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Regression Analysis and the Analysis of Variance

In: Engineering Statistics

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  • Edward B. Magrab

    (University of Maryland)

Abstract

In this chapter, we provide derivations of the formulas for simple and multiple linear regression. In obtaining these results, the partitioning of the data using the sum of squares identities and the analysis of variance (ANOVA) are introduced. The confidence intervals of the model’s parameters are determined and how an analysis of the residuals is used to confirm that the model is appropriate. Prior to obtaining the analytical results, we discuss why it is necessary to plot data before attempting to model it, state general guidelines and limits of a straight-line model to data, and show how one determines whether plotted data that appear to be nonlinear could be intrinsically linear. Hypothesis tests are introduced to determine which parameters in the model are the most influential.

Suggested Citation

  • Edward B. Magrab, 2022. "Regression Analysis and the Analysis of Variance," Springer Books, in: Engineering Statistics, chapter 0, pages 93-124, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-05010-7_3
    DOI: 10.1007/978-3-031-05010-7_3
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