to maintenance cycles within engine, and flight segment to flight segment within maintenance cycle. The EHM data provide an opportunity to explain the various sources of variability through appropriate regression models. Different EHM variables explain different contributions to the variability in the residuals, which provides fundamental insights as to the causes of the degradation over time. The resulting combination of the pure thermodynamics model with proper modeling based on the EHM data yield significantly better predictions of the observed TGT, allowing analysts to see the impact of the causes of the degradation much more clearly. / Doctor of Philosophy / AEM is major civilian aircraft gas turbine engine manufacturer, serving different airliners and airlines. However, one of its newest models has had performance issues; the engines degraded faster than their in-house model had anticipated, leading to more frequent maintenance and causing significant financial losses to the company. The key objectives of our research project are to produce a model that has higher predictive capabilities than AEM's in-house predictive model (DTGT), and develop a model selection algorithm that allows for direct comparisons among models of vastly different architecture. There are three major components to our research: 1) interdisciplinary studies merging the theory of thermodynamics and regression, 2) the sequential modeling, and 3) the modified Mallows's Cp. We propose a layered sequential approach to the regression modeling, where one regression model is followed by another regression on the residuals of the previous model. We also propose the modified Mallows's Cp, a modification of the Mallows's Cp, as a viable model selection criterion. Our results demonstrated that the sequential approach both outperformed the AEM's in-house model and was found to be more useful than the traditional multiple linear regression. Our results also demonstrated that the modified Mallows's Cp prefer smaller number of parameters than other standard model selection criterion without sacrificing predictive capabilities of its models.