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Pearson's correlation between three variables; using students' basic knowledge of geometry for an exercise in mathematical statistics

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Abstract:

When studying correlations, how do the three bivariate correlation coefficients between three variables relate? After transforming Pearson's correlation coefficient r into a Euclidean distance, undergraduate students can tackle this problem using their secondary school knowledge of geometry (Pythagoras' theorem and similarity of triangles). Through a geometric interpretation, we start from two correlation coefficients rAB and rBC and then estimate a range for the third correlation rAC. In the case of three records (n = 3), the third correlation rAC can only attain two possible values. Crossing borders between mathematical disciplines, such as statistics and geometry, can assist students in deepening their conceptual knowledge.

Keywords: bivariate correlation; correlative distance; person space; range restrictions; trans-disciplinarity

Document Type: Research Article

DOI: http://dx.doi.org/10.1080/00207390802419578

Affiliations: AMSTEL Institute, University of Amsterdam, The Netherlands

Publication date: January 1, 2009

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