Daniel KAHNEMAN, Olivier SIBONY, and Cass R. SUNSTEIN "Noise": Excellent Book, but Missing r² and R²

 “r² = (explained variation)² + MSE”

Dear Daniel KAHNEMAN, Olivier SIBONY, and Cass R. SUNSTEIN!
Congratulations to your excellent book “Noise” published recently (Little, Brown Spark 2021):

May I propose an advancement referring to Part III pages 107 continued: You increase the consistency with your excellent formula “MSE = bias² + noise²” (page 62; figure 7; …) if you consider the “squared correlation” r² as “shared variation of two variables” not related to MSE. “Percentage concordant” is less efficient compared to r² in most applications of bivariate or multivariate analysis; however predictive analysis might allow to use “percentage concordant” in some cases; my question to you: How do you define “percent concordant” in regression and correlation analysis, especially when looking at BAYES’ theorem, and the concepts of Jean-Paul BENZÉCRI?

On the other hand, may I introduce the term “correlation fallacy”, or “MSE^(1/2 * 2) fallacy”. This “correlation fallacy” refers to the fact that MSE is squared, while r is not, and the misunderstanding gained by the difference “squared” and “not squared”: mean error = MSE^1/2 = MeanSquaredError^1/2.

 

r² is often called “determination coefficient”. R² is the “multiple determination coefficient”. Both are very useful in constructing a real representation of the world by statistical data.

 

The interpretation of r (in contrast to r²) as shared variance is often used in the social sciencies, but this use holds no further mathematical analysis. However, r² represents the number intended (see correlation and regression analysis, e.g. my teacher in statistics, experimental psychology, and mathematical psychology Werner SCHUBÖ, e.g. “Einfache und komplexe statistische Analyse” UTB 1985). Note that my approach related to Werner SCHUBÖ, and others, and – in retrospect - to You (e.g. Your figure 16 on page 211) allows to demonstrate a HIGGS field component in GEIER’s NEWTON’s cradle; please, read my Facebook account 30. Mai 2021.

Yours Stefan Geier, Haidholzen

 

 

See Wikipedia:
1.1.        r²: Explained variance (variation)

1.2.   unexplained variance (variation): MSE
2. “In statistics, the coefficient of determination, denoted R^2 or r^2 and pronounced "R squared", is the proportion of the variance in the dependent variable that is predictable from the independent variable(s).“
Wikipedia 24.06.2021 15:25