In the context of linear regression models, a novel methodology is presented for the decomposition of indicator R2 in terms of independent variables. The methodology is based on the existence of an orthogonal base of singular vectors for the space generated by the independent variables expressed in terms of deviations from their mean. This methodology allows to quantify the explanatory power or the participation of each one of the independent variables in the explanation of the variation of the dependent variable, reason why in practice it is extremely useful in the analysis of the determinants of the dependent variable and the decision of decisions in any field where a linear model is used. Two applications are presented, one related to the determinants of the decision to distribute dividends in a group of companies, and another related to the determinants of labor income in urban areas of Bolivia. Special emphasis is placed on evaluating the new methodology regarding the decomposition proposed by G. Fields, as a representative of decomposition methodologies that admit negative participations by an independent variable, which has become popular in recent years, quickly being applied in various studies throughout of all the world. The new decomposition methodology guarantees non-negativity of the direct explanatory power of a variable, on the one hand, and recognizes and quantifies the effect generated by the correlation between independent variables, on the other.
 
References about the project: CIEE Director