The Cholesky Factorization of the Inverse Correlation or Covariance Matrix in Multiple Regression

The lower-triangular Cholesky inverse root (CIR) of the correlation matrix of the dependent and independent variables in a multiple regression problem is shown to be an excellent summary statistic yielding information about the full multiple regression and subsets. In particular, the CIR may be used to select variables and identify alternative subsets. It is also useful for interrelationship analysis.