Transformation to Achieve Perfect Correlation

Authors : Satyendra Chakrabartty, Anish Chakrabarty

Pages : 1-12

View : 54 | Download : 94

Publication Date : 2025-12-31

Article Type : Research Paper

Abstract :Correlation and linear regression are common means to evaluate association and empirical relationships between two or more variables. Such relationships often show significant departure of |r_XY | from unity. Existing transformations to increase correlation fail to achieve perfect correlation. For a bivariate data, the paper proposes transforming Y to y=G.‖x‖‖y‖, which gives r_(X y)=1 where G is the G-inverse of the matrix A=x.x^Tand x, y denote vectors of deviation scores. The concept is extended to perfect linearity between a dependent variable (Y) and a set of independent variables (Multiple linear regressions) or between set of dependent variables and set of independent variables (Canonical regression), avoiding problems of insignificant beta coefficients in univariate and multivariate regression models and outliers. Empirical illustration of G-inverse and extensions for multiple linear regressions and Canonical regressions are also given. The proposed transformation is a novel method of introducing perfect correlation between two variables. Extension of the concept in multiple linear regressions and canonical regression will go a long way in empirical researches in various branches of science. Future studies may include finding distribution of the proposed perfect correlations and comparison of efficacy of our suggested approach against other traditional ones by providing quantitative evidences.
Keywords : Korelasyon katsayısı, Genelleştirilmiş ters, Çoklu doğrusal regresyonlar, Kanonik regresyon, Normal dağılım

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