June 12, 2005
June 12, 2005
June 15, 2005
10.865.1 - 10.865.10
LABORATORY USE OF A SPECIALLY PROGRAMMED EXCEL USER FORM FOR POLYNOMIAL REGRESSION AND FOR EVALUATING THE UNCERTAINTY OF POLYNOMIAL REGRESSION MODELS
Sheldon M. Jeter
Georgia Institute of Technology
Regression models are widely used in engineering practice, especially in mechanical and chemical engineering and in related fields. They are used to represent data and to calibrate instruments among other applications. Standard textbooks address linear regression models well, and some also address the associated statistical uncertainties of linear models. This uncertainty of a model is the range of uncertainty about the systematic dependence of the dependent variable on the independent variable(s).
Unfortunately, none of the popular texts reviewed for this paper adequately address polynomial models and their uncertainties, probably because polynomial models seem to be common mostly in engineering applications. In contrast, polynomial models are not so common in fields such as medicine and social sciences that seem to attract more interest from professional statisticians. Nevertheless, it has been shown elsewhere (Jeter, 2003) that Error Propagation Analysis (EPA), which is already familiar to most experimental engineers, can be used to find the uncertainty of both linear and polynomial models.
While the underlying philosophy and mathematics concerning the uncertainty of polynomial regression models is not especially complicated, the practical implementation requires multiple executions of auxiliary regressions. These extra steps are quite time consuming when each step must be defined manually, and the extra manual steps are likely to induce procedural errors. To make the calculation and plotting of the results simple and easy, a special Excel utility routine called a User Form that is described in this paper was programmed.
In the balance of this paper, the statistical and mathematical background for this technique will be reviewed, the algorithm for the implementing the technique will be outlined, and a couple of representative practical examples from mechanical engineering will be presented.
Proceedings of the 2005 American Society for Engineering Education Annual Conference & Exposition Copyright 2005, American Society for Engineering Education
Jeter, S. (2005, June), Laboratory Use Of A Specially Programmed Excel User Form For Polynomial Regression Paper presented at 2005 Annual Conference, Portland, Oregon. https://peer.asee.org/14780
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