Sum of Squares and Cross Products for Hypothesis and Error for Split Plot MANOVA in R

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.
In general, when you get the message "System is singular" from some LAPACK routine, that means you can decompose the matrix in certain ways. You're probably running into an issue that you can't do the decomposition necessary (whatever it may be), so that's why you get your error. This is more of a general comment, since I've never used R.

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