Direction dependence in a regression line

Abstract

In this paper, we derive some simple formulae to express the association between two random variables in the case of a linear relationship, One of these representations, the cube of the correlation coefficient, is given as the ratio of the skewness of the response variable to that of the explanatory variable. This result, along with other expressions of the correlation coefficient presented in this paper, has implications for choosing the response variable in a linear regression modelling.

Keywords:

• Correlation
• Least squares
• Linear regression
• Response variable
• Direction dependence regression
• Skewness

Additional information

Notes on contributors

Yadolah Dodge