An innovative R2 decomposition technique is presented in linear regression models. It is assumed that R2 is invariant before coplanar rotations of the observation vectors of the variables, so it is natural to decompose R2 simultaneously with respect to the directions of greatest variance both in the space of the variables and of the individuals, which leads to the Dual Decomposition of R2. This decomposition quantifies the explanatory power of each variable and individual simultaneously and, in particular, allows identifying the variables and individuals with the highest explanatory power in the model. In the first case, it is very useful to guide policy measures; in the second, it allows the identification of atypical individuals who, when concentrating too much explanatory power, could be generating incorrect readings for the whole. These results and their application to the study of determinants of the distribution of business dividends, show that all linear regression analysis should be accompanied by their respective dual decomposition analysis.
 
Published in Research & Development, No 8, 2008, pp. 5 - 22​