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Data X:
11 8 7 18 12 20 4 0.5 1 0.67 0.67 0 0.5 12.9 19 18 20 23 20 19 4 0.5 0.89 0.83 0.33 0.5 1 12.2 16 12 9 22 14 18 5 0.4 0.89 1 0.67 0 1 12.8 24 24 19 22 25 24 4 0.5 0.89 0.83 0 0 0 7.4 15 16 12 19 15 20 4 0.7 0.89 0.67 0 1 1 6.7 17 19 16 25 20 20 9 0.3 0.78 0 0 0.5 0.5 12.6 19 16 17 28 21 24 8 0.4 0.89 0.83 0.67 0.5 0 14.8 19 15 9 16 15 21 11 0.4 1 0.5 0.67 1 1 13.3 28 28 28 28 28 28 4 0.7 0.89 0.83 0 0.5 0 11.1 26 21 20 21 11 10 4 0.6 0.78 0.33 0.67 0.5 0.5 8.2 15 18 16 22 22 22 6 0.6 1 0.5 1 0 0.5 11.4 26 22 22 24 22 19 4 0.2 0.78 0.67 0 0.5 0.5 6.4 16 19 17 24 27 27 8 0.4 0.89 1 0 0.5 0.5 10.6 24 22 12 26 24 23 4 0.4 0.89 0.5 0.67 0 1 12 25 25 18 28 23 24 4 0.5 0.89 0.67 0.33 0 0 6.3 22 20 20 24 24 24 11 0.3 0.89 0.17 0.67 0 0.5 11.3 15 16 12 20 21 25 4 0.4 0.89 0.83 0.33 0.5 0.5 11.9 21 19 16 26 20 24 4 0.7 0.67 0.67 0.33 0.5 1 9.3 22 18 16 21 19 21 6 0.5 1 0.67 0.33 0 1 9.6 27 26 21 28 25 28 6 0.2 0.78 0.67 0 0 1 10 26 24 15 27 16 28 4 0.3 0.78 0.5 0.67 0 0.5 6.4 26 20 17 23 24 22 8 0.6 0.89 1 0.33 0 1 13.8 22 19 17 24 21 26 5 0.6 0.78 0.83 0.33 0 1 10.8 21 19 17 24 22 26 4 0.2 0.89 0.83 0.33 0 1 13.8 22 23 18 22 25 21 9 0.7 0.89 1 0.67 1 0 11.7 20 18 15 21 23 26 4 0.2 0.33 0.67 0 0 0 10.9 21 16 20 25 20 23 7 1 1 1 0.33 1 1 16.1 20 18 13 20 21 20 10 0.4 0.89 0.83 0.67 0 0.5 13.4 22 21 21 21 22 24 4 0.4 0.89 1 1 0 1 9.9 21 20 12 26 25 25 4 0.2 0.67 0.83 0.67 0 0.5 11.5 8 15 6 23 23 24 7 0.4 0.56 0.67 0.33 0 1 8.3 22 19 13 21 19 20 12 0.4 0.89 0.67 0 0.5 1 11.7 20 19 19 27 21 24 7 0.7 0.89 1 0.67 0.5 0.5 9 24 7 12 25 19 25 5 0.2 1 0.67 0.67 0 0.5 9.7 17 20 14 23 25 23 8 0.6 0.78 1 1 0 0.5 10.8 20 20 13 25 16 21 5 0.3 0.78 1 1 0.5 0.5 10.3 23 19 12 23 24 23 4 0.3 0.33 0.5 0.33 0 0 10.4 20 19 17 19 24 21 9 0.2 0.78 0.67 0 0.5 0 12.7 22 20 19 22 18 18 7 0.5 0.89 0.83 0.67 0.5 0.5 9.3 19 18 10 24 28 24 4 0.7 0.89 1 0.67 0.5 1 11.8 15 14 10 19 15 18 4 0.6 0.78 1 0.67 0.5 0.5 5.9 20 17 11 21 17 21 4 0.4 0.89 1 0.67 0.5 1 11.4 22 17 11 27 18 23 4 0.6 0.89 1 0.33 0.5 1 13 17 8 10 25 26 25 4 0.4 1 1 1 0 1 10.8 14 9 7 25 18 22 7 0.3 0.67 0.83 0.67 0 1 12.3 24 22 22 23 22 22 4 0.5 1 0.83 0.67 0.5 0.5 11.3 17 20 12 17 19 23 7 0.2 0.89 0.5 0 0 1 11.8 23 20 18 28 17 24 4 0.3 0.89 0.83 0 0.5 1 7.9 25 22 20 25 26 25 4 0.5 0.89 0.17 0 0 1 12.7 16 22 9 20 21 22 4 0.7 0.78 0.83 1 0.5 1 12.3 18 22 16 25 26 24 4 0.4 0.89 1 0.67 1 0.5 11.6 20 16 14 21 21 21 8 0.3 0.78 1 0 0 0.5 6.7 18 14 11 24 12 24 4 0.2 0.78 0.67 0.67 1 1 10.9 23 24 20 28 20 25 4 0.5 1 1 0 0 0.5 12.1 24 21 17 20 20 23 4 0.4 0.78 1 0 0.5 0 13.3 23 20 14 19 24 27 4 0.6 1 1 0.67 1 1 10.1 13 20 8 24 24 27 7 0.4 0.78 0.83 1 0 1 5.7 20 18 16 21 22 23 12 0.4 0.67 0.33 0 0 0.5 14.3 20 14 11 24 21 18 4 0.2 0.33 0.33 0.33 0 0 8 19 19 10 23 20 20 4 0.9 1 1 0.67 0.5 1 13.3 22 24 15 18 23 23 4 0.8 1 1 0.67 1 0.5 9.3 22 19 15 27 19 24 5 0.8 0.78 0.83 0 0.5 1 12.5 15 16 10 25 24 26 15 0.3 0.67 1 1 0.5 1 7.6 17 16 10 20 21 20 5 0.2 1 0.83 0.67 0 0.5 15.9 19 16 18 21 16 23 10 0.4 0.89 0.67 0 0.5 1 9.2 20 14 10 23 17 22 9 0.2 0.89 0.83 1 0 1 9.1 22 22 22 27 23 23 8 0.2 0.78 0.67 0.67 0.5 1 11.1 21 21 16 24 20 17 4 0.1 1 0.83 0.67 0 1 13 21 15 10 27 19 20 5 0.4 0.56 0.67 1 0.5 0 14.5 16 14 7 24 18 22 4 0.5 0.67 1 0 0.5 0.5 12.2 20 15 16 23 18 18 9 0.8 0.89 0.83 0.33 0.5 1 12.3 21 14 16 24 21 19 4 0.4 0.89 0.67 0.67 0 0.5 11.4 20 20 16 21 20 19 10 0.6 0.89 0.83 0.33 0.5 0.5 8.8 23 21 22 23 17 16 4 0.5 0.89 0.83 0.67 0.5 1 14.6 18 14 5 27 25 26 4 0.3 0.78 0.67 0 0 0 12.6 22 19 18 24 15 14 6 0.8 0.89 1 1 0.5 1 NA 16 16 10 25 17 25 7 0.4 1 0.33 0 0.5 0 13 17 13 8 19 17 23 5 0.6 1 0.83 0.67 0.5 0.5 12.6 24 26 16 24 24 18 4 0.4 0.89 1 0.33 0 0.5 13.2 13 13 8 25 21 22 4 0.3 0.44 0.83 0 0 0 9.9 19 18 16 23 22 26 4 0.8 0.78 0.83 0 1 1 7.7 20 15 14 23 18 25 4 0.6 0.89 0.5 0.33 1 1 10.5 22 18 15 25 22 26 4 0.3 0.67 0.5 0 0 0 13.4 19 21 9 26 20 26 4 0.5 0.78 0.83 0.67 0.5 1 10.9 21 17 21 26 21 24 6 0.4 0.78 1 0.33 0 1 4.3 15 18 7 16 21 22 10 0.3 0.33 0.33 0.67 0 0 10.3 21 20 17 23 20 21 7 0.7 0.89 1 0.33 0 0.5 11.8 24 18 18 26 18 22 4 0.2 0.89 0.67 0.33 0.5 0.5 11.2 22 25 16 25 25 28 4 0.4 0.89 0.83 1 0 1 11.4 20 20 16 23 23 22 7 0.6 0.89 1 0.67 0.5 0.5 8.6 21 19 14 26 21 26 4 0.6 0.56 0.83 0 0 1 13.2 19 18 15 22 20 20 8 0.6 0.67 0.83 0.67 0.5 0.5 12.6 14 12 8 20 21 24 11 0.4 0.67 1 0.33 0.5 1 5.6 25 22 22 27 20 21 6 0.6 0.78 0.83 0 0 1 9.9 11 16 5 20 22 23 14 0.5 0.78 1 0.33 0.5 1 8.8 17 18 13 22 15 23 5 0.5 0.78 0.83 0 0 1 7.7 22 23 22 24 24 23 4 0.6 0.89 0.67 0 0 1 9 20 20 18 21 22 22 8 0.8 1 0.83 0.33 0.5 1 7.3 22 20 15 24 21 23 9 0.5 0.89 0.83 0.67 1 0.5 11.4 15 16 11 26 17 21 4 0.6 0.89 0.83 0.67 0.5 1 13.6 23 22 19 24 23 27 4 0.4 0.78 0.83 0.67 0.5 1 7.9 20 19 19 24 22 23 5 0.3 1 0.67 0.67 0.5 1 10.7 22 23 21 27 23 26 4 0.3 0.78 0.83 1 0 0.5 10.3 16 6 4 25 16 27 5 0.2 0.67 0 0 0 0 8.3 25 19 17 27 18 27 4 0.4 0.78 0.83 0 0 0.5 9.6 18 24 10 19 25 23 4 0.5 0.89 1 0 0 0.5 14.2 19 19 13 22 18 23 7 0.3 0.67 0.17 0 0.5 0 8.5 25 15 15 22 14 23 10 0.4 0.22 0.17 0 0.5 0 13.5 21 18 11 25 20 28 4 0.5 0.44 0.5 1 0 0 4.9 22 18 20 23 19 24 5 0.3 0.89 0.5 0.67 0 1 6.4 21 22 13 24 18 20 4 0.5 0.67 1 0 0 0.5 9.6 22 23 18 24 22 23 4 0.4 0.89 0.67 0.67 0 0.5 11.6 23 18 20 23 21 22 4 0.4 0.67 0.83 0.67 0 1 11.1 20 17 15 22 14 15 6 0.6 0.78 1 0 1 1 4.35 6 6 4 24 5 27 4 0.3 0.78 1 0.67 1 1 12.7 15 22 9 19 25 23 8 0.4 0.78 1 0.33 1 0.5 18.1 18 20 18 25 21 23 5 0.3 1 1 1 1 1 17.85 24 16 12 26 11 20 4 1 0.78 1 1 1 1 16.6 22 16 17 18 20 18 17 0.4 0.67 1 0 0 0.5 12.6 21 17 12 24 9 22 4 0.8 0.89 0.83 1 0.5 1 17.1 23 20 16 28 15 20 4 0.3 0.89 1 0.67 1 1 19.1 20 23 17 23 23 21 8 0.5 1 0.83 0.67 0 1 16.1 20 18 14 19 21 25 4 0.4 0.78 1 0 0 0.5 13.35 18 13 13 19 9 19 7 0.3 0.67 0.83 0.67 0 1 18.4 25 22 20 27 24 25 4 0.5 0.89 0.83 1 0 1 14.7 16 20 16 24 16 24 4 0.3 0.67 1 0.67 0 1 10.6 20 20 15 26 20 22 5 0.3 0.67 0.67 0 0 1 12.6 14 13 10 21 15 28 7 0.4 1 0.83 0 0 1 16.2 22 16 16 25 18 22 4 0.3 0.67 1 0 0 0.5 13.6 26 25 21 28 22 21 4 0.6 1 1 0.33 0.5 0.5 18.9 20 16 15 19 21 23 7 0.6 0.89 0.83 0.67 1 1 14.1 17 15 16 20 21 19 11 0.4 0.89 1 1 1 1 14.5 22 19 19 26 21 21 7 0.4 1 1 0 0 0 16.15 22 19 9 27 20 25 4 0.4 0.67 1 0.67 0 0.5 14.75 20 24 19 23 24 23 4 0.3 0.44 0.67 0.67 0.5 1 14.8 17 9 7 18 15 28 4 0.2 0.89 1 0.33 1 0 12.45 22 22 23 23 24 14 4 0.5 0.56 0.83 0.67 0 1 12.65 17 15 14 21 18 23 4 0.4 0.78 1 0.67 1 1 17.35 22 22 10 23 24 24 4 0.4 1 1 0.67 0 0 8.6 21 22 16 22 24 25 6 0.4 1 0.83 0.67 0 1 18.4 25 24 12 21 15 15 8 0.3 0.89 0.67 0.67 0.5 0.5 16.1 11 12 10 14 19 23 23 0.4 0.67 0.83 0.67 1 0.5 11.6 19 21 7 24 20 26 4 0.2 0.89 1 0.33 0.5 1 17.75 24 25 20 26 26 21 8 0 0.33 0 0 0 0 15.25 17 26 9 24 26 26 6 0.4 0.89 1 0.67 0.5 1 17.65 22 21 12 22 23 23 4 0.6 0.78 1 0 1 1 16.35 17 14 10 20 13 15 7 0.4 1 0.67 0.67 0 0.5 17.65 26 28 19 20 16 16 4 0.4 0.44 1 0 0 0.5 13.6 20 21 11 18 22 20 4 0.4 0.67 0.83 0 0.5 0 14.35 19 16 15 18 21 20 4 0.2 0.33 0.17 0 0.5 0 14.75 21 16 14 25 11 21 10 0.4 0.89 0.83 1 1 1 18.25 24 25 11 28 23 28 6 0.3 0.89 0.83 0 0 0.5 9.9 21 21 14 23 18 19 5 0.6 1 0.83 0.67 1 0 16 19 22 15 20 19 21 5 0.6 0.89 0.83 1 0 1 18.25 13 9 7 22 15 22 4 0.4 0.89 0.83 0 0 1 16.85 24 20 22 27 8 27 4 0.5 1 1 0.67 1 0.5 14.6 28 19 19 24 15 20 5 0.4 0.89 0.83 0 0.5 1 13.85 27 24 22 23 21 17 5 0.6 1 1 1 1 1 18.95 22 22 11 20 25 26 5 0.6 0.78 0.83 0.67 0.5 1 15.6 23 22 19 22 14 21 5 0.9 0.78 1 0.67 0.5 1 14.85 19 12 9 21 21 24 4 0.4 0.67 0.83 0.67 0.5 0 11.75 18 17 11 24 18 21 6 0.8 0.89 1 1 0.5 1 18.45 23 18 17 26 18 25 4 0.5 0.67 0.83 1 0 1 15.9 21 10 12 24 12 22 4 0.4 0.78 0.83 1 0 0 17.1 22 22 17 18 24 17 4 0.4 0.89 1 0.67 1 0.5 16.1 17 24 10 17 17 14 9 0.7 0.89 1 1 1 0.5 19.9 15 18 17 23 20 23 18 0.4 0.78 1 0.33 1 1 10.95 21 18 13 21 24 28 6 0.8 1 1 0.67 0.5 1 18.45 20 23 11 21 22 24 5 0.4 1 1 1 1 0.5 15.1 26 21 19 24 15 22 4 0.3 1 1 0.67 0 0.5 15 19 21 21 22 22 24 11 0.5 0.67 1 0.67 0.5 1 11.35 28 28 24 24 26 25 4 0.8 0.89 1 0.67 1 1 15.95 21 17 13 24 17 21 10 0.4 1 0.83 0.33 0 0.5 18.1 19 21 16 24 23 22 6 1 1 1 1 0.5 0 14.6 22 21 13 23 19 16 8 0.5 0.89 1 0.67 1 1 15.4 21 20 15 21 21 18 8 0.5 0.89 1 0.67 1 1 15.4 20 18 15 24 23 27 6 0.3 0.89 1 0.33 0 1 17.6 19 17 11 19 19 17 8 0.3 0.89 0.83 0.33 0.5 1 13.35 11 7 7 19 18 25 4 0.3 0.89 0.5 0 0 1 19.1 17 17 13 23 16 24 4 0.4 1 0.67 0.33 0.5 0.5 15.35 19 14 13 25 23 21 9 0.5 0.67 1 0.33 0 1 7.6 20 18 12 24 13 21 9 0.5 1 0.67 0.67 0.5 1 13.4 17 14 8 21 18 19 5 0.4 0.89 1 0 0 0 13.9 21 23 7 18 23 27 4 0.7 0.89 1 1 0.5 0 19.1 21 20 17 23 21 28 4 0.5 0.89 0.5 0.33 0 0.5 15.25 12 14 9 20 23 19 15 0.4 0.89 0.67 0.33 1 0 12.9 23 17 18 23 16 23 10 0.7 1 0.67 1 0 1 16.1 22 21 17 23 17 25 9 0.7 1 0.67 1 0 1 17.35 22 23 17 23 20 26 7 0.7 1 0.67 1 0 1 13.15 21 24 18 23 18 25 9 0.7 0.89 0.67 1 0 1 12.15 20 21 12 27 20 25 6 0.7 0.89 0.67 0 0 0 12.6 18 14 14 19 19 24 4 0.7 0.89 1 0.67 0.5 1 10.35 21 24 22 25 26 24 7 0.1 0.33 0.67 0.33 0.5 0 15.4 24 16 19 25 9 24 4 0.2 0.67 0.67 0.67 0.5 1 9.6 22 21 21 21 23 22 7 0.3 0.56 0.33 0.33 0 1 18.2 20 8 10 25 9 21 4 0.6 0.44 0.83 0.33 0 0.5 13.6 17 17 16 17 13 17 15 0.8 1 1 1 1 1 14.85 19 18 11 22 27 23 4 0.8 0.89 1 0.33 0.5 0.5 14.75 16 17 15 23 22 17 9 0 0.33 0.17 0 0 0 14.1 19 16 12 27 12 25 4 0.3 0.67 0.67 0.33 0 1 14.9 23 22 21 27 18 19 4 0.6 0.67 0.83 0.33 0.5 1 16.25 8 17 22 5 6 8 28 0.5 1 0.83 0.67 0 1 19.25 22 21 20 19 17 14 4 0.7 0.78 1 0.33 0 0.5 13.6 23 20 15 24 22 22 4 0.3 0.67 0.83 0 0.5 1 13.6 15 20 9 23 22 25 4 0.3 1 1 0.67 0 0 15.65 17 19 15 28 23 28 5 0.4 0.78 1 0.67 0 0.5 12.75 21 8 14 25 19 25 4 0.4 0.89 0.83 1 0 1 14.6 25 19 11 27 20 24 4 0.1 0.89 0.83 0 0 1 9.85 18 11 9 16 17 15 12 0.5 0.89 1 0.67 0 1 12.65 20 13 12 25 24 24 4 0 0 0 0 0 0 19.2 21 18 11 26 20 28 6 0.4 0.67 1 0.33 0.5 0 16.6 21 19 14 24 18 24 6 0.6 1 0.83 0.67 1 0.5 11.2 24 23 10 23 23 25 5 0.4 1 1 0.33 0.5 1 15.25 22 20 18 24 27 23 4 0.1 0.67 0.33 0 0.5 1 11.9 22 22 11 27 25 26 4 0.3 0.89 0.83 0 0 1 13.2 23 19 14 25 24 26 4 0.7 0.89 0.83 0.67 0 1 16.35 17 16 16 19 12 22 10 0.3 0.56 0.17 0 0 1 12.4 15 11 11 19 16 25 7 0.5 0.67 0.83 0.33 0.5 0 15.85 22 21 16 24 24 22 4 0.3 1 0.83 0.67 1 1 18.15 19 14 13 20 23 26 7 0.6 1 0.67 0.67 0.5 1 11.15 18 21 12 21 24 20 4 0.9 1 1 1 0 1 15.65 21 20 17 28 24 26 4 0.4 0.67 0.83 0 0.5 1 17.75 20 21 23 26 26 26 12 0.3 0.44 1 0 0.5 0.5 7.65 19 20 14 19 19 21 5 0.9 0.89 1 0.67 1 1 12.35 19 19 10 23 28 21 8 0.5 0.44 1 0 0.5 0 15.6 16 19 16 23 23 24 6 0.3 0.56 1 1 0.5 0.5 19.3 18 18 11 21 21 21 17 0.6 0.89 0.83 0.67 0 0.5 15.2 23 20 16 26 19 18 4 0.2 0.67 1 0.33 0 0.5 17.1 22 21 19 25 23 23 5 0.4 0.89 0.83 1 0.5 1 15.6 23 22 17 25 23 26 4 0.5 1 0.83 0.67 0.5 0.5 18.4 20 19 12 24 20 23 5 0.4 0.78 0.83 0.67 0 0.5 19.05 24 23 17 23 18 25 5 0 0.44 0 0 0 0 18.55 25 16 11 22 20 20 6 0.2 0.89 1 0.33 0.5 1 19.1 25 23 19 27 28 25 4 0.5 0.89 1 0.67 0.5 1 13.1 20 18 12 26 21 26 4 0.3 0.89 1 0.67 0 0.5 12.85 23 23 8 23 25 19 4 0 0.44 0 0 0 0 9.5 21 20 17 22 18 21 6 0.5 1 0.83 1 0 1 4.5 23 20 13 26 24 23 8 0.6 0.89 0.83 0.33 0 1 11.85 23 23 17 22 28 24 10 0.3 0.67 0.83 0 0.5 0.5 13.6 11 13 7 17 9 6 4 0 0.33 0 0 0 0 11.7 21 21 23 25 22 22 5 0.3 0.78 0.67 0 0.5 0 12.4 27 26 18 22 26 21 4 0.5 0.89 1 0.67 0.5 1 13.35 19 18 13 28 28 28 4 0.4 0.78 0.67 0 0 1 11.4 21 19 17 22 18 24 4 0.5 0.78 0.83 0.67 0 0.5 14.9 16 18 13 21 23 14 16 0.7 0.89 1 1 1 0.5 19.9 21 18 8 24 15 20 7 0.8 0.78 1 0.67 0.5 1 11.2 22 19 16 26 24 28 4 0.6 0.78 1 0.33 0.5 1 14.6 16 13 14 26 12 19 4 0.4 0.67 0.83 0.33 0 0.5 17.6 18 10 13 24 12 24 14 0.5 0.89 0.83 0.33 0.5 0 14.05 23 21 19 27 20 21 5 0.5 0.89 1 0 0.5 1 16.1 24 24 15 22 25 21 5 0.3 0.78 1 0.33 0 1 13.35 20 21 15 23 24 26 5 0.6 1 1 0 0.5 1 11.85 20 23 8 22 23 24 5 0.3 1 0.67 0.67 0 0.5 11.95 18 18 14 23 18 26 7 0.6 0.78 0.83 1 0.5 0.5 14.75 4 11 7 15 20 25 19 0.3 0.78 0.33 0.33 0 1 15.15 14 16 11 20 22 23 16 0.7 0.89 1 0.67 1 1 13.2 22 20 17 22 20 24 4 0.7 0.89 1 1 0 1 16.85 17 20 19 25 25 24 4 0.6 0.67 0.67 1 0.5 1 7.85 23 26 17 27 28 26 7 0.5 1 1 0.33 0.5 0 7.7 20 21 12 24 25 23 9 0.5 0.67 0.83 0.33 0 0.5 12.6 18 12 12 21 14 20 5 0.4 0.56 0.67 0 0 1 7.85 19 15 18 17 16 16 14 0.4 0.78 1 0.33 1 1 10.95 20 18 16 26 24 24 4 0.7 1 1 1 0 1 12.35 15 14 15 20 13 20 16 0.2 0.67 0.17 0 0.5 0 9.95 24 18 20 22 19 23 10 0.5 0.78 0.83 0.67 0 0.5 14.9 21 16 16 24 18 23 5 0.4 0.56 0.83 0.67 0.5 0 16.65 19 19 12 23 16 18 6 0.2 1 1 0.67 1 1 13.4 19 7 10 22 8 21 4 0.5 0.89 0.67 0.67 0 0 13.95 27 21 28 28 27 25 4 0.4 0.44 0.5 0 0 1 15.7 23 24 19 21 23 23 4 0.7 1 0.67 1 1 1 16.85 23 21 18 24 20 26 5 0.6 0.89 0.83 0.67 1 0 10.95 20 20 19 28 20 26 4 0.4 0.78 0.83 0 0 0 15.35 17 22 8 25 26 24 4 0.5 0.89 1 0.67 1 1 12.2 21 17 17 24 23 23 5 0 0.11 0.17 0 0 0 15.1 23 19 16 24 24 21 4 0.7 0.89 1 0.67 0.5 1 17.75 22 20 18 21 21 23 4 0.4 0.89 0.67 0.67 0 1 15.2 16 16 12 20 15 20 5 0.5 1 0.67 1 0 1 14.6 20 20 17 26 22 23 8 0.6 0.89 0.83 0.67 0 0.5 16.65 16 16 13 16 25 24 15 0.8 1 0.5 0.67 0.5 0.5 8.1
Names of X columns:
AMS.I1 AMS.I2 AMS.I3 AMS.E1 AMS.E2 AMS.E3 AMS.A Algebraic_Reasoning Calculation Graphical_Interpretation Proportionality_and_Ratio Probability_and_Sampling Estimation TOT
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$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '') myeq <- paste(myeq, signif(mysum$coefficients[i,1],6), 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,signif(mysum$coefficients[i,1],6)) a<-table.element(a, signif(mysum$coefficients[i,2],6)) a<-table.element(a, signif(mysum$coefficients[i,3],4)) a<-table.element(a, signif(mysum$coefficients[i,4],6)) a<-table.element(a, signif(mysum$coefficients[i,4]/2,6)) a<-table.row.end(a) } a<-table.end(a) table.save(a,file='mytable2.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Multiple R',1,TRUE) a<-table.element(a, signif(sqrt(mysum$r.squared),6)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'R-squared',1,TRUE) a<-table.element(a, signif(mysum$r.squared,6)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Adjusted R-squared',1,TRUE) a<-table.element(a, signif(mysum$adj.r.squared,6)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (value)',1,TRUE) a<-table.element(a, signif(mysum$fstatistic[1],6)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE) a<-table.element(a, signif(mysum$fstatistic[2],6)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE) a<-table.element(a, signif(mysum$fstatistic[3],6)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'p-value',1,TRUE) a<-table.element(a, signif(1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]),6)) 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, signif(mysum$sigma,6)) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Sum Squared Residuals',1,TRUE) a<-table.element(a, signif(sum(myerror*myerror),6)) a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable3.tab') a<-table.start() a<-table.row.start(a) a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a, 'Time or Index', 1, TRUE) a<-table.element(a, 'Actuals', 1, TRUE) a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE) a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE) a<-table.row.end(a) for (i in 1:n) { a<-table.row.start(a) a<-table.element(a,i, 1, TRUE) a<-table.element(a,signif(x[i],6)) a<-table.element(a,signif(x[i]-mysum$resid[i],6)) a<-table.element(a,signif(mysum$resid[i],6)) 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,signif(gqarr[mypoint-kp3+1,1],6)) a<-table.element(a,signif(gqarr[mypoint-kp3+1,2],6)) a<-table.element(a,signif(gqarr[mypoint-kp3+1,3],6)) 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,signif(numsignificant1,6)) a<-table.element(a,signif(numsignificant1/numgqtests,6)) 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,signif(numsignificant5,6)) a<-table.element(a,signif(numsignificant5/numgqtests,6)) 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,signif(numsignificant10,6)) a<-table.element(a,signif(numsignificant10/numgqtests,6)) 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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