The PCovR biplot: a graphical tool for principal covariates regression

Biplots are useful tools because they provide a visual representation of both individuals and variables simultaneously, making it easier to explore relationships and patterns within multidimensional datasets. This paper extends their use to examine the relationship between a set of predictors <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>X</mml:mi></mml:mrow> </mml:math> and a set of response variables <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Y</mml:mi></mml:mrow> </mml:math> using Principal Covariates Regression analysis (PCovR). The PCovR biplot provides a simultaneous graphical representation of individuals, predictor variables and response variables. It also provides the ability to examine the relationship between both types of variables in the form of the regression coefficient matrix.