Regression Analysis—Inference for Curve- and Surface-Fitting

Stephen B. Vardeman & J. Marcus Jobe

This chapter is part of: Vardeman S. & Jobe J. 2023. Basic Engineering Data Collection and Analysis

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The two previous chapters began a study of inference methods for multisample studies by considering first those which make no explicit use of structure relating several samples and then discussing some directed at the analysis of factorial structure. The discussion in this chapter will primarily consider inference methods for multisample studies where factors involved are inherently quantitative and it is reasonable to believe that some approximate functional relationship holds between the values of the system/input/independent variables and observed system responses. That is, this chapter introduces and applies inference methods for the curve- and surface-fitting contexts discussed in Sections 4.1 and 4.2. The chapter begins with a discussion of the simplest situation of this type—namely, where a response variable y is approximately linearly related to a single quantitative input variable x. In this specific context, it is possible to give explicit formulas and illustrate in concrete terms what is possible in the way of inference methods for surface-fitting analyses. The second section then treats the general problem of statistical inferences in multiple regression (curve- and surface-fitting) analyses. In the general case, it is not expedient to produce many computational formulas. So the exposition relies instead on summary measures commonly appearing on multiple regression printouts from statistical packages. A final section further illustrates the broad utility of the multiple regression methods by applying them to “response surface,” and then factorial, analyses.
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    Published Published By Pages
    Jan. 12, 2023 Iowa State University Digital Press 78
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    © 2001 Stephen B. Vardeman and J. Marcus Jobe. Basic Engineering Data Collection and Analysis is available under a Creative Commons Attribution NonCommercial ShareAlike (CC BY-NC-SA) 4.0 International license. You may share and adapt the material, so long as you provide appropriate credit to the original authors, do not use the material for commercial purposes, and any adaptations or remixes of the material which you create are distributed under the same license as the original.
    Citation
    Vardeman S. & Jobe J. 2023. Regression Analysis—Inference for Curve- and Surface-Fitting. In Vardeman S. & Jobe J. 2023. Basic Engineering Data Collection and Analysis