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Data X:
7 0.27 0.36 20.7 0.045 45 170 1.001 3 0.45 8.8 6 6.3 0.3 0.34 1.6 0.049 14 132 0.994 3.3 0.49 9.5 6 8.1 0.28 0.4 6.9 0.05 30 97 0.9951 3.26 0.44 10.1 6 7.2 0.23 0.32 8.5 0.058 47 186 0.9956 3.19 0.4 9.9 6 7.2 0.23 0.32 8.5 0.058 47 186 0.9956 3.19 0.4 9.9 6 8.1 0.28 0.4 6.9 0.05 30 97 0.9951 3.26 0.44 10.1 6 6.2 0.32 0.16 7 0.045 30 136 0.9949 3.18 0.47 9.6 6 7 0.27 0.36 20.7 0.045 45 170 1.001 3 0.45 8.8 6 6.3 0.3 0.34 1.6 0.049 14 132 0.994 3.3 0.49 9.5 6 8.1 0.22 0.43 1.5 0.044 28 129 0.9938 3.22 0.45 11 6 8.1 0.27 0.41 1.45 0.033 11 63 0.9908 2.99 0.56 12 5 8.6 0.23 0.4 4.2 0.035 17 109 0.9947 3.14 0.53 9.7 5 7.9 0.18 0.37 1.2 0.04 16 75 0.992 3.18 0.63 10.8 5 6.6 0.16 0.4 1.5 0.044 48 143 0.9912 3.54 0.52 12.4 7 8.3 0.42 0.62 19.25 0.04 41 172 1.0002 2.98 0.67 9.7 5 6.6 0.17 0.38 1.5 0.032 28 112 0.9914 3.25 0.55 11.4 7 6.3 0.48 0.04 1.1 0.046 30 99 0.9928 3.24 0.36 9.6 6 6.2 0.66 0.48 1.2 0.029 29 75 0.9892 3.33 0.39 12.8 8 7.4 0.34 0.42 1.1 0.033 17 171 0.9917 3.12 0.53 11.3 6 6.5 0.31 0.14 7.5 0.044 34 133 0.9955 3.22 0.5 9.5 5 6.2 0.66 0.48 1.2 0.029 29 75 0.9892 3.33 0.39 12.8 8 6.4 0.31 0.38 2.9 0.038 19 102 0.9912 3.17 0.35 11 7 6.8 0.26 0.42 1.7 0.049 41 122 0.993 3.47 0.48 10.5 8 7.6 0.67 0.14 1.5 0.074 25 168 0.9937 3.05 0.51 9.3 5 6.6 0.27 0.41 1.3 0.052 16 142 0.9951 3.42 0.47 10 6 7 0.25 0.32 9 0.046 56 245 0.9955 3.25 0.5 10.4 6 6.9 0.24 0.35 1 0.052 35 146 0.993 3.45 0.44 10 6 7 0.28 0.39 8.7 0.051 32 141 0.9961 3.38 0.53 10.5 6 7.4 0.27 0.48 1.1 0.047 17 132 0.9914 3.19 0.49 11.6 6 7.2 0.32 0.36 2 0.033 37 114 0.9906 3.1 0.71 12.3 7 8.5 0.24 0.39 10.4 0.044 20 142 0.9974 3.2 0.53 10 6 8.3 0.14 0.34 1.1 0.042 7 47 0.9934 3.47 0.4 10.2 6 7.4 0.25 0.36 2.05 0.05 31 100 0.992 3.19 0.44 10.8 6 6.2 0.12 0.34 1.5 0.045 43 117 0.9939 3.42 0.51 9 6 5.8 0.27 0.2 14.95 0.044 22 179 0.9962 3.37 0.37 10.2 5 7.3 0.28 0.43 1.7 0.08 21 123 0.9905 3.19 0.42 12.8 5 6.5 0.39 0.23 5.4 0.051 25 149 0.9934 3.24 0.35 10 5 7 0.33 0.32 1.2 0.053 38 138 0.9906 3.13 0.28 11.2 6 7.3 0.24 0.39 17.95 0.057 45 149 0.9999 3.21 0.36 8.6 5 7.3 0.24 0.39 17.95 0.057 45 149 0.9999 3.21 0.36 8.6 5 6.7 0.23 0.39 2.5 0.172 63 158 0.9937 3.11 0.36 9.4 6 6.7 0.24 0.39 2.9 0.173 63 157 0.9937 3.1 0.34 9.4 6 7 0.31 0.26 7.4 0.069 28 160 0.9954 3.13 0.46 9.8 6 6.6 0.24 0.27 1.4 0.057 33 152 0.9934 3.22 0.56 9.5 6 6.7 0.23 0.26 1.4 0.06 33 154 0.9934 3.24 0.56 9.5 6 7.4 0.18 0.31 1.4 0.058 38 167 0.9931 3.16 0.53 10 7 6.2 0.45 0.26 4.4 0.063 63 206 0.994 3.27 0.52 9.8 4 6.2 0.46 0.25 4.4 0.066 62 207 0.9939 3.25 0.52 9.8 5 7 0.31 0.26 7.4 0.069 28 160 0.9954 3.13 0.46 9.8 6 6.9 0.19 0.35 5 0.067 32 150 0.995 3.36 0.48 9.8 5 7.2 0.19 0.31 1.6 0.062 31 173 0.9917 3.35 0.44 11.7 6 6.6 0.25 0.29 1.1 0.068 39 124 0.9914 3.34 0.58 11 7 6.2 0.16 0.33 1.1 0.057 21 82 0.991 3.32 0.46 10.9 7 6.4 0.18 0.35 1 0.045 39 108 0.9911 3.31 0.35 10.9 6 6.8 0.2 0.59 0.9 0.147 38 132 0.993 3.05 0.38 9.1 6 6.9 0.25 0.35 1.3 0.039 29 191 0.9908 3.13 0.52 11 6 7.2 0.21 0.34 11.9 0.043 37 213 0.9962 3.09 0.5 9.6 6 6 0.19 0.26 12.4 0.048 50 147 0.9972 3.3 0.36 8.9 6 6.6 0.38 0.15 4.6 0.044 25 78 0.9931 3.11 0.38 10.2 6 7.4 0.2 0.36 1.2 0.038 44 111 0.9926 3.36 0.34 9.9 6 6.8 0.22 0.24 4.9 0.092 30 123 0.9951 3.03 0.46 8.6 6 6 0.19 0.26 12.4 0.048 50 147 0.9972 3.3 0.36 8.9 6 7 0.47 0.07 1.1 0.035 17 151 0.991 3.02 0.34 10.5 5 6.6 0.38 0.15 4.6 0.044 25 78 0.9931 3.11 0.38 10.2 6 7.2 0.24 0.27 1.4 0.038 31 122 0.9927 3.15 0.46 10.3 6 6.2 0.35 0.03 1.2 0.064 29 120 0.9934 3.22 0.54 9.1 5 6.4 0.26 0.24 6.4 0.04 27 124 0.9903 3.22 0.49 12.6 7 6.7 0.25 0.13 1.2 0.041 81 174 0.992 3.14 0.42 9.8 5 6.7 0.23 0.31 2.1 0.046 30 96 0.9926 3.33 0.64 10.7 8 7.4 0.24 0.29 10.1 0.05 21 105 0.9962 3.13 0.35 9.5 5 6.2 0.27 0.43 7.8 0.056 48 244 0.9956 3.1 0.51 9 6 6.8 0.3 0.23 4.6 0.061 50.5 238.5 0.9958 3.32 0.6 9.5 5 6 0.27 0.28 4.8 0.063 31 201 0.9964 3.69 0.71 10 5 8.6 0.23 0.46 1 0.054 9 72 0.9941 2.95 0.49 9.1 6 6.7 0.23 0.31 2.1 0.046 30 96 0.9926 3.33 0.64 10.7 8 7.4 0.24 0.29 10.1 0.05 21 105 0.9962 3.13 0.35 9.5 5 7.1 0.18 0.36 1.4 0.043 31 87 0.9898 3.26 0.37 12.7 7 7 0.32 0.34 1.3 0.042 20 69 0.9912 3.31 0.65 12 7 7.4 0.18 0.3 8.8 0.064 26 103 0.9961 2.94 0.56 9.3 5 6.7 0.54 0.28 5.4 0.06 21 105 0.9949 3.27 0.37 9 5 6.8 0.22 0.31 1.4 0.053 34 114 0.9929 3.39 0.77 10.6 6 7.1 0.2 0.34 16 0.05 51 166 0.9985 3.21 0.6 9.2 6 7.1 0.34 0.2 6.1 0.063 47 164 0.9946 3.17 0.42 10 5 7.3 0.22 0.3 8.2 0.047 42 207 0.9966 3.33 0.46 9.5 6 7.1 0.43 0.61 11.8 0.045 54 155 0.9974 3.11 0.45 8.7 5 7.1 0.44 0.62 11.8 0.044 52 152 0.9975 3.12 0.46 8.7 6 7.2 0.39 0.63 11 0.044 55 156 0.9974 3.09 0.44 8.7 6 6.8 0.25 0.31 13.3 0.05 69 202 0.9972 3.22 0.48 9.7 6 7.1 0.43 0.61 11.8 0.045 54 155 0.9974 3.11 0.45 8.7 5 7.1 0.44 0.62 11.8 0.044 52 152 0.9975 3.12 0.46 8.7 6 7.2 0.39 0.63 11 0.044 55 156 0.9974 3.09 0.44 8.7 6 6.1 0.27 0.43 7.5 0.049 65 243 0.9957 3.12 0.47 9 5 6.9 0.24 0.33 1.7 0.035 47 136 0.99 3.26 0.4 12.6 7 6.9 0.21 0.33 1.8 0.034 48 136 0.9899 3.25 0.41 12.6 7 7.5 0.17 0.32 1.7 0.04 51 148 0.9916 3.21 0.44 11.5 7 7.1 0.26 0.29 12.4 0.044 62 240 0.9969 3.04 0.42 9.2 6 6 0.34 0.66 15.9 0.046 26 164 0.9979 3.14 0.5 8.8 6 8.6 0.265 0.36 1.2 0.034 15 80 0.9913 2.95 0.36 11.4 7 9.8 0.36 0.46 10.5 0.038 4 83 0.9956 2.89 0.3 10.1 4 6 0.34 0.66 15.9 0.046 26 164 0.9979 3.14 0.5 8.8 6 7.4 0.25 0.37 13.5 0.06 52 192 0.9975 3 0.44 9.1 5 7.1 0.12 0.32 9.6 0.054 64 162 0.9962 3.4 0.41 9.4 5 6 0.21 0.24 12.1 0.05 55 164 0.997 3.34 0.39 9.4 5 7.5 0.305 0.4 18.9 0.059 44 170 1 2.99 0.46 9 5 7.4 0.25 0.37 13.5 0.06 52 192 0.9975 3 0.44 9.1 5 7.3 0.13 0.32 14.4 0.051 34 109 0.9974 3.2 0.35 9.2 6 7.1 0.12 0.32 9.6 0.054 64 162 0.9962 3.4 0.41 9.4 5 7.1 0.23 0.35 16.5 0.04 60 171 0.999 3.16 0.59 9.1 6 7.1 0.23 0.35 16.5 0.04 60 171 0.999 3.16 0.59 9.1 6 6.9 0.33 0.28 1.3 0.051 37 187 0.9927 3.27 0.6 10.3 5 6.5 0.17 0.54 8.5 0.082 64 163 0.9959 2.89 0.39 8.8 6 7.2 0.27 0.46 18.75 0.052 45 255 1 3.04 0.52 8.9 5 7.2 0.31 0.5 13.3 0.056 68 195 0.9982 3.01 0.47 9.2 5 6.7 0.41 0.34 9.2 0.049 29 150 0.9968 3.22 0.51 9.1 5 6.7 0.41 0.34 9.2 0.049 29 150 0.9968 3.22 0.51 9.1 5 5.5 0.485 0 1.5 0.065 8 103 0.994 3.63 0.4 9.7 4 6 0.31 0.24 3.3 0.041 25 143 0.9914 3.31 0.44 11.3 6 7 0.14 0.4 1.7 0.035 16 85 0.9911 3.19 0.42 11.8 6 7.2 0.31 0.5 13.3 0.056 68 195 0.9982 3.01 0.47 9.2 5 7.3 0.32 0.48 13.3 0.06 57 196 0.9982 3.04 0.5 9.2 5 5.9 0.36 0.04 5.7 0.046 21 87 0.9934 3.22 0.51 10.2 5 7.8 0.24 0.32 12.2 0.054 42 138 0.9984 3.01 0.54 8.8 5 7.4 0.16 0.31 6.85 0.059 31 131 0.9952 3.29 0.34 9.7 5 6.9 0.19 0.28 5 0.058 14 146 0.9952 3.29 0.36 9.1 6 6.4 0.13 0.47 1.6 0.092 40 158 0.9928 3.21 0.36 9.8 6 6.7 0.19 0.36 1.1 0.026 63 143 0.9912 3.27 0.48 11 6 7.4 0.39 0.23 7 0.033 29 126 0.994 3.14 0.42 10.5 5 6.5 0.24 0.32 7.6 0.038 48 203 0.9958 3.45 0.54 9.7 7 6.1 0.3 0.56 2.8 0.044 47 179 0.9924 3.3 0.57 10.9 7 6.1 0.3 0.56 2.7 0.046 46 184 0.9924 3.31 0.57 10.9 6 5.7 0.26 0.25 10.4 0.02 7 57 0.994 3.39 0.37 10.6 5 6.5 0.24 0.32 7.6 0.038 48 203 0.9958 3.45 0.54 9.7 7 6.5 0.425 0.4 13.1 0.038 59 241 0.9979 3.23 0.57 9 5 6.6 0.24 0.27 15.8 0.035 46 188 0.9982 3.24 0.51 9.2 5 6.8 0.27 0.22 8.1 0.034 55 203 0.9961 3.19 0.52 8.9 5 6.7 0.27 0.31 15.7 0.036 44 179 0.9979 3.26 0.56 9.6 5 8.2 0.23 0.4 1.2 0.027 36 121 0.992 3.12 0.38 10.7 6 7.1 0.37 0.67 10.5 0.045 49 155 0.9975 3.16 0.44 8.7 5 6.8 0.19 0.36 1.9 0.035 30 96 0.9917 3.15 0.54 10.8 7 8.1 0.28 0.39 1.9 0.029 18 79 0.9923 3.23 0.52 11.8 6 6.3 0.31 0.34 2.2 0.045 20 77 0.9927 3.3 0.43 10.2 5 7.1 0.37 0.67 10.5 0.045 49 155 0.9975 3.16 0.44 8.7 5 7.9 0.21 0.4 1.2 0.039 38 107 0.992 3.21 0.54 10.8 6 8.5 0.21 0.41 4.3 0.036 24 99 0.9947 3.18 0.53 9.7 6 8.1 0.2 0.4 2 0.037 19 87 0.9921 3.12 0.54 11.2 6 6.3 0.255 0.37 1.1 0.04 37 114 0.9905 3 0.39 10.9 6 5.6 0.16 0.27 1.4 0.044 53 168 0.9918 3.28 0.37 10.1 6 6.4 0.595 0.14 5.2 0.058 15 97 0.9951 3.38 0.36 9 4 6.3 0.34 0.33 4.6 0.034 19 80 0.9917 3.38 0.58 12 7 6.9 0.25 0.3 4.1 0.054 23 116 0.994 2.99 0.38 9.4 6 7.9 0.22 0.38 8 0.043 46 152 0.9934 3.12 0.32 11.5 7 7.6 0.18 0.46 10.2 0.055 58 135 0.9968 3.14 0.43 9.9 6 6.9 0.25 0.3 4.1 0.054 23 116 0.994 2.99 0.38 9.4 6 7.2 0.18 0.41 1.2 0.048 41 97 0.9919 3.14 0.45 10.4 5 8.2 0.23 0.4 7.5 0.049 12 76 0.9966 3.06 0.84 9.7 6 7.4 0.24 0.42 14 0.066 48 198 0.9979 2.89 0.42 8.9 6 7.4 0.24 0.42 14 0.066 48 198 0.9979 2.89 0.42 8.9 6 6.1 0.32 0.24 1.5 0.036 38 124 0.9898 3.29 0.42 12.4 7 5.2 0.44 0.04 1.4 0.036 43 119 0.9894 3.36 0.33 12.1 8 5.2 0.44 0.04 1.4 0.036 43 119 0.9894 3.36 0.33 12.1 8 6.1 0.32 0.24 1.5 0.036 38 124 0.9898 3.29 0.42 12.4 7 6.4 0.22 0.56 14.5 0.055 27 159 0.998 2.98 0.4 9.1 5 6.3 0.36 0.3 4.8 0.049 14 85 0.9932 3.28 0.39 10.6 5 7.4 0.24 0.42 14 0.066 48 198 0.9979 2.89 0.42 8.9 6 6.7 0.24 0.35 13.1 0.05 64 205 0.997 3.15 0.5 9.5 5 7 0.23 0.36 13 0.051 72 177 0.9972 3.16 0.49 9.8 5 8.4 0.27 0.46 8.7 0.048 39 197 0.9974 3.14 0.59 9.6 6 6.7 0.46 0.18 2.4 0.034 25 98 0.9896 3.08 0.44 12.6 7 7.5 0.29 0.31 8.95 0.055 20 151 0.9968 3.08 0.54 9.3 5 9.8 0.42 0.48 9.85 0.034 5 110 0.9958 2.87 0.29 10 5 7.1 0.3 0.46 1.5 0.066 29 133 0.9906 3.12 0.54 12.7 6 7.9 0.19 0.45 1.5 0.045 17 96 0.9917 3.13 0.39 11 6 7.6 0.48 0.37 0.8 0.037 4 100 0.9902 3.03 0.39 11.4 4 6.3 0.22 0.43 4.55 0.038 31 130 0.9918 3.35 0.33 11.5 7 7.5 0.27 0.31 17.7 0.051 33 173 0.999 3.09 0.64 10.2 5 6.9 0.23 0.4 7.5 0.04 50 151 0.9927 3.11 0.27 11.4 6 7.2 0.32 0.47 5.1 0.044 19 65 0.991 3.03 0.41 12.6 4 5.9 0.23 0.3 12.9 0.054 57 170 0.9972 3.28 0.39 9.4 5 6 0.67 0.07 1.2 0.06 9 108 0.9931 3.11 0.35 8.7 4 6.4 0.25 0.32 5.5 0.049 41 176 0.995 3.19 0.68 9.2 6 6.4 0.33 0.31 5.5 0.048 42 173 0.9951 3.19 0.66 9.3 6 7.1 0.34 0.15 1.2 0.053 61 183 0.9936 3.09 0.43 9.2 5 6.8 0.28 0.4 22 0.048 48 167 1.001 2.93 0.5 8.7 5 6.9 0.27 0.4 14 0.05 64 227 0.9979 3.18 0.58 9.6 6 6.8 0.26 0.56 11.9 0.043 64 226 0.997 3.02 0.63 9.3 5 6.8 0.29 0.56 11.9 0.043 66 230 0.9972 3.02 0.63 9.3 5 6.7 0.24 0.41 9.4 0.04 49 166 0.9954 3.12 0.61 9.9 6 5.9 0.3 0.23 4.2 0.038 42 119 0.9924 3.15 0.5 11 5 6.8 0.53 0.35 3.8 0.034 26 109 0.9906 3.26 0.57 12.7 8 6.5 0.28 0.28 8.5 0.047 54 210 0.9962 3.09 0.54 8.9 4 6.6 0.28 0.28 8.5 0.052 55 211 0.9962 3.09 0.55 8.9 6 6.8 0.28 0.4 22 0.048 48 167 1.001 2.93 0.5 8.7 5 6.8 0.28 0.36 8 0.045 28 123 0.9928 3.02 0.37 11.4 6 6.6 0.15 0.34 5.1 0.055 34 125 0.9942 3.36 0.42 9.6 5 6.4 0.29 0.44 3.6 0.2 75 181 0.9942 3.02 0.41 9.1 5 6.4 0.3 0.45 3.5 0.197 76 180 0.9942 3.02 0.39 9.1 6 6.4 0.29 0.44 3.6 0.197 75 183 0.9942 3.01 0.38 9.1 5 6.8 0.26 0.24 7.8 0.052 54 214 0.9961 3.13 0.47 8.9 5 7.1 0.32 0.24 13.1 0.05 52 204 0.998 3.1 0.49 8.8 5 6.8 0.26 0.24 7.8 0.052 54 214 0.9961 3.13 0.47 8.9 5 6.8 0.27 0.26 16.1 0.049 55 196 0.9984 3.15 0.5 9.3 5 7.1 0.32 0.24 13.1 0.05 52 204 0.998 3.1 0.49 8.8 5 6.9 0.54 0.32 13.2 0.05 53 236 0.9973 3.2 0.5 9.6 5 6.8 0.26 0.34 13.9 0.034 39 134 0.9949 3.33 0.53 12 6 5.8 0.28 0.35 2.3 0.053 36 114 0.9924 3.28 0.5 10.2 4 6.4 0.21 0.5 11.6 0.042 45 153 0.9972 3.15 0.43 8.8 5 7 0.16 0.32 8.3 0.045 38 126 0.9958 3.21 0.34 9.2 5 10.2 0.44 0.88 6.2 0.049 20 124 0.9968 2.99 0.51 9.9 4 6.8 0.57 0.29 2.2 0.04 15 77 0.9938 3.32 0.74 10.2 5 6.1 0.4 0.31 0.9 0.048 23 170 0.993 3.22 0.77 9.5 6 5.6 0.245 0.25 9.7 0.032 12 68 0.994 3.31 0.34 10.5 5 6.8 0.18 0.38 1.4 0.038 35 111 0.9918 3.32 0.59 11.2 7 7 0.16 0.32 8.3 0.045 38 126 0.9958 3.21 0.34 9.2 5 6.7 0.13 0.29 5.3 0.051 31 122 0.9944 3.44 0.37 9.7 6 6.2 0.25 0.25 1.4 0.03 35 105 0.9912 3.3 0.44 11.1 7 5.8 0.26 0.24 9.2 0.044 55 152 0.9961 3.31 0.38 9.4 5 7.5 0.27 0.36 7 0.036 45 164 0.9939 3.03 0.33 11 5 5.8 0.26 0.24 9.2 0.044 55 152 0.9961 3.31 0.38 9.4 5 5.7 0.28 0.24 17.5 0.044 60 167 0.9989 3.31 0.44 9.4 5 7.5 0.23 0.36 7 0.036 43 161 0.9938 3.04 0.32 11 5 7.5 0.27 0.36 7 0.036 45 164 0.9939 3.03 0.33 11 5 7.2 0.685 0.21 9.5 0.07 33 172 0.9971 3 0.55 9.1 6 6.2 0.25 0.25 1.4 0.03 35 105 0.9912 3.3 0.44 11.1 7 6.5 0.19 0.3 0.8 0.043 33 144 0.9936 3.42 0.39 9.1 6 6.3 0.495 0.22 1.8 0.046 31 140 0.9929 3.39 0.54 10.4 6 7.1 0.24 0.41 17.8 0.046 39 145 0.9998 3.32 0.39 8.7 5 6.4 0.17 0.32 2.4 0.048 41 200 0.9938 3.5 0.5 9.7 6 7.1 0.25 0.32 10.3 0.041 66 272 0.9969 3.17 0.52 9.1 6 6.4 0.17 0.32 2.4 0.048 41 200 0.9938 3.5 0.5 9.7 6 7.1 0.24 0.41 17.8 0.046 39 145 0.9998 3.32 0.39 8.7 5 6.8 0.64 0.08 9.7 0.062 26 142 0.9972 3.37 0.46 8.9 4 8.3 0.28 0.4 7.8 0.041 38 194 0.9976 3.34 0.51 9.6 6 8.2 0.27 0.39 7.8 0.039 49 208 0.9976 3.31 0.51 9.5 6 7.2 0.23 0.38 14.3 0.058 55 194 0.9979 3.09 0.44 9 6 7.2 0.23 0.38 14.3 0.058 55 194 0.9979 3.09 0.44 9 6 7.2 0.23 0.38 14.3 0.058 55 194 0.9979 3.09 0.44 9 6 7.2 0.23 0.38 14.3 0.058 55 194 0.9979 3.09 0.44 9 6 6.8 0.52 0.32 13.2 0.044 54 221 0.9972 3.27 0.5 9.6 6 7 0.26 0.59 1.4 0.037 40 120 0.9918 3.34 0.41 11.1 7 6.2 0.25 0.21 15.55 0.039 28 159 0.9982 3.48 0.64 9.6 6 7.3 0.32 0.23 13.7 0.05 49 197 0.9985 3.2 0.46 8.7 5 7.7 0.31 0.26 7.8 0.031 23 90 0.9944 3.13 0.5 10.4 5 7.1 0.21 0.37 2.4 0.026 23 100 0.9903 3.15 0.38 11.4 7 6.8 0.24 0.34 2.7 0.047 64.5 218.5 0.9934 3.3 0.58 9.7 6 6.9 0.4 0.56 11.2 0.043 40 142 0.9975 3.14 0.46 8.7 5 6.1 0.18 0.36 2 0.038 20 249.5 0.9923 3.37 0.79 11.3 6 6.8 0.21 0.27 2.1 0.03 26 139 0.99 3.16 0.61 12.6 7 5.8 0.2 0.27 1.4 0.031 12 77 0.9905 3.25 0.36 10.9 7 5.6 0.19 0.26 1.4 0.03 12 76 0.9905 3.25 0.37 10.9 7 6.1 0.41 0.14 10.4 0.037 18 119 0.996 3.38 0.45 10 5 5.9 0.21 0.28 4.6 0.053 40 199 0.9964 3.72 0.7 10 4 8.5 0.26 0.21 16.2 0.074 41 197 0.998 3.02 0.5 9.8 3 6.9 0.4 0.56 11.2 0.043 40 142 0.9975 3.14 0.46 8.7 5 5.8 0.24 0.44 3.5 0.029 5 109 0.9913 3.53 0.43 11.7 3 5.8 0.24 0.39 1.5 0.054 37 158 0.9932 3.21 0.52 9.3 6 6.7 0.26 0.39 1.1 0.04 45 147 0.9935 3.32 0.58 9.6 8 6.3 0.35 0.3 5.7 0.035 8 97 0.9927 3.27 0.41 11 7 6.3 0.35 0.3 5.7 0.035 8 97 0.9927 3.27 0.41 11 7 6.4 0.23 0.39 1.8 0.032 23 118 0.9912 3.32 0.5 11.8 6 5.8 0.36 0.38 0.9 0.037 3 75 0.9904 3.28 0.34 11.4 4 6.9 0.115 0.35 5.4 0.048 36 108 0.9939 3.32 0.42 10.2 6 6.9 0.29 0.4 19.45 0.043 36 156 0.9996 2.93 0.47 8.9 5 6.9 0.28 0.4 8.2 0.036 15 95 0.9944 3.17 0.33 10.2 5 7.2 0.29 0.4 13.6 0.045 66 231 0.9977 3.08 0.59 9.6 6 6.2 0.24 0.35 1.2 0.038 22 167 0.9912 3.1 0.48 10.6 6 6.9 0.29 0.4 19.45 0.043 36 156 0.9996 2.93 0.47 8.9 5 6.9 0.32 0.26 8.3 0.053 32 180 0.9965 3.25 0.51 9.2 6 5.3 0.58 0.07 6.9 0.043 34 149 0.9944 3.34 0.57 9.7 5 5.3 0.585 0.07 7.1 0.044 34 145 0.9945 3.34 0.57 9.7 6 5.4 0.59 0.07 7 0.045 36 147 0.9944 3.34 0.57 9.7 6 6.9 0.32 0.26 8.3 0.053 32 180 0.9965 3.25 0.51 9.2 6 5.2 0.6 0.07 7 0.044 33 147 0.9944 3.33 0.58 9.7 5 5.8 0.25 0.26 13.1 0.051 44 148 0.9972 3.29 0.38 9.3 5 6.6 0.58 0.3 5.1 0.057 30 123 0.9949 3.24 0.38 9 5 7 0.29 0.54 10.7 0.046 59 234 0.9966 3.05 0.61 9.5 5 6.6 0.19 0.41 8.9 0.046 51 169 0.9954 3.14 0.57 9.8 6 6.7 0.2 0.41 9.1 0.044 50 166 0.9954 3.14 0.58 9.8 6 7.7 0.26 0.4 1.1 0.042 9 60 0.9915 2.89 0.5 10.6 5 6.8 0.32 0.34 1.2 0.044 14 67 0.9919 3.05 0.47 10.6 4 7 0.3 0.49 4.7 0.036 17 105 0.9916 3.26 0.68 12.4 7 7 0.24 0.36 2.8 0.034 22 112 0.99 3.19 0.38 12.6 8 6.1 0.31 0.58 5 0.039 36 114 0.9909 3.3 0.6 12.3 8 6.8 0.44 0.37 5.1 0.047 46 201 0.9938 3.08 0.65 10.5 4 6.7 0.34 0.3 15.6 0.054 51 196 0.9982 3.19 0.49 9.3 5 7.1 0.35 0.24 15.4 0.055 46 198 0.9988 3.12 0.49 8.8 5 7.3 0.32 0.25 7.2 0.056 47 180 0.9961 3.08 0.47 8.8 5 6.5 0.28 0.33 15.7 0.053 51 190 0.9978 3.22 0.51 9.7 6 7.2 0.23 0.39 14.2 0.058 49 192 0.9979 2.98 0.48 9 7 7.2 0.23 0.39 14.2 0.058 49 192 0.9979 2.98 0.48 9 7 7.2 0.23 0.39 14.2 0.058 49 192 0.9979 2.98 0.48 9 7 7.2 0.23 0.39 14.2 0.058 49 192 0.9979 2.98 0.48 9 7 5.9 0.15 0.31 5.8 0.041 53 155 0.9945 3.52 0.46 10.5 6 7.4 0.28 0.42 19.8 0.066 53 195 1 2.96 0.44 9.1 5 6.2 0.28 0.22 7.3 0.041 26 157 0.9957 3.44 0.64 9.8 7 9.1 0.59 0.38 1.6 0.066 34 182 0.9968 3.23 0.38 8.5 3 6.3 0.33 0.27 1.2 0.046 34 175 0.9934 3.37 0.54 9.4 6 8.3 0.39 0.7 10.6 0.045 33 169 0.9976 3.09 0.57 9.4 5 7.2 0.19 0.46 3.8 0.041 82 187 0.9932 3.19 0.6 11.2 7
Names of X columns:
fixedAcidity volatileAcidity citricAcid residualSugar chlorides freeSulfurDioxide totSulfurDioxide density pH sulphates alcohol quality
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') }
Compute
Summary of computational transaction
Raw Input
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Raw Output
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Computing time
0 seconds
R Server
Big Analytics Cloud Computing Center
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