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Where only bivariate collinear relations exist, a matrix of correlation coefficients is a perfectly adequate diagnostic tool for identifying collinearity. However, they are incapable of diagnosing a collinear relationship involving more than two indepdendent variables. This is the advantage of auxilliary regression. They allow a researcher to detect a collinear relationship between as many independent variables as the researcher requires.

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Q: Why are auxiliary regressions more general means of identifying collinear relationships between variables than correlation coefficients?
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