LABORATORY USE OF A SPECIALLY PROGRAMMED EXCEL USER FORM FOR POLYNOMIAL REGRESSION AND FOR EVALUATING THE UNCERTAINTY OF POLYNOMIAL REGRESSION MODELS

摘要

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.