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Bias in least squares regression. Williams, Douglas Harold

Abstract

Much of the data analysed by least squares regression methods violates the assumption that independent variables are known without error. Also, it has been demonstrated that parameter estimates based on minimum residual sums of squares have a high probability of being unsatisfactory if the independent variables are not orthogonal. Both situations are examined jointly by Monte Carlo simulation and bias in least squares estimate of regression coefficients and error sums of squares is demonstrated. Techniques for regression under these conditions are reviewed but the literature does not present a practical algorithm in either case.

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