Related Experiment Videos
An extremely strange observation on the equations for calculation of correlation coefficient
1Laboratoire de Toxicocinétique et Pharmacocinétique, Faculté de Pharmacie, Université de la Méditerraneé Aix-Marseille II, Marseilles, France.
European Journal of Drug Metabolism and Pharmacokinetics
|July 25, 2003
Summary
This study explores alternative formulas for calculating the correlation coefficient (r) and coefficient of determination (r²). Unexpected results emerged, questioning the standard interpretation of these statistical measures.
Area of Science:
- Statistics
- Data Analysis
Background:
- Standard formulas for correlation coefficient (r) and coefficient of determination (r²) are widely accepted.
- The equivalence of various computational methods for these statistics is generally presumed.
Purpose of the Study:
- To investigate the impact of using specific alternative formulas for calculating r and r².
- To highlight and present extraordinary findings derived from these alternative calculations.
Main Methods:
- Utilized the formulas r = sqrt((Σ(ŷi - y)²) / (Σ(yi - y)²)) and r² = (Σ(yi - y)² - Σ(yi - ŷi)²) / (Σ(yi - y)²).
- Applied these formulas in the context of regression analysis, including cases within confidence bands.
Main Results:
- Observed extraordinary and unexpected results when applying the specified alternative formulas.
- Demonstrated scenarios, such as a line within a 95% confidence band, yielding peculiar outcomes.
Conclusions:
- The results challenge the conventional understanding and nomenclature of correlation and determination coefficients.
- The presented findings warrant further discussion and consideration within statistical practice.