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An alternative to Principal Components Regression based on Regression Biplot

Abstract:

An alternative estimation method, herein termed Regression Biplots, is shown to approximate a data matrix biplot fitting bilinear models. The biplots and the Principal Components Regression are similar methods when the variables have a symmetrical role, a normal distribution and a convenient meter is introduced in their space. The advantage offered by the Regression Biplots arises from the possibility of being able to demon strate in graphic form the association, linear or not, between subjects and/or variables. For the interpretation of the graphic representation, its geometry was analyzed in the classic form and in terms of projections onto the best-fitted subspaces. Finally, a comparison is made through two practical applications, showing the usefulness of the method in diverse fields of natural and social sciences research.