Least squares computations based on the cholesky decomposition of the correlation matrix

Methods for obtaining the estimates of coefficients and other statistics in the usual least squares regression model are disucussed which proceed by forming a version of the Cholesky decomposition of the correlation matrix, and are well adapted to updating as predictot variables are added to or deleted from the regression. Connection with jordan elimination and with methods based on Householder decompositions are explored. Brief comments are made on the relevance of the methods for the computations of multivariate analysis.