A Generalization of Pythagoras's Theorem and Application to Explanations of Variance Contributions in Linear Models. Research Report. ETS RR-14-18

Autor/in	Carlson, James E.
Titel	A Generalization of Pythagoras's Theorem and Application to Explanations of Variance Contributions in Linear Models. Research Report. ETS RR-14-18
Quelle	In: ETS Research Report Series, (2014), (19 Seiten)Infoseite zur Zeitschrift PDF als Volltext kostenfreie Datei Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	2330-8516
Schlagwörter	Least Squares Statistics; Geometry; Geometric Concepts; Statistical Analysis; Regression (Statistics); Mathematical Models; Mathematical Formulas + Suchen Sie Ihr Suchwort? Geometrie; Elementare Geometrie; Statistische Analyse; Regression; Regressionsanalyse; Mathematical model; Mathematisches Modell; Mathematische Formel
Abstract	Many aspects of the geometry of linear statistical models and least squares estimation are well known. Discussions of the geometry may be found in many sources. Some aspects of the geometry relating to the partitioning of variation that can be explained using a little-known theorem of Pappus and have not been discussed previously are the topic of this report. I discuss, using the theorem, how geometric explanation helps us understand issues relating to contributions of independent variables to explanation of variance in a dependent variable. A particular concern that the theorem helps explain involves nonorthogonal linear models including correlated regressors and analysis of variance. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01