# x33.txt # # Reference: # # Helmut Spaeth, # Mathematical Algorithms for Linear Regression, # Academic Press, 1991, # ISBN 0-12-656460-4. # # Helmut Spaeth, # Cluster Dissection and Analysis: Theory, Fortran Programs, Examples, # Horwood, 1985, pages 208-209. # # Discussion: # # The matrix A was randomly generated. The right hand side B was # determined by multiplying rows of A by different vectors X: # Rows X # 1 - 48 ( 2, 1, 50, 1 ) # 49 - 84 ( 1, 80, 3, -60 ) # 85 - 96 ( 70, -1, 1, -4 ) # and then perturbing the computed value of B by a uniform distribution. # # There are 96 rows of data. The data include: # # I, the index; # A1, column 1; # A2, column 2; # A3, column 3; # A4, column 4; # B, the right hand side. # # We seek a model of the form: # # B = A1 * X1 + A2 * X2 + A3 * X3 + A4 * X4 # 6 columns 96 rows Index A1 A2 A3 A4 B 1 75 91 6 85 4815 2 6 48 48 48 234 3 5 60 24 40 160 4 74 48 8 86 4794 5 10 74 70 11 659 6 67 89 32 19 4551 7 49 36 32 68 3150 8 90 49 95 82 6014 9 74 90 9 19 5017 10 94 49 19 47 6353 11 21 3 90 38 1399 12 95 21 60 34 6550 13 14 50 7 84 606 14 89 46 65 44 6081 15 38 83 62 63 2392 16 48 67 33 33 3194 17 70 88 91 86 4553 18 92 41 62 53 6244 19 92 3 4 17 6379 20 43 54 7 93 2594 21 40 75 86 15 2750 22 74 64 72 39 5024 23 50 61 46 71 3191 24 78 5 60 20 5440 25 32 13 14 56 2014 26 21 34 18 78 1140 27 88 96 17 1 6084 28 71 4 74 67 4773 29 43 29 10 19 2909 30 3 32 96 29 164 31 5 82 22 72 11 32 50 54 64 2 3507 33 48 33 54 67 3107 34 42 82 8 46 2690 35 65 88 23 79 4162 36 32 33 35 86 1898 37 44 89 35 32 2902 38 61 9 85 46 4162 39 52 14 62 65 3427 40 56 69 66 13 3861 41 23 86 23 72 1268 42 54 64 24 47 3549 43 80 26 56 22 5538 44 24 22 94 65 1484 45 50 87 32 21 3363 46 77 88 9 78 4990 47 86 88 21 54 5739 48 79 47 66 65 5287 49 372 273 48 39 3450 50 232 226 172 64 9340 51 160 162 146 31 7806 52 76 291 92 59 5089 53 128 186 164 63 8200 54 224 30 110 3 5980 55 292 123 52 37 3351 56 336 96 142 54 7925 57 388 255 78 96 5030 58 180 165 110 16 6031 59 248 219 46 27 3051 60 88 60 34 40 1969 61 288 216 102 75 5961 62 312 261 168 58 9330 63 12 141 44 66 2433 64 384 99 70 62 4422 65 196 39 100 56 5490 66 196 183 190 88 10155 67 16 30 138 18 6972 68 376 114 28 76 2341 69 152 183 2 64 662 70 276 297 188 48 10302 71 392 3 54 42 3524 72 344 273 82 48 5117 73 220 105 50 1 3057 74 388 144 112 60 6589 75 56 33 16 73 1005 76 160 192 120 60 6568 77 128 87 88 59 4790 78 164 132 132 80 7151 79 232 45 8 77 982 80 132 174 46 2 2745 81 138 55 16 15 3691 82 66 95 12 57 4284 83 6 50 44 36 1981 84 36 70 96 51 2859 85 60 100 64 69 4105 86 36 55 0 15 3544 87 138 120 20 42 7278 88 6 115 72 12 8697 89 126 85 4 72 2625 90 36 5 64 66 -3326 91 132 110 16 63 5197 92 36 0 88 6 -51 93 42 70 28 9 5185 94 24 85 48 69 2823 95 60 45 72 3 3697 96 132 35 4 48 65