# x42.txt # # Reference: # # Y T Chen, # Iterative Methods for Linear Least Squares Problems, # Research Report CS-75-04, # Departhment of Computer Science, # University of Waterloo, Ontario, Canada, # 1975, page 191. # # Helmut Spaeth, # Mathematical Algorithms for Linear Regression, # Academic Press, 1991, # ISBN 0-12-656460-4. # # Discussion: # # The linear system A * X = B. # By the method of least squared deviations, the solution is # X = (83.125, 2.625, 3.125, 3.75, -2.0, -4.375, 0.0, 1.5, -0.25 ). # # There are 16 rows of data. The data include: # # I, the index; # A1, column 1; # A2, column 2; # A3, column 3; # A4, column 4; # A5, column 5; # A6, column 6; # A7, column 7; # A8, column 8; # A9, column 9; # B, the right hand side. # # We seek a model of the form: # # B = A1 * X1 + A2 * X2 + A3 * X3 + A4 * X4 + A5 * X5 # + A6 * X6 + A7 * X7 + A8 * X8 + A9 * X9 # 11 columns 16 rows Index A1 A2 A3 A4 A5 A6 A7 A8 A9 B 1 1 -1 -1 0 0 1 0 0 0 67 2 1 1 -1 0 0 -1 0 0 0 83 3 1 -1 1 0 0 -1 0 0 0 95 4 1 1 1 0 0 1 0 0 0 89 5 1 -1 -1 1 0 1 -1 -1 1 71 6 1 1 -1 1 0 -1 1 -1 -1 85 7 1 -1 1 1 0 -1 -1 1 -1 98 8 1 1 1 1 0 1 1 1 1 92 9 1 -1 -1 0 1 1 0 0 0 77 10 1 1 -1 0 1 -1 0 0 0 89 11 1 -1 1 0 1 -1 0 0 0 79 12 1 1 1 0 1 1 0 0 0 78 13 1 -1 -1 1 1 1 -1 -1 1 77 14 1 1 -1 1 1 -1 1 -1 -1 92 15 1 -1 1 1 1 -1 -1 1 -1 87 16 1 1 1 1 1 1 1 1 1 85