Collinearity and Least Squares Regression

In this paper we introduce certain numbers, called collinearity indices, which are useful in detecting near collinearities in regression problems. The coefficients enter adversely into formulas concerning signif- icance testing and the effects of errors in the regression variables. Thus they provide simple regression diagnostics, suitable for incorporation in regression packages.

[1]  H. H. Steinour,et al.  Effect of Composition of Portland Cement on Heat Evolved during hardening , 1932 .

[2]  C. Eckart,et al.  The approximation of one matrix by another of lower rank , 1936 .

[3]  A. Turing ROUNDING-OFF ERRORS IN MATRIX PROCESSES , 1948 .

[4]  L. Mirsky SYMMETRIC GAUGE FUNCTIONS AND UNITARILY INVARIANT NORMS , 1960 .

[5]  Xiaomei Yang Rounding Errors in Algebraic Processes , 1964, Nature.

[6]  J. H. Wilkinson,et al.  Note on the iterative refinement of least squares solution , 1966 .

[7]  A. Sluis Condition numbers and equilibration of matrices , 1969 .

[8]  Donald W. Marquaridt Generalized Inverses, Ridge Regression, Biased Linear Estimation, and Nonlinear Estimation , 1970 .

[9]  Donald B. Rubin,et al.  THE ACCEPTABILITY OF REGRESSION SOLUTIONS: ANOTHER LOOK AT COMPUTATIONAL ACCURACY , 1972 .

[10]  Benee F. Swindel,et al.  Rounding Errors in the Independent Variables in a General Linear Model , 1972 .

[11]  P. G. Moore,et al.  Data Uncertainties and Least Squares Regression , 1972 .

[12]  G. Stewart Introduction to matrix computations , 1973 .

[13]  Robert B. Davies,et al.  The effect of errors in the independent variables in linear regression , 1975 .

[14]  G. Stewart On the Perturbation of Pseudo-Inverses, Projections and Linear Least Squares Problems , 1977 .

[15]  V. Klema LINPACK user's guide , 1980 .

[16]  M. J. R. Healy,et al.  Fitting Equations to Data, 2Nd Ed , 1980 .

[17]  T. W. Anderson Estimating Linear Statistical Relationships , 1984 .

[18]  David A. Belsley Demeaning Conditioning Diagnostics through Centering , 1984 .

[19]  Jack Dongarra,et al.  LINPACK Users' Guide , 1987 .

[20]  G. Stewart,et al.  A generalization of the Eckart-Young-Mirsky matrix approximation theorem , 1987 .