Latent Root Regression Analysis

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Abstract
Least squares estimates of parameters of a multiple linear regression model are known to be highly variable when the matrix of independent variables is near singular. Using the latent roots and latent vectors of the “correlation matrix” of the dependent and independent variables a modified least squares estimation procedure is introduced. This technique enables one to determine whether the near singularity has predictive value and examine alternate prediction equations in which the effect of the near singrtlarity has been removed from the estimates of the regression coefficients. In addition a method for performing backward elimination of variables using standard least squares or the modified procedure is presented.

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