A COMPUTATIONAL STRATEGY FOR INVERSION OF CORRELATION MATRICES HAVING LINEAR DEPENDENCIES
Correlation matrices having linear dependencies are a common occurrence in educational research. For such matrices there is no unique solution for the multiple regression coefficients; however, there is an infinity of solutions which satisfy the least squares criterion and yield the identical multiple-R and R-square. Traditional strategies for deriving the multiple regression coefficients do not ordinarily function in the presence of linear dependencies. The common practice is to use an iterative technique in which a series of approximations is car ried out repeatedly until a solution is achieved. The authors have modified the Gauss-Jordan procedure to func tion in the presence of linear dependencies. The modified procedure is much simpler than the iterative procedure and has the added advantage of identifying each redundant variable with a zero regression coefficient.