Regression versus Correlation

Abstract

Idea of the linear regression. Auxiliary material - straight lines in Cartesian geometry. The concept of distance - geometrical distance and equivalent distances in two orthogonal directions - as a prerequisite to the concept of two regression lines. Frequent errors in interpreting two regression lines. The least square concept - Adrien Marie Legendre, Francis Galton, Karl Pearson [2]. Formal derivation of the two regression lines. Correlation coefficient as a geometrical mean of the two directional coefficients of regression lines. Which in fact measures the correlation coefficient? Udny Yule [1] and his warnings regarding abuse of correlation analysis. Further reading [3-4], [6-9]. © Springer-Verlag Berlin Heidelberg 2013.