What question did this study set out to answer?

The aim is to explore the historical development and different definitions of the correlation coefficient.

Thirteen Ways to Look at the Correlation Coefficient

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This article presents various definitions and perspectives on the correlation coefficient, suggesting versatile interpretations.

The aim is to explore the historical development and different definitions of the correlation coefficient.
Historical overview of the concept of regression and correlation.
Presentation of 13 alternative formulas defining correlation.
Examination of correlation from algebraic, geometric, and trigonometric perspectives.
Demonstrates correlation coefficient can be viewed as a special type of mean and variance.
Shows differing interpretations such as the ratio of means and the slope of a line.
Illustrates correlation's relationship to geometric concepts like the cosine of an angle.

Rodgers et al. (1988) studied this question.

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