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Data X:
10.708 12.3 23 154.25 67.75 36.2 93.1 85.2 94.5 59.0 37.3 21.9 32.0 27.4 17.1 10.853 6.1 22 173.25 72.25 38.5 93.6 83.0 98.7 58.7 37.3 23.4 30.5 28.9 18.2 10.414 25.3 22 154.00 66.25 34.0 95.8 87.9 99.2 59.6 38.9 24.0 28.8 25.2 16.6 10.751 10.4 26 184.75 72.25 37.4 101.8 86.4 101.2 60.1 37.3 22.8 32.4 29.4 18.2 10.340 28.7 24 184.25 71.25 34.4 97.3 100.0 101.9 63.2 42.2 24.0 32.2 27.7 17.7 10.502 20.9 24 210.25 74.75 39.0 104.5 94.4 107.8 66.0 42.0 25.6 35.7 30.6 18.8 10.549 19.2 26 181.00 69.75 36.4 105.1 90.7 100.3 58.4 38.3 22.9 31.9 27.8 17.7 10.704 12.4 25 176.00 72.50 37.8 99.6 88.5 97.1 60.0 39.4 23.2 30.5 29.0 18.8 10.900 4.1 25 191.00 74.00 38.1 100.9 82.5 99.9 62.9 38.3 23.8 35.9 31.1 18.2 10.722 11.7 23 198.25 73.50 42.1 99.6 88.6 104.1 63.1 41.7 25.0 35.6 30.0 19.2 10.830 7.1 26 186.25 74.50 38.5 101.5 83.6 98.2 59.7 39.7 25.2 32.8 29.4 18.5 10.812 7.8 27 216.00 76.00 39.4 103.6 90.9 107.7 66.2 39.2 25.9 37.2 30.2 19.0 10.513 20.8 32 180.50 69.50 38.4 102.0 91.6 103.9 63.4 38.3 21.5 32.5 28.6 17.7 10.505 21.2 30 205.25 71.25 39.4 104.1 101.8 108.6 66.0 41.5 23.7 36.9 31.6 18.8 10.484 22.1 35 187.75 69.50 40.5 101.3 96.4 100.1 69.0 39.0 23.1 36.1 30.5 18.2 10.512 20.9 35 162.75 66.00 36.4 99.1 92.8 99.2 63.1 38.7 21.7 31.1 26.4 16.9 10.333 29.0 34 195.75 71.00 38.9 101.9 96.4 105.2 64.8 40.8 23.1 36.2 30.8 17.3 10.468 22.9 32 209.25 71.00 42.1 107.6 97.5 107.0 66.9 40.0 24.4 38.2 31.6 19.3 10.622 16.0 28 183.75 67.75 38.0 106.8 89.6 102.4 64.2 38.7 22.9 37.2 30.5 18.5 10.610 16.5 33 211.75 73.50 40.0 106.2 100.5 109.0 65.8 40.6 24.0 37.1 30.1 18.2 10.551 19.1 28 179.00 68.00 39.1 103.3 95.9 104.9 63.5 38.0 22.1 32.5 30.3 18.4 10.640 15.2 28 200.50 69.75 41.3 111.4 98.8 104.8 63.4 40.6 24.6 33.0 32.8 19.9 10.631 15.6 31 140.25 68.25 33.9 86.0 76.4 94.6 57.4 35.3 22.2 27.9 25.9 16.7 10.584 17.7 32 148.75 70.00 35.5 86.7 80.0 93.4 54.9 36.2 22.1 29.8 26.7 17.1 10.668 14.0 28 151.25 67.75 34.5 90.2 76.3 95.8 58.4 35.5 22.9 31.1 28.0 17.6 10.911 3.7 27 159.25 71.50 35.7 89.6 79.7 96.5 55.0 36.7 22.5 29.9 28.2 17.7 10.811 7.9 34 131.50 67.50 36.2 88.6 74.6 85.3 51.7 34.7 21.4 28.7 27.0 16.5 10.468 22.9 31 148.00 67.50 38.8 97.4 88.7 94.7 57.5 36.0 21.0 29.2 26.6 17.0 10.910 3.7 27 133.25 64.75 36.4 93.5 73.9 88.5 50.1 34.5 21.3 30.5 27.9 17.2 10.790 8.8 29 160.75 69.00 36.7 97.4 83.5 98.7 58.9 35.3 22.6 30.1 26.7 17.6 10.716 11.9 32 182.00 73.75 38.7 100.5 88.7 99.8 57.5 38.7 33.9 32.5 27.7 18.4 10.862 5.7 29 160.25 71.25 37.3 93.5 84.5 100.6 58.5 38.8 21.5 30.1 26.4 17.9 10.719 11.8 27 168.00 71.25 38.1 93.0 79.1 94.5 57.3 36.2 24.5 29.0 30.0 18.8 10.502 21.3 41 218.50 71.00 39.8 111.7 100.5 108.3 67.1 44.2 25.2 37.5 31.5 18.7 10.263 32.3 41 247.25 73.50 42.1 117.0 115.6 116.1 71.2 43.3 26.3 37.3 31.7 19.7 10.101 40.1 49 191.75 65.00 38.4 118.5 113.1 113.8 61.9 38.3 21.9 32.0 29.8 17.0 10.438 24.2 40 202.25 70.00 38.5 106.5 100.9 106.2 63.5 39.9 22.6 35.1 30.6 19.0 10.346 28.4 50 196.75 68.25 42.1 105.6 98.8 104.8 66.0 41.5 24.7 33.2 30.5 19.4 10.202 35.2 46 363.15 72.25 51.2 136.2 148.1 147.7 87.3 49.1 29.6 45.0 29.0 21.4 10.258 32.6 50 203.00 67.00 40.2 114.8 108.1 102.5 61.3 41.1 24.7 34.1 31.0 18.3 10.217 34.5 45 262.75 68.75 43.2 128.3 126.2 125.6 72.5 39.6 26.6 36.4 32.7 21.4 10.250 32.9 44 205.00 29.50 36.6 106.0 104.3 115.5 70.6 42.5 23.7 33.6 28.7 17.4 10.279 31.6 48 217.00 70.00 37.3 113.3 111.2 114.1 67.7 40.9 25.0 36.7 29.8 18.4 10.269 32.0 41 212.00 71.50 41.5 106.6 104.3 106.0 65.0 40.2 23.0 35.8 31.5 18.8 10.814 7.7 39 125.25 68.00 31.5 85.1 76.0 88.2 50.0 34.7 21.0 26.1 23.1 16.1 10.670 13.9 43 164.25 73.25 35.7 96.6 81.5 97.2 58.4 38.2 23.4 29.7 27.4 18.3 10.742 10.8 40 133.50 67.50 33.6 88.2 73.7 88.5 53.3 34.5 22.5 27.9 26.2 17.3 10.665 5.6 39 148.50 71.25 34.6 89.8 79.5 92.7 52.7 37.5 21.9 28.8 26.8 17.9 10.678 13.6 45 135.75 68.50 32.8 92.3 83.4 90.4 52.0 35.8 20.6 28.8 25.5 16.3 10.903 4.0 47 127.50 66.75 34.0 83.4 70.4 87.2 50.6 34.4 21.9 26.8 25.8 16.8 10.756 10.2 47 158.25 72.25 34.9 90.2 86.7 98.3 52.6 37.2 22.4 26.0 25.8 17.3 10.840 6.6 40 139.25 69.00 34.3 89.2 77.9 91.0 51.4 34.9 21.0 26.7 26.1 17.2 10.807 8.0 51 137.25 67.75 36.5 89.7 82.0 89.1 49.3 33.7 21.4 29.6 26.0 16.9 10.848 6.3 49 152.75 73.50 35.1 93.3 79.6 91.6 52.6 37.6 22.6 38.5 27.4 18.5 10.906 3.9 42 136.25 67.50 37.8 87.6 77.6 88.6 51.9 34.9 22.5 27.7 27.5 18.5 10.473 22.6 54 198.00 72.00 39.9 107.6 100.0 99.6 57.2 38.0 22.0 35.9 30.2 18.9 10.524 20.4 58 181.50 68.00 39.1 100.0 99.8 102.5 62.1 39.6 22.5 33.1 28.3 18.5 10.356 28.0 62 201.25 69.50 40.5 111.5 104.2 105.8 61.8 39.8 22.7 37.7 30.9 19.2 10.280 31.5 54 202.50 70.75 40.5 115.4 105.3 97.0 59.1 38.0 22.5 31.6 28.8 18.2 10.430 24.6 61 179.75 65.75 38.4 104.8 98.3 99.6 60.6 37.7 22.9 34.5 29.6 18.5 10.396 26.1 62 216.00 73.25 41.4 112.3 104.8 103.1 61.6 40.9 23.1 36.2 31.8 20.2 10.317 29.8 56 178.75 68.50 35.6 102.9 94.7 100.8 60.9 38.0 22.1 32.5 29.8 18.3 10.298 30.7 54 193.25 70.25 38.0 107.6 102.4 99.4 61.0 39.4 23.6 32.7 29.9 19.1 10.403 25.8 61 178.00 67.00 37.4 105.3 99.7 99.7 60.8 40.1 22.7 33.6 29.0 18.8 10.264 32.3 57 205.50 70.00 40.1 105.3 105.5 108.3 65.0 41.2 24.7 35.3 31.1 18.4 10.313 30.0 55 183.50 67.50 40.9 103.0 100.3 104.2 64.8 40.2 22.7 34.8 30.1 18.7 10.499 21.5 54 151.50 70.75 35.6 90.0 83.9 93.9 55.0 36.1 21.7 29.6 27.4 17.4 10.673 13.8 55 154.75 71.50 36.9 95.4 86.6 91.8 54.3 35.4 21.5 32.8 27.4 18.7 10.847 6.3 54 155.25 69.25 37.5 89.3 78.4 96.1 56.0 37.4 22.4 32.6 28.1 18.1 10.693 12.9 55 156.75 71.50 36.3 94.4 84.6 94.3 51.2 37.4 21.6 27.3 27.1 17.3 10.439 24.3 62 167.50 71.50 35.5 97.6 91.5 98.5 56.6 38.6 22.4 31.5 27.3 18.6 10.788 8.8 55 146.75 68.75 38.7 88.5 82.8 95.5 58.9 37.6 21.6 30.3 27.3 18.3 10.796 8.5 56 160.75 73.75 36.4 93.6 82.9 96.3 52.9 37.5 23.1 29.7 27.3 18.2 10.680 13.5 55 125.00 64.00 33.2 87.7 76.0 88.6 50.9 35.4 19.1 29.3 25.7 16.9 10.720 11.8 61 143.00 65.75 36.5 93.4 83.3 93.0 55.5 35.2 20.9 29.4 27.0 16.8 10.666 18.5 61 148.25 67.50 36.0 91.6 81.8 94.8 54.5 37.0 21.4 29.3 27.0 18.3 10.790 8.8 57 162.50 69.50 38.7 91.6 78.8 94.3 56.7 39.7 24.2 30.2 29.2 18.1 10.483 22.2 69 177.75 68.50 38.7 102.0 95.0 98.3 55.0 38.3 21.8 30.8 25.7 18.8 10.498 21.5 81 161.25 70.25 37.8 96.4 95.4 99.3 53.5 37.5 21.5 31.4 26.8 18.3 10.560 18.8 66 171.25 69.25 37.4 102.7 98.6 100.2 56.5 39.3 22.7 30.3 28.7 19.0 10.283 31.4 67 163.75 67.75 38.4 97.7 95.8 97.1 54.8 38.2 23.7 29.4 27.2 19.0 10.382 26.8 64 150.25 67.25 38.1 97.1 89.0 96.9 54.8 38.0 22.0 29.9 25.2 17.7 10.568 18.4 64 190.25 72.75 39.3 103.1 97.8 99.6 58.9 39.0 23.0 34.3 29.6 19.0 10.377 27.0 70 170.75 70.00 38.7 101.8 94.9 95.0 56.0 36.5 24.1 31.2 27.3 19.2 10.378 27.0 72 168.00 69.25 38.5 101.4 99.8 96.2 56.3 36.6 22.0 29.7 26.3 18.0 10.386 26.6 67 167.00 67.50 36.5 98.9 89.7 96.2 54.7 37.8 33.7 32.4 27.7 18.2 10.648 14.9 72 157.75 67.25 37.7 97.5 88.1 96.9 57.2 37.7 21.8 32.6 28.0 18.8 10.462 23.1 64 160.00 65.75 36.5 104.3 90.9 93.8 57.8 39.5 23.3 29.2 28.4 18.1 10.800 8.3 46 176.75 72.50 38.0 97.3 86.0 99.3 61.0 38.4 23.8 30.2 29.3 18.8 10.666 14.1 48 176.00 73.00 36.7 96.7 86.5 98.3 60.4 39.9 24.4 28.8 29.6 18.7 10.520 20.5 46 177.00 70.00 37.2 99.7 95.6 102.2 58.3 38.2 22.5 29.1 27.7 17.7 10.573 18.2 44 179.75 69.50 39.2 101.9 93.2 100.6 58.9 39.7 23.1 31.4 28.4 18.8 10.795 8.5 47 165.25 70.50 37.5 97.2 83.1 95.4 56.9 38.3 22.1 30.1 28.2 18.4 10.424 24.9 46 192.50 71.75 38.0 106.6 97.5 100.6 58.9 40.5 24.5 33.3 29.6 19.1 10.785 9.0 47 184.25 74.50 37.3 99.6 88.8 101.4 57.4 39.6 24.6 30.3 27.9 17.8 10.991 17.4 53 224.50 77.75 41.1 113.2 99.2 107.5 61.7 42.3 23.2 32.9 30.8 20.4 10.770 9.6 38 188.75 73.25 37.5 99.1 91.6 102.4 60.6 39.4 22.9 31.6 30.1 18.5 10.730 11.3 50 162.50 66.50 38.7 99.4 86.7 96.2 62.1 39.3 23.3 30.6 27.8 18.2 10.582 17.8 46 156.50 68.25 35.9 95.1 88.2 92.8 54.7 37.3 21.9 31.6 27.5 18.2 10.484 22.2 47 197.00 72.00 40.0 107.5 94.0 103.7 62.7 39.0 22.3 35.3 30.9 18.3 10.506 21.2 49 198.50 73.50 40.1 106.5 95.0 101.7 59.0 39.4 22.3 32.2 31.0 18.6 10.524 20.4 48 173.75 72.00 37.0 99.1 92.0 98.3 59.3 38.4 22.4 27.9 26.2 17.0 10.530 20.1 41 172.75 71.25 36.3 96.7 89.2 98.3 60.0 38.4 23.2 31.0 29.2 18.4 10.480 22.3 49 196.75 73.75 40.7 103.5 95.5 101.6 59.1 39.8 25.4 31.0 30.3 19.7 10.412 25.4 43 177.00 69.25 39.6 104.0 98.6 99.5 59.5 36.1 22.0 30.1 27.2 17.7 10.578 18.0 43 165.50 68.50 31.1 93.1 87.3 96.6 54.7 39.0 24.8 31.0 29.4 18.8 10.547 19.3 43 200.25 73.50 38.6 105.2 102.8 103.6 61.2 39.3 23.5 30.5 28.5 18.1 10.569 18.3 52 203.25 74.25 42.0 110.0 101.6 100.7 55.8 38.7 23.4 35.1 29.6 19.1 10.593 17.3 43 194.00 75.50 38.5 110.1 88.7 102.1 57.5 40.0 24.8 35.1 30.7 19.2 10.500 21.4 40 168.50 69.25 34.2 97.8 92.3 100.6 57.5 36.8 22.8 32.1 26.0 17.3 10.538 19.7 43 170.75 68.50 37.2 96.3 90.6 99.3 61.9 38.0 22.3 33.3 28.2 18.1 10.355 28.0 43 183.25 70.00 37.1 108.0 105.0 103.0 63.7 40.0 23.6 33.5 27.8 17.4 10.486 22.1 47 178.25 70.00 40.2 99.7 95.0 98.6 62.3 38.1 23.9 35.3 31.1 19.8 10.503 21.3 42 163.00 70.25 35.3 93.5 89.6 99.8 61.5 37.8 21.9 30.7 27.6 17.4 10.384 26.7 48 175.25 71.75 38.0 100.7 92.4 97.5 59.3 38.1 21.8 31.8 27.3 17.5 10.607 16.7 40 158.00 69.25 36.3 97.0 86.6 92.6 55.9 36.3 22.1 29.8 26.3 17.3 10.529 20.1 48 177.25 72.75 36.8 96.0 90.0 99.7 58.8 38.4 22.8 29.9 28.0 18.1 10.671 13.9 51 179.00 72.00 41.0 99.2 90.0 96.4 56.8 38.8 23.3 33.4 29.8 19.5 10.404 25.8 40 191.00 74.00 38.3 95.4 92.4 104.3 64.6 41.1 24.8 33.6 29.5 18.5 10.575 18.1 44 187.50 72.25 38.0 101.8 87.5 101.0 58.5 39.2 24.5 32.1 28.6 18.0 10.358 27.9 52 206.50 74.50 40.8 104.3 99.2 104.1 58.5 39.3 24.6 33.9 31.2 19.5 10.414 25.3 44 185.25 71.50 39.5 99.2 98.1 101.4 57.1 40.5 23.2 33.0 29.6 18.4 10.652 14.7 40 160.25 68.75 36.9 99.3 83.3 97.5 60.5 38.7 22.6 34.4 28.0 17.6 10.623 16.0 47 151.50 66.75 36.9 94.0 86.1 95.2 58.1 36.5 22.1 30.6 27.5 17.6 10.674 13.8 50 161.00 66.50 37.7 98.9 84.1 94.0 58.5 36.6 23.5 34.4 29.2 18.0 10.587 17.5 46 167.00 67.00 36.6 101.0 89.9 100.0 60.7 36.0 21.9 35.6 30.2 17.6 10.373 27.2 42 177.50 68.75 38.9 98.7 92.1 98.5 60.7 36.8 22.2 33.8 30.3 17.2 10.590 17.4 43 152.25 67.75 37.5 95.9 78.0 93.2 53.5 35.8 20.8 33.9 28.2 17.4 10.515 20.8 40 192.25 73.25 39.8 103.9 93.5 99.5 61.7 39.0 21.8 33.3 29.6 18.1 10.648 14.9 42 165.25 69.75 38.3 96.2 87.0 97.8 57.4 36.9 22.2 31.6 27.8 17.7 10.575 18.1 49 171.75 71.50 35.5 97.8 90.1 95.8 57.0 38.7 23.2 27.5 26.5 17.6 10.472 22.7 40 171.25 70.50 36.3 94.6 90.3 99.1 60.3 38.5 23.0 31.2 28.4 17.1 10.452 23.6 47 197.00 73.25 37.8 103.6 99.8 103.2 61.2 38.1 22.6 33.5 28.6 17.9 10.398 26.1 50 157.00 66.75 37.8 100.4 89.4 92.3 56.1 35.6 20.5 33.6 29.3 17.3 10.435 24.4 41 168.25 69.50 36.5 98.4 87.2 98.4 56.0 36.9 23.0 34.0 29.8 18.1 10.374 27.1 44 186.00 69.75 37.8 104.6 101.1 102.1 58.9 37.9 22.7 30.9 28.8 17.6 10.491 21.8 39 166.75 70.75 37.0 92.9 86.1 95.6 58.8 36.1 22.4 32.7 28.3 17.1 10.325 29.4 43 187.75 74.00 37.7 97.8 98.6 100.6 63.6 39.2 23.8 34.3 28.4 17.7 10.481 22.4 40 168.25 71.25 34.3 98.3 88.5 98.3 58.1 38.4 22.5 31.7 27.4 17.6 10.522 20.4 49 212.75 75.00 40.8 104.7 106.6 107.7 66.5 42.5 24.5 35.5 29.8 18.7 10.422 24.9 40 176.75 71.00 37.4 98.6 93.1 101.6 59.1 39.6 21.6 30.8 27.9 16.6 10.571 18.3 40 173.25 69.50 36.5 99.5 93.0 99.3 60.4 38.2 22.0 32.0 28.5 17.8 10.459 23.3 52 167.00 67.75 37.5 102.7 91.0 98.9 57.1 36.7 22.3 31.6 27.5 17.9 10.775 9.4 23 159.75 72.25 35.5 92.1 77.1 93.9 56.1 36.1 22.7 30.5 27.2 18.2 10.754 10.3 23 188.15 77.50 38.0 96.6 85.3 102.5 59.1 37.6 23.2 31.8 29.7 18.3 10.664 14.2 24 156.00 70.75 35.7 92.7 81.9 95.3 56.4 36.5 22.0 33.5 28.3 17.3 10.550 19.2 24 208.50 72.75 39.2 102.0 99.1 110.1 71.2 43.5 25.2 36.1 30.3 18.7 10.322 29.6 25 206.50 69.75 40.9 110.9 100.5 106.2 68.4 40.8 24.6 33.3 29.7 18.4 10.873 5.3 25 143.75 72.50 35.2 92.3 76.5 92.1 51.9 35.7 22.0 25.8 25.2 16.9 10.416 25.2 26 223.00 70.25 40.6 114.1 106.8 113.9 67.6 42.7 24.7 36.0 30.4 18.4 10.776 9.4 26 152.25 69.00 35.4 92.9 77.6 93.5 56.9 35.9 20.4 31.6 29.0 17.8 10.542 19.6 26 241.75 74.50 41.8 108.3 102.9 114.4 72.9 43.5 25.1 38.5 33.8 19.6 10.758 10.1 27 146.00 72.25 34.1 88.5 72.8 91.1 53.6 36.8 23.8 27.8 26.3 17.4 10.610 16.5 27 156.75 67.25 37.9 94.0 88.2 95.2 56.8 37.4 22.8 30.6 28.3 17.9 10.510 21.0 27 200.25 73.50 38.2 101.1 100.1 105.0 62.1 40.0 24.9 33.7 29.2 19.4 10.594 17.3 28 171.50 75.25 35.6 92.1 83.5 98.3 57.3 37.8 21.7 32.2 27.7 17.7 10.287 31.2 28 205.75 69.00 38.5 105.6 105.0 106.4 68.6 40.0 25.2 35.2 30.7 19.1 10.761 10.0 28 182.50 72.25 37.0 98.5 90.8 102.5 60.8 38.5 25.0 31.6 28.0 18.6 10.704 12.5 30 136.50 68.75 35.9 88.7 76.6 89.8 50.1 34.8 21.8 27.0 34.9 16.9 10.477 22.5 31 177.25 71.50 36.2 101.1 92.4 99.3 59.4 39.0 24.6 30.1 28.2 18.2 10.775 9.4 31 151.25 72.25 35.0 94.0 81.2 91.5 52.5 36.6 21.0 27.0 26.3 16.5 10.653 14.6 33 196.00 73.00 38.5 103.8 95.6 105.1 61.4 40.6 25.0 31.3 29.2 19.1 10.690 13.0 33 184.25 68.75 40.7 98.9 92.1 103.5 64.0 37.3 23.5 33.5 30.6 19.7 10.644 15.1 34 140.00 70.50 36.0 89.2 83.4 89.6 52.4 35.6 20.4 28.3 26.2 16.5 10.370 27.3 34 218.75 72.00 39.5 111.4 106.0 108.8 63.8 42.0 23.4 34.0 31.2 18.5 10.549 19.2 35 217.00 73.75 40.5 107.5 95.1 104.5 64.8 41.3 25.6 36.4 33.7 19.4 10.492 21.8 35 166.25 68.00 38.5 99.1 90.4 95.6 55.5 34.2 21.9 30.2 28.7 17.7 10.525 20.3 35 224.75 72.25 43.9 108.2 100.4 106.8 63.3 41.7 24.6 37.2 33.1 19.8 10.180 34.3 35 228.25 69.50 40.4 114.9 115.9 111.9 74.4 40.6 24.0 36.1 31.8 18.8 10.610 16.5 35 172.75 69.50 37.6 99.1 90.8 98.1 60.1 39.1 23.4 32.5 29.8 17.4 10.926 3.0 35 152.25 67.75 37.0 92.2 81.9 92.8 54.7 36.2 22.1 30.4 27.4 17.7 10.983 .7 35 125.75 65.50 34.0 90.8 75.0 89.2 50.0 34.8 22.0 24.8 25.9 16.9 10.521 20.5 35 177.25 71.00 38.4 100.5 90.3 98.7 57.8 37.3 22.4 31.0 28.7 17.7 10.603 16.9 36 176.25 71.50 38.7 98.2 90.3 99.9 59.2 37.7 21.5 32.4 28.4 17.8 10.414 25.3 36 226.75 71.75 41.5 115.3 108.8 114.4 69.2 42.4 24.0 35.4 21.0 20.1 10.763 9.9 37 145.25 69.25 36.0 96.8 79.4 89.2 50.3 34.8 22.2 31.0 26.9 16.9 10.689 13.1 37 151.00 67.00 35.3 92.6 83.2 96.4 60.0 38.1 22.0 31.5 26.6 16.7 10.316 29.9 37 241.25 71.50 42.1 119.2 110.3 113.9 69.8 42.6 24.8 34.4 29.5 18.4 10.477 22.5 38 187.25 69.25 38.0 102.7 92.7 101.9 64.7 39.5 24.7 34.8 30.3 18.1 10.603 16.9 39 234.75 74.50 42.8 109.5 104.5 109.9 69.5 43.1 25.8 39.1 32.5 19.9 10.387 26.6 39 219.25 74.25 40.0 108.5 104.6 109.8 68.1 42.8 24.1 35.6 29.0 19.0 11.089 .0 40 118.50 68.00 33.8 79.3 69.4 85.0 47.2 33.5 20.2 27.7 24.6 16.5 10.725 11.5 40 145.75 67.25 35.5 95.5 83.6 91.6 54.1 36.2 21.8 31.4 28.3 17.2 10.713 12.1 40 159.25 69.75 35.3 92.3 86.8 96.1 58.0 39.4 22.7 30.0 26.4 17.4 10.587 17.5 40 170.50 74.25 37.7 98.9 90.4 95.5 55.4 38.9 22.4 30.5 28.9 17.7 10.794 8.6 40 167.50 71.50 39.4 89.5 83.7 98.1 57.3 39.7 22.6 32.9 29.3 18.2 10.453 23.6 41 232.75 74.25 41.9 117.5 109.3 108.8 67.7 41.3 24.7 37.2 31.8 20.0 10.524 20.4 41 210.50 72.00 38.5 107.4 98.9 104.1 63.5 39.8 23.5 36.4 30.4 19.1 10.520 20.5 41 202.25 72.50 40.8 109.2 98.0 101.8 62.8 41.3 24.8 36.6 32.4 18.8 10.434 24.4 41 185.00 68.25 38.0 103.4 101.2 103.1 61.5 40.4 22.9 33.4 29.2 18.5 10.728 11.4 41 153.00 69.25 36.4 91.4 80.6 92.3 54.3 36.3 21.8 29.6 27.3 17.9 10.140 38.1 42 244.25 76.00 41.8 115.2 113.7 112.4 68.5 45.0 25.5 37.1 31.2 19.9 10.624 15.9 42 193.50 70.50 40.7 104.9 94.1 102.7 60.6 38.6 24.7 34.0 30.1 18.7 10.429 24.7 42 224.75 74.75 38.5 106.7 105.7 111.8 65.3 43.3 26.0 33.7 29.9 18.5 10.470 22.8 42 162.75 72.75 35.4 92.2 85.6 96.5 60.2 38.9 22.4 31.7 27.1 17.1 10.411 25.5 42 180.00 68.25 38.5 101.6 96.6 100.6 61.1 38.4 24.1 32.9 29.8 18.8 10.488 22.0 42 156.25 69.00 35.5 97.8 86.0 96.2 57.7 38.6 24.0 31.2 27.3 17.4 10.583 17.7 42 168.00 71.50 36.5 92.0 89.7 101.0 62.3 38.0 22.3 30.8 27.8 16.9 10.841 6.6 42 167.25 72.75 37.6 94.0 78.0 99.0 57.5 40.0 22.5 30.6 30.0 18.5 10.462 23.6 43 170.75 67.50 37.4 103.7 89.7 94.2 58.5 39.0 24.1 33.8 28.8 18.8 10.709 12.2 43 178.25 70.25 37.8 102.7 89.2 99.2 60.2 39.2 23.8 31.7 28.4 18.6 10.484 22.1 43 150.00 69.25 35.2 91.1 85.7 96.9 55.5 35.7 22.0 29.4 26.6 17.4 10.340 28.7 43 200.50 71.50 37.9 107.2 103.1 105.5 68.8 38.3 23.7 32.1 28.9 18.7 10.854 6.0 44 184.00 74.00 37.9 100.8 89.1 102.6 60.6 39.0 24.0 32.9 29.2 18.4 10.209 34.8 44 223.00 69.75 40.9 121.6 113.9 107.1 63.5 40.3 21.8 34.8 30.7 17.4 10.610 16.6 44 208.75 73.00 41.9 105.6 96.3 102.0 63.3 39.8 24.1 37.3 23.1 19.4 10.250 32.9 44 166.00 65.50 39.1 100.6 93.9 100.1 58.9 37.6 21.4 33.1 29.5 17.3 10.254 32.8 47 195.00 72.50 40.2 102.7 101.3 101.7 60.7 39.4 23.3 36.7 31.6 18.4 10.771 9.6 47 160.50 70.25 36.0 99.8 83.9 91.8 53.0 36.2 22.5 31.4 27.5 17.7 10.742 10.8 47 159.75 70.75 34.5 92.9 84.4 94.0 56.0 38.2 22.6 29.0 26.2 17.6 10.829 7.1 49 140.50 68.00 35.8 91.2 79.4 89.0 51.1 35.0 21.7 30.9 28.8 17.4 10.373 27.2 49 216.25 74.50 40.2 115.6 104.0 109.0 63.7 40.3 23.2 36.8 31.0 18.9 10.543 19.5 49 168.25 71.75 38.3 98.3 89.7 99.1 56.3 38.8 23.0 29.5 27.9 18.6 10.561 18.7 50 194.75 70.75 39.0 103.7 97.6 104.2 60.0 40.9 25.5 32.7 30.0 19.0 10.543 19.5 50 172.75 73.00 37.4 98.7 87.6 96.1 57.1 38.1 21.8 28.6 26.7 18.0 0.9950 47.5 51 219.00 64.00 41.2 119.8 122.1 112.8 62.5 36.9 23.6 34.7 29.1 18.4 10.678 13.6 51 149.25 69.75 34.8 92.8 81.1 96.3 53.8 36.5 21.5 31.3 26.3 17.8 10.819 7.5 51 154.50 70.00 36.9 93.3 81.5 94.4 54.7 39.0 22.6 27.5 25.9 18.6 10.433 24.5 52 199.25 71.75 39.4 106.8 100.0 105.0 63.9 39.2 22.9 35.7 30.4 19.2 10.646 15.0 53 154.50 69.25 37.6 93.9 88.7 94.5 53.7 36.2 22.0 28.5 25.7 17.1 10.706 12.4 54 153.25 70.50 38.5 99.0 91.8 96.2 57.7 38.1 23.9 31.4 29.9 18.9 10.399 26.0 54 230.00 72.25 42.5 119.9 110.4 105.5 64.2 42.7 27.0 38.4 32.0 19.6 10.726 11.5 54 161.75 67.50 37.4 94.2 87.6 95.6 59.7 40.2 23.4 27.9 27.0 17.8 10.874 5.2 55 142.25 67.25 35.2 92.7 82.8 91.9 54.4 35.2 22.5 29.4 26.8 17.0 10.740 10.9 55 179.75 68.75 41.1 106.9 95.3 98.2 57.4 37.1 21.8 34.1 31.1 19.2 10.703 12.5 55 126.50 66.75 33.4 88.8 78.2 87.5 50.8 33.0 19.7 25.3 22.0 15.8 10.650 14.8 55 169.50 68.25 37.2 101.7 91.1 97.1 56.6 38.5 22.6 33.4 29.3 18.8 10.418 25.2 55 198.50 74.25 38.3 105.3 96.7 106.6 64.0 42.6 23.4 33.2 30.0 18.4 10.647 14.9 56 174.50 69.50 38.1 104.0 89.4 98.4 58.4 37.4 22.5 34.6 30.1 18.8 10.601 17.0 56 167.75 68.50 37.4 98.6 93.0 97.0 55.4 38.8 23.2 32.4 29.7 19.0 10.745 10.6 57 147.75 65.75 35.2 99.6 86.4 90.1 53.0 35.0 21.3 31.7 27.3 16.9 10.620 16.1 57 182.25 71.75 39.4 103.4 96.7 100.7 59.3 38.6 22.8 31.8 29.1 19.0 10.636 15.4 58 175.50 71.50 38.0 100.2 88.1 97.8 57.1 38.9 23.6 30.9 29.6 18.0 10.384 26.7 58 161.75 67.25 35.1 94.9 94.9 100.2 56.8 35.9 21.0 27.8 26.1 17.6 10.403 25.8 60 157.75 67.50 40.4 97.2 93.3 94.0 54.3 35.7 21.0 31.3 28.7 18.3 10.563 18.6 62 168.75 67.50 38.3 104.7 95.6 93.7 54.4 37.1 22.7 30.3 26.3 18.3 10.424 24.8 62 191.50 72.25 40.6 104.0 98.2 101.1 59.3 40.3 23.0 32.6 28.5 19.0 10.372 27.3 63 219.15 69.50 40.2 117.6 113.8 111.8 63.4 41.1 22.3 35.1 29.6 18.5 10.705 12.4 64 155.25 69.50 37.9 95.8 82.8 94.5 61.2 39.1 22.3 29.8 28.9 18.3 10.316 29.9 65 189.75 65.75 40.8 106.4 100.5 100.5 59.2 38.1 24.0 35.9 30.5 19.1 10.599 17.0 65 127.50 65.75 34.7 93.0 79.7 87.6 50.7 33.4 20.1 28.5 24.8 16.5 10.207 35.0 65 224.50 68.25 38.8 119.6 118.0 114.3 61.3 42.1 23.4 34.9 30.1 19.4 10.304 30.4 66 234.25 72.00 41.4 119.7 109.0 109.1 63.7 42.4 24.6 35.6 30.7 19.5 10.256 32.6 67 227.75 72.75 41.3 115.8 113.4 109.8 65.6 46.0 25.4 35.3 29.8 19.5 10.334 29.0 67 199.50 68.50 40.7 118.3 106.1 101.6 58.2 38.8 24.1 32.1 29.3 18.5 10.641 15.2 68 155.50 69.25 36.3 97.4 84.3 94.4 54.3 37.5 22.6 29.2 27.3 18.5 10.308 30.2 69 215.50 70.50 40.8 113.7 107.6 110.0 63.3 44.0 22.6 37.5 32.6 18.8 10.736 11.0 70 134.25 67.00 34.9 89.2 83.6 88.8 49.6 34.8 21.5 25.6 25.7 18.5 10.236 33.6 72 201.00 69.75 40.9 108.5 105.0 104.5 59.6 40.8 23.2 35.2 28.6 20.1 10.328 29.3 72 186.75 66.00 38.9 111.1 111.5 101.7 60.3 37.3 21.5 31.3 27.2 18.0 10.399 26.0 72 190.75 70.50 38.9 108.3 101.3 97.8 56.0 41.6 22.7 30.5 29.4 19.8 10.271 31.9 74 207.50 70.00 40.8 112.4 108.5 107.1 59.3 42.2 24.6 33.7 30.0 20.9
Names of X columns:
Density Fat Age Weight Height Neck Chest Abdomen Hip Thigh Knee Ankle Biceps Forearm Wrist
Sample Range:
(leave blank to include all observations)
From:
To:
Column Number of Endogenous Series
(?)
Fixed Seasonal Effects
Do not include Seasonal Dummies
Do not include Seasonal Dummies
Include Seasonal Dummies
Type of Equation
No Linear Trend
No Linear Trend
Linear Trend
First Differences
Seasonal Differences (s)
First and Seasonal Differences (s)
Degree of Predetermination (lagged endogenous variables)
Degree of Seasonal Predetermination
Seasonality
12
1
2
3
4
5
6
7
8
9
10
11
12
Chart options
R Code
library(lattice) library(lmtest) n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test par1 <- as.numeric(par1) x <- t(y) k <- length(x[1,]) n <- length(x[,1]) x1 <- cbind(x[,par1], x[,1:k!=par1]) mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1]) colnames(x1) <- mycolnames #colnames(x)[par1] x <- x1 if (par3 == 'First Differences'){ x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep=''))) for (i in 1:n-1) { for (j in 1:k) { x2[i,j] <- x[i+1,j] - x[i,j] } } x <- x2 } if (par2 == 'Include Monthly Dummies'){ x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep =''))) for (i in 1:11){ x2[seq(i,n,12),i] <- 1 } x <- cbind(x, x2) } if (par2 == 'Include Quarterly Dummies'){ x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep =''))) for (i in 1:3){ x2[seq(i,n,4),i] <- 1 } x <- cbind(x, x2) } k <- length(x[1,]) if (par3 == 'Linear Trend'){ x <- cbind(x, c(1:n)) colnames(x)[k+1] <- 't' } x k <- length(x[1,]) df <- as.data.frame(x) (mylm <- lm(df)) (mysum <- summary(mylm)) if (n > n25) { kp3 <- k + 3 nmkm3 <- n - k - 3 gqarr <- array(NA, dim=c(nmkm3-kp3+1,3)) numgqtests <- 0 numsignificant1 <- 0 numsignificant5 <- 0 numsignificant10 <- 0 for (mypoint in kp3:nmkm3) { j <- 0 numgqtests <- numgqtests + 1 for (myalt in c('greater', 'two.sided', 'less')) { j <- j + 1 gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value } if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1 if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1 if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1 } gqarr } bitmap(file='test0.png') plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index') points(x[,1]-mysum$resid) grid() dev.off() bitmap(file='test1.png') plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index') grid() dev.off() bitmap(file='test2.png') hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals') grid() dev.off() bitmap(file='test3.png') densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals') dev.off() bitmap(file='test4.png') qqnorm(mysum$resid, main='Residual Normal Q-Q Plot') qqline(mysum$resid) grid() dev.off() (myerror <- as.ts(mysum$resid)) bitmap(file='test5.png') dum <- cbind(lag(myerror,k=1),myerror) dum dum1 <- dum[2:length(myerror),] dum1 z <- as.data.frame(dum1) z plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals') lines(lowess(z)) abline(lm(z)) grid() dev.off() bitmap(file='test6.png') acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function') grid() dev.off() bitmap(file='test7.png') pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function') grid() dev.off() bitmap(file='test8.png') opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0)) plot(mylm, las = 1, sub='Residual Diagnostics') par(opar) dev.off() if (n > n25) { bitmap(file='test9.png') plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint') grid() dev.off() } load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE) a<-table.row.end(a) myeq <- colnames(x)[1] myeq <- paste(myeq, '[t] = ', sep='') for (i in 1:k){ if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ') if (rownames(mysum$coefficients)[i] != '(Intercept)') { myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='') if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='') } } myeq <- paste(myeq, ' + e[t]') a<-table.row.start(a) a<-table.element(a, myeq) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable1.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Variable',header=TRUE) a<-table.element(a,'Parameter',header=TRUE) a<-table.element(a,'S.D.',header=TRUE) a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE) a<-table.element(a,'2-tail p-value',header=TRUE) a<-table.element(a,'1-tail p-value',header=TRUE) a<-table.row.end(a) for (i in 1:k){ a<-table.row.start(a) a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE) a<-table.element(a,mysum$coefficients[i,1]) a<-table.element(a, round(mysum$coefficients[i,2],6)) a<-table.element(a, round(mysum$coefficients[i,3],4)) a<-table.element(a, round(mysum$coefficients[i,4],6)) a<-table.element(a, round(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, sqrt(mysum$r.squared)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, mysum$r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, mysum$adj.r.squared) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, mysum$fstatistic[1]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, mysum$fstatistic[2]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, mysum$fstatistic[3]) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3])) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Residual Standard Deviation',1,TRUE) a<-table.element(a, mysum$sigma) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, sum(myerror*myerror)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,x[i]) a<-table.element(a,x[i]-mysum$resid[i]) a<-table.element(a,mysum$resid[i]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable4.tab') if (n > n25) { a<-table.start() a<-table.row.start(a) a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'p-values',header=TRUE) a<-table.element(a,'Alternative Hypothesis',3,header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'breakpoint index',header=TRUE) a<-table.element(a,'greater',header=TRUE) a<-table.element(a,'2-sided',header=TRUE) a<-table.element(a,'less',header=TRUE) a<-table.row.end(a) for (mypoint in kp3:nmkm3) { a<-table.row.start(a) a<-table.element(a,mypoint,header=TRUE) a<-table.element(a,gqarr[mypoint-kp3+1,1]) a<-table.element(a,gqarr[mypoint-kp3+1,2]) a<-table.element(a,gqarr[mypoint-kp3+1,3]) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable5.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Description',header=TRUE) a<-table.element(a,'# significant tests',header=TRUE) a<-table.element(a,'% significant tests',header=TRUE) a<-table.element(a,'OK/NOK',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'1% type I error level',header=TRUE) a<-table.element(a,numsignificant1) a<-table.element(a,numsignificant1/numgqtests) if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'5% type I error level',header=TRUE) a<-table.element(a,numsignificant5) a<-table.element(a,numsignificant5/numgqtests) if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'10% type I error level',header=TRUE) a<-table.element(a,numsignificant10) a<-table.element(a,numsignificant10/numgqtests) if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK' a<-table.element(a,dum) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable6.tab') }
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