Regressió a la mediocritat, ara i abans

Abstract

[en] Regression towards mediocrity is a widely known statistical phenomenon, considered trivial when deeply understood. Regardless of its apparent simplicity, its interpretation seems unclear and continues to confuse people by producing fallacious reasoning. This dissertation begins by showing a historical approach on the issue focusing on the origin of the regression theory and its most related topics: correlation and covariance. Next, the mathematical bases which structure the regression method are shown from a geometrical point of view as well as its probabilistic equivalent. The Least Squares method, along with its historical motivation, is exposed as the most celebrated regression method. After that, a discussion is presented on the subtlety of the regression method, which makes it be considered one of the most reproduced fallacy in the history of economic statistics and data visualization. Moreover, the most mistaken and surprising interpretations that have taken place since its appearance until nowadays are exposed. In order to achieve a good comprehension of the paradox, a simulation is run so the reader can relate the mentioned concepts with empirical data. Finally, the relationship that binds the regression method with latter ones, such as Shrinkage or James-Stein estimator, is introduced. Such methods may be interpreted as an improvement of the regression method. As well as the method’s rigorous explanation and proof, its Galtonian deduction is also referred.