An overview of the elementary statistics of correlation, R-squared, cosine, sine, and regression through the origin, with application to votes and seats for Parliament

Thomas Colignatus ()

MPRA Paper from University Library of Munich, Germany

Abstract: The correlation between two vectors is the cosine of the angle between the centered data. While the cosine is a measure of association, the literature has spent little attention to the use of the sine as a measure of distance. A key application of the sine is a new “sine-diagonal inequality / disproportionality” (SDID) measure for votes and their assigned seats for parties for Parliament. This application has nonnegative data and uses regression through the origin (RTO) with non-centered data. Textbooks are advised to discuss this case because the geometry will improve the understanding of both regression and the distinction between descriptive statistics and statistical decision theory. Regression may better be introduced and explained by looking at the angles relevant for a vector and its estimate rather than looking at the Euclidean distance and the sum of squared errors. The paper provides an overview of the issues involved. Also a new relation between the sine and the Euclidean distance is derived.

Keywords: General Economics; Social Choice; Social Welfare; Election; Parliament; Party System; Representation; Sine Diagonal Inequality / Disproportionality; SDID; Proportion; District; Voting; Seat; Euclid; Distance; Cosine; Sine; Gallagher; Loosemore-Hanby; Sainte-Laguë; Webster; Jefferson; Hamilton; Largest Remainder; Correlation; Diagonal regression; Regression through the origin; Apportionment; Disproportionality; Equity; Inequality (search for similar items in EconPapers)
JEL-codes: A10 D63 D71 D72 (search for similar items in EconPapers)
Date: 2018-02-20, Revised 2018-02-20
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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https://mpra.ub.uni-muenchen.de/86307/1/MPRA_paper_86307.pdf revised version (application/pdf)

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