On Asymmetric Properties of the Correlation Coeffcient in the Regression Setting

Although correlation is a symmetric concept of two variables, this is not the case for regression where we distinguish a response from an explanatory variable. This article presents several ways of expressing the correlation coefficient as an asymmetric formula of the two variables involved in the regression setting. Contrary to some well-known results, those are not necessarily preserved in the sample when the model is wrong. As a consequence, they may be used for model checking or model selection. In particular, we propose a criterion for choosing the response variable in a simple linear regression problem. An example from the domain of finance illustrates our purpose. We find evidence under our model that the U.S. dollar influenced other currencies during the period of consideration.