Artículo: The Correlation Coefficient – An Overview

30 05 2009

Resumen del Artículo:

 

Correlation and regression are different, but not mutually exclusive, techniques. Roughly, regression
is used for prediction (which does not extrapolate beyond the data used in the analysis)
whereas correlation is used to determine the degree of association. There situations in which the
x variable is not fixed or readily chosen by the experimenter, but instead is a random covariate
to the y variable. This paper shows the relationships between the coefficient of determination,
the multiple correlation coefficient, the covariance, the correlation coefficient and the coefficient
of alienation, for the case of two related variables x and y. It discusses the uses of the
correlation coefficient r , either as a way to infer correlation, or to test linearity. A number of
graphical examples are provided as well as examples of actual chemical applications. The paper
recommends the use of z Fisher transformation instead of r values because r is not normally
distributed but z is (at least in approximation). For either correlation or for regression models,
the same expressions are valid, although they differ significantly in meaning

 

Correlation and regression are different, but not mutually exclusive, techniques. Roughly, regression is used for prediction (which does not extrapolate beyond the data used in the analysis) whereas correlation is used to determine the degree of association. There situations in which the x variable is not fixed or readily chosen by the experimenter, but instead is a random covariate to the y variable. This paper shows the relationships between the coefficient of determination, the multiple correlation coefficient, the covariance, the correlation coefficient and the coefficient of alienation, for the case of two related variables x and y. It discusses the uses of the correlation coefficient r , either as a way to infer correlation, or to test linearity. A number of graphical examples are provided as well as examples of actual chemical applications. The paper recommends the use of z Fisher transformation instead of r values because r is not normally distributed but z is (at least in approximation). For either correlation or for regression models, the same expressions are valid, although they differ significantly in meaning.

 

Autores: Asuero, Sagayo y González

Año: 2006

Revista: Critical Reviews in Analytical Chemistry

Enlace de Descarga: The Correlation Coefficient An Overview

  


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