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Data X:
11 8 7 18 12 20 1.00 0.50 0.67 0.67 0.00 0.50 12.9 149 4 19 18 20 23 20 19 0.89 0.50 0.83 0.33 0.50 1.00 12.2 139 4 16 12 9 22 14 18 0.89 0.40 1.00 0.67 0.00 1.00 12.8 148 5 24 24 19 22 25 24 0.89 0.50 0.83 0.00 0.00 0.00 7.4 158 4 15 16 12 19 15 20 0.89 0.70 0.67 0.00 1.00 1.00 6.7 128 4 17 19 16 25 20 20 0.78 0.30 0.00 0.00 0.50 0.50 12.6 224 9 19 16 17 28 21 24 0.89 0.40 0.83 0.67 0.50 0.00 14.8 159 8 19 15 9 16 15 21 1.00 0.40 0.50 0.67 1.00 1.00 13.3 105 11 28 28 28 28 28 28 0.89 0.70 0.83 0.00 0.50 0.00 11.1 159 4 26 21 20 21 11 10 0.78 0.60 0.33 0.67 0.50 0.50 8.2 167 4 15 18 16 22 22 22 1.00 0.60 0.50 1.00 0.00 0.50 11.4 165 6 26 22 22 24 22 19 0.78 0.20 0.67 0.00 0.50 0.50 6.4 159 4 16 19 17 24 27 27 0.89 0.40 1.00 0.00 0.50 0.50 10.6 119 8 24 22 12 26 24 23 0.89 0.40 0.50 0.67 0.00 1.00 12.0 176 4 25 25 18 28 23 24 0.89 0.50 0.67 0.33 0.00 0.00 6.3 54 4 22 20 20 24 24 24 0.89 0.30 0.17 0.67 0.00 0.50 11.3 91 11 15 16 12 20 21 25 0.89 0.40 0.83 0.33 0.50 0.50 11.9 163 4 21 19 16 26 20 24 0.67 0.70 0.67 0.33 0.50 1.00 9.3 124 4 22 18 16 21 19 21 1.00 0.50 0.67 0.33 0.00 1.00 9.6 137 6 27 26 21 28 25 28 0.78 0.20 0.67 0.00 0.00 1.00 10.0 121 6 26 24 15 27 16 28 0.78 0.30 0.50 0.67 0.00 0.50 6.4 153 4 26 20 17 23 24 22 0.89 0.60 1.00 0.33 0.00 1.00 13.8 148 8 22 19 17 24 21 26 0.78 0.60 0.83 0.33 0.00 1.00 10.8 221 5 21 19 17 24 22 26 0.89 0.20 0.83 0.33 0.00 1.00 13.8 188 4 22 23 18 22 25 21 0.89 0.70 1.00 0.67 1.00 0.00 11.7 149 9 20 18 15 21 23 26 0.33 0.20 0.67 0.00 0.00 0.00 10.9 244 4 21 16 20 25 20 23 1.00 1.00 1.00 0.33 1.00 1.00 16.1 148 7 20 18 13 20 21 20 0.89 0.40 0.83 0.67 0.00 0.50 13.4 92 10 22 21 21 21 22 24 0.89 0.40 1.00 1.00 0.00 1.00 9.9 150 4 21 20 12 26 25 25 0.67 0.20 0.83 0.67 0.00 0.50 11.5 153 4 8 15 6 23 23 24 0.56 0.40 0.67 0.33 0.00 1.00 8.3 94 7 22 19 13 21 19 20 0.89 0.40 0.67 0.00 0.50 1.00 11.7 156 12 20 19 19 27 21 24 0.89 0.70 1.00 0.67 0.50 0.50 9.0 132 7 24 7 12 25 19 25 1.00 0.20 0.67 0.67 0.00 0.50 9.7 161 5 17 20 14 23 25 23 0.78 0.60 1.00 1.00 0.00 0.50 10.8 105 8 20 20 13 25 16 21 0.78 0.30 1.00 1.00 0.50 0.50 10.3 97 5 23 19 12 23 24 23 0.33 0.30 0.50 0.33 0.00 0.00 10.4 151 4 20 19 17 19 24 21 0.78 0.20 0.67 0.00 0.50 0.00 12.7 131 9 22 20 19 22 18 18 0.89 0.50 0.83 0.67 0.50 0.50 9.3 166 7 19 18 10 24 28 24 0.89 0.70 1.00 0.67 0.50 1.00 11.8 157 4 15 14 10 19 15 18 0.78 0.60 1.00 0.67 0.50 0.50 5.9 111 4 20 17 11 21 17 21 0.89 0.40 1.00 0.67 0.50 1.00 11.4 145 4 22 17 11 27 18 23 0.89 0.60 1.00 0.33 0.50 1.00 13.0 162 4 17 8 10 25 26 25 1.00 0.40 1.00 1.00 0.00 1.00 10.8 163 4 14 9 7 25 18 22 0.67 0.30 0.83 0.67 0.00 1.00 12.3 59 7 24 22 22 23 22 22 1.00 0.50 0.83 0.67 0.50 0.50 11.3 187 4 17 20 12 17 19 23 0.89 0.20 0.50 0.00 0.00 1.00 11.8 109 7 23 20 18 28 17 24 0.89 0.30 0.83 0.00 0.50 1.00 7.9 90 4 25 22 20 25 26 25 0.89 0.50 0.17 0.00 0.00 1.00 12.7 105 4 16 22 9 20 21 22 0.78 0.70 0.83 1.00 0.50 1.00 12.3 83 4 18 22 16 25 26 24 0.89 0.40 1.00 0.67 1.00 0.50 11.6 116 4 20 16 14 21 21 21 0.78 0.30 1.00 0.00 0.00 0.50 6.7 42 8 18 14 11 24 12 24 0.78 0.20 0.67 0.67 1.00 1.00 10.9 148 4 23 24 20 28 20 25 1.00 0.50 1.00 0.00 0.00 0.50 12.1 155 4 24 21 17 20 20 23 0.78 0.40 1.00 0.00 0.50 0.00 13.3 125 4 23 20 14 19 24 27 1.00 0.60 1.00 0.67 1.00 1.00 10.1 116 4 13 20 8 24 24 27 0.78 0.40 0.83 1.00 0.00 1.00 5.7 128 7 20 18 16 21 22 23 0.67 0.40 0.33 0.00 0.00 0.50 14.3 138 12 20 14 11 24 21 18 0.33 0.20 0.33 0.33 0.00 0.00 8.0 49 4 19 19 10 23 20 20 1.00 0.90 1.00 0.67 0.50 1.00 13.3 96 4 22 24 15 18 23 23 1.00 0.80 1.00 0.67 1.00 0.50 9.3 164 4 22 19 15 27 19 24 0.78 0.80 0.83 0.00 0.50 1.00 12.5 162 5 15 16 10 25 24 26 0.67 0.30 1.00 1.00 0.50 1.00 7.6 99 15 17 16 10 20 21 20 1.00 0.20 0.83 0.67 0.00 0.50 15.9 202 5 19 16 18 21 16 23 0.89 0.40 0.67 0.00 0.50 1.00 9.2 186 10 20 14 10 23 17 22 0.89 0.20 0.83 1.00 0.00 1.00 9.1 66 9 22 22 22 27 23 23 0.78 0.20 0.67 0.67 0.50 1.00 11.1 183 8 21 21 16 24 20 17 1.00 0.10 0.83 0.67 0.00 1.00 13.0 214 4 21 15 10 27 19 20 0.56 0.40 0.67 1.00 0.50 0.00 14.5 188 5 16 14 7 24 18 22 0.67 0.50 1.00 0.00 0.50 0.50 12.2 104 4 20 15 16 23 18 18 0.89 0.80 0.83 0.33 0.50 1.00 12.3 177 9 21 14 16 24 21 19 0.89 0.40 0.67 0.67 0.00 0.50 11.4 126 4 20 20 16 21 20 19 0.89 0.60 0.83 0.33 0.50 0.50 8.8 76 10 23 21 22 23 17 16 0.89 0.50 0.83 0.67 0.50 1.00 14.6 99 4 18 14 5 27 25 26 0.78 0.30 0.67 0.00 0.00 0.00 12.6 139 4 22 19 18 24 15 14 0.89 0.80 1.00 1.00 0.50 1.00 NA 78 6 16 16 10 25 17 25 1.00 0.40 0.33 0.00 0.50 0.00 13.0 162 7 17 13 8 19 17 23 1.00 0.60 0.83 0.67 0.50 0.50 12.6 108 5 24 26 16 24 24 18 0.89 0.40 1.00 0.33 0.00 0.50 13.2 159 4 13 13 8 25 21 22 0.44 0.30 0.83 0.00 0.00 0.00 9.9 74 4 19 18 16 23 22 26 0.78 0.80 0.83 0.00 1.00 1.00 7.7 110 4 20 15 14 23 18 25 0.89 0.60 0.50 0.33 1.00 1.00 10.5 96 4 22 18 15 25 22 26 0.67 0.30 0.50 0.00 0.00 0.00 13.4 116 4 19 21 9 26 20 26 0.78 0.50 0.83 0.67 0.50 1.00 10.9 87 4 21 17 21 26 21 24 0.78 0.40 1.00 0.33 0.00 1.00 4.3 97 6 15 18 7 16 21 22 0.33 0.30 0.33 0.67 0.00 0.00 10.3 127 10 21 20 17 23 20 21 0.89 0.70 1.00 0.33 0.00 0.50 11.8 106 7 24 18 18 26 18 22 0.89 0.20 0.67 0.33 0.50 0.50 11.2 80 4 22 25 16 25 25 28 0.89 0.40 0.83 1.00 0.00 1.00 11.4 74 4 20 20 16 23 23 22 0.89 0.60 1.00 0.67 0.50 0.50 8.6 91 7 21 19 14 26 21 26 0.56 0.60 0.83 0.00 0.00 1.00 13.2 133 4 19 18 15 22 20 20 0.67 0.60 0.83 0.67 0.50 0.50 12.6 74 8 14 12 8 20 21 24 0.67 0.40 1.00 0.33 0.50 1.00 5.6 114 11 25 22 22 27 20 21 0.78 0.60 0.83 0.00 0.00 1.00 9.9 140 6 11 16 5 20 22 23 0.78 0.50 1.00 0.33 0.50 1.00 8.8 95 14 17 18 13 22 15 23 0.78 0.50 0.83 0.00 0.00 1.00 7.7 98 5 22 23 22 24 24 23 0.89 0.60 0.67 0.00 0.00 1.00 9.0 121 4 20 20 18 21 22 22 1.00 0.80 0.83 0.33 0.50 1.00 7.3 126 8 22 20 15 24 21 23 0.89 0.50 0.83 0.67 1.00 0.50 11.4 98 9 15 16 11 26 17 21 0.89 0.60 0.83 0.67 0.50 1.00 13.6 95 4 23 22 19 24 23 27 0.78 0.40 0.83 0.67 0.50 1.00 7.9 110 4 20 19 19 24 22 23 1.00 0.30 0.67 0.67 0.50 1.00 10.7 70 5 22 23 21 27 23 26 0.78 0.30 0.83 1.00 0.00 0.50 10.3 102 4 16 6 4 25 16 27 0.67 0.20 0.00 0.00 0.00 0.00 8.3 86 5 25 19 17 27 18 27 0.78 0.40 0.83 0.00 0.00 0.50 9.6 130 4 18 24 10 19 25 23 0.89 0.50 1.00 0.00 0.00 0.50 14.2 96 4 19 19 13 22 18 23 0.67 0.30 0.17 0.00 0.50 0.00 8.5 102 7 25 15 15 22 14 23 0.22 0.40 0.17 0.00 0.50 0.00 13.5 100 10 21 18 11 25 20 28 0.44 0.50 0.50 1.00 0.00 0.00 4.9 94 4 22 18 20 23 19 24 0.89 0.30 0.50 0.67 0.00 1.00 6.4 52 5 21 22 13 24 18 20 0.67 0.50 1.00 0.00 0.00 0.50 9.6 98 4 22 23 18 24 22 23 0.89 0.40 0.67 0.67 0.00 0.50 11.6 118 4 23 18 20 23 21 22 0.67 0.40 0.83 0.67 0.00 1.00 11.1 99 4 20 17 15 22 14 15 0.78 0.60 1.00 0.00 1.00 1.00 4.35 48 6 6 6 4 24 5 27 0.78 0.30 1.00 0.67 1.00 1.00 12.7 50 4 15 22 9 19 25 23 0.78 0.40 1.00 0.33 1.00 0.50 18.1 150 8 18 20 18 25 21 23 1.00 0.30 1.00 1.00 1.00 1.00 17.85 154 5 24 16 12 26 11 20 0.78 1.00 1.00 1.00 1.00 1.00 16.6 109 4 22 16 17 18 20 18 0.67 0.40 1.00 0.00 0.00 0.50 12.6 68 17 21 17 12 24 9 22 0.89 0.80 0.83 1.00 0.50 1.00 17.1 194 4 23 20 16 28 15 20 0.89 0.30 1.00 0.67 1.00 1.00 19.1 158 4 20 23 17 23 23 21 1.00 0.50 0.83 0.67 0.00 1.00 16.1 159 8 20 18 14 19 21 25 0.78 0.40 1.00 0.00 0.00 0.50 13.35 67 4 18 13 13 19 9 19 0.67 0.30 0.83 0.67 0.00 1.00 18.4 147 7 25 22 20 27 24 25 0.89 0.50 0.83 1.00 0.00 1.00 14.7 39 4 16 20 16 24 16 24 0.67 0.30 1.00 0.67 0.00 1.00 10.6 100 4 20 20 15 26 20 22 0.67 0.30 0.67 0.00 0.00 1.00 12.6 111 5 14 13 10 21 15 28 1.00 0.40 0.83 0.00 0.00 1.00 16.2 138 7 22 16 16 25 18 22 0.67 0.30 1.00 0.00 0.00 0.50 13.6 101 4 26 25 21 28 22 21 1.00 0.60 1.00 0.33 0.50 0.50 18.9 131 4 20 16 15 19 21 23 0.89 0.60 0.83 0.67 1.00 1.00 14.1 101 7 17 15 16 20 21 19 0.89 0.40 1.00 1.00 1.00 1.00 14.5 114 11 22 19 19 26 21 21 1.00 0.40 1.00 0.00 0.00 0.00 16.15 165 7 22 19 9 27 20 25 0.67 0.40 1.00 0.67 0.00 0.50 14.75 114 4 20 24 19 23 24 23 0.44 0.30 0.67 0.67 0.50 1.00 14.8 111 4 17 9 7 18 15 28 0.89 0.20 1.00 0.33 1.00 0.00 12.45 75 4 22 22 23 23 24 14 0.56 0.50 0.83 0.67 0.00 1.00 12.65 82 4 17 15 14 21 18 23 0.78 0.40 1.00 0.67 1.00 1.00 17.35 121 4 22 22 10 23 24 24 1.00 0.40 1.00 0.67 0.00 0.00 8.6 32 4 21 22 16 22 24 25 1.00 0.40 0.83 0.67 0.00 1.00 18.4 150 6 25 24 12 21 15 15 0.89 0.30 0.67 0.67 0.50 0.50 16.1 117 8 11 12 10 14 19 23 0.67 0.40 0.83 0.67 1.00 0.50 11.6 71 23 19 21 7 24 20 26 0.89 0.20 1.00 0.33 0.50 1.00 17.75 165 4 24 25 20 26 26 21 0.33 0.00 0.00 0.00 0.00 0.00 15.25 154 8 17 26 9 24 26 26 0.89 0.40 1.00 0.67 0.50 1.00 17.65 126 6 22 21 12 22 23 23 0.78 0.60 1.00 0.00 1.00 1.00 16.35 149 4 17 14 10 20 13 15 1.00 0.40 0.67 0.67 0.00 0.50 17.65 145 7 26 28 19 20 16 16 0.44 0.40 1.00 0.00 0.00 0.50 13.6 120 4 20 21 11 18 22 20 0.67 0.40 0.83 0.00 0.50 0.00 14.35 109 4 19 16 15 18 21 20 0.33 0.20 0.17 0.00 0.50 0.00 14.75 132 4 21 16 14 25 11 21 0.89 0.40 0.83 1.00 1.00 1.00 18.25 172 10 24 25 11 28 23 28 0.89 0.30 0.83 0.00 0.00 0.50 9.9 169 6 21 21 14 23 18 19 1.00 0.60 0.83 0.67 1.00 0.00 16 114 5 19 22 15 20 19 21 0.89 0.60 0.83 1.00 0.00 1.00 18.25 156 5 13 9 7 22 15 22 0.89 0.40 0.83 0.00 0.00 1.00 16.85 172 4 24 20 22 27 8 27 1.00 0.50 1.00 0.67 1.00 0.50 14.6 68 4 28 19 19 24 15 20 0.89 0.40 0.83 0.00 0.50 1.00 13.85 89 5 27 24 22 23 21 17 1.00 0.60 1.00 1.00 1.00 1.00 18.95 167 5 22 22 11 20 25 26 0.78 0.60 0.83 0.67 0.50 1.00 15.6 113 5 23 22 19 22 14 21 0.78 0.90 1.00 0.67 0.50 1.00 14.85 115 5 19 12 9 21 21 24 0.67 0.40 0.83 0.67 0.50 0.00 11.75 78 4 18 17 11 24 18 21 0.89 0.80 1.00 1.00 0.50 1.00 18.45 118 6 23 18 17 26 18 25 0.67 0.50 0.83 1.00 0.00 1.00 15.9 87 4 21 10 12 24 12 22 0.78 0.40 0.83 1.00 0.00 0.00 17.1 173 4 22 22 17 18 24 17 0.89 0.40 1.00 0.67 1.00 0.50 16.1 2 4 17 24 10 17 17 14 0.89 0.70 1.00 1.00 1.00 0.50 19.9 162 9 15 18 17 23 20 23 0.78 0.40 1.00 0.33 1.00 1.00 10.95 49 18 21 18 13 21 24 28 1.00 0.80 1.00 0.67 0.50 1.00 18.45 122 6 20 23 11 21 22 24 1.00 0.40 1.00 1.00 1.00 0.50 15.1 96 5 26 21 19 24 15 22 1.00 0.30 1.00 0.67 0.00 0.50 15 100 4 19 21 21 22 22 24 0.67 0.50 1.00 0.67 0.50 1.00 11.35 82 11 28 28 24 24 26 25 0.89 0.80 1.00 0.67 1.00 1.00 15.95 100 4 21 17 13 24 17 21 1.00 0.40 0.83 0.33 0.00 0.50 18.1 115 10 19 21 16 24 23 22 1.00 1.00 1.00 1.00 0.50 0.00 14.6 141 6 22 21 13 23 19 16 0.89 0.50 1.00 0.67 1.00 1.00 15.4 165 8 21 20 15 21 21 18 0.89 0.50 1.00 0.67 1.00 1.00 15.4 165 8 20 18 15 24 23 27 0.89 0.30 1.00 0.33 0.00 1.00 17.6 110 6 19 17 11 19 19 17 0.89 0.30 0.83 0.33 0.50 1.00 13.35 118 8 11 7 7 19 18 25 0.89 0.30 0.50 0.00 0.00 1.00 19.1 158 4 17 17 13 23 16 24 1.00 0.40 0.67 0.33 0.50 0.50 15.35 146 4 19 14 13 25 23 21 0.67 0.50 1.00 0.33 0.00 1.00 7.6 49 9 20 18 12 24 13 21 1.00 0.50 0.67 0.67 0.50 1.00 13.4 90 9 17 14 8 21 18 19 0.89 0.40 1.00 0.00 0.00 0.00 13.9 121 5 21 23 7 18 23 27 0.89 0.70 1.00 1.00 0.50 0.00 19.1 155 4 21 20 17 23 21 28 0.89 0.50 0.50 0.33 0.00 0.50 15.25 104 4 12 14 9 20 23 19 0.89 0.40 0.67 0.33 1.00 0.00 12.9 147 15 23 17 18 23 16 23 1.00 0.70 0.67 1.00 0.00 1.00 16.1 110 10 22 21 17 23 17 25 1.00 0.70 0.67 1.00 0.00 1.00 17.35 108 9 22 23 17 23 20 26 1.00 0.70 0.67 1.00 0.00 1.00 13.15 113 7 21 24 18 23 18 25 0.89 0.70 0.67 1.00 0.00 1.00 12.15 115 9 20 21 12 27 20 25 0.89 0.70 0.67 0.00 0.00 0.00 12.6 61 6 18 14 14 19 19 24 0.89 0.70 1.00 0.67 0.50 1.00 10.35 60 4 21 24 22 25 26 24 0.33 0.10 0.67 0.33 0.50 0.00 15.4 109 7 24 16 19 25 9 24 0.67 0.20 0.67 0.67 0.50 1.00 9.6 68 4 22 21 21 21 23 22 0.56 0.30 0.33 0.33 0.00 1.00 18.2 111 7 20 8 10 25 9 21 0.44 0.60 0.83 0.33 0.00 0.50 13.6 77 4 17 17 16 17 13 17 1.00 0.80 1.00 1.00 1.00 1.00 14.85 73 15 19 18 11 22 27 23 0.89 0.80 1.00 0.33 0.50 0.50 14.75 151 4 16 17 15 23 22 17 0.33 0.00 0.17 0.00 0.00 0.00 14.1 89 9 19 16 12 27 12 25 0.67 0.30 0.67 0.33 0.00 1.00 14.9 78 4 23 22 21 27 18 19 0.67 0.60 0.83 0.33 0.50 1.00 16.25 110 4 8 17 22 5 6 8 1.00 0.50 0.83 0.67 0.00 1.00 19.25 220 28 22 21 20 19 17 14 0.78 0.70 1.00 0.33 0.00 0.50 13.6 65 4 23 20 15 24 22 22 0.67 0.30 0.83 0.00 0.50 1.00 13.6 141 4 15 20 9 23 22 25 1.00 0.30 1.00 0.67 0.00 0.00 15.65 117 4 17 19 15 28 23 28 0.78 0.40 1.00 0.67 0.00 0.50 12.75 122 5 21 8 14 25 19 25 0.89 0.40 0.83 1.00 0.00 1.00 14.6 63 4 25 19 11 27 20 24 0.89 0.10 0.83 0.00 0.00 1.00 9.85 44 4 18 11 9 16 17 15 0.89 0.50 1.00 0.67 0.00 1.00 12.65 52 12 20 13 12 25 24 24 0.00 0.00 0.00 0.00 0.00 0.00 19.2 131 4 21 18 11 26 20 28 0.67 0.40 1.00 0.33 0.50 0.00 16.6 101 6 21 19 14 24 18 24 1.00 0.60 0.83 0.67 1.00 0.50 11.2 42 6 24 23 10 23 23 25 1.00 0.40 1.00 0.33 0.50 1.00 15.25 152 5 22 20 18 24 27 23 0.67 0.10 0.33 0.00 0.50 1.00 11.9 107 4 22 22 11 27 25 26 0.89 0.30 0.83 0.00 0.00 1.00 13.2 77 4 23 19 14 25 24 26 0.89 0.70 0.83 0.67 0.00 1.00 16.35 154 4 17 16 16 19 12 22 0.56 0.30 0.17 0.00 0.00 1.00 12.4 103 10 15 11 11 19 16 25 0.67 0.50 0.83 0.33 0.50 0.00 15.85 96 7 22 21 16 24 24 22 1.00 0.30 0.83 0.67 1.00 1.00 18.15 175 4 19 14 13 20 23 26 1.00 0.60 0.67 0.67 0.50 1.00 11.15 57 7 18 21 12 21 24 20 1.00 0.90 1.00 1.00 0.00 1.00 15.65 112 4 21 20 17 28 24 26 0.67 0.40 0.83 0.00 0.50 1.00 17.75 143 4 20 21 23 26 26 26 0.44 0.30 1.00 0.00 0.50 0.50 7.65 49 12 19 20 14 19 19 21 0.89 0.90 1.00 0.67 1.00 1.00 12.35 110 5 19 19 10 23 28 21 0.44 0.50 1.00 0.00 0.50 0.00 15.6 131 8 16 19 16 23 23 24 0.56 0.30 1.00 1.00 0.50 0.50 19.3 167 6 18 18 11 21 21 21 0.89 0.60 0.83 0.67 0.00 0.50 15.2 56 17 23 20 16 26 19 18 0.67 0.20 1.00 0.33 0.00 0.50 17.1 137 4 22 21 19 25 23 23 0.89 0.40 0.83 1.00 0.50 1.00 15.6 86 5 23 22 17 25 23 26 1.00 0.50 0.83 0.67 0.50 0.50 18.4 121 4 20 19 12 24 20 23 0.78 0.40 0.83 0.67 0.00 0.50 19.05 149 5 24 23 17 23 18 25 0.44 0.00 0.00 0.00 0.00 0.00 18.55 168 5 25 16 11 22 20 20 0.89 0.20 1.00 0.33 0.50 1.00 19.1 140 6 25 23 19 27 28 25 0.89 0.50 1.00 0.67 0.50 1.00 13.1 88 4 20 18 12 26 21 26 0.89 0.30 1.00 0.67 0.00 0.50 12.85 168 4 23 23 8 23 25 19 0.44 0.00 0.00 0.00 0.00 0.00 9.5 94 4 21 20 17 22 18 21 1.00 0.50 0.83 1.00 0.00 1.00 4.5 51 6 23 20 13 26 24 23 0.89 0.60 0.83 0.33 0.00 1.00 11.85 48 8 23 23 17 22 28 24 0.67 0.30 0.83 0.00 0.50 0.50 13.6 145 10 11 13 7 17 9 6 0.33 0.00 0.00 0.00 0.00 0.00 11.7 66 4 21 21 23 25 22 22 0.78 0.30 0.67 0.00 0.50 0.00 12.4 85 5 27 26 18 22 26 21 0.89 0.50 1.00 0.67 0.50 1.00 13.35 109 4 19 18 13 28 28 28 0.78 0.40 0.67 0.00 0.00 1.00 11.4 63 4 21 19 17 22 18 24 0.78 0.50 0.83 0.67 0.00 0.50 14.9 102 4 16 18 13 21 23 14 0.89 0.70 1.00 1.00 1.00 0.50 19.9 162 16 21 18 8 24 15 20 0.78 0.80 1.00 0.67 0.50 1.00 11.2 86 7 22 19 16 26 24 28 0.78 0.60 1.00 0.33 0.50 1.00 14.6 114 4 16 13 14 26 12 19 0.67 0.40 0.83 0.33 0.00 0.50 17.6 164 4 18 10 13 24 12 24 0.89 0.50 0.83 0.33 0.50 0.00 14.05 119 14 23 21 19 27 20 21 0.89 0.50 1.00 0.00 0.50 1.00 16.1 126 5 24 24 15 22 25 21 0.78 0.30 1.00 0.33 0.00 1.00 13.35 132 5 20 21 15 23 24 26 1.00 0.60 1.00 0.00 0.50 1.00 11.85 142 5 20 23 8 22 23 24 1.00 0.30 0.67 0.67 0.00 0.50 11.95 83 5 18 18 14 23 18 26 0.78 0.60 0.83 1.00 0.50 0.50 14.75 94 7 4 11 7 15 20 25 0.78 0.30 0.33 0.33 0.00 1.00 15.15 81 19 14 16 11 20 22 23 0.89 0.70 1.00 0.67 1.00 1.00 13.2 166 16 22 20 17 22 20 24 0.89 0.70 1.00 1.00 0.00 1.00 16.85 110 4 17 20 19 25 25 24 0.67 0.60 0.67 1.00 0.50 1.00 7.85 64 4 23 26 17 27 28 26 1.00 0.50 1.00 0.33 0.50 0.00 7.7 93 7 20 21 12 24 25 23 0.67 0.50 0.83 0.33 0.00 0.50 12.6 104 9 18 12 12 21 14 20 0.56 0.40 0.67 0.00 0.00 1.00 7.85 105 5 19 15 18 17 16 16 0.78 0.40 1.00 0.33 1.00 1.00 10.95 49 14 20 18 16 26 24 24 1.00 0.70 1.00 1.00 0.00 1.00 12.35 88 4 15 14 15 20 13 20 0.67 0.20 0.17 0.00 0.50 0.00 9.95 95 16 24 18 20 22 19 23 0.78 0.50 0.83 0.67 0.00 0.50 14.9 102 10 21 16 16 24 18 23 0.56 0.40 0.83 0.67 0.50 0.00 16.65 99 5 19 19 12 23 16 18 1.00 0.20 1.00 0.67 1.00 1.00 13.4 63 6 19 7 10 22 8 21 0.89 0.50 0.67 0.67 0.00 0.00 13.95 76 4 27 21 28 28 27 25 0.44 0.40 0.50 0.00 0.00 1.00 15.7 109 4 23 24 19 21 23 23 1.00 0.70 0.67 1.00 1.00 1.00 16.85 117 4 23 21 18 24 20 26 0.89 0.60 0.83 0.67 1.00 0.00 10.95 57 5 20 20 19 28 20 26 0.78 0.40 0.83 0.00 0.00 0.00 15.35 120 4 17 22 8 25 26 24 0.89 0.50 1.00 0.67 1.00 1.00 12.2 73 4 21 17 17 24 23 23 0.11 0.00 0.17 0.00 0.00 0.00 15.1 91 5 23 19 16 24 24 21 0.89 0.70 1.00 0.67 0.50 1.00 17.75 108 4 22 20 18 21 21 23 0.89 0.40 0.67 0.67 0.00 1.00 15.2 105 4 16 16 12 20 15 20 1.00 0.50 0.67 1.00 0.00 1.00 14.6 117 5 20 20 17 26 22 23 0.89 0.60 0.83 0.67 0.00 0.50 16.65 119 8
Names of X columns:
AMS.I1 AMS.I2 AMS.I3 AMS.E1 AMS.E2 AMS.E3 Calculation Algebraic_Reasoning Graphical_Interpretation Proportionality_and_Ratio Probability_and_Sampling Estimation TOT LFM AMS.A
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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R Server
Big Analytics Cloud Computing Center
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