R 中裂区多元方差分析的假设和误差的平方和和叉积
我正在 R 中使用以下数据
Data <- read.table(tc <- textConnection("
A Rep B Y1 Y2 Y3 Y4 Y5
A1 1 B1 10.946 22.467 762.548 1.345 20.033
A1 1 B2 10.786 19.975 761.904 1.363 16.378
A1 1 B3 10.241 23.4 776.061 1.37 17.518
A1 1 B4 10.214 23.675 743.886 1.331 26.721
A1 1 B5 10.45 22.425 758.687 1.371 21.799
A1 1 B6 9.652 22.925 718.79 1.346 23.467
A1 1 B7 11.353 29.15 741.312 1.354 22.454
A1 1 B8 9.726 24.55 768.983 1.362 21.277
A1 1 B9 10.409 28.275 775.418 1.358 20.278
A1 1 B10 11.194 27.75 743.243 1.34 20.14
A1 1 B11 10.296 24.15 736.808 1.341 27.561
A1 1 B12 10.476 24.2 741.312 1.338 24.083
A1 1 B13 9.684 19.125 769.626 1.356 18.235
A1 1 B14 8.712 24.65 737.451 1.372 17.431
A1 1 B15 11.25 22.35 756.756 1.355 23.744
A1 1 B16 10.067 24.225 762.548 1.358 16.288
A1 2 B15 11.149 24.1 759.33 1.351 22.232
A1 2 B2 10.782 19.4 759.33 1.368 17.903
A1 2 B10 10.834 27.95 763.191 1.351 21.558
A1 2 B13 10.077 19.7 748.391 1.362 16.45
A1 2 B11 10.202 24.275 747.747 1.348 25.252
A1 2 B5 11.056 23.15 754.826 1.354 24.118
A1 2 B12 9.976 23.225 760.617 1.35 21.212
A1 2 B14 9.791 25.35 750.321 1.382 18.348
A1 2 B8 10.895 25.075 761.261 1.357 20.827
A1 2 B6 9.609 25.125 758.043 1.364 25.108
A1 2 B4 8.852 23.883 758.687 1.348 22.48
A1 2 B16 10.438 20.925 768.983 1.358 16.858
A1 2 B1 10.109 24.675 767.696 1.346 20.561
A1 2 B9 10.882 23.975 784.427 1.355 21.78
A1 2 B7 11.724 25.925 761.904 1.362 19.476
A1 2 B3 9.873 24 772.844 1.356 17.524
A1 3 B13 9.644 21.167 762.805 1.346 19.92
A1 3 B6 9.991 26.5 744.53 1.362 24.05
A1 3 B5 11.265 24.15 758.043 1.333 24.505
A1 3 B14 10.49 25.8 751.608 1.366 15.401
A1 3 B8 10.772 26.525 761.261 1.352 19.184
A1 3 B11 10.604 25.925 753.539 1.352 26.824
A1 3 B3 10.686 23.45 778.635 1.366 17.328
A1 3 B16 9.443 28.75 767.696 1.371 16.968
A1 3 B4 11.723 24.975 752.252 1.342 23.929
A1 3 B7 11.911 28.675 770.913 1.362 20.636
A1 3 B10 11.044 27.925 763.191 1.351 21.936
A1 3 B9 10.1 28.15 774.774 1.359 21.258
A1 3 B1 8.653 22.475 767.696 1.331 20.223
A1 3 B15 10.775 24.15 752.895 1.345 24.161
A1 3 B2 10.24 18.15 774.774 1.366 20.323
A1 3 B12 11.252 25.25 754.826 1.34 23.289
A2 1 B11 1.667 10.1 589.446 1.174 71.956
A2 1 B9 1.595 12.25 671.171 1.204 62.015
A2 1 B7 1.239 9.1 468.992 1.156
A2 1 B8 0.422 11.5 573.075 1.167
A2 1 B10 0.342 9.025 587.511 1.203
A2 1 B13 1.423 9.575 612.612 1.153 74.968
A2 1 B6 1.166 10.025 555.984 1.201 69.652
A2 1 B3 0.98 8.325 581.081 1.162 75.744
A2 1 B2 0.582 7.425 573.075 1.108
A2 1 B4 0.446 8.125 587.511 1.152 90
A2 1 B14 1.221 7.975 593.307 1.176 60.277
A2 1 B1 2.015 9.95 619.691 1.202 76.751
A2 1 B16 1.309 9.075 605.533 1.174 77.219
A2 1 B15 1.1 9.475 595.238 1.149 84.298
A2 1 B12 0.884 6.125 576.099 1.148 80.095
A2 1 B5 0.288 8.475 507.902 1.118
A2 2 B6 0.74 9.325 613.899 1.271 67.744
A2 2 B8 0.508 6.8 673.101 1.223 65.377
A2 2 B3 0.238 5.35 602.96 1.15 76.194
A2 2 B1 0.925 5.45 602.96 1.2 80.177
A2 2 B14 0.475 4.575 1.136 61.903
A2 2 B16 4.518 11.35 649.935 1.187 72.118
A2 2 B2 2.607 8.25 599.742 1.162 82.612
A2 2 B7 1.664 10.7 590.09 1.172 73.57
A2 2 B13 1.584 7.625 559.845 1.157 81.399
A2 2 B9 2.039 15.575 675.675 1.254 60.811
A2 2 B15 2.648 10.1 609.395 1.164 77.74
A2 2 B11 2.277 16.5 633.204 1.205 69.425
A2 2 B5 1.442 9.15 1.146 75.663
A2 2 B12 2.073 10.775 631.274 1.175 68.576
A2 2 B10 1.644 11.45 638.996 1.191 66.842
A2 2 B4 1.312 8 574.646 1.146 79.375
A2 3 B9 3.286 16.775 721.364 1.275 61.76
A2 3 B2 1.931 7.475 599.099 1.157 82.169
A2 3 B13 1.018 6.675 1.144 81.615
A2 3 B1 2.197 11.85 627.413 1.202 82.249
A2 3 B14 0.966 9.85 611.325 1.179 58.796
A2 3 B12 1.024 7.35 1.14 82.797
A2 3 B6 1.498 11.725 637.065 1.251 66.161
A2 3 B16 1.284 9.5 579.15 1.17 73.011
A2 3 B11 1.791 10.775 589.06 1.179 69.603
A2 3 B8 1.679 13 666.666 1.223 64.473
A2 3 B15 1.845 11.1 607.464 1.16 78.837
A2 3 B5 0.98 6.325 1.132 81.264
A2 3 B7 0.831 8.2 1.162 75.246
A2 3 B4 0.873 6.625 553.825 1.122 85.433
A2 3 B3 1.439 11.3 624.195 1.196 61.882
A2 3 B10 1.506 10.825 646.074 1.196 70.917
A3 1 B16 5.183 20.575 773.487 1.333 21.848
A3 1 B6 5.538 20.45 794.079 1.347 23.38
A3 1 B8 6.527 22.325 770.27 1.332 27.505
A3 1 B1 6.076 18.75 784.427 1.346 19.53
A3 1 B14 4.2 21.325 784.427 1.364 17.889
A3 1 B10 6.816 22.225 759.33 1.314 27.247
A3 1 B9 6.629 24.025 794.079 1.357 20.466
A3 1 B5 4.053 14.45 712.998 1.278 34.904
A3 1 B2 6.288 15.5 750.321 1.342 22.114
A3 1 B11 5.62 20.325 767.696 1.323 33.483
A3 1 B13 4.377 13.025 658.301 1.242 45.57
A3 1 B12 5.59 21.075 785.07 1.34 23.19
A3 1 B15 3.83 15.025 722.007 1.288 37.806
A3 1 B7 6.676 20.275 767.696 1.329 27.785
A3 1 B3 5.051 20.75 803.088 1.364 18.018
A3 1 B4 4.691 15.1 709.781 1.284 37.364
A3 2 B1 5.786 19.475 785.07 1.348 19.692
A3 2 B16 5.433 20.55 783.14 1.35 19.014
A3 2 B4 4.784 15.25 703.346 1.263 38.752
A3 2 B5 4.937 15.7 726.512 1.299 33.649
A3 2 B13 5.503 15.95 734.877 1.318 29.355
A3 2 B8 6.365 19.875 769.626 1.325 28.599
A3 2 B2 5.198 14 738.738 1.329 25.158
A3 2 B7 7.124 23.225 775.418 1.33 25.612
A3 2 B9 5.301 21.575 784.427 1.344 24.722
A3 2 B6 5.549 22.075 791.505 1.344 26.306
A3 2 B14 4.559 20.225 784.427 1.368 19.346
A3 2 B3 5.881 18.85 797.297 1.351 24.062
A3 2 B10 5.982 21.225 754.826 1.303 28.48
A3 2 B11 6.196 21.425 766.409 1.32 34.234
A3 2 B12 6.117 21.5 769.626 1.324 26.425
A3 2 B15 5.816 15.625 724.581 1.293 34.943
A3 3 B1 6.181 19.925 789.575 1.34 20.271
A3 3 B11 6.961 20.8 776.705 1.338 31.354
A3 3 B8 6.617 23.25 780.566 1.338 26.629
A3 3 B6 6.959 26 778.635 1.344 23.185
A3 3 B5 5.608 15.475 722.651 1.298 35.883
A3 3 B14 6.548 22.625 789.575 1.374 15.987
A3 3 B4 4.59 13.975 648.005 1.228 48.702
A3 3 B2 6.684 14.1 735.521 1.329 25.888
A3 3 B7 6.774 22.35 763.835 1.325 27.918
A3 3 B16 5.773 22.15 784.427 1.344 21.004
A3 3 B12 7.172 21.925 787.001 1.332 23.976
A3 3 B9 6.584 23.675 796.653 1.349 20.609
A3 3 B13 4.622 14.875 715.572 1.301 31.807
A3 3 B3 5.921 21.55 792.792 1.36 21.521
A3 3 B10 6.278 23.625 769.626 1.315 28.586
A3 3 B15 5.07 15.65 720.077 1.29 35.372
A4 1 B7 10.174 29.15 803.732 1.374 20.431
A4 1 B5 10.025 21.75 785.07 1.348 24.449
A4 1 B1 7.727 30.675 795.366 1.34 23.269
A4 1 B8 9.9 25.2 799.227 1.357 17.634
A4 1 B12 9.7 23.783 793.436 1.348 22.657
A4 1 B15 8.771 21.575 792.792 1.355 22.612
A4 1 B16 10.124 24.35 808.88 1.354 16.704
A4 1 B10 9.621 28.875 803.732 1.359 19.26
A4 1 B4 9.763 21.875 781.853 1.344 25.39
A4 1 B2 9.639 16.775 786.357 1.355 19.489
A4 1 B3 10.835 21.675 795.366 1.353 20.44
A4 1 B6 10.996 25.2 754.826 1.341 34.872
A4 1 B14 9.913 25.9 803.732 1.373 14.841
A4 1 B11 16.508 21.6 787.644 1.349 30.582
A4 1 B13 10.981 20.975 788.288 1.364 15.359
A4 1 B9 10.94 27.5 814.028 1.374 14.328
A4 2 B2 10.606 22.025 796.01 1.359 18.222
A4 2 B15 8.086 21.5 788.288 1.354 23.742
A4 2 B7 9.288 27.717 803.088 1.366 20.544
A4 2 B16 10.224 24.875 811.454 1.356 14.521
A4 2 B6 10.429 27.725 767.052 1.337 28.561
A4 2 B1 10.916 19.1 791.505 1.344 21.068
A4 2 B9 9.913 27.25 816.602 1.371 16.655
A4 2 B8 11.46 25.825 798.584 1.359 19.354
A4 2 B10 9.175 27.575 805.662 1.375 19.988
A4 2 B11 9.41 21.125 780.566 1.328 33.694
A4 2 B4 8.524 21.575 785.07 1.353 24.372
A4 2 B12 9.947 25.6 796.653 1.348 21.886
A4 2 B5 7.93 22.3 791.505 1.361 21.973
A4 2 B13 7.879 21.7 794.079 1.365 15.912
A4 2 B14 11.022 27.875 791.505 1.368 14.528
A4 2 B3 10.699 20.425 794.079 1.352 22.81
A4 3 B10 9.203 29.1 803.088 1.358 18.451
A4 3 B7 8.261 28.875 814.028 1.369 17.177
A4 3 B3 10.8 21.45 795.366 1.359 22.341
A4 3 B13 9.883 21.85 783.14 1.36 15.446
A4 3 B11 8.182 21.3 776.705 1.327 33.511
A4 3 B16 10.23 27.1 805.019 1.35 16.389
A4 3 B14 10.419 26 801.801 1.387 15.209
A4 3 B1 10.556 20.225 794.079 1.344 21.278
A4 3 B12 10.734 25.45 798.584 1.357 20.884
A4 3 B15 10.432 20.75 792.149 1.364 21.516
A4 3 B8 10.359 24.7 796.01 1.356 19.032
A4 3 B9 11.011 25.45 819.176 1.367 16.18
A4 3 B4 12.165 21.875 796.01 1.357 22.221
A4 3 B2 10.919 16.75 790.862 1.354 19.671
A4 3 B6 10.017 27.55 769.626 1.332 32.058
A4 3 B5 10.245 22.025 787.644 1.35 23.351
A5 1 B16 2.03 20.625 755.941 1.36 18.358
A5 1 B6 2.399 21.95 760.479 1.363 17.784
A5 1 B8 4.047 22.65 780.566 1.356 17.449
A5 1 B1 3.651 22.15 794.079 1.359 15.4
A5 1 B14 3.62 21.2 785.07 1.368 14.513
A5 1 B10 4.781 24.525 794.723 1.356 20.509
A5 1 B9 3.255 23.125 814.671 1.38 13.658
A5 1 B5 0.771 714.968 1.326 41.98
A5 1 B2 2.172 19.95 792.149 1.373 14.747
A5 1 B11 3.428 23.75 787.644 1.355 22.675
A5 1 B13 1.981 20.9 769.626 1.352 19.245
A5 1 B12 1.328 26.5 790.862 1.359 18.084
A5 1 B15 2.053 23.225 745.173 1.325 27.575
A5 1 B7 2.96 21.85 784.427 1.364 17.643
A5 1 B3 3.949 19.4 800.514 1.366 13.362
A5 1 B4 2.797 22.475 750.965 1.331 26.011
A5 2 B1 4.22 19.925 801.158 1.364 15.974
A5 2 B16 1.207 22.5 790.218 1.359 15.471
A5 2 B4 3.34
A5 2 B5 1.286 21.6 775.418 1.353 22.037
A5 2 B13 0.992 19.725 761.261 1.353 16.896
A5 2 B8 0.862 22.2 750.992 1.36 14.992
A5 2 B2 1.076 740.405 1.325 29.78
A5 2 B7 2.156 26.45 783.783 1.365 17.274
A5 2 B9 3.567 20.875 802.445 1.374 15.411
A5 2 B6 3.911 19.05 774.774 1.348 19.857
A5 2 B14 2.916 21.25 783.783 1.369 13.759
A5 2 B3 3.133 16.125 795.366 1.369 14.838
A5 2 B10 2.27 29.15 802.445 1.365 16.55
A5 2 B11 5.476 27.175 797.297 1.371 18.261
A5 2 B12 1.669 23.325 792.792 1.349 17.488
A5 2 B15 7.583 24.3 772.844 1.349 18.701
A5 3 B1 5.304 17.5 790.218 1.354 16.79
A5 3 B11 4.444 17 773.487 1.339 23.587
A5 3 B8 5.473 19.025 779.922 1.349 17.47
A5 3 B6 5.948 19.95 766.409 1.336 28.229
A5 3 B5 13.925 662.162 1.252 52.154
A5 3 B14 21.175 747.747 1.337 23.447
A5 3 B4 3.251 16.7 714.929 1.29 37.962
A5 3 B2 4.174 15.45 765.122 1.373 14.603
A5 3 B7 7.771 23.375 725.225 1.365 17.809
A5 3 B16 4.439 22.725 803.732 1.373 12.581
A5 3 B12 5.292 25.05 797.94 1.356 16.857
A5 3 B9 6.437 20.1 799.227 1.368 16.454
A5 3 B13 4.988 16.85 759.974 1.351 19.3
A5 3 B3 0.669 19.3 788.931 1.356 20.689
A5 3 B10 0.849 26.15 787.644 1.347 22.238
A5 3 B15 0.666 21.075 763.835 1.334 28.851
A6 1 B3 8.822 23.55 799.227 1.368 20.441
A6 1 B13 9.368 22.067 806.306 1.376 18.265
A6 1 B14 6.572 23.7 809.523 1.392 14.031
A6 1 B16 7.1 23.017 787.001 1.344 21.233
A6 1 B9 9.701 26.725 803.732 1.37 17.701
A6 1 B8 10.685 30.35 810.81 1.367 14.775
A6 1 B4 11.035 24.475 798.798 1.375 16.635
A6 1 B12 8.921 27.85 799.871 1.357 19.567
A6 1 B10 9.431 31.025 807.378 1.374 15.811
A6 1 B1 8.343 20 781.209 1.339 23.81
A6 1 B5 10.72 25.75 820.463 1.381 15.697
A6 1 B15 10.487 24.3 811.454 1.379 17.006
A6 1 B6 9.197 23.5 796.653 1.356 28.012
A6 1 B2 10.977 19.25 794.079 1.375 17.683
A6 1 B7 10.571 28.567 814.671 1.379 17.013
A6 1 B11 9.843 22.4 799.227 1.354 26.885
A6 2 B13 10.439 23.1 801.801 1.375 16.915
A6 2 B3 8.449 22.475 808.88 1.375 18.681
A6 2 B11 9.457 26.9 798.584 1.361 22.328
A6 2 B12 9.983 28.367 796.653 1.362 19.106
A6 2 B4 9.692 27.433 814.671 1.378 17.106
A6 2 B1 8.706 21.4 783.783 1.359 21.951
A6 2 B10 10.243 32.15 817.889 1.372 15.932
A6 2 B8 11.87 29.775 811.454 1.373 14.88
A6 2 B9 9.954 25.825 803.517 1.377 16.093
A6 2 B7 10.43 27.9 815.958 1.376 17.634
A6 2 B2 10.937 17.675 806.306 1.373 16.022
A6 2 B6 8.6 22.55 777.348 1.342 29.022
A6 2 B15 9.09 25.3 814.028 1.383 16.605
A6 2 B5 9.564 23.575 811.454 1.383 15.611
A6 2 B16 9.275 25.75 804.375 1.362 15.699
A6 2 B14 8.185 22.8 815.315 1.39 14.105
A6 3 B7 10.497 27 815.315 1.376 16.85
A6 3 B13 9.357 21.167 795.366 1.37 15.266
A6 3 B9 8.674 25.583 813.384 1.373 16.03
A6 3 B10 9.304 31.2 815.315 1.378 15.696
A6 3 B1 8.148 19.825 797.297 1.355 20.923
A6 3 B4 10.532 25.75 811.454 1.382 15.296
A6 3 B14 6.254 23.667 806.306 1.387 13.405
A6 3 B12 7.008 25.5 794.079 1.353 20.211
A6 3 B16 8.132 24.5 801.158 1.36 17.368
A6 3 B11 10.383 24.875 806.949 1.362 21.382
A6 3 B6 8.785 24.3 783.783 1.35 23.681
A6 3 B8 11.635 28.275 807.593 1.372 14.423
A6 3 B3 8.501 20.625 804.375 1.374 21.299
A6 3 B5 9.802 26.8 821.75 1.386 14.861
A6 3 B15 10.078 25.35 822.393 1.382 16.044
A6 3 B2 10.015 17.675 806.949 1.379 15.585
A7 1 B11 9.971 26.825 796.01 1.36 20.541
A7 1 B15 9.565 28.25 813.384 1.379 15.433
A7 1 B8 9.893 33.825 832.26 1.364 15.04
A7 1 B9 7.135 29.1 810.81 1.38 16.703
A7 1 B16 7.563 33.425 815.958 1.373 17.447
A7 1 B6 6.581 27.225 777.348 1.355 21.014
A7 1 B2 9.134 22.475 806.306 1.381 15.128
A7 1 B7 9.807 29.175 810.167 1.381 18.353
A7 1 B13 8.032 21.475 799.227 1.381 18.199
A7 1 B12 7.676 30.25 801.158 1.361 17.286
A7 1 B4 8.595 26.65 810.167 1.379 16.822
A7 1 B14 8.37 25.975 809.523 1.386 14.919
A7 1 B1 6.825 23.325 801.158 1.368 16.936
A7 1 B5 9.224 26.675 814.671 1.382 15.219
A7 1 B3 7.281 23.1 817.889 1.393 15.15
A7 1 B10 9.044 35.7 815.315 1.377 16.436
A7 2 B9 9.089 29.325 815.958 1.381 14.726
A7 2 B2 8.79 22.175 802.445 1.379 16.568
A7 2 B10 10.738 33.975 825.611 1.331 16.463
A7 2 B5 9.008 28.775 809.523 1.382 15.846
A7 2 B12 9.294 31.8 805.662 1.367 15.586
A7 2 B1 6.913 22.85 804.375 1.374 16.089
A7 2 B4 8.191 29.225 811.454 1.38 16.729
A7 2 B11 8.889 25.675 792.792 1.364 20.47
A7 2 B13 9.394 24.7 794.079 1.379 18.963
A7 2 B3 8.156 30.375 812.097 1.378 18.086
A7 2 B14 7.843 26.2 808.236 1.387 16.248
A7 2 B16 7.31 26.1 818.532 1.38 14.936
A7 2 B6 6.641 30.175 812.741 1.36 20.799
A7 2 B8 10.107 31.775 803.732 1.369 16.201
A7 2 B7 9.16 22.175 811.454 1.387 17.612
A7 2 B15 8.244 28.425 807.593 1.384 15.442
A7 3 B12 9.057 28.65 811.454 1.366 18.134
A7 3 B1 6.861 23.5 812.097 1.375 17.135
A7 3 B13 8.484 24.617 798.584 1.378 17.695
A7 3 B11 8.201 26.375 798.584 1.362 20.516
A7 3 B8 8.38 34.3 814.028 1.371 14.961
A7 3 B3 6.751 22.625 822.393 1.389 17.498
A7 3 B2 9.503 22.375 798.584 1.38 16.528
A7 3 B9 7.798 27.275 800.514 1.386 16.209
A7 3 B15 9.029 28.65 810.167 1.382 16.719
A7 3 B7 8.97 30.225 802.445 1.377 17.245
A7 3 B5 10.04 28.933 814.028 1.38 16.864
A7 3 B16 6.908 28.325 809.523 1.377 14.784
A7 3 B4 9.098 27.8 814.671 1.389 15.216
A7 3 B6 6.012 29.35 777.348 1.358 23.69
A7 3 B14 7.264 28.4 803.732 1.386 16.866
A7 3 B10 7.66 37.5 810.167 1.379 16.339
A8 1 B16 4.247 27 811.454 1.371 17.469
A8 1 B2 6.722 18.225 797.297 1.373 20.396
A8 1 B7 6.945 24.317 792.149 1.354 27.105
A8 1 B1 4.804 20.95 805.662 1.352 20.438
A8 1 B6 4.613 29.05 805.019 1.36 25.11
A8 1 B13 4.577 19.45 759.33 1.35 24.746
A8 1 B4 5.943 23.55 801.801 1.367 23.586
A8 1 B3 3.989 18.65 806.306 1.371 21.225
A8 1 B9 4.229 27.3 824.967 1.382 20.241
A8 1 B10 6.54 29.525 814.028 1.367 23.41
A8 1 B11 6.021 24.3 800.514 1.342 32.493
A8 1 B5 6.104 22.825 792.792 1.352 23.37
A8 1 B12 6.922 27.875 804.375 1.352 23.875
A8 1 B15 6.754 24.275 801.801 1.372 20.248
A8 1 B8 5.455 31.2 803.088 1.345 19.463
A8 1 B14 4.517 24.725 803.088 1.379 19.739
A8 2 B3 4.529 22.675 808.88 1.367 22.658
A8 2 B13 4.746 17.675 731.016 1.324 28.432
A8 2 B7 6.877 25.9 791.505 1.351 27.525
A8 2 B6 3.261 25.85 792.149 1.35 24.247
A8 2 B16 3.92 25.85 814.028 1.37 15.893
A8 2 B8 6.081 28.25 807.593 1.367 20.304
A8 2 B9 5.918 28.15 825.611 1.38 19.622
A8 2 B2 5.317 17.975 799.227 1.373 19.205
A8 2 B11 6.528 26.375 796.01 1.345 29.784
A8 2 B15 6.217 24.325 805.662 1.376 21.344
A8 2 B4 4.487 21.567 785.07 1.352 26.007
A8 2 B5 6.087 24.25 809.523 1.374 20.456
A8 2 B10 5.994 29.763 817.245 1.368 21.037
A8 2 B14 6.135 23.95 805.662 1.385 19.042
A8 2 B12 6.528 27.133 810.81 1.362 22.466
A8 2 B1 4.76 22.85 815.315 1.368 20.528
A8 3 B13 3.455 20.25 743.886 1.341 26.73
A8 3 B1 4.942 22.1 807.593 1.365 19.639
A8 3 B10 5.776 30.925 807.593 1.368 22.756
A8 3 B5 6.545 24.275 800.514 1.377 22.103
A8 3 B9 3.878 28 816.602 1.378 22.725
A8 3 B4 4.916 24.6 801.801 1.373 21.726
A8 3 B3 5.748 21.625 815.958 1.378 20.842
A8 3 B15 7.568 24.675 803.088 1.376 21.039
A8 3 B12 6.084 27.575 803.088 1.358 22.309
A8 3 B16 4.063 26.725 795.366 1.356 23.763
A8 3 B6 3.612 29.275 788.288 1.353 28.822
A8 3 B11 5.466 26.45 798.584 1.347 32.859
A8 3 B7 5.939 26.625 797.297 1.358 27.659
A8 3 B8 5.661 30.025 811.454 1.368 20.423
A8 3 B14 2.533 23.15 799.227 1.377 19.143
A8 3 B2 5.301 16.95 784.427 1.369 22.939
A9 1 B8 8.908 28.175 799.871 1.368 12.955
A9 1 B4 8.273 24.35 802.445 1.373 13.235
A9 1 B1 7.472 20.8 797.297 1.369 14.353
A9 1 B5 8.808 23.475 812.741 1.378 12.292
A9 1 B14 8.067 24.625 809.523 1.389 13.665
A9 1 B15 8.995 26.225 804.375 1.377 13.469
A9 1 B2 6.206 19.175 799.871 1.377 14.69
A9 1 B7 9.778 27.6 801.801 1.371 16.124
A9 1 B13 8.18 25.3 785.714 1.368 18.33
A9 1 B3 7.936 22.975 810.167 1.386 11.341
A9 1 B16 8.787 25.45 823.037 1.381 11.62
A9 1 B11 8.071 24.25 790.218 1.361 15.167
A9 1 B6 7.473 25.6 795.366 1.359 16.692
A9 1 B9 8.79 26.375 823.68 1.387 11.944
A9 1 B12 7.895 26.025 801.158 1.368 14.529
A9 1 B10 9.099 31.85 806.306 1.375 12.969
A9 2 B12 8.991 29.575 816.602 1.371 13.701
A9 2 B4 8.844 26.5 802.445 1.381 12.056
A9 2 B9 8.278 26.725 824.967 1.385 14.12
A9 2 B8 8.527 28.925 808.88 1.374 13.366
A9 2 B5 8.311 26.95 805.019 1.383 14.069
A9 2 B6 6.499 24.625 790.862 1.358 17.618
A9 2 B2 9.412 20.475 796.653 1.376 13.741
A9 2 B16 8.009 26.375 817.245 1.382 11.936
A9 2 B15 10.036 27.15 805.019 1.38 13.556
A9 2 B10 9.479 33.75 821.75 1.386 12.528
A9 2 B14 6.617 26.1 805.662 1.393 13.299
A9 2 B3 7.67 22.35 821.106 1.397 11.727
A9 2 B11 9.042 24.65 797.94 1.363 17.142
A9 2 B1 8.015 22.3 814.671 1.381 13.444
A9 2 B7 7.75 29.7 799.227 1.374 16.425
A9 2 B13 8.168 21.25 790.862 1.377 16.372
A9 3 B1 6.881 21.1 790.862 1.368 14.115
A9 3 B11 9.169 24.825 797.94 1.358 16.476
A9 3 B4 9.129 26.8 802.445 1.381 13.853
A9 3 B14 7.555 24.25 800.514 1.387 14.93
A9 3 B16 8.377 26.275 801.801 1.387 11.885
A9 3 B7 7.36 27.3 796.653 1.382 11.223
A9 3 B5 10.215 28.25 808.88 1.374 17.517
A9 3 B12 9.753 25.75 814.028 1.379 14.708
A9 3 B2 7.671 25.475 797.94 1.37 15.711
A9 3 B8 8.549 21.15 800.514 1.378 15.154
A9 3 B6 8.801 28.775 797.94 1.365 14.123
A9 3 B10 5.741 25.625 791.505 1.349 18.78
A9 3 B3 9.379 31.2 814.028 1.381 13.838
A9 3 B9 8.652 23.575 816.602 1.387 12.983
A9 3 B13 7.843 22.2 780.566 1.374 18.146
A9 3 B15 9.432 24.75 804.375 1.38 15.123
A10 1 B10 11.286 28.075 819.819 1.354 14.646
A10 1 B1 9.574 18.475 792.792 1.37 17.585
A10 1 B12 10.99 22.25 788.288 1.36 20.025
A10 1 B8 10.909 23.925 797.297 1.369 16.103
A10 1 B15 11.221 24.833 805.662 1.384 15.419
A10 1 B16 9.432 23.575 802.445 1.374 13.821
A10 1 B14 9.216 21.075 790.862 1.39 14.995
A10 1 B7 11.493 26.625 815.958 1.386 16.563
A10 1 B6 8.5 18.65 761.261 1.334 32.261
A10 1 B5 12.232 21.9 815.958 1.386 15.209
A10 1 B3 11.139 19.75 805.662 1.386 16.083
A10 1 B13 11.046 21.15 794.723 1.387 14.934
A10 1 B4 11.4 23.525 805.019 1.391 14.507
A10 1 B9 9.462 22.5 804.375 1.376 15.48
A10 1 B2 11.723 16.075 797.297 1.38 16.237
A10 1 B11 9.953 22.35 791.505 1.359 23.063
A10 2 B2 11.614 16.317 793.436 1.381 14.826
A10 2 B11 9.543 20.025 786.357 1.347 28.834
A10 2 B14 10.173 20.925 803.732 1.398 14.818
A10 2 B16 10.031 21.9 801.801 1.377 13.178
A10 2 B1 9.276 17.6 788.931 1.364 19.5
A10 2 B3 9.993 18.75 794.723 1.384 17.542
A10 2 B9 9.893 22.475 798.584 1.376 15.575
A10 2 B8 11.701 26.05 803.088 1.379 14.768
A10 2 B13 10.657 19.725 794.723 1.39 15.132
A10 2 B7 11.521 25.5 806.949 1.388 15.757
A10 2 B5 11.492 23.1 805.662 1.391 14.931
A10 2 B6 8.728 19.55 768.983 1.349 27.698
A10 2 B15 10.747 23.85 801.158 1.387 15.78
A10 2 B10 10.163 28.5 815.315 1.385 15.52
A10 2 B4 11.379 23.175 809.523 1.39 14.324
A10 2 B12 10.276 21.317 791.505 1.355 21.603
A10 3 B6 8.973 19.475 772.844 1.344 27.594
A10 3 B13 10.731 18.55 793.436 1.388 14.397
A10 3 B10 10.946 26.667 808.236 1.388 14.519
A10 3 B9 9.23 24.175 808.236 1.38 14.59
A10 3 B8 10.987 25.125 799.227 1.375 15.066
A10 3 B7 11.173 25.625 807.593 1.389 15.947
A10 3 B14 8.376 21.725 806.306 1.397 14.206
A10 3 B16 9.127 21.925 803.732 1.373 14.4
A10 3 B15 12.365 23.125 803.732 1.388 15.078
A10 3 B5 11.926 22.475 806.306 1.39 14.644
A10 3 B3 9.65 18.7 794.079 1.384 17.816
A10 3 B12 10.412 23.05 778.635 1.358 22.357
A10 3 B4 12.465 24.125 809.523 1.391 15.282
A10 3 B11 9.918 21.05 779.279 1.351 26.552
A10 3 B1 8.996 17.925 783.783 1.368 18.58
A10 3 B2 10.812 16.575 794.079 1.389 13.945
A11 1 B14 7.758 26.875 797.94 1.388 12.362
A11 1 B15 8.897 27.7 800.514 1.367 16.409
A11 1 B9 8.85 23.8 798.584 1.374 16.224
A11 1 B12 9.975 26.075 785.07 1.36 20.065
A11 1 B16 9.259 24.35 797.94 1.372 14.972
A11 1 B4 9.206 27.275 802.445 1.373 15.97
A11 1 B6 7.813 22.625 785.714 1.348 25.304
A11 1 B11 8.249 19.15 797.94 1.352 23.845
A11 1 B3 9.254 21.175 812.097 1.383 41.784
A11 1 B1 9.609 25.675 799.871 1.377 16.683
A11 1 B10 10.368 29.75 815.315 1.378 17.591
A11 1 B5 10.46 25.3 801.158 1.38 66.391
A11 1 B8 10.876 27.15 802.445 1.37 16.227
A11 1 B7 4.247 27.925 788.288 1.359 16.951
A11 1 B2 10.425 17.95 783.14 1.382 14.525
A11 1 B13 9.749 23.075 785.714 1.383 17.901
A11 2 B3 9.119 18.35 805.662 1.388 14.69
A11 2 B6 8.499 26.125 772.2 1.353 23.519
A11 2 B12 10.243 26.05 793.436 1.363 20.628
A11 2 B7 10.481 26.925 802.445 1.382 17.585
A11 2 B10 11.13 30.25 815.958 1.386 16.183
A11 2 B4 11.089 25.125 805.662 1.383 16.403
A11 2 B2 9.514 18.55 793.436 1.378 17.209
A11 2 B8 10.492 25.425 800.514 1.37 16.851
A11 2 B15 8.33 29.5 797.94 1.374 16.764
A11 2 B13 9.616 21.95 787.644 1.383 17.671
A11 2 B9 8.824 23.825 800.514 1.376 15.565
A11 2 B11 8.563 23.175 789.575 1.357 24.682
A11 2 B14 9.632 23.775 803.088 1.395 13.853
A11 2 B5 8.594 24.125 812.741 1.386 15.241
A11 2 B1 10.978 20.975 805.662 1.376 16.638
A11 2 B16 8.955 23.425 801.158 1.385 15.373
A11 3 B16 9.401 23.8 803.732 1.38 15.236
A11 3 B1 9.064 20.375 801.801 1.379 16.128
A11 3 B3 8.823 19.475 806.306 1.387 17.477
A11 3 B10 9.3 29.667 811.454 1.383 15.748
A11 3 B14 7.616 24.1 798.584 1.394 13.213
A11 3 B13 10.5 21.833 794.079 1.384 16.934
A11 3 B12 10.626 26.525 792.149 1.369 18.901
A11 3 B2 10.319 18.1 793.436 1.385 15.925
A11 3 B11 10.434 20.8 783.783 1.353 25.08
A11 3 B15 8.286 30.467 794.723 1.372 18.128
A11 3 B6 10.77 26.675 797.297 1.365 20.25
A11 3 B8 10.879 27.375 794.079 1.374 16.859
A11 3 B7 10.961 24.55 803.732 1.387 17.66
A11 3 B4 9.187 25.575 803.732 1.383 16.772
A11 3 B9 9.333 23.975 797.297 1.378 15.092
A11 3 B5 9.471 25.525 808.88 1.38 18.376
A12 1 B13 5.677 26.45 777.992 1.349 14.333
A12 1 B4 1.286 27.775 787.001 1.356 14.091
A12 1 B10 6.479 32.9 812.097 1.371 11.569
A12 1 B3 8.146 20.9 824.967 1.387 12.077
A12 1 B14 8.205 25.525 801.158 1.38 13.808
A12 1 B5 7.675 25.325 808.88 1.384 12.905
A12 1 B1 8.731 21.425 795.366 1.369 13.229
A12 1 B7 9.355 27.65 812.741 1.381 13.418
A12 1 B9 9.453 25.25 824.967 1.388 11.146
A12 1 B16 0.978 23.35 822.393 1.38 10.709
A12 1 B11 7.062 23.55 802.445 1.358 15.353
A12 1 B15 7.529 26.9 799.227 1.372 12.867
A12 1 B2 9.643 20.575 796.653 1.377 14.282
A12 1 B6 7.643 22.925 793.436 1.353 17.352
A12 1 B8 9.544 29.125 805.019 1.37 12.081
A12 1 B12 7.62 29.275 799.871 1.36 13.22
A12 2 B8 8.95 26.625 806.306 1.369 12.867
A12 2 B2 9.255 18.7 799.227 1.381 12.721
A12 2 B7 9.873 25.75 814.671 1.384 13.943
A12 2 B14 5.188 25.4 799.227 1.369 18.655
A12 2 B9 7.27 25.8 828.828 1.39 10.801
A12 2 B4 5.203 22.225 787.644 1.356 15.177
A12 2 B1 4.691 21.15 810.167 1.373 11.514
A12 2 B3 7.677 20.775 815.958 1.397 10.753
A12 2 B16 7.875 24 823.68 1.384 12.272
A12 2 B5 8.341 25.525 810.167 1.382 12.059
A12 2 B6 7.241 22.1 775.418 1.355 16.251
A12 2 B11 8.46 23.375 803.088 1.362 14.43
A12 2 B10 8.193 34.375 813.384 1.377 13.667
A12 2 B15 8.272 26.95 810.167 1.382 13.194
A12 2 B13 7.107 25.5 781.853 1.359 14.81
A12 2 B12 5.24 27.35 808.236 1.369 12.293
A12 3 B10 7.87 31.575 811.454 1.363 13.712
A12 3 B7 5.632 25.875 806.949 1.382 13.734
A12 3 B1 5.316 19.85 816.602 1.386 12.005
A12 3 B2 6.548 20.8 788.931 1.373 12.9
A12 3 B5 7.093 23.825 802.445 1.383 11.034
A12 3 B11 8.385 24.2 798.584 1.36 16.748
A12 3 B13 8.394 26.15 796.653 1.371 14.601
A12 3 B16 7.584 24.325 823.68 1.388 11.101
A12 3 B15 8.206 27 798.584 1.378 12.704
A12 3 B14 4.895 28.65 788.288 1.371 16.782
A12 3 B12 8.745 28.825 808.236 1.368 12.503
A12 3 B3 6.562 20.05 823.037 1.396 11.316
A12 3 B8 9.485 30.475 796.653 1.368 13.013
A12 3 B6 6.91 22.817 794.723 1.35 18.594
A12 3 B4 3.957 24.875 770.27 1.347 18.442
A12 3 B9 8.452 25.975 825.611 1.393 11.019"), header = TRUE, fill = TRUE); close(tc)
和以下 R 代码
Fit <- manova(formula = cbind(Y1, Y2, Y3, Y4, Y5) ~ A + Rep:A + B + A: B, data = Data)
summary.aov(Fit)
summary(Fit, test="Wilks")
summary.manova(Fit)
进行裂区多元方差分析到目前为止，一切正常。现在我想通过使用以下代码获得假设的平方和和叉积（对于 A、Rep(A)、B、AB）和错误，
library(car)
MANOVA <- Manova(mod = Fit, type = "II")
并收到以下错误消息：
Error in solve.default(wcrossprod(model.matrix(mod), w = wts)) :
Lapack routine dgesv: system is exactly singular
我无法理解为什么会收到此 消息错误信息。还有其他方法可以获取这些 SSCP吗？当我在 SAS 中进行相同的分析时，一切都很好。 SAS 代码是
PROC GLM DATA = Data;
CLASS A Rep B;
MODEL Y1 Y2 Y3 Y4 Y5 = A Rep(A) B A*B;
MANOVA H =_all_ /PRINTE PRINTH;
RUN;
但我想在 R 中执行此操作。任何帮助将不胜感激。提前致谢。
I'm doing the split-plot MANOVA in R by using the following data
Data <- read.table(tc <- textConnection("
A Rep B Y1 Y2 Y3 Y4 Y5
A1 1 B1 10.946 22.467 762.548 1.345 20.033
A1 1 B2 10.786 19.975 761.904 1.363 16.378
A1 1 B3 10.241 23.4 776.061 1.37 17.518
A1 1 B4 10.214 23.675 743.886 1.331 26.721
A1 1 B5 10.45 22.425 758.687 1.371 21.799
A1 1 B6 9.652 22.925 718.79 1.346 23.467
A1 1 B7 11.353 29.15 741.312 1.354 22.454
A1 1 B8 9.726 24.55 768.983 1.362 21.277
A1 1 B9 10.409 28.275 775.418 1.358 20.278
A1 1 B10 11.194 27.75 743.243 1.34 20.14
A1 1 B11 10.296 24.15 736.808 1.341 27.561
A1 1 B12 10.476 24.2 741.312 1.338 24.083
A1 1 B13 9.684 19.125 769.626 1.356 18.235
A1 1 B14 8.712 24.65 737.451 1.372 17.431
A1 1 B15 11.25 22.35 756.756 1.355 23.744
A1 1 B16 10.067 24.225 762.548 1.358 16.288
A1 2 B15 11.149 24.1 759.33 1.351 22.232
A1 2 B2 10.782 19.4 759.33 1.368 17.903
A1 2 B10 10.834 27.95 763.191 1.351 21.558
A1 2 B13 10.077 19.7 748.391 1.362 16.45
A1 2 B11 10.202 24.275 747.747 1.348 25.252
A1 2 B5 11.056 23.15 754.826 1.354 24.118
A1 2 B12 9.976 23.225 760.617 1.35 21.212
A1 2 B14 9.791 25.35 750.321 1.382 18.348
A1 2 B8 10.895 25.075 761.261 1.357 20.827
A1 2 B6 9.609 25.125 758.043 1.364 25.108
A1 2 B4 8.852 23.883 758.687 1.348 22.48
A1 2 B16 10.438 20.925 768.983 1.358 16.858
A1 2 B1 10.109 24.675 767.696 1.346 20.561
A1 2 B9 10.882 23.975 784.427 1.355 21.78
A1 2 B7 11.724 25.925 761.904 1.362 19.476
A1 2 B3 9.873 24 772.844 1.356 17.524
A1 3 B13 9.644 21.167 762.805 1.346 19.92
A1 3 B6 9.991 26.5 744.53 1.362 24.05
A1 3 B5 11.265 24.15 758.043 1.333 24.505
A1 3 B14 10.49 25.8 751.608 1.366 15.401
A1 3 B8 10.772 26.525 761.261 1.352 19.184
A1 3 B11 10.604 25.925 753.539 1.352 26.824
A1 3 B3 10.686 23.45 778.635 1.366 17.328
A1 3 B16 9.443 28.75 767.696 1.371 16.968
A1 3 B4 11.723 24.975 752.252 1.342 23.929
A1 3 B7 11.911 28.675 770.913 1.362 20.636
A1 3 B10 11.044 27.925 763.191 1.351 21.936
A1 3 B9 10.1 28.15 774.774 1.359 21.258
A1 3 B1 8.653 22.475 767.696 1.331 20.223
A1 3 B15 10.775 24.15 752.895 1.345 24.161
A1 3 B2 10.24 18.15 774.774 1.366 20.323
A1 3 B12 11.252 25.25 754.826 1.34 23.289
A2 1 B11 1.667 10.1 589.446 1.174 71.956
A2 1 B9 1.595 12.25 671.171 1.204 62.015
A2 1 B7 1.239 9.1 468.992 1.156
A2 1 B8 0.422 11.5 573.075 1.167
A2 1 B10 0.342 9.025 587.511 1.203
A2 1 B13 1.423 9.575 612.612 1.153 74.968
A2 1 B6 1.166 10.025 555.984 1.201 69.652
A2 1 B3 0.98 8.325 581.081 1.162 75.744
A2 1 B2 0.582 7.425 573.075 1.108
A2 1 B4 0.446 8.125 587.511 1.152 90
A2 1 B14 1.221 7.975 593.307 1.176 60.277
A2 1 B1 2.015 9.95 619.691 1.202 76.751
A2 1 B16 1.309 9.075 605.533 1.174 77.219
A2 1 B15 1.1 9.475 595.238 1.149 84.298
A2 1 B12 0.884 6.125 576.099 1.148 80.095
A2 1 B5 0.288 8.475 507.902 1.118
A2 2 B6 0.74 9.325 613.899 1.271 67.744
A2 2 B8 0.508 6.8 673.101 1.223 65.377
A2 2 B3 0.238 5.35 602.96 1.15 76.194
A2 2 B1 0.925 5.45 602.96 1.2 80.177
A2 2 B14 0.475 4.575 1.136 61.903
A2 2 B16 4.518 11.35 649.935 1.187 72.118
A2 2 B2 2.607 8.25 599.742 1.162 82.612
A2 2 B7 1.664 10.7 590.09 1.172 73.57
A2 2 B13 1.584 7.625 559.845 1.157 81.399
A2 2 B9 2.039 15.575 675.675 1.254 60.811
A2 2 B15 2.648 10.1 609.395 1.164 77.74
A2 2 B11 2.277 16.5 633.204 1.205 69.425
A2 2 B5 1.442 9.15 1.146 75.663
A2 2 B12 2.073 10.775 631.274 1.175 68.576
A2 2 B10 1.644 11.45 638.996 1.191 66.842
A2 2 B4 1.312 8 574.646 1.146 79.375
A2 3 B9 3.286 16.775 721.364 1.275 61.76
A2 3 B2 1.931 7.475 599.099 1.157 82.169
A2 3 B13 1.018 6.675 1.144 81.615
A2 3 B1 2.197 11.85 627.413 1.202 82.249
A2 3 B14 0.966 9.85 611.325 1.179 58.796
A2 3 B12 1.024 7.35 1.14 82.797
A2 3 B6 1.498 11.725 637.065 1.251 66.161
A2 3 B16 1.284 9.5 579.15 1.17 73.011
A2 3 B11 1.791 10.775 589.06 1.179 69.603
A2 3 B8 1.679 13 666.666 1.223 64.473
A2 3 B15 1.845 11.1 607.464 1.16 78.837
A2 3 B5 0.98 6.325 1.132 81.264
A2 3 B7 0.831 8.2 1.162 75.246
A2 3 B4 0.873 6.625 553.825 1.122 85.433
A2 3 B3 1.439 11.3 624.195 1.196 61.882
A2 3 B10 1.506 10.825 646.074 1.196 70.917
A3 1 B16 5.183 20.575 773.487 1.333 21.848
A3 1 B6 5.538 20.45 794.079 1.347 23.38
A3 1 B8 6.527 22.325 770.27 1.332 27.505
A3 1 B1 6.076 18.75 784.427 1.346 19.53
A3 1 B14 4.2 21.325 784.427 1.364 17.889
A3 1 B10 6.816 22.225 759.33 1.314 27.247
A3 1 B9 6.629 24.025 794.079 1.357 20.466
A3 1 B5 4.053 14.45 712.998 1.278 34.904
A3 1 B2 6.288 15.5 750.321 1.342 22.114
A3 1 B11 5.62 20.325 767.696 1.323 33.483
A3 1 B13 4.377 13.025 658.301 1.242 45.57
A3 1 B12 5.59 21.075 785.07 1.34 23.19
A3 1 B15 3.83 15.025 722.007 1.288 37.806
A3 1 B7 6.676 20.275 767.696 1.329 27.785
A3 1 B3 5.051 20.75 803.088 1.364 18.018
A3 1 B4 4.691 15.1 709.781 1.284 37.364
A3 2 B1 5.786 19.475 785.07 1.348 19.692
A3 2 B16 5.433 20.55 783.14 1.35 19.014
A3 2 B4 4.784 15.25 703.346 1.263 38.752
A3 2 B5 4.937 15.7 726.512 1.299 33.649
A3 2 B13 5.503 15.95 734.877 1.318 29.355
A3 2 B8 6.365 19.875 769.626 1.325 28.599
A3 2 B2 5.198 14 738.738 1.329 25.158
A3 2 B7 7.124 23.225 775.418 1.33 25.612
A3 2 B9 5.301 21.575 784.427 1.344 24.722
A3 2 B6 5.549 22.075 791.505 1.344 26.306
A3 2 B14 4.559 20.225 784.427 1.368 19.346
A3 2 B3 5.881 18.85 797.297 1.351 24.062
A3 2 B10 5.982 21.225 754.826 1.303 28.48
A3 2 B11 6.196 21.425 766.409 1.32 34.234
A3 2 B12 6.117 21.5 769.626 1.324 26.425
A3 2 B15 5.816 15.625 724.581 1.293 34.943
A3 3 B1 6.181 19.925 789.575 1.34 20.271
A3 3 B11 6.961 20.8 776.705 1.338 31.354
A3 3 B8 6.617 23.25 780.566 1.338 26.629
A3 3 B6 6.959 26 778.635 1.344 23.185
A3 3 B5 5.608 15.475 722.651 1.298 35.883
A3 3 B14 6.548 22.625 789.575 1.374 15.987
A3 3 B4 4.59 13.975 648.005 1.228 48.702
A3 3 B2 6.684 14.1 735.521 1.329 25.888
A3 3 B7 6.774 22.35 763.835 1.325 27.918
A3 3 B16 5.773 22.15 784.427 1.344 21.004
A3 3 B12 7.172 21.925 787.001 1.332 23.976
A3 3 B9 6.584 23.675 796.653 1.349 20.609
A3 3 B13 4.622 14.875 715.572 1.301 31.807
A3 3 B3 5.921 21.55 792.792 1.36 21.521
A3 3 B10 6.278 23.625 769.626 1.315 28.586
A3 3 B15 5.07 15.65 720.077 1.29 35.372
A4 1 B7 10.174 29.15 803.732 1.374 20.431
A4 1 B5 10.025 21.75 785.07 1.348 24.449
A4 1 B1 7.727 30.675 795.366 1.34 23.269
A4 1 B8 9.9 25.2 799.227 1.357 17.634
A4 1 B12 9.7 23.783 793.436 1.348 22.657
A4 1 B15 8.771 21.575 792.792 1.355 22.612
A4 1 B16 10.124 24.35 808.88 1.354 16.704
A4 1 B10 9.621 28.875 803.732 1.359 19.26
A4 1 B4 9.763 21.875 781.853 1.344 25.39
A4 1 B2 9.639 16.775 786.357 1.355 19.489
A4 1 B3 10.835 21.675 795.366 1.353 20.44
A4 1 B6 10.996 25.2 754.826 1.341 34.872
A4 1 B14 9.913 25.9 803.732 1.373 14.841
A4 1 B11 16.508 21.6 787.644 1.349 30.582
A4 1 B13 10.981 20.975 788.288 1.364 15.359
A4 1 B9 10.94 27.5 814.028 1.374 14.328
A4 2 B2 10.606 22.025 796.01 1.359 18.222
A4 2 B15 8.086 21.5 788.288 1.354 23.742
A4 2 B7 9.288 27.717 803.088 1.366 20.544
A4 2 B16 10.224 24.875 811.454 1.356 14.521
A4 2 B6 10.429 27.725 767.052 1.337 28.561
A4 2 B1 10.916 19.1 791.505 1.344 21.068
A4 2 B9 9.913 27.25 816.602 1.371 16.655
A4 2 B8 11.46 25.825 798.584 1.359 19.354
A4 2 B10 9.175 27.575 805.662 1.375 19.988
A4 2 B11 9.41 21.125 780.566 1.328 33.694
A4 2 B4 8.524 21.575 785.07 1.353 24.372
A4 2 B12 9.947 25.6 796.653 1.348 21.886
A4 2 B5 7.93 22.3 791.505 1.361 21.973
A4 2 B13 7.879 21.7 794.079 1.365 15.912
A4 2 B14 11.022 27.875 791.505 1.368 14.528
A4 2 B3 10.699 20.425 794.079 1.352 22.81
A4 3 B10 9.203 29.1 803.088 1.358 18.451
A4 3 B7 8.261 28.875 814.028 1.369 17.177
A4 3 B3 10.8 21.45 795.366 1.359 22.341
A4 3 B13 9.883 21.85 783.14 1.36 15.446
A4 3 B11 8.182 21.3 776.705 1.327 33.511
A4 3 B16 10.23 27.1 805.019 1.35 16.389
A4 3 B14 10.419 26 801.801 1.387 15.209
A4 3 B1 10.556 20.225 794.079 1.344 21.278
A4 3 B12 10.734 25.45 798.584 1.357 20.884
A4 3 B15 10.432 20.75 792.149 1.364 21.516
A4 3 B8 10.359 24.7 796.01 1.356 19.032
A4 3 B9 11.011 25.45 819.176 1.367 16.18
A4 3 B4 12.165 21.875 796.01 1.357 22.221
A4 3 B2 10.919 16.75 790.862 1.354 19.671
A4 3 B6 10.017 27.55 769.626 1.332 32.058
A4 3 B5 10.245 22.025 787.644 1.35 23.351
A5 1 B16 2.03 20.625 755.941 1.36 18.358
A5 1 B6 2.399 21.95 760.479 1.363 17.784
A5 1 B8 4.047 22.65 780.566 1.356 17.449
A5 1 B1 3.651 22.15 794.079 1.359 15.4
A5 1 B14 3.62 21.2 785.07 1.368 14.513
A5 1 B10 4.781 24.525 794.723 1.356 20.509
A5 1 B9 3.255 23.125 814.671 1.38 13.658
A5 1 B5 0.771 714.968 1.326 41.98
A5 1 B2 2.172 19.95 792.149 1.373 14.747
A5 1 B11 3.428 23.75 787.644 1.355 22.675
A5 1 B13 1.981 20.9 769.626 1.352 19.245
A5 1 B12 1.328 26.5 790.862 1.359 18.084
A5 1 B15 2.053 23.225 745.173 1.325 27.575
A5 1 B7 2.96 21.85 784.427 1.364 17.643
A5 1 B3 3.949 19.4 800.514 1.366 13.362
A5 1 B4 2.797 22.475 750.965 1.331 26.011
A5 2 B1 4.22 19.925 801.158 1.364 15.974
A5 2 B16 1.207 22.5 790.218 1.359 15.471
A5 2 B4 3.34
A5 2 B5 1.286 21.6 775.418 1.353 22.037
A5 2 B13 0.992 19.725 761.261 1.353 16.896
A5 2 B8 0.862 22.2 750.992 1.36 14.992
A5 2 B2 1.076 740.405 1.325 29.78
A5 2 B7 2.156 26.45 783.783 1.365 17.274
A5 2 B9 3.567 20.875 802.445 1.374 15.411
A5 2 B6 3.911 19.05 774.774 1.348 19.857
A5 2 B14 2.916 21.25 783.783 1.369 13.759
A5 2 B3 3.133 16.125 795.366 1.369 14.838
A5 2 B10 2.27 29.15 802.445 1.365 16.55
A5 2 B11 5.476 27.175 797.297 1.371 18.261
A5 2 B12 1.669 23.325 792.792 1.349 17.488
A5 2 B15 7.583 24.3 772.844 1.349 18.701
A5 3 B1 5.304 17.5 790.218 1.354 16.79
A5 3 B11 4.444 17 773.487 1.339 23.587
A5 3 B8 5.473 19.025 779.922 1.349 17.47
A5 3 B6 5.948 19.95 766.409 1.336 28.229
A5 3 B5 13.925 662.162 1.252 52.154
A5 3 B14 21.175 747.747 1.337 23.447
A5 3 B4 3.251 16.7 714.929 1.29 37.962
A5 3 B2 4.174 15.45 765.122 1.373 14.603
A5 3 B7 7.771 23.375 725.225 1.365 17.809
A5 3 B16 4.439 22.725 803.732 1.373 12.581
A5 3 B12 5.292 25.05 797.94 1.356 16.857
A5 3 B9 6.437 20.1 799.227 1.368 16.454
A5 3 B13 4.988 16.85 759.974 1.351 19.3
A5 3 B3 0.669 19.3 788.931 1.356 20.689
A5 3 B10 0.849 26.15 787.644 1.347 22.238
A5 3 B15 0.666 21.075 763.835 1.334 28.851
A6 1 B3 8.822 23.55 799.227 1.368 20.441
A6 1 B13 9.368 22.067 806.306 1.376 18.265
A6 1 B14 6.572 23.7 809.523 1.392 14.031
A6 1 B16 7.1 23.017 787.001 1.344 21.233
A6 1 B9 9.701 26.725 803.732 1.37 17.701
A6 1 B8 10.685 30.35 810.81 1.367 14.775
A6 1 B4 11.035 24.475 798.798 1.375 16.635
A6 1 B12 8.921 27.85 799.871 1.357 19.567
A6 1 B10 9.431 31.025 807.378 1.374 15.811
A6 1 B1 8.343 20 781.209 1.339 23.81
A6 1 B5 10.72 25.75 820.463 1.381 15.697
A6 1 B15 10.487 24.3 811.454 1.379 17.006
A6 1 B6 9.197 23.5 796.653 1.356 28.012
A6 1 B2 10.977 19.25 794.079 1.375 17.683
A6 1 B7 10.571 28.567 814.671 1.379 17.013
A6 1 B11 9.843 22.4 799.227 1.354 26.885
A6 2 B13 10.439 23.1 801.801 1.375 16.915
A6 2 B3 8.449 22.475 808.88 1.375 18.681
A6 2 B11 9.457 26.9 798.584 1.361 22.328
A6 2 B12 9.983 28.367 796.653 1.362 19.106
A6 2 B4 9.692 27.433 814.671 1.378 17.106
A6 2 B1 8.706 21.4 783.783 1.359 21.951
A6 2 B10 10.243 32.15 817.889 1.372 15.932
A6 2 B8 11.87 29.775 811.454 1.373 14.88
A6 2 B9 9.954 25.825 803.517 1.377 16.093
A6 2 B7 10.43 27.9 815.958 1.376 17.634
A6 2 B2 10.937 17.675 806.306 1.373 16.022
A6 2 B6 8.6 22.55 777.348 1.342 29.022
A6 2 B15 9.09 25.3 814.028 1.383 16.605
A6 2 B5 9.564 23.575 811.454 1.383 15.611
A6 2 B16 9.275 25.75 804.375 1.362 15.699
A6 2 B14 8.185 22.8 815.315 1.39 14.105
A6 3 B7 10.497 27 815.315 1.376 16.85
A6 3 B13 9.357 21.167 795.366 1.37 15.266
A6 3 B9 8.674 25.583 813.384 1.373 16.03
A6 3 B10 9.304 31.2 815.315 1.378 15.696
A6 3 B1 8.148 19.825 797.297 1.355 20.923
A6 3 B4 10.532 25.75 811.454 1.382 15.296
A6 3 B14 6.254 23.667 806.306 1.387 13.405
A6 3 B12 7.008 25.5 794.079 1.353 20.211
A6 3 B16 8.132 24.5 801.158 1.36 17.368
A6 3 B11 10.383 24.875 806.949 1.362 21.382
A6 3 B6 8.785 24.3 783.783 1.35 23.681
A6 3 B8 11.635 28.275 807.593 1.372 14.423
A6 3 B3 8.501 20.625 804.375 1.374 21.299
A6 3 B5 9.802 26.8 821.75 1.386 14.861
A6 3 B15 10.078 25.35 822.393 1.382 16.044
A6 3 B2 10.015 17.675 806.949 1.379 15.585
A7 1 B11 9.971 26.825 796.01 1.36 20.541
A7 1 B15 9.565 28.25 813.384 1.379 15.433
A7 1 B8 9.893 33.825 832.26 1.364 15.04
A7 1 B9 7.135 29.1 810.81 1.38 16.703
A7 1 B16 7.563 33.425 815.958 1.373 17.447
A7 1 B6 6.581 27.225 777.348 1.355 21.014
A7 1 B2 9.134 22.475 806.306 1.381 15.128
A7 1 B7 9.807 29.175 810.167 1.381 18.353
A7 1 B13 8.032 21.475 799.227 1.381 18.199
A7 1 B12 7.676 30.25 801.158 1.361 17.286
A7 1 B4 8.595 26.65 810.167 1.379 16.822
A7 1 B14 8.37 25.975 809.523 1.386 14.919
A7 1 B1 6.825 23.325 801.158 1.368 16.936
A7 1 B5 9.224 26.675 814.671 1.382 15.219
A7 1 B3 7.281 23.1 817.889 1.393 15.15
A7 1 B10 9.044 35.7 815.315 1.377 16.436
A7 2 B9 9.089 29.325 815.958 1.381 14.726
A7 2 B2 8.79 22.175 802.445 1.379 16.568
A7 2 B10 10.738 33.975 825.611 1.331 16.463
A7 2 B5 9.008 28.775 809.523 1.382 15.846
A7 2 B12 9.294 31.8 805.662 1.367 15.586
A7 2 B1 6.913 22.85 804.375 1.374 16.089
A7 2 B4 8.191 29.225 811.454 1.38 16.729
A7 2 B11 8.889 25.675 792.792 1.364 20.47
A7 2 B13 9.394 24.7 794.079 1.379 18.963
A7 2 B3 8.156 30.375 812.097 1.378 18.086
A7 2 B14 7.843 26.2 808.236 1.387 16.248
A7 2 B16 7.31 26.1 818.532 1.38 14.936
A7 2 B6 6.641 30.175 812.741 1.36 20.799
A7 2 B8 10.107 31.775 803.732 1.369 16.201
A7 2 B7 9.16 22.175 811.454 1.387 17.612
A7 2 B15 8.244 28.425 807.593 1.384 15.442
A7 3 B12 9.057 28.65 811.454 1.366 18.134
A7 3 B1 6.861 23.5 812.097 1.375 17.135
A7 3 B13 8.484 24.617 798.584 1.378 17.695
A7 3 B11 8.201 26.375 798.584 1.362 20.516
A7 3 B8 8.38 34.3 814.028 1.371 14.961
A7 3 B3 6.751 22.625 822.393 1.389 17.498
A7 3 B2 9.503 22.375 798.584 1.38 16.528
A7 3 B9 7.798 27.275 800.514 1.386 16.209
A7 3 B15 9.029 28.65 810.167 1.382 16.719
A7 3 B7 8.97 30.225 802.445 1.377 17.245
A7 3 B5 10.04 28.933 814.028 1.38 16.864
A7 3 B16 6.908 28.325 809.523 1.377 14.784
A7 3 B4 9.098 27.8 814.671 1.389 15.216
A7 3 B6 6.012 29.35 777.348 1.358 23.69
A7 3 B14 7.264 28.4 803.732 1.386 16.866
A7 3 B10 7.66 37.5 810.167 1.379 16.339
A8 1 B16 4.247 27 811.454 1.371 17.469
A8 1 B2 6.722 18.225 797.297 1.373 20.396
A8 1 B7 6.945 24.317 792.149 1.354 27.105
A8 1 B1 4.804 20.95 805.662 1.352 20.438
A8 1 B6 4.613 29.05 805.019 1.36 25.11
A8 1 B13 4.577 19.45 759.33 1.35 24.746
A8 1 B4 5.943 23.55 801.801 1.367 23.586
A8 1 B3 3.989 18.65 806.306 1.371 21.225
A8 1 B9 4.229 27.3 824.967 1.382 20.241
A8 1 B10 6.54 29.525 814.028 1.367 23.41
A8 1 B11 6.021 24.3 800.514 1.342 32.493
A8 1 B5 6.104 22.825 792.792 1.352 23.37
A8 1 B12 6.922 27.875 804.375 1.352 23.875
A8 1 B15 6.754 24.275 801.801 1.372 20.248
A8 1 B8 5.455 31.2 803.088 1.345 19.463
A8 1 B14 4.517 24.725 803.088 1.379 19.739
A8 2 B3 4.529 22.675 808.88 1.367 22.658
A8 2 B13 4.746 17.675 731.016 1.324 28.432
A8 2 B7 6.877 25.9 791.505 1.351 27.525
A8 2 B6 3.261 25.85 792.149 1.35 24.247
A8 2 B16 3.92 25.85 814.028 1.37 15.893
A8 2 B8 6.081 28.25 807.593 1.367 20.304
A8 2 B9 5.918 28.15 825.611 1.38 19.622
A8 2 B2 5.317 17.975 799.227 1.373 19.205
A8 2 B11 6.528 26.375 796.01 1.345 29.784
A8 2 B15 6.217 24.325 805.662 1.376 21.344
A8 2 B4 4.487 21.567 785.07 1.352 26.007
A8 2 B5 6.087 24.25 809.523 1.374 20.456
A8 2 B10 5.994 29.763 817.245 1.368 21.037
A8 2 B14 6.135 23.95 805.662 1.385 19.042
A8 2 B12 6.528 27.133 810.81 1.362 22.466
A8 2 B1 4.76 22.85 815.315 1.368 20.528
A8 3 B13 3.455 20.25 743.886 1.341 26.73
A8 3 B1 4.942 22.1 807.593 1.365 19.639
A8 3 B10 5.776 30.925 807.593 1.368 22.756
A8 3 B5 6.545 24.275 800.514 1.377 22.103
A8 3 B9 3.878 28 816.602 1.378 22.725
A8 3 B4 4.916 24.6 801.801 1.373 21.726
A8 3 B3 5.748 21.625 815.958 1.378 20.842
A8 3 B15 7.568 24.675 803.088 1.376 21.039
A8 3 B12 6.084 27.575 803.088 1.358 22.309
A8 3 B16 4.063 26.725 795.366 1.356 23.763
A8 3 B6 3.612 29.275 788.288 1.353 28.822
A8 3 B11 5.466 26.45 798.584 1.347 32.859
A8 3 B7 5.939 26.625 797.297 1.358 27.659
A8 3 B8 5.661 30.025 811.454 1.368 20.423
A8 3 B14 2.533 23.15 799.227 1.377 19.143
A8 3 B2 5.301 16.95 784.427 1.369 22.939
A9 1 B8 8.908 28.175 799.871 1.368 12.955
A9 1 B4 8.273 24.35 802.445 1.373 13.235
A9 1 B1 7.472 20.8 797.297 1.369 14.353
A9 1 B5 8.808 23.475 812.741 1.378 12.292
A9 1 B14 8.067 24.625 809.523 1.389 13.665
A9 1 B15 8.995 26.225 804.375 1.377 13.469
A9 1 B2 6.206 19.175 799.871 1.377 14.69
A9 1 B7 9.778 27.6 801.801 1.371 16.124
A9 1 B13 8.18 25.3 785.714 1.368 18.33
A9 1 B3 7.936 22.975 810.167 1.386 11.341
A9 1 B16 8.787 25.45 823.037 1.381 11.62
A9 1 B11 8.071 24.25 790.218 1.361 15.167
A9 1 B6 7.473 25.6 795.366 1.359 16.692
A9 1 B9 8.79 26.375 823.68 1.387 11.944
A9 1 B12 7.895 26.025 801.158 1.368 14.529
A9 1 B10 9.099 31.85 806.306 1.375 12.969
A9 2 B12 8.991 29.575 816.602 1.371 13.701
A9 2 B4 8.844 26.5 802.445 1.381 12.056
A9 2 B9 8.278 26.725 824.967 1.385 14.12
A9 2 B8 8.527 28.925 808.88 1.374 13.366
A9 2 B5 8.311 26.95 805.019 1.383 14.069
A9 2 B6 6.499 24.625 790.862 1.358 17.618
A9 2 B2 9.412 20.475 796.653 1.376 13.741
A9 2 B16 8.009 26.375 817.245 1.382 11.936
A9 2 B15 10.036 27.15 805.019 1.38 13.556
A9 2 B10 9.479 33.75 821.75 1.386 12.528
A9 2 B14 6.617 26.1 805.662 1.393 13.299
A9 2 B3 7.67 22.35 821.106 1.397 11.727
A9 2 B11 9.042 24.65 797.94 1.363 17.142
A9 2 B1 8.015 22.3 814.671 1.381 13.444
A9 2 B7 7.75 29.7 799.227 1.374 16.425
A9 2 B13 8.168 21.25 790.862 1.377 16.372
A9 3 B1 6.881 21.1 790.862 1.368 14.115
A9 3 B11 9.169 24.825 797.94 1.358 16.476
A9 3 B4 9.129 26.8 802.445 1.381 13.853
A9 3 B14 7.555 24.25 800.514 1.387 14.93
A9 3 B16 8.377 26.275 801.801 1.387 11.885
A9 3 B7 7.36 27.3 796.653 1.382 11.223
A9 3 B5 10.215 28.25 808.88 1.374 17.517
A9 3 B12 9.753 25.75 814.028 1.379 14.708
A9 3 B2 7.671 25.475 797.94 1.37 15.711
A9 3 B8 8.549 21.15 800.514 1.378 15.154
A9 3 B6 8.801 28.775 797.94 1.365 14.123
A9 3 B10 5.741 25.625 791.505 1.349 18.78
A9 3 B3 9.379 31.2 814.028 1.381 13.838
A9 3 B9 8.652 23.575 816.602 1.387 12.983
A9 3 B13 7.843 22.2 780.566 1.374 18.146
A9 3 B15 9.432 24.75 804.375 1.38 15.123
A10 1 B10 11.286 28.075 819.819 1.354 14.646
A10 1 B1 9.574 18.475 792.792 1.37 17.585
A10 1 B12 10.99 22.25 788.288 1.36 20.025
A10 1 B8 10.909 23.925 797.297 1.369 16.103
A10 1 B15 11.221 24.833 805.662 1.384 15.419
A10 1 B16 9.432 23.575 802.445 1.374 13.821
A10 1 B14 9.216 21.075 790.862 1.39 14.995
A10 1 B7 11.493 26.625 815.958 1.386 16.563
A10 1 B6 8.5 18.65 761.261 1.334 32.261
A10 1 B5 12.232 21.9 815.958 1.386 15.209
A10 1 B3 11.139 19.75 805.662 1.386 16.083
A10 1 B13 11.046 21.15 794.723 1.387 14.934
A10 1 B4 11.4 23.525 805.019 1.391 14.507
A10 1 B9 9.462 22.5 804.375 1.376 15.48
A10 1 B2 11.723 16.075 797.297 1.38 16.237
A10 1 B11 9.953 22.35 791.505 1.359 23.063
A10 2 B2 11.614 16.317 793.436 1.381 14.826
A10 2 B11 9.543 20.025 786.357 1.347 28.834
A10 2 B14 10.173 20.925 803.732 1.398 14.818
A10 2 B16 10.031 21.9 801.801 1.377 13.178
A10 2 B1 9.276 17.6 788.931 1.364 19.5
A10 2 B3 9.993 18.75 794.723 1.384 17.542
A10 2 B9 9.893 22.475 798.584 1.376 15.575
A10 2 B8 11.701 26.05 803.088 1.379 14.768
A10 2 B13 10.657 19.725 794.723 1.39 15.132
A10 2 B7 11.521 25.5 806.949 1.388 15.757
A10 2 B5 11.492 23.1 805.662 1.391 14.931
A10 2 B6 8.728 19.55 768.983 1.349 27.698
A10 2 B15 10.747 23.85 801.158 1.387 15.78
A10 2 B10 10.163 28.5 815.315 1.385 15.52
A10 2 B4 11.379 23.175 809.523 1.39 14.324
A10 2 B12 10.276 21.317 791.505 1.355 21.603
A10 3 B6 8.973 19.475 772.844 1.344 27.594
A10 3 B13 10.731 18.55 793.436 1.388 14.397
A10 3 B10 10.946 26.667 808.236 1.388 14.519
A10 3 B9 9.23 24.175 808.236 1.38 14.59
A10 3 B8 10.987 25.125 799.227 1.375 15.066
A10 3 B7 11.173 25.625 807.593 1.389 15.947
A10 3 B14 8.376 21.725 806.306 1.397 14.206
A10 3 B16 9.127 21.925 803.732 1.373 14.4
A10 3 B15 12.365 23.125 803.732 1.388 15.078
A10 3 B5 11.926 22.475 806.306 1.39 14.644
A10 3 B3 9.65 18.7 794.079 1.384 17.816
A10 3 B12 10.412 23.05 778.635 1.358 22.357
A10 3 B4 12.465 24.125 809.523 1.391 15.282
A10 3 B11 9.918 21.05 779.279 1.351 26.552
A10 3 B1 8.996 17.925 783.783 1.368 18.58
A10 3 B2 10.812 16.575 794.079 1.389 13.945
A11 1 B14 7.758 26.875 797.94 1.388 12.362
A11 1 B15 8.897 27.7 800.514 1.367 16.409
A11 1 B9 8.85 23.8 798.584 1.374 16.224
A11 1 B12 9.975 26.075 785.07 1.36 20.065
A11 1 B16 9.259 24.35 797.94 1.372 14.972
A11 1 B4 9.206 27.275 802.445 1.373 15.97
A11 1 B6 7.813 22.625 785.714 1.348 25.304
A11 1 B11 8.249 19.15 797.94 1.352 23.845
A11 1 B3 9.254 21.175 812.097 1.383 41.784
A11 1 B1 9.609 25.675 799.871 1.377 16.683
A11 1 B10 10.368 29.75 815.315 1.378 17.591
A11 1 B5 10.46 25.3 801.158 1.38 66.391
A11 1 B8 10.876 27.15 802.445 1.37 16.227
A11 1 B7 4.247 27.925 788.288 1.359 16.951
A11 1 B2 10.425 17.95 783.14 1.382 14.525
A11 1 B13 9.749 23.075 785.714 1.383 17.901
A11 2 B3 9.119 18.35 805.662 1.388 14.69
A11 2 B6 8.499 26.125 772.2 1.353 23.519
A11 2 B12 10.243 26.05 793.436 1.363 20.628
A11 2 B7 10.481 26.925 802.445 1.382 17.585
A11 2 B10 11.13 30.25 815.958 1.386 16.183
A11 2 B4 11.089 25.125 805.662 1.383 16.403
A11 2 B2 9.514 18.55 793.436 1.378 17.209
A11 2 B8 10.492 25.425 800.514 1.37 16.851
A11 2 B15 8.33 29.5 797.94 1.374 16.764
A11 2 B13 9.616 21.95 787.644 1.383 17.671
A11 2 B9 8.824 23.825 800.514 1.376 15.565
A11 2 B11 8.563 23.175 789.575 1.357 24.682
A11 2 B14 9.632 23.775 803.088 1.395 13.853
A11 2 B5 8.594 24.125 812.741 1.386 15.241
A11 2 B1 10.978 20.975 805.662 1.376 16.638
A11 2 B16 8.955 23.425 801.158 1.385 15.373
A11 3 B16 9.401 23.8 803.732 1.38 15.236
A11 3 B1 9.064 20.375 801.801 1.379 16.128
A11 3 B3 8.823 19.475 806.306 1.387 17.477
A11 3 B10 9.3 29.667 811.454 1.383 15.748
A11 3 B14 7.616 24.1 798.584 1.394 13.213
A11 3 B13 10.5 21.833 794.079 1.384 16.934
A11 3 B12 10.626 26.525 792.149 1.369 18.901
A11 3 B2 10.319 18.1 793.436 1.385 15.925
A11 3 B11 10.434 20.8 783.783 1.353 25.08
A11 3 B15 8.286 30.467 794.723 1.372 18.128
A11 3 B6 10.77 26.675 797.297 1.365 20.25
A11 3 B8 10.879 27.375 794.079 1.374 16.859
A11 3 B7 10.961 24.55 803.732 1.387 17.66
A11 3 B4 9.187 25.575 803.732 1.383 16.772
A11 3 B9 9.333 23.975 797.297 1.378 15.092
A11 3 B5 9.471 25.525 808.88 1.38 18.376
A12 1 B13 5.677 26.45 777.992 1.349 14.333
A12 1 B4 1.286 27.775 787.001 1.356 14.091
A12 1 B10 6.479 32.9 812.097 1.371 11.569
A12 1 B3 8.146 20.9 824.967 1.387 12.077
A12 1 B14 8.205 25.525 801.158 1.38 13.808
A12 1 B5 7.675 25.325 808.88 1.384 12.905
A12 1 B1 8.731 21.425 795.366 1.369 13.229
A12 1 B7 9.355 27.65 812.741 1.381 13.418
A12 1 B9 9.453 25.25 824.967 1.388 11.146
A12 1 B16 0.978 23.35 822.393 1.38 10.709
A12 1 B11 7.062 23.55 802.445 1.358 15.353
A12 1 B15 7.529 26.9 799.227 1.372 12.867
A12 1 B2 9.643 20.575 796.653 1.377 14.282
A12 1 B6 7.643 22.925 793.436 1.353 17.352
A12 1 B8 9.544 29.125 805.019 1.37 12.081
A12 1 B12 7.62 29.275 799.871 1.36 13.22
A12 2 B8 8.95 26.625 806.306 1.369 12.867
A12 2 B2 9.255 18.7 799.227 1.381 12.721
A12 2 B7 9.873 25.75 814.671 1.384 13.943
A12 2 B14 5.188 25.4 799.227 1.369 18.655
A12 2 B9 7.27 25.8 828.828 1.39 10.801
A12 2 B4 5.203 22.225 787.644 1.356 15.177
A12 2 B1 4.691 21.15 810.167 1.373 11.514
A12 2 B3 7.677 20.775 815.958 1.397 10.753
A12 2 B16 7.875 24 823.68 1.384 12.272
A12 2 B5 8.341 25.525 810.167 1.382 12.059
A12 2 B6 7.241 22.1 775.418 1.355 16.251
A12 2 B11 8.46 23.375 803.088 1.362 14.43
A12 2 B10 8.193 34.375 813.384 1.377 13.667
A12 2 B15 8.272 26.95 810.167 1.382 13.194
A12 2 B13 7.107 25.5 781.853 1.359 14.81
A12 2 B12 5.24 27.35 808.236 1.369 12.293
A12 3 B10 7.87 31.575 811.454 1.363 13.712
A12 3 B7 5.632 25.875 806.949 1.382 13.734
A12 3 B1 5.316 19.85 816.602 1.386 12.005
A12 3 B2 6.548 20.8 788.931 1.373 12.9
A12 3 B5 7.093 23.825 802.445 1.383 11.034
A12 3 B11 8.385 24.2 798.584 1.36 16.748
A12 3 B13 8.394 26.15 796.653 1.371 14.601
A12 3 B16 7.584 24.325 823.68 1.388 11.101
A12 3 B15 8.206 27 798.584 1.378 12.704
A12 3 B14 4.895 28.65 788.288 1.371 16.782
A12 3 B12 8.745 28.825 808.236 1.368 12.503
A12 3 B3 6.562 20.05 823.037 1.396 11.316
A12 3 B8 9.485 30.475 796.653 1.368 13.013
A12 3 B6 6.91 22.817 794.723 1.35 18.594
A12 3 B4 3.957 24.875 770.27 1.347 18.442
A12 3 B9 8.452 25.975 825.611 1.393 11.019"), header = TRUE, fill = TRUE); close(tc)
and the following R Code
Fit <- manova(formula = cbind(Y1, Y2, Y3, Y4, Y5) ~ A + Rep:A + B + A: B, data = Data)
summary.aov(Fit)
summary(Fit, test="Wilks")
summary.manova(Fit)
Up to this point everything is okay. Now I want to get the Sum of Squares and Cross Products for Hypothesis (for A, Rep(A), B, AB) and Error by using the following code
library(car)
MANOVA <- Manova(mod = Fit, type = "II")
and getting the following error message:
Error in solve.default(wcrossprod(model.matrix(mod), w = wts)) :
Lapack routine dgesv: system is exactly singular
I could not understand why I am getting this error message. Is there any other way to get these SSCPs? When I did the same analysis in SAS everything is fine. The SAS code is
PROC GLM DATA = Data;
CLASS A Rep B;
MODEL Y1 Y2 Y3 Y4 Y5 = A Rep(A) B A*B;
MANOVA H =_all_ /PRINTE PRINTH;
RUN;
But I'd like to do this in R. Any help will be highly appreciated. Thanks in advance.
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来自 SAS 文档：http://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_glm_sect038.htm
“用于使用多元方差分析或重复进行分析语句，或者使用 PROC GLM 语句中的 MANOVA 选项，如果所有因变量和自变量中使用的所有变量的值均不缺失，则 PROC GLM 使用观察值的影响。”
要进行检查，如果将 R 限制为完整案例，请查看 R 是否生成与 SAS 相同的值。
例如
我得到的结果是：
From the SAS docs: http://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_glm_sect038.htm
"for an analysis with the MANOVA or REPEATED statement, or with the MANOVA option in the PROC GLM statement, PROC GLM uses an observation if values are nonmissing for all dependent variables and all the variables used in independent effects."
To check, see if R produces the same value as SAS does if you restrict it to complete cases.
e.g.
The results I get for this are: