Least Squares Geometry and the Overall ANOVA

Dale L. Zimmerman
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Dale L. Zimmerman: University of Iowa, Department of Statistics and Actuarial Science

Chapter 8 in Linear Model Theory, 2020, pp 149-168 from Springer

Abstract: Abstract In Chap. 7 , we defined least squares estimators associated with a given model algebraically, i.e., in terms of the problem of minimizing the residual sum of squares function for the model. But least squares also have a geometric interpretation, which is demonstrated in this chapter. This additional interpretation of least squares yields new insights and suggests a decomposition of the total variability of the response vector into components attributable to the model’s mean structure and error structure, which is known as the overall analysis of variance (or overall ANOVA). It also leads to an estimator of the residual variance in the Gauss–Markov model {y, Xβ, σ 2I} that is unbiased under that model.

Date: 2020
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DOI: 10.1007/978-3-030-52063-2_8

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