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

摘要

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 r_(AB) and r_(BC) and then estimate a range for the third correlation r_(AC). In the case of three records (n = 3), the third correlation r_(AC) can only attain two possible values. Crossing borders between mathematical disciplines, such as statistics and geometry, can assist students in deepening their conceptual knowledge.