## Least squares computations using orthogonalization methodsOrthogonalization, elimination, least squares and correlation. The least suqares problem. Back substitution, forward solution inversion. Classical gram-schmidt vs. modified gram-schmidt. Connection between gram-schmidt, householder and plane rotations. The gram-schmidt algorithm. The inverse matrix. Generalized matrix inversion by gram-schmidt. Singular value decomposition. Advantages and disadvantages of reducing. Programming considerations. |

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1,NPROJ ABAR(J BETA coefficients bidiagonal matrix CALL MPLY CARD Classical Gram-Schmidt COEFFICIENT OF DETERMINATION coefficient of nondetermination CONDITION NUMBER DABS data matrix diagonal elements equations ERROR OF FORECAST F-RATIOS follows FORTRAN Gram-Schmidt orthogonalization Gram-Schmidt process Gramian Householder transformations IMPLICIT REAL*8 A-H,O-Z inner products iterations Lawson and Hanson least squares LEFT GIVENS length of regressand length of vector Longley Problem matrix of orthonormal multiple coefficient n x n NMGSA normalized data NPROJ OPTION orthonormal vectors OVERFLOW produced R(IK regression coefficients regressor variables residual vector RETURN END rows SCALED 10 EXP SDBHAT shifts in origin side statistics singular value decomposition singular values solution square root standard deviations STANDARD ERROR Stewart's Sensitivity Index SUBROUTINE SKINNY SUBROUTINE SUM TAMP TEMP terms of normalized tolerance values TOMP trace and determinant triangular inverse matrix TUMP underflow unexplained variance upper triangular inverse upper triangular matrix VARIANCE-COVARIANCE MATRIX zero