library(MASS)
Boston
## crim zn indus chas nox rm age dis rad tax ptratio black
## 1 0.00632 18.0 2.31 0 0.5380 6.575 65.2 4.0900 1 296 15.3 396.90
## 2 0.02731 0.0 7.07 0 0.4690 6.421 78.9 4.9671 2 242 17.8 396.90
## 3 0.02729 0.0 7.07 0 0.4690 7.185 61.1 4.9671 2 242 17.8 392.83
## 4 0.03237 0.0 2.18 0 0.4580 6.998 45.8 6.0622 3 222 18.7 394.63
## 5 0.06905 0.0 2.18 0 0.4580 7.147 54.2 6.0622 3 222 18.7 396.90
## 6 0.02985 0.0 2.18 0 0.4580 6.430 58.7 6.0622 3 222 18.7 394.12
## 7 0.08829 12.5 7.87 0 0.5240 6.012 66.6 5.5605 5 311 15.2 395.60
## 8 0.14455 12.5 7.87 0 0.5240 6.172 96.1 5.9505 5 311 15.2 396.90
## 9 0.21124 12.5 7.87 0 0.5240 5.631 100.0 6.0821 5 311 15.2 386.63
## 10 0.17004 12.5 7.87 0 0.5240 6.004 85.9 6.5921 5 311 15.2 386.71
## 11 0.22489 12.5 7.87 0 0.5240 6.377 94.3 6.3467 5 311 15.2 392.52
## 12 0.11747 12.5 7.87 0 0.5240 6.009 82.9 6.2267 5 311 15.2 396.90
## 13 0.09378 12.5 7.87 0 0.5240 5.889 39.0 5.4509 5 311 15.2 390.50
## 14 0.62976 0.0 8.14 0 0.5380 5.949 61.8 4.7075 4 307 21.0 396.90
## 15 0.63796 0.0 8.14 0 0.5380 6.096 84.5 4.4619 4 307 21.0 380.02
## 16 0.62739 0.0 8.14 0 0.5380 5.834 56.5 4.4986 4 307 21.0 395.62
## 17 1.05393 0.0 8.14 0 0.5380 5.935 29.3 4.4986 4 307 21.0 386.85
## 18 0.78420 0.0 8.14 0 0.5380 5.990 81.7 4.2579 4 307 21.0 386.75
## 19 0.80271 0.0 8.14 0 0.5380 5.456 36.6 3.7965 4 307 21.0 288.99
## 20 0.72580 0.0 8.14 0 0.5380 5.727 69.5 3.7965 4 307 21.0 390.95
## 21 1.25179 0.0 8.14 0 0.5380 5.570 98.1 3.7979 4 307 21.0 376.57
## 22 0.85204 0.0 8.14 0 0.5380 5.965 89.2 4.0123 4 307 21.0 392.53
## 23 1.23247 0.0 8.14 0 0.5380 6.142 91.7 3.9769 4 307 21.0 396.90
## 24 0.98843 0.0 8.14 0 0.5380 5.813 100.0 4.0952 4 307 21.0 394.54
## 25 0.75026 0.0 8.14 0 0.5380 5.924 94.1 4.3996 4 307 21.0 394.33
## 26 0.84054 0.0 8.14 0 0.5380 5.599 85.7 4.4546 4 307 21.0 303.42
## 27 0.67191 0.0 8.14 0 0.5380 5.813 90.3 4.6820 4 307 21.0 376.88
## 28 0.95577 0.0 8.14 0 0.5380 6.047 88.8 4.4534 4 307 21.0 306.38
## 29 0.77299 0.0 8.14 0 0.5380 6.495 94.4 4.4547 4 307 21.0 387.94
## 30 1.00245 0.0 8.14 0 0.5380 6.674 87.3 4.2390 4 307 21.0 380.23
## 31 1.13081 0.0 8.14 0 0.5380 5.713 94.1 4.2330 4 307 21.0 360.17
## 32 1.35472 0.0 8.14 0 0.5380 6.072 100.0 4.1750 4 307 21.0 376.73
## 33 1.38799 0.0 8.14 0 0.5380 5.950 82.0 3.9900 4 307 21.0 232.60
## 34 1.15172 0.0 8.14 0 0.5380 5.701 95.0 3.7872 4 307 21.0 358.77
## 35 1.61282 0.0 8.14 0 0.5380 6.096 96.9 3.7598 4 307 21.0 248.31
## 36 0.06417 0.0 5.96 0 0.4990 5.933 68.2 3.3603 5 279 19.2 396.90
## 37 0.09744 0.0 5.96 0 0.4990 5.841 61.4 3.3779 5 279 19.2 377.56
## 38 0.08014 0.0 5.96 0 0.4990 5.850 41.5 3.9342 5 279 19.2 396.90
## 39 0.17505 0.0 5.96 0 0.4990 5.966 30.2 3.8473 5 279 19.2 393.43
## 40 0.02763 75.0 2.95 0 0.4280 6.595 21.8 5.4011 3 252 18.3 395.63
## 41 0.03359 75.0 2.95 0 0.4280 7.024 15.8 5.4011 3 252 18.3 395.62
## 42 0.12744 0.0 6.91 0 0.4480 6.770 2.9 5.7209 3 233 17.9 385.41
## 43 0.14150 0.0 6.91 0 0.4480 6.169 6.6 5.7209 3 233 17.9 383.37
## 44 0.15936 0.0 6.91 0 0.4480 6.211 6.5 5.7209 3 233 17.9 394.46
## 45 0.12269 0.0 6.91 0 0.4480 6.069 40.0 5.7209 3 233 17.9 389.39
## 46 0.17142 0.0 6.91 0 0.4480 5.682 33.8 5.1004 3 233 17.9 396.90
## 47 0.18836 0.0 6.91 0 0.4480 5.786 33.3 5.1004 3 233 17.9 396.90
## 48 0.22927 0.0 6.91 0 0.4480 6.030 85.5 5.6894 3 233 17.9 392.74
## 49 0.25387 0.0 6.91 0 0.4480 5.399 95.3 5.8700 3 233 17.9 396.90
## 50 0.21977 0.0 6.91 0 0.4480 5.602 62.0 6.0877 3 233 17.9 396.90
## 51 0.08873 21.0 5.64 0 0.4390 5.963 45.7 6.8147 4 243 16.8 395.56
## 52 0.04337 21.0 5.64 0 0.4390 6.115 63.0 6.8147 4 243 16.8 393.97
## 53 0.05360 21.0 5.64 0 0.4390 6.511 21.1 6.8147 4 243 16.8 396.90
## 54 0.04981 21.0 5.64 0 0.4390 5.998 21.4 6.8147 4 243 16.8 396.90
## 55 0.01360 75.0 4.00 0 0.4100 5.888 47.6 7.3197 3 469 21.1 396.90
## 56 0.01311 90.0 1.22 0 0.4030 7.249 21.9 8.6966 5 226 17.9 395.93
## 57 0.02055 85.0 0.74 0 0.4100 6.383 35.7 9.1876 2 313 17.3 396.90
## 58 0.01432 100.0 1.32 0 0.4110 6.816 40.5 8.3248 5 256 15.1 392.90
## 59 0.15445 25.0 5.13 0 0.4530 6.145 29.2 7.8148 8 284 19.7 390.68
## 60 0.10328 25.0 5.13 0 0.4530 5.927 47.2 6.9320 8 284 19.7 396.90
## 61 0.14932 25.0 5.13 0 0.4530 5.741 66.2 7.2254 8 284 19.7 395.11
## 62 0.17171 25.0 5.13 0 0.4530 5.966 93.4 6.8185 8 284 19.7 378.08
## 63 0.11027 25.0 5.13 0 0.4530 6.456 67.8 7.2255 8 284 19.7 396.90
## 64 0.12650 25.0 5.13 0 0.4530 6.762 43.4 7.9809 8 284 19.7 395.58
## 65 0.01951 17.5 1.38 0 0.4161 7.104 59.5 9.2229 3 216 18.6 393.24
## 66 0.03584 80.0 3.37 0 0.3980 6.290 17.8 6.6115 4 337 16.1 396.90
## 67 0.04379 80.0 3.37 0 0.3980 5.787 31.1 6.6115 4 337 16.1 396.90
## 68 0.05789 12.5 6.07 0 0.4090 5.878 21.4 6.4980 4 345 18.9 396.21
## 69 0.13554 12.5 6.07 0 0.4090 5.594 36.8 6.4980 4 345 18.9 396.90
## 70 0.12816 12.5 6.07 0 0.4090 5.885 33.0 6.4980 4 345 18.9 396.90
## 71 0.08826 0.0 10.81 0 0.4130 6.417 6.6 5.2873 4 305 19.2 383.73
## 72 0.15876 0.0 10.81 0 0.4130 5.961 17.5 5.2873 4 305 19.2 376.94
## 73 0.09164 0.0 10.81 0 0.4130 6.065 7.8 5.2873 4 305 19.2 390.91
## 74 0.19539 0.0 10.81 0 0.4130 6.245 6.2 5.2873 4 305 19.2 377.17
## 75 0.07896 0.0 12.83 0 0.4370 6.273 6.0 4.2515 5 398 18.7 394.92
## 76 0.09512 0.0 12.83 0 0.4370 6.286 45.0 4.5026 5 398 18.7 383.23
## 77 0.10153 0.0 12.83 0 0.4370 6.279 74.5 4.0522 5 398 18.7 373.66
## 78 0.08707 0.0 12.83 0 0.4370 6.140 45.8 4.0905 5 398 18.7 386.96
## 79 0.05646 0.0 12.83 0 0.4370 6.232 53.7 5.0141 5 398 18.7 386.40
## 80 0.08387 0.0 12.83 0 0.4370 5.874 36.6 4.5026 5 398 18.7 396.06
## 81 0.04113 25.0 4.86 0 0.4260 6.727 33.5 5.4007 4 281 19.0 396.90
## 82 0.04462 25.0 4.86 0 0.4260 6.619 70.4 5.4007 4 281 19.0 395.63
## 83 0.03659 25.0 4.86 0 0.4260 6.302 32.2 5.4007 4 281 19.0 396.90
## 84 0.03551 25.0 4.86 0 0.4260 6.167 46.7 5.4007 4 281 19.0 390.64
## 85 0.05059 0.0 4.49 0 0.4490 6.389 48.0 4.7794 3 247 18.5 396.90
## 86 0.05735 0.0 4.49 0 0.4490 6.630 56.1 4.4377 3 247 18.5 392.30
## 87 0.05188 0.0 4.49 0 0.4490 6.015 45.1 4.4272 3 247 18.5 395.99
## 88 0.07151 0.0 4.49 0 0.4490 6.121 56.8 3.7476 3 247 18.5 395.15
## 89 0.05660 0.0 3.41 0 0.4890 7.007 86.3 3.4217 2 270 17.8 396.90
## 90 0.05302 0.0 3.41 0 0.4890 7.079 63.1 3.4145 2 270 17.8 396.06
## 91 0.04684 0.0 3.41 0 0.4890 6.417 66.1 3.0923 2 270 17.8 392.18
## 92 0.03932 0.0 3.41 0 0.4890 6.405 73.9 3.0921 2 270 17.8 393.55
## 93 0.04203 28.0 15.04 0 0.4640 6.442 53.6 3.6659 4 270 18.2 395.01
## 94 0.02875 28.0 15.04 0 0.4640 6.211 28.9 3.6659 4 270 18.2 396.33
## 95 0.04294 28.0 15.04 0 0.4640 6.249 77.3 3.6150 4 270 18.2 396.90
## 96 0.12204 0.0 2.89 0 0.4450 6.625 57.8 3.4952 2 276 18.0 357.98
## 97 0.11504 0.0 2.89 0 0.4450 6.163 69.6 3.4952 2 276 18.0 391.83
## 98 0.12083 0.0 2.89 0 0.4450 8.069 76.0 3.4952 2 276 18.0 396.90
## 99 0.08187 0.0 2.89 0 0.4450 7.820 36.9 3.4952 2 276 18.0 393.53
## 100 0.06860 0.0 2.89 0 0.4450 7.416 62.5 3.4952 2 276 18.0 396.90
## 101 0.14866 0.0 8.56 0 0.5200 6.727 79.9 2.7778 5 384 20.9 394.76
## 102 0.11432 0.0 8.56 0 0.5200 6.781 71.3 2.8561 5 384 20.9 395.58
## 103 0.22876 0.0 8.56 0 0.5200 6.405 85.4 2.7147 5 384 20.9 70.80
## 104 0.21161 0.0 8.56 0 0.5200 6.137 87.4 2.7147 5 384 20.9 394.47
## 105 0.13960 0.0 8.56 0 0.5200 6.167 90.0 2.4210 5 384 20.9 392.69
## 106 0.13262 0.0 8.56 0 0.5200 5.851 96.7 2.1069 5 384 20.9 394.05
## 107 0.17120 0.0 8.56 0 0.5200 5.836 91.9 2.2110 5 384 20.9 395.67
## 108 0.13117 0.0 8.56 0 0.5200 6.127 85.2 2.1224 5 384 20.9 387.69
## 109 0.12802 0.0 8.56 0 0.5200 6.474 97.1 2.4329 5 384 20.9 395.24
## 110 0.26363 0.0 8.56 0 0.5200 6.229 91.2 2.5451 5 384 20.9 391.23
## 111 0.10793 0.0 8.56 0 0.5200 6.195 54.4 2.7778 5 384 20.9 393.49
## 112 0.10084 0.0 10.01 0 0.5470 6.715 81.6 2.6775 6 432 17.8 395.59
## 113 0.12329 0.0 10.01 0 0.5470 5.913 92.9 2.3534 6 432 17.8 394.95
## 114 0.22212 0.0 10.01 0 0.5470 6.092 95.4 2.5480 6 432 17.8 396.90
## 115 0.14231 0.0 10.01 0 0.5470 6.254 84.2 2.2565 6 432 17.8 388.74
## 116 0.17134 0.0 10.01 0 0.5470 5.928 88.2 2.4631 6 432 17.8 344.91
## 117 0.13158 0.0 10.01 0 0.5470 6.176 72.5 2.7301 6 432 17.8 393.30
## 118 0.15098 0.0 10.01 0 0.5470 6.021 82.6 2.7474 6 432 17.8 394.51
## 119 0.13058 0.0 10.01 0 0.5470 5.872 73.1 2.4775 6 432 17.8 338.63
## 120 0.14476 0.0 10.01 0 0.5470 5.731 65.2 2.7592 6 432 17.8 391.50
## 121 0.06899 0.0 25.65 0 0.5810 5.870 69.7 2.2577 2 188 19.1 389.15
## 122 0.07165 0.0 25.65 0 0.5810 6.004 84.1 2.1974 2 188 19.1 377.67
## 123 0.09299 0.0 25.65 0 0.5810 5.961 92.9 2.0869 2 188 19.1 378.09
## 124 0.15038 0.0 25.65 0 0.5810 5.856 97.0 1.9444 2 188 19.1 370.31
## 125 0.09849 0.0 25.65 0 0.5810 5.879 95.8 2.0063 2 188 19.1 379.38
## 126 0.16902 0.0 25.65 0 0.5810 5.986 88.4 1.9929 2 188 19.1 385.02
## 127 0.38735 0.0 25.65 0 0.5810 5.613 95.6 1.7572 2 188 19.1 359.29
## 128 0.25915 0.0 21.89 0 0.6240 5.693 96.0 1.7883 4 437 21.2 392.11
## 129 0.32543 0.0 21.89 0 0.6240 6.431 98.8 1.8125 4 437 21.2 396.90
## 130 0.88125 0.0 21.89 0 0.6240 5.637 94.7 1.9799 4 437 21.2 396.90
## 131 0.34006 0.0 21.89 0 0.6240 6.458 98.9 2.1185 4 437 21.2 395.04
## 132 1.19294 0.0 21.89 0 0.6240 6.326 97.7 2.2710 4 437 21.2 396.90
## 133 0.59005 0.0 21.89 0 0.6240 6.372 97.9 2.3274 4 437 21.2 385.76
## 134 0.32982 0.0 21.89 0 0.6240 5.822 95.4 2.4699 4 437 21.2 388.69
## 135 0.97617 0.0 21.89 0 0.6240 5.757 98.4 2.3460 4 437 21.2 262.76
## 136 0.55778 0.0 21.89 0 0.6240 6.335 98.2 2.1107 4 437 21.2 394.67
## 137 0.32264 0.0 21.89 0 0.6240 5.942 93.5 1.9669 4 437 21.2 378.25
## 138 0.35233 0.0 21.89 0 0.6240 6.454 98.4 1.8498 4 437 21.2 394.08
## 139 0.24980 0.0 21.89 0 0.6240 5.857 98.2 1.6686 4 437 21.2 392.04
## 140 0.54452 0.0 21.89 0 0.6240 6.151 97.9 1.6687 4 437 21.2 396.90
## 141 0.29090 0.0 21.89 0 0.6240 6.174 93.6 1.6119 4 437 21.2 388.08
## 142 1.62864 0.0 21.89 0 0.6240 5.019 100.0 1.4394 4 437 21.2 396.90
## 143 3.32105 0.0 19.58 1 0.8710 5.403 100.0 1.3216 5 403 14.7 396.90
## 144 4.09740 0.0 19.58 0 0.8710 5.468 100.0 1.4118 5 403 14.7 396.90
## 145 2.77974 0.0 19.58 0 0.8710 4.903 97.8 1.3459 5 403 14.7 396.90
## 146 2.37934 0.0 19.58 0 0.8710 6.130 100.0 1.4191 5 403 14.7 172.91
## 147 2.15505 0.0 19.58 0 0.8710 5.628 100.0 1.5166 5 403 14.7 169.27
## 148 2.36862 0.0 19.58 0 0.8710 4.926 95.7 1.4608 5 403 14.7 391.71
## 149 2.33099 0.0 19.58 0 0.8710 5.186 93.8 1.5296 5 403 14.7 356.99
## 150 2.73397 0.0 19.58 0 0.8710 5.597 94.9 1.5257 5 403 14.7 351.85
## 151 1.65660 0.0 19.58 0 0.8710 6.122 97.3 1.6180 5 403 14.7 372.80
## 152 1.49632 0.0 19.58 0 0.8710 5.404 100.0 1.5916 5 403 14.7 341.60
## 153 1.12658 0.0 19.58 1 0.8710 5.012 88.0 1.6102 5 403 14.7 343.28
## 154 2.14918 0.0 19.58 0 0.8710 5.709 98.5 1.6232 5 403 14.7 261.95
## 155 1.41385 0.0 19.58 1 0.8710 6.129 96.0 1.7494 5 403 14.7 321.02
## 156 3.53501 0.0 19.58 1 0.8710 6.152 82.6 1.7455 5 403 14.7 88.01
## 157 2.44668 0.0 19.58 0 0.8710 5.272 94.0 1.7364 5 403 14.7 88.63
## 158 1.22358 0.0 19.58 0 0.6050 6.943 97.4 1.8773 5 403 14.7 363.43
## 159 1.34284 0.0 19.58 0 0.6050 6.066 100.0 1.7573 5 403 14.7 353.89
## 160 1.42502 0.0 19.58 0 0.8710 6.510 100.0 1.7659 5 403 14.7 364.31
## 161 1.27346 0.0 19.58 1 0.6050 6.250 92.6 1.7984 5 403 14.7 338.92
## 162 1.46336 0.0 19.58 0 0.6050 7.489 90.8 1.9709 5 403 14.7 374.43
## 163 1.83377 0.0 19.58 1 0.6050 7.802 98.2 2.0407 5 403 14.7 389.61
## 164 1.51902 0.0 19.58 1 0.6050 8.375 93.9 2.1620 5 403 14.7 388.45
## 165 2.24236 0.0 19.58 0 0.6050 5.854 91.8 2.4220 5 403 14.7 395.11
## 166 2.92400 0.0 19.58 0 0.6050 6.101 93.0 2.2834 5 403 14.7 240.16
## 167 2.01019 0.0 19.58 0 0.6050 7.929 96.2 2.0459 5 403 14.7 369.30
## 168 1.80028 0.0 19.58 0 0.6050 5.877 79.2 2.4259 5 403 14.7 227.61
## 169 2.30040 0.0 19.58 0 0.6050 6.319 96.1 2.1000 5 403 14.7 297.09
## 170 2.44953 0.0 19.58 0 0.6050 6.402 95.2 2.2625 5 403 14.7 330.04
## 171 1.20742 0.0 19.58 0 0.6050 5.875 94.6 2.4259 5 403 14.7 292.29
## 172 2.31390 0.0 19.58 0 0.6050 5.880 97.3 2.3887 5 403 14.7 348.13
## 173 0.13914 0.0 4.05 0 0.5100 5.572 88.5 2.5961 5 296 16.6 396.90
## 174 0.09178 0.0 4.05 0 0.5100 6.416 84.1 2.6463 5 296 16.6 395.50
## 175 0.08447 0.0 4.05 0 0.5100 5.859 68.7 2.7019 5 296 16.6 393.23
## 176 0.06664 0.0 4.05 0 0.5100 6.546 33.1 3.1323 5 296 16.6 390.96
## 177 0.07022 0.0 4.05 0 0.5100 6.020 47.2 3.5549 5 296 16.6 393.23
## 178 0.05425 0.0 4.05 0 0.5100 6.315 73.4 3.3175 5 296 16.6 395.60
## 179 0.06642 0.0 4.05 0 0.5100 6.860 74.4 2.9153 5 296 16.6 391.27
## 180 0.05780 0.0 2.46 0 0.4880 6.980 58.4 2.8290 3 193 17.8 396.90
## 181 0.06588 0.0 2.46 0 0.4880 7.765 83.3 2.7410 3 193 17.8 395.56
## 182 0.06888 0.0 2.46 0 0.4880 6.144 62.2 2.5979 3 193 17.8 396.90
## 183 0.09103 0.0 2.46 0 0.4880 7.155 92.2 2.7006 3 193 17.8 394.12
## 184 0.10008 0.0 2.46 0 0.4880 6.563 95.6 2.8470 3 193 17.8 396.90
## 185 0.08308 0.0 2.46 0 0.4880 5.604 89.8 2.9879 3 193 17.8 391.00
## 186 0.06047 0.0 2.46 0 0.4880 6.153 68.8 3.2797 3 193 17.8 387.11
## 187 0.05602 0.0 2.46 0 0.4880 7.831 53.6 3.1992 3 193 17.8 392.63
## 188 0.07875 45.0 3.44 0 0.4370 6.782 41.1 3.7886 5 398 15.2 393.87
## 189 0.12579 45.0 3.44 0 0.4370 6.556 29.1 4.5667 5 398 15.2 382.84
## 190 0.08370 45.0 3.44 0 0.4370 7.185 38.9 4.5667 5 398 15.2 396.90
## 191 0.09068 45.0 3.44 0 0.4370 6.951 21.5 6.4798 5 398 15.2 377.68
## 192 0.06911 45.0 3.44 0 0.4370 6.739 30.8 6.4798 5 398 15.2 389.71
## 193 0.08664 45.0 3.44 0 0.4370 7.178 26.3 6.4798 5 398 15.2 390.49
## 194 0.02187 60.0 2.93 0 0.4010 6.800 9.9 6.2196 1 265 15.6 393.37
## 195 0.01439 60.0 2.93 0 0.4010 6.604 18.8 6.2196 1 265 15.6 376.70
## 196 0.01381 80.0 0.46 0 0.4220 7.875 32.0 5.6484 4 255 14.4 394.23
## 197 0.04011 80.0 1.52 0 0.4040 7.287 34.1 7.3090 2 329 12.6 396.90
## 198 0.04666 80.0 1.52 0 0.4040 7.107 36.6 7.3090 2 329 12.6 354.31
## 199 0.03768 80.0 1.52 0 0.4040 7.274 38.3 7.3090 2 329 12.6 392.20
## 200 0.03150 95.0 1.47 0 0.4030 6.975 15.3 7.6534 3 402 17.0 396.90
## 201 0.01778 95.0 1.47 0 0.4030 7.135 13.9 7.6534 3 402 17.0 384.30
## 202 0.03445 82.5 2.03 0 0.4150 6.162 38.4 6.2700 2 348 14.7 393.77
## 203 0.02177 82.5 2.03 0 0.4150 7.610 15.7 6.2700 2 348 14.7 395.38
## 204 0.03510 95.0 2.68 0 0.4161 7.853 33.2 5.1180 4 224 14.7 392.78
## 205 0.02009 95.0 2.68 0 0.4161 8.034 31.9 5.1180 4 224 14.7 390.55
## 206 0.13642 0.0 10.59 0 0.4890 5.891 22.3 3.9454 4 277 18.6 396.90
## 207 0.22969 0.0 10.59 0 0.4890 6.326 52.5 4.3549 4 277 18.6 394.87
## 208 0.25199 0.0 10.59 0 0.4890 5.783 72.7 4.3549 4 277 18.6 389.43
## 209 0.13587 0.0 10.59 1 0.4890 6.064 59.1 4.2392 4 277 18.6 381.32
## 210 0.43571 0.0 10.59 1 0.4890 5.344 100.0 3.8750 4 277 18.6 396.90
## 211 0.17446 0.0 10.59 1 0.4890 5.960 92.1 3.8771 4 277 18.6 393.25
## 212 0.37578 0.0 10.59 1 0.4890 5.404 88.6 3.6650 4 277 18.6 395.24
## 213 0.21719 0.0 10.59 1 0.4890 5.807 53.8 3.6526 4 277 18.6 390.94
## 214 0.14052 0.0 10.59 0 0.4890 6.375 32.3 3.9454 4 277 18.6 385.81
## 215 0.28955 0.0 10.59 0 0.4890 5.412 9.8 3.5875 4 277 18.6 348.93
## 216 0.19802 0.0 10.59 0 0.4890 6.182 42.4 3.9454 4 277 18.6 393.63
## 217 0.04560 0.0 13.89 1 0.5500 5.888 56.0 3.1121 5 276 16.4 392.80
## 218 0.07013 0.0 13.89 0 0.5500 6.642 85.1 3.4211 5 276 16.4 392.78
## 219 0.11069 0.0 13.89 1 0.5500 5.951 93.8 2.8893 5 276 16.4 396.90
## 220 0.11425 0.0 13.89 1 0.5500 6.373 92.4 3.3633 5 276 16.4 393.74
## 221 0.35809 0.0 6.20 1 0.5070 6.951 88.5 2.8617 8 307 17.4 391.70
## 222 0.40771 0.0 6.20 1 0.5070 6.164 91.3 3.0480 8 307 17.4 395.24
## 223 0.62356 0.0 6.20 1 0.5070 6.879 77.7 3.2721 8 307 17.4 390.39
## 224 0.61470 0.0 6.20 0 0.5070 6.618 80.8 3.2721 8 307 17.4 396.90
## 225 0.31533 0.0 6.20 0 0.5040 8.266 78.3 2.8944 8 307 17.4 385.05
## 226 0.52693 0.0 6.20 0 0.5040 8.725 83.0 2.8944 8 307 17.4 382.00
## 227 0.38214 0.0 6.20 0 0.5040 8.040 86.5 3.2157 8 307 17.4 387.38
## 228 0.41238 0.0 6.20 0 0.5040 7.163 79.9 3.2157 8 307 17.4 372.08
## 229 0.29819 0.0 6.20 0 0.5040 7.686 17.0 3.3751 8 307 17.4 377.51
## 230 0.44178 0.0 6.20 0 0.5040 6.552 21.4 3.3751 8 307 17.4 380.34
## 231 0.53700 0.0 6.20 0 0.5040 5.981 68.1 3.6715 8 307 17.4 378.35
## 232 0.46296 0.0 6.20 0 0.5040 7.412 76.9 3.6715 8 307 17.4 376.14
## 233 0.57529 0.0 6.20 0 0.5070 8.337 73.3 3.8384 8 307 17.4 385.91
## 234 0.33147 0.0 6.20 0 0.5070 8.247 70.4 3.6519 8 307 17.4 378.95
## 235 0.44791 0.0 6.20 1 0.5070 6.726 66.5 3.6519 8 307 17.4 360.20
## 236 0.33045 0.0 6.20 0 0.5070 6.086 61.5 3.6519 8 307 17.4 376.75
## 237 0.52058 0.0 6.20 1 0.5070 6.631 76.5 4.1480 8 307 17.4 388.45
## 238 0.51183 0.0 6.20 0 0.5070 7.358 71.6 4.1480 8 307 17.4 390.07
## 239 0.08244 30.0 4.93 0 0.4280 6.481 18.5 6.1899 6 300 16.6 379.41
## 240 0.09252 30.0 4.93 0 0.4280 6.606 42.2 6.1899 6 300 16.6 383.78
## 241 0.11329 30.0 4.93 0 0.4280 6.897 54.3 6.3361 6 300 16.6 391.25
## 242 0.10612 30.0 4.93 0 0.4280 6.095 65.1 6.3361 6 300 16.6 394.62
## 243 0.10290 30.0 4.93 0 0.4280 6.358 52.9 7.0355 6 300 16.6 372.75
## 244 0.12757 30.0 4.93 0 0.4280 6.393 7.8 7.0355 6 300 16.6 374.71
## 245 0.20608 22.0 5.86 0 0.4310 5.593 76.5 7.9549 7 330 19.1 372.49
## 246 0.19133 22.0 5.86 0 0.4310 5.605 70.2 7.9549 7 330 19.1 389.13
## 247 0.33983 22.0 5.86 0 0.4310 6.108 34.9 8.0555 7 330 19.1 390.18
## 248 0.19657 22.0 5.86 0 0.4310 6.226 79.2 8.0555 7 330 19.1 376.14
## 249 0.16439 22.0 5.86 0 0.4310 6.433 49.1 7.8265 7 330 19.1 374.71
## 250 0.19073 22.0 5.86 0 0.4310 6.718 17.5 7.8265 7 330 19.1 393.74
## 251 0.14030 22.0 5.86 0 0.4310 6.487 13.0 7.3967 7 330 19.1 396.28
## 252 0.21409 22.0 5.86 0 0.4310 6.438 8.9 7.3967 7 330 19.1 377.07
## 253 0.08221 22.0 5.86 0 0.4310 6.957 6.8 8.9067 7 330 19.1 386.09
## 254 0.36894 22.0 5.86 0 0.4310 8.259 8.4 8.9067 7 330 19.1 396.90
## 255 0.04819 80.0 3.64 0 0.3920 6.108 32.0 9.2203 1 315 16.4 392.89
## 256 0.03548 80.0 3.64 0 0.3920 5.876 19.1 9.2203 1 315 16.4 395.18
## 257 0.01538 90.0 3.75 0 0.3940 7.454 34.2 6.3361 3 244 15.9 386.34
## 258 0.61154 20.0 3.97 0 0.6470 8.704 86.9 1.8010 5 264 13.0 389.70
## 259 0.66351 20.0 3.97 0 0.6470 7.333 100.0 1.8946 5 264 13.0 383.29
## 260 0.65665 20.0 3.97 0 0.6470 6.842 100.0 2.0107 5 264 13.0 391.93
## 261 0.54011 20.0 3.97 0 0.6470 7.203 81.8 2.1121 5 264 13.0 392.80
## 262 0.53412 20.0 3.97 0 0.6470 7.520 89.4 2.1398 5 264 13.0 388.37
## 263 0.52014 20.0 3.97 0 0.6470 8.398 91.5 2.2885 5 264 13.0 386.86
## 264 0.82526 20.0 3.97 0 0.6470 7.327 94.5 2.0788 5 264 13.0 393.42
## 265 0.55007 20.0 3.97 0 0.6470 7.206 91.6 1.9301 5 264 13.0 387.89
## 266 0.76162 20.0 3.97 0 0.6470 5.560 62.8 1.9865 5 264 13.0 392.40
## 267 0.78570 20.0 3.97 0 0.6470 7.014 84.6 2.1329 5 264 13.0 384.07
## 268 0.57834 20.0 3.97 0 0.5750 8.297 67.0 2.4216 5 264 13.0 384.54
## 269 0.54050 20.0 3.97 0 0.5750 7.470 52.6 2.8720 5 264 13.0 390.30
## 270 0.09065 20.0 6.96 1 0.4640 5.920 61.5 3.9175 3 223 18.6 391.34
## 271 0.29916 20.0 6.96 0 0.4640 5.856 42.1 4.4290 3 223 18.6 388.65
## 272 0.16211 20.0 6.96 0 0.4640 6.240 16.3 4.4290 3 223 18.6 396.90
## 273 0.11460 20.0 6.96 0 0.4640 6.538 58.7 3.9175 3 223 18.6 394.96
## 274 0.22188 20.0 6.96 1 0.4640 7.691 51.8 4.3665 3 223 18.6 390.77
## 275 0.05644 40.0 6.41 1 0.4470 6.758 32.9 4.0776 4 254 17.6 396.90
## 276 0.09604 40.0 6.41 0 0.4470 6.854 42.8 4.2673 4 254 17.6 396.90
## 277 0.10469 40.0 6.41 1 0.4470 7.267 49.0 4.7872 4 254 17.6 389.25
## 278 0.06127 40.0 6.41 1 0.4470 6.826 27.6 4.8628 4 254 17.6 393.45
## 279 0.07978 40.0 6.41 0 0.4470 6.482 32.1 4.1403 4 254 17.6 396.90
## 280 0.21038 20.0 3.33 0 0.4429 6.812 32.2 4.1007 5 216 14.9 396.90
## 281 0.03578 20.0 3.33 0 0.4429 7.820 64.5 4.6947 5 216 14.9 387.31
## 282 0.03705 20.0 3.33 0 0.4429 6.968 37.2 5.2447 5 216 14.9 392.23
## 283 0.06129 20.0 3.33 1 0.4429 7.645 49.7 5.2119 5 216 14.9 377.07
## 284 0.01501 90.0 1.21 1 0.4010 7.923 24.8 5.8850 1 198 13.6 395.52
## 285 0.00906 90.0 2.97 0 0.4000 7.088 20.8 7.3073 1 285 15.3 394.72
## 286 0.01096 55.0 2.25 0 0.3890 6.453 31.9 7.3073 1 300 15.3 394.72
## 287 0.01965 80.0 1.76 0 0.3850 6.230 31.5 9.0892 1 241 18.2 341.60
## 288 0.03871 52.5 5.32 0 0.4050 6.209 31.3 7.3172 6 293 16.6 396.90
## 289 0.04590 52.5 5.32 0 0.4050 6.315 45.6 7.3172 6 293 16.6 396.90
## 290 0.04297 52.5 5.32 0 0.4050 6.565 22.9 7.3172 6 293 16.6 371.72
## 291 0.03502 80.0 4.95 0 0.4110 6.861 27.9 5.1167 4 245 19.2 396.90
## 292 0.07886 80.0 4.95 0 0.4110 7.148 27.7 5.1167 4 245 19.2 396.90
## 293 0.03615 80.0 4.95 0 0.4110 6.630 23.4 5.1167 4 245 19.2 396.90
## 294 0.08265 0.0 13.92 0 0.4370 6.127 18.4 5.5027 4 289 16.0 396.90
## 295 0.08199 0.0 13.92 0 0.4370 6.009 42.3 5.5027 4 289 16.0 396.90
## 296 0.12932 0.0 13.92 0 0.4370 6.678 31.1 5.9604 4 289 16.0 396.90
## 297 0.05372 0.0 13.92 0 0.4370 6.549 51.0 5.9604 4 289 16.0 392.85
## 298 0.14103 0.0 13.92 0 0.4370 5.790 58.0 6.3200 4 289 16.0 396.90
## 299 0.06466 70.0 2.24 0 0.4000 6.345 20.1 7.8278 5 358 14.8 368.24
## 300 0.05561 70.0 2.24 0 0.4000 7.041 10.0 7.8278 5 358 14.8 371.58
## 301 0.04417 70.0 2.24 0 0.4000 6.871 47.4 7.8278 5 358 14.8 390.86
## 302 0.03537 34.0 6.09 0 0.4330 6.590 40.4 5.4917 7 329 16.1 395.75
## 303 0.09266 34.0 6.09 0 0.4330 6.495 18.4 5.4917 7 329 16.1 383.61
## 304 0.10000 34.0 6.09 0 0.4330 6.982 17.7 5.4917 7 329 16.1 390.43
## 305 0.05515 33.0 2.18 0 0.4720 7.236 41.1 4.0220 7 222 18.4 393.68
## 306 0.05479 33.0 2.18 0 0.4720 6.616 58.1 3.3700 7 222 18.4 393.36
## 307 0.07503 33.0 2.18 0 0.4720 7.420 71.9 3.0992 7 222 18.4 396.90
## 308 0.04932 33.0 2.18 0 0.4720 6.849 70.3 3.1827 7 222 18.4 396.90
## 309 0.49298 0.0 9.90 0 0.5440 6.635 82.5 3.3175 4 304 18.4 396.90
## 310 0.34940 0.0 9.90 0 0.5440 5.972 76.7 3.1025 4 304 18.4 396.24
## 311 2.63548 0.0 9.90 0 0.5440 4.973 37.8 2.5194 4 304 18.4 350.45
## 312 0.79041 0.0 9.90 0 0.5440 6.122 52.8 2.6403 4 304 18.4 396.90
## 313 0.26169 0.0 9.90 0 0.5440 6.023 90.4 2.8340 4 304 18.4 396.30
## 314 0.26938 0.0 9.90 0 0.5440 6.266 82.8 3.2628 4 304 18.4 393.39
## 315 0.36920 0.0 9.90 0 0.5440 6.567 87.3 3.6023 4 304 18.4 395.69
## 316 0.25356 0.0 9.90 0 0.5440 5.705 77.7 3.9450 4 304 18.4 396.42
## 317 0.31827 0.0 9.90 0 0.5440 5.914 83.2 3.9986 4 304 18.4 390.70
## 318 0.24522 0.0 9.90 0 0.5440 5.782 71.7 4.0317 4 304 18.4 396.90
## 319 0.40202 0.0 9.90 0 0.5440 6.382 67.2 3.5325 4 304 18.4 395.21
## 320 0.47547 0.0 9.90 0 0.5440 6.113 58.8 4.0019 4 304 18.4 396.23
## 321 0.16760 0.0 7.38 0 0.4930 6.426 52.3 4.5404 5 287 19.6 396.90
## 322 0.18159 0.0 7.38 0 0.4930 6.376 54.3 4.5404 5 287 19.6 396.90
## 323 0.35114 0.0 7.38 0 0.4930 6.041 49.9 4.7211 5 287 19.6 396.90
## 324 0.28392 0.0 7.38 0 0.4930 5.708 74.3 4.7211 5 287 19.6 391.13
## 325 0.34109 0.0 7.38 0 0.4930 6.415 40.1 4.7211 5 287 19.6 396.90
## 326 0.19186 0.0 7.38 0 0.4930 6.431 14.7 5.4159 5 287 19.6 393.68
## 327 0.30347 0.0 7.38 0 0.4930 6.312 28.9 5.4159 5 287 19.6 396.90
## 328 0.24103 0.0 7.38 0 0.4930 6.083 43.7 5.4159 5 287 19.6 396.90
## 329 0.06617 0.0 3.24 0 0.4600 5.868 25.8 5.2146 4 430 16.9 382.44
## 330 0.06724 0.0 3.24 0 0.4600 6.333 17.2 5.2146 4 430 16.9 375.21
## 331 0.04544 0.0 3.24 0 0.4600 6.144 32.2 5.8736 4 430 16.9 368.57
## 332 0.05023 35.0 6.06 0 0.4379 5.706 28.4 6.6407 1 304 16.9 394.02
## 333 0.03466 35.0 6.06 0 0.4379 6.031 23.3 6.6407 1 304 16.9 362.25
## 334 0.05083 0.0 5.19 0 0.5150 6.316 38.1 6.4584 5 224 20.2 389.71
## 335 0.03738 0.0 5.19 0 0.5150 6.310 38.5 6.4584 5 224 20.2 389.40
## 336 0.03961 0.0 5.19 0 0.5150 6.037 34.5 5.9853 5 224 20.2 396.90
## 337 0.03427 0.0 5.19 0 0.5150 5.869 46.3 5.2311 5 224 20.2 396.90
## 338 0.03041 0.0 5.19 0 0.5150 5.895 59.6 5.6150 5 224 20.2 394.81
## 339 0.03306 0.0 5.19 0 0.5150 6.059 37.3 4.8122 5 224 20.2 396.14
## 340 0.05497 0.0 5.19 0 0.5150 5.985 45.4 4.8122 5 224 20.2 396.90
## 341 0.06151 0.0 5.19 0 0.5150 5.968 58.5 4.8122 5 224 20.2 396.90
## 342 0.01301 35.0 1.52 0 0.4420 7.241 49.3 7.0379 1 284 15.5 394.74
## 343 0.02498 0.0 1.89 0 0.5180 6.540 59.7 6.2669 1 422 15.9 389.96
## 344 0.02543 55.0 3.78 0 0.4840 6.696 56.4 5.7321 5 370 17.6 396.90
## 345 0.03049 55.0 3.78 0 0.4840 6.874 28.1 6.4654 5 370 17.6 387.97
## 346 0.03113 0.0 4.39 0 0.4420 6.014 48.5 8.0136 3 352 18.8 385.64
## 347 0.06162 0.0 4.39 0 0.4420 5.898 52.3 8.0136 3 352 18.8 364.61
## 348 0.01870 85.0 4.15 0 0.4290 6.516 27.7 8.5353 4 351 17.9 392.43
## 349 0.01501 80.0 2.01 0 0.4350 6.635 29.7 8.3440 4 280 17.0 390.94
## 350 0.02899 40.0 1.25 0 0.4290 6.939 34.5 8.7921 1 335 19.7 389.85
## 351 0.06211 40.0 1.25 0 0.4290 6.490 44.4 8.7921 1 335 19.7 396.90
## 352 0.07950 60.0 1.69 0 0.4110 6.579 35.9 10.7103 4 411 18.3 370.78
## 353 0.07244 60.0 1.69 0 0.4110 5.884 18.5 10.7103 4 411 18.3 392.33
## 354 0.01709 90.0 2.02 0 0.4100 6.728 36.1 12.1265 5 187 17.0 384.46
## 355 0.04301 80.0 1.91 0 0.4130 5.663 21.9 10.5857 4 334 22.0 382.80
## 356 0.10659 80.0 1.91 0 0.4130 5.936 19.5 10.5857 4 334 22.0 376.04
## 357 8.98296 0.0 18.10 1 0.7700 6.212 97.4 2.1222 24 666 20.2 377.73
## 358 3.84970 0.0 18.10 1 0.7700 6.395 91.0 2.5052 24 666 20.2 391.34
## 359 5.20177 0.0 18.10 1 0.7700 6.127 83.4 2.7227 24 666 20.2 395.43
## 360 4.26131 0.0 18.10 0 0.7700 6.112 81.3 2.5091 24 666 20.2 390.74
## 361 4.54192 0.0 18.10 0 0.7700 6.398 88.0 2.5182 24 666 20.2 374.56
## 362 3.83684 0.0 18.10 0 0.7700 6.251 91.1 2.2955 24 666 20.2 350.65
## 363 3.67822 0.0 18.10 0 0.7700 5.362 96.2 2.1036 24 666 20.2 380.79
## 364 4.22239 0.0 18.10 1 0.7700 5.803 89.0 1.9047 24 666 20.2 353.04
## 365 3.47428 0.0 18.10 1 0.7180 8.780 82.9 1.9047 24 666 20.2 354.55
## 366 4.55587 0.0 18.10 0 0.7180 3.561 87.9 1.6132 24 666 20.2 354.70
## 367 3.69695 0.0 18.10 0 0.7180 4.963 91.4 1.7523 24 666 20.2 316.03
## 368 13.52220 0.0 18.10 0 0.6310 3.863 100.0 1.5106 24 666 20.2 131.42
## 369 4.89822 0.0 18.10 0 0.6310 4.970 100.0 1.3325 24 666 20.2 375.52
## 370 5.66998 0.0 18.10 1 0.6310 6.683 96.8 1.3567 24 666 20.2 375.33
## 371 6.53876 0.0 18.10 1 0.6310 7.016 97.5 1.2024 24 666 20.2 392.05
## 372 9.23230 0.0 18.10 0 0.6310 6.216 100.0 1.1691 24 666 20.2 366.15
## 373 8.26725 0.0 18.10 1 0.6680 5.875 89.6 1.1296 24 666 20.2 347.88
## 374 11.10810 0.0 18.10 0 0.6680 4.906 100.0 1.1742 24 666 20.2 396.90
## 375 18.49820 0.0 18.10 0 0.6680 4.138 100.0 1.1370 24 666 20.2 396.90
## 376 19.60910 0.0 18.10 0 0.6710 7.313 97.9 1.3163 24 666 20.2 396.90
## 377 15.28800 0.0 18.10 0 0.6710 6.649 93.3 1.3449 24 666 20.2 363.02
## 378 9.82349 0.0 18.10 0 0.6710 6.794 98.8 1.3580 24 666 20.2 396.90
## 379 23.64820 0.0 18.10 0 0.6710 6.380 96.2 1.3861 24 666 20.2 396.90
## 380 17.86670 0.0 18.10 0 0.6710 6.223 100.0 1.3861 24 666 20.2 393.74
## 381 88.97620 0.0 18.10 0 0.6710 6.968 91.9 1.4165 24 666 20.2 396.90
## 382 15.87440 0.0 18.10 0 0.6710 6.545 99.1 1.5192 24 666 20.2 396.90
## 383 9.18702 0.0 18.10 0 0.7000 5.536 100.0 1.5804 24 666 20.2 396.90
## 384 7.99248 0.0 18.10 0 0.7000 5.520 100.0 1.5331 24 666 20.2 396.90
## 385 20.08490 0.0 18.10 0 0.7000 4.368 91.2 1.4395 24 666 20.2 285.83
## 386 16.81180 0.0 18.10 0 0.7000 5.277 98.1 1.4261 24 666 20.2 396.90
## 387 24.39380 0.0 18.10 0 0.7000 4.652 100.0 1.4672 24 666 20.2 396.90
## 388 22.59710 0.0 18.10 0 0.7000 5.000 89.5 1.5184 24 666 20.2 396.90
## 389 14.33370 0.0 18.10 0 0.7000 4.880 100.0 1.5895 24 666 20.2 372.92
## 390 8.15174 0.0 18.10 0 0.7000 5.390 98.9 1.7281 24 666 20.2 396.90
## 391 6.96215 0.0 18.10 0 0.7000 5.713 97.0 1.9265 24 666 20.2 394.43
## 392 5.29305 0.0 18.10 0 0.7000 6.051 82.5 2.1678 24 666 20.2 378.38
## 393 11.57790 0.0 18.10 0 0.7000 5.036 97.0 1.7700 24 666 20.2 396.90
## 394 8.64476 0.0 18.10 0 0.6930 6.193 92.6 1.7912 24 666 20.2 396.90
## 395 13.35980 0.0 18.10 0 0.6930 5.887 94.7 1.7821 24 666 20.2 396.90
## 396 8.71675 0.0 18.10 0 0.6930 6.471 98.8 1.7257 24 666 20.2 391.98
## 397 5.87205 0.0 18.10 0 0.6930 6.405 96.0 1.6768 24 666 20.2 396.90
## 398 7.67202 0.0 18.10 0 0.6930 5.747 98.9 1.6334 24 666 20.2 393.10
## 399 38.35180 0.0 18.10 0 0.6930 5.453 100.0 1.4896 24 666 20.2 396.90
## 400 9.91655 0.0 18.10 0 0.6930 5.852 77.8 1.5004 24 666 20.2 338.16
## 401 25.04610 0.0 18.10 0 0.6930 5.987 100.0 1.5888 24 666 20.2 396.90
## 402 14.23620 0.0 18.10 0 0.6930 6.343 100.0 1.5741 24 666 20.2 396.90
## 403 9.59571 0.0 18.10 0 0.6930 6.404 100.0 1.6390 24 666 20.2 376.11
## 404 24.80170 0.0 18.10 0 0.6930 5.349 96.0 1.7028 24 666 20.2 396.90
## 405 41.52920 0.0 18.10 0 0.6930 5.531 85.4 1.6074 24 666 20.2 329.46
## 406 67.92080 0.0 18.10 0 0.6930 5.683 100.0 1.4254 24 666 20.2 384.97
## 407 20.71620 0.0 18.10 0 0.6590 4.138 100.0 1.1781 24 666 20.2 370.22
## 408 11.95110 0.0 18.10 0 0.6590 5.608 100.0 1.2852 24 666 20.2 332.09
## 409 7.40389 0.0 18.10 0 0.5970 5.617 97.9 1.4547 24 666 20.2 314.64
## 410 14.43830 0.0 18.10 0 0.5970 6.852 100.0 1.4655 24 666 20.2 179.36
## 411 51.13580 0.0 18.10 0 0.5970 5.757 100.0 1.4130 24 666 20.2 2.60
## 412 14.05070 0.0 18.10 0 0.5970 6.657 100.0 1.5275 24 666 20.2 35.05
## 413 18.81100 0.0 18.10 0 0.5970 4.628 100.0 1.5539 24 666 20.2 28.79
## 414 28.65580 0.0 18.10 0 0.5970 5.155 100.0 1.5894 24 666 20.2 210.97
## 415 45.74610 0.0 18.10 0 0.6930 4.519 100.0 1.6582 24 666 20.2 88.27
## 416 18.08460 0.0 18.10 0 0.6790 6.434 100.0 1.8347 24 666 20.2 27.25
## 417 10.83420 0.0 18.10 0 0.6790 6.782 90.8 1.8195 24 666 20.2 21.57
## 418 25.94060 0.0 18.10 0 0.6790 5.304 89.1 1.6475 24 666 20.2 127.36
## 419 73.53410 0.0 18.10 0 0.6790 5.957 100.0 1.8026 24 666 20.2 16.45
## 420 11.81230 0.0 18.10 0 0.7180 6.824 76.5 1.7940 24 666 20.2 48.45
## 421 11.08740 0.0 18.10 0 0.7180 6.411 100.0 1.8589 24 666 20.2 318.75
## 422 7.02259 0.0 18.10 0 0.7180 6.006 95.3 1.8746 24 666 20.2 319.98
## 423 12.04820 0.0 18.10 0 0.6140 5.648 87.6 1.9512 24 666 20.2 291.55
## 424 7.05042 0.0 18.10 0 0.6140 6.103 85.1 2.0218 24 666 20.2 2.52
## 425 8.79212 0.0 18.10 0 0.5840 5.565 70.6 2.0635 24 666 20.2 3.65
## 426 15.86030 0.0 18.10 0 0.6790 5.896 95.4 1.9096 24 666 20.2 7.68
## 427 12.24720 0.0 18.10 0 0.5840 5.837 59.7 1.9976 24 666 20.2 24.65
## 428 37.66190 0.0 18.10 0 0.6790 6.202 78.7 1.8629 24 666 20.2 18.82
## 429 7.36711 0.0 18.10 0 0.6790 6.193 78.1 1.9356 24 666 20.2 96.73
## 430 9.33889 0.0 18.10 0 0.6790 6.380 95.6 1.9682 24 666 20.2 60.72
## 431 8.49213 0.0 18.10 0 0.5840 6.348 86.1 2.0527 24 666 20.2 83.45
## 432 10.06230 0.0 18.10 0 0.5840 6.833 94.3 2.0882 24 666 20.2 81.33
## 433 6.44405 0.0 18.10 0 0.5840 6.425 74.8 2.2004 24 666 20.2 97.95
## 434 5.58107 0.0 18.10 0 0.7130 6.436 87.9 2.3158 24 666 20.2 100.19
## 435 13.91340 0.0 18.10 0 0.7130 6.208 95.0 2.2222 24 666 20.2 100.63
## 436 11.16040 0.0 18.10 0 0.7400 6.629 94.6 2.1247 24 666 20.2 109.85
## 437 14.42080 0.0 18.10 0 0.7400 6.461 93.3 2.0026 24 666 20.2 27.49
## 438 15.17720 0.0 18.10 0 0.7400 6.152 100.0 1.9142 24 666 20.2 9.32
## 439 13.67810 0.0 18.10 0 0.7400 5.935 87.9 1.8206 24 666 20.2 68.95
## 440 9.39063 0.0 18.10 0 0.7400 5.627 93.9 1.8172 24 666 20.2 396.90
## 441 22.05110 0.0 18.10 0 0.7400 5.818 92.4 1.8662 24 666 20.2 391.45
## 442 9.72418 0.0 18.10 0 0.7400 6.406 97.2 2.0651 24 666 20.2 385.96
## 443 5.66637 0.0 18.10 0 0.7400 6.219 100.0 2.0048 24 666 20.2 395.69
## 444 9.96654 0.0 18.10 0 0.7400 6.485 100.0 1.9784 24 666 20.2 386.73
## 445 12.80230 0.0 18.10 0 0.7400 5.854 96.6 1.8956 24 666 20.2 240.52
## 446 10.67180 0.0 18.10 0 0.7400 6.459 94.8 1.9879 24 666 20.2 43.06
## 447 6.28807 0.0 18.10 0 0.7400 6.341 96.4 2.0720 24 666 20.2 318.01
## 448 9.92485 0.0 18.10 0 0.7400 6.251 96.6 2.1980 24 666 20.2 388.52
## 449 9.32909 0.0 18.10 0 0.7130 6.185 98.7 2.2616 24 666 20.2 396.90
## 450 7.52601 0.0 18.10 0 0.7130 6.417 98.3 2.1850 24 666 20.2 304.21
## 451 6.71772 0.0 18.10 0 0.7130 6.749 92.6 2.3236 24 666 20.2 0.32
## 452 5.44114 0.0 18.10 0 0.7130 6.655 98.2 2.3552 24 666 20.2 355.29
## 453 5.09017 0.0 18.10 0 0.7130 6.297 91.8 2.3682 24 666 20.2 385.09
## 454 8.24809 0.0 18.10 0 0.7130 7.393 99.3 2.4527 24 666 20.2 375.87
## 455 9.51363 0.0 18.10 0 0.7130 6.728 94.1 2.4961 24 666 20.2 6.68
## 456 4.75237 0.0 18.10 0 0.7130 6.525 86.5 2.4358 24 666 20.2 50.92
## 457 4.66883 0.0 18.10 0 0.7130 5.976 87.9 2.5806 24 666 20.2 10.48
## 458 8.20058 0.0 18.10 0 0.7130 5.936 80.3 2.7792 24 666 20.2 3.50
## 459 7.75223 0.0 18.10 0 0.7130 6.301 83.7 2.7831 24 666 20.2 272.21
## 460 6.80117 0.0 18.10 0 0.7130 6.081 84.4 2.7175 24 666 20.2 396.90
## 461 4.81213 0.0 18.10 0 0.7130 6.701 90.0 2.5975 24 666 20.2 255.23
## 462 3.69311 0.0 18.10 0 0.7130 6.376 88.4 2.5671 24 666 20.2 391.43
## 463 6.65492 0.0 18.10 0 0.7130 6.317 83.0 2.7344 24 666 20.2 396.90
## 464 5.82115 0.0 18.10 0 0.7130 6.513 89.9 2.8016 24 666 20.2 393.82
## 465 7.83932 0.0 18.10 0 0.6550 6.209 65.4 2.9634 24 666 20.2 396.90
## 466 3.16360 0.0 18.10 0 0.6550 5.759 48.2 3.0665 24 666 20.2 334.40
## 467 3.77498 0.0 18.10 0 0.6550 5.952 84.7 2.8715 24 666 20.2 22.01
## 468 4.42228 0.0 18.10 0 0.5840 6.003 94.5 2.5403 24 666 20.2 331.29
## 469 15.57570 0.0 18.10 0 0.5800 5.926 71.0 2.9084 24 666 20.2 368.74
## 470 13.07510 0.0 18.10 0 0.5800 5.713 56.7 2.8237 24 666 20.2 396.90
## 471 4.34879 0.0 18.10 0 0.5800 6.167 84.0 3.0334 24 666 20.2 396.90
## 472 4.03841 0.0 18.10 0 0.5320 6.229 90.7 3.0993 24 666 20.2 395.33
## 473 3.56868 0.0 18.10 0 0.5800 6.437 75.0 2.8965 24 666 20.2 393.37
## 474 4.64689 0.0 18.10 0 0.6140 6.980 67.6 2.5329 24 666 20.2 374.68
## 475 8.05579 0.0 18.10 0 0.5840 5.427 95.4 2.4298 24 666 20.2 352.58
## 476 6.39312 0.0 18.10 0 0.5840 6.162 97.4 2.2060 24 666 20.2 302.76
## 477 4.87141 0.0 18.10 0 0.6140 6.484 93.6 2.3053 24 666 20.2 396.21
## 478 15.02340 0.0 18.10 0 0.6140 5.304 97.3 2.1007 24 666 20.2 349.48
## 479 10.23300 0.0 18.10 0 0.6140 6.185 96.7 2.1705 24 666 20.2 379.70
## 480 14.33370 0.0 18.10 0 0.6140 6.229 88.0 1.9512 24 666 20.2 383.32
## 481 5.82401 0.0 18.10 0 0.5320 6.242 64.7 3.4242 24 666 20.2 396.90
## 482 5.70818 0.0 18.10 0 0.5320 6.750 74.9 3.3317 24 666 20.2 393.07
## 483 5.73116 0.0 18.10 0 0.5320 7.061 77.0 3.4106 24 666 20.2 395.28
## 484 2.81838 0.0 18.10 0 0.5320 5.762 40.3 4.0983 24 666 20.2 392.92
## 485 2.37857 0.0 18.10 0 0.5830 5.871 41.9 3.7240 24 666 20.2 370.73
## 486 3.67367 0.0 18.10 0 0.5830 6.312 51.9 3.9917 24 666 20.2 388.62
## 487 5.69175 0.0 18.10 0 0.5830 6.114 79.8 3.5459 24 666 20.2 392.68
## 488 4.83567 0.0 18.10 0 0.5830 5.905 53.2 3.1523 24 666 20.2 388.22
## 489 0.15086 0.0 27.74 0 0.6090 5.454 92.7 1.8209 4 711 20.1 395.09
## 490 0.18337 0.0 27.74 0 0.6090 5.414 98.3 1.7554 4 711 20.1 344.05
## 491 0.20746 0.0 27.74 0 0.6090 5.093 98.0 1.8226 4 711 20.1 318.43
## 492 0.10574 0.0 27.74 0 0.6090 5.983 98.8 1.8681 4 711 20.1 390.11
## 493 0.11132 0.0 27.74 0 0.6090 5.983 83.5 2.1099 4 711 20.1 396.90
## 494 0.17331 0.0 9.69 0 0.5850 5.707 54.0 2.3817 6 391 19.2 396.90
## 495 0.27957 0.0 9.69 0 0.5850 5.926 42.6 2.3817 6 391 19.2 396.90
## 496 0.17899 0.0 9.69 0 0.5850 5.670 28.8 2.7986 6 391 19.2 393.29
## 497 0.28960 0.0 9.69 0 0.5850 5.390 72.9 2.7986 6 391 19.2 396.90
## 498 0.26838 0.0 9.69 0 0.5850 5.794 70.6 2.8927 6 391 19.2 396.90
## 499 0.23912 0.0 9.69 0 0.5850 6.019 65.3 2.4091 6 391 19.2 396.90
## 500 0.17783 0.0 9.69 0 0.5850 5.569 73.5 2.3999 6 391 19.2 395.77
## 501 0.22438 0.0 9.69 0 0.5850 6.027 79.7 2.4982 6 391 19.2 396.90
## 502 0.06263 0.0 11.93 0 0.5730 6.593 69.1 2.4786 1 273 21.0 391.99
## 503 0.04527 0.0 11.93 0 0.5730 6.120 76.7 2.2875 1 273 21.0 396.90
## 504 0.06076 0.0 11.93 0 0.5730 6.976 91.0 2.1675 1 273 21.0 396.90
## 505 0.10959 0.0 11.93 0 0.5730 6.794 89.3 2.3889 1 273 21.0 393.45
## 506 0.04741 0.0 11.93 0 0.5730 6.030 80.8 2.5050 1 273 21.0 396.90
## lstat medv
## 1 4.98 24.0
## 2 9.14 21.6
## 3 4.03 34.7
## 4 2.94 33.4
## 5 5.33 36.2
## 6 5.21 28.7
## 7 12.43 22.9
## 8 19.15 27.1
## 9 29.93 16.5
## 10 17.10 18.9
## 11 20.45 15.0
## 12 13.27 18.9
## 13 15.71 21.7
## 14 8.26 20.4
## 15 10.26 18.2
## 16 8.47 19.9
## 17 6.58 23.1
## 18 14.67 17.5
## 19 11.69 20.2
## 20 11.28 18.2
## 21 21.02 13.6
## 22 13.83 19.6
## 23 18.72 15.2
## 24 19.88 14.5
## 25 16.30 15.6
## 26 16.51 13.9
## 27 14.81 16.6
## 28 17.28 14.8
## 29 12.80 18.4
## 30 11.98 21.0
## 31 22.60 12.7
## 32 13.04 14.5
## 33 27.71 13.2
## 34 18.35 13.1
## 35 20.34 13.5
## 36 9.68 18.9
## 37 11.41 20.0
## 38 8.77 21.0
## 39 10.13 24.7
## 40 4.32 30.8
## 41 1.98 34.9
## 42 4.84 26.6
## 43 5.81 25.3
## 44 7.44 24.7
## 45 9.55 21.2
## 46 10.21 19.3
## 47 14.15 20.0
## 48 18.80 16.6
## 49 30.81 14.4
## 50 16.20 19.4
## 51 13.45 19.7
## 52 9.43 20.5
## 53 5.28 25.0
## 54 8.43 23.4
## 55 14.80 18.9
## 56 4.81 35.4
## 57 5.77 24.7
## 58 3.95 31.6
## 59 6.86 23.3
## 60 9.22 19.6
## 61 13.15 18.7
## 62 14.44 16.0
## 63 6.73 22.2
## 64 9.50 25.0
## 65 8.05 33.0
## 66 4.67 23.5
## 67 10.24 19.4
## 68 8.10 22.0
## 69 13.09 17.4
## 70 8.79 20.9
## 71 6.72 24.2
## 72 9.88 21.7
## 73 5.52 22.8
## 74 7.54 23.4
## 75 6.78 24.1
## 76 8.94 21.4
## 77 11.97 20.0
## 78 10.27 20.8
## 79 12.34 21.2
## 80 9.10 20.3
## 81 5.29 28.0
## 82 7.22 23.9
## 83 6.72 24.8
## 84 7.51 22.9
## 85 9.62 23.9
## 86 6.53 26.6
## 87 12.86 22.5
## 88 8.44 22.2
## 89 5.50 23.6
## 90 5.70 28.7
## 91 8.81 22.6
## 92 8.20 22.0
## 93 8.16 22.9
## 94 6.21 25.0
## 95 10.59 20.6
## 96 6.65 28.4
## 97 11.34 21.4
## 98 4.21 38.7
## 99 3.57 43.8
## 100 6.19 33.2
## 101 9.42 27.5
## 102 7.67 26.5
## 103 10.63 18.6
## 104 13.44 19.3
## 105 12.33 20.1
## 106 16.47 19.5
## 107 18.66 19.5
## 108 14.09 20.4
## 109 12.27 19.8
## 110 15.55 19.4
## 111 13.00 21.7
## 112 10.16 22.8
## 113 16.21 18.8
## 114 17.09 18.7
## 115 10.45 18.5
## 116 15.76 18.3
## 117 12.04 21.2
## 118 10.30 19.2
## 119 15.37 20.4
## 120 13.61 19.3
## 121 14.37 22.0
## 122 14.27 20.3
## 123 17.93 20.5
## 124 25.41 17.3
## 125 17.58 18.8
## 126 14.81 21.4
## 127 27.26 15.7
## 128 17.19 16.2
## 129 15.39 18.0
## 130 18.34 14.3
## 131 12.60 19.2
## 132 12.26 19.6
## 133 11.12 23.0
## 134 15.03 18.4
## 135 17.31 15.6
## 136 16.96 18.1
## 137 16.90 17.4
## 138 14.59 17.1
## 139 21.32 13.3
## 140 18.46 17.8
## 141 24.16 14.0
## 142 34.41 14.4
## 143 26.82 13.4
## 144 26.42 15.6
## 145 29.29 11.8
## 146 27.80 13.8
## 147 16.65 15.6
## 148 29.53 14.6
## 149 28.32 17.8
## 150 21.45 15.4
## 151 14.10 21.5
## 152 13.28 19.6
## 153 12.12 15.3
## 154 15.79 19.4
## 155 15.12 17.0
## 156 15.02 15.6
## 157 16.14 13.1
## 158 4.59 41.3
## 159 6.43 24.3
## 160 7.39 23.3
## 161 5.50 27.0
## 162 1.73 50.0
## 163 1.92 50.0
## 164 3.32 50.0
## 165 11.64 22.7
## 166 9.81 25.0
## 167 3.70 50.0
## 168 12.14 23.8
## 169 11.10 23.8
## 170 11.32 22.3
## 171 14.43 17.4
## 172 12.03 19.1
## 173 14.69 23.1
## 174 9.04 23.6
## 175 9.64 22.6
## 176 5.33 29.4
## 177 10.11 23.2
## 178 6.29 24.6
## 179 6.92 29.9
## 180 5.04 37.2
## 181 7.56 39.8
## 182 9.45 36.2
## 183 4.82 37.9
## 184 5.68 32.5
## 185 13.98 26.4
## 186 13.15 29.6
## 187 4.45 50.0
## 188 6.68 32.0
## 189 4.56 29.8
## 190 5.39 34.9
## 191 5.10 37.0
## 192 4.69 30.5
## 193 2.87 36.4
## 194 5.03 31.1
## 195 4.38 29.1
## 196 2.97 50.0
## 197 4.08 33.3
## 198 8.61 30.3
## 199 6.62 34.6
## 200 4.56 34.9
## 201 4.45 32.9
## 202 7.43 24.1
## 203 3.11 42.3
## 204 3.81 48.5
## 205 2.88 50.0
## 206 10.87 22.6
## 207 10.97 24.4
## 208 18.06 22.5
## 209 14.66 24.4
## 210 23.09 20.0
## 211 17.27 21.7
## 212 23.98 19.3
## 213 16.03 22.4
## 214 9.38 28.1
## 215 29.55 23.7
## 216 9.47 25.0
## 217 13.51 23.3
## 218 9.69 28.7
## 219 17.92 21.5
## 220 10.50 23.0
## 221 9.71 26.7
## 222 21.46 21.7
## 223 9.93 27.5
## 224 7.60 30.1
## 225 4.14 44.8
## 226 4.63 50.0
## 227 3.13 37.6
## 228 6.36 31.6
## 229 3.92 46.7
## 230 3.76 31.5
## 231 11.65 24.3
## 232 5.25 31.7
## 233 2.47 41.7
## 234 3.95 48.3
## 235 8.05 29.0
## 236 10.88 24.0
## 237 9.54 25.1
## 238 4.73 31.5
## 239 6.36 23.7
## 240 7.37 23.3
## 241 11.38 22.0
## 242 12.40 20.1
## 243 11.22 22.2
## 244 5.19 23.7
## 245 12.50 17.6
## 246 18.46 18.5
## 247 9.16 24.3
## 248 10.15 20.5
## 249 9.52 24.5
## 250 6.56 26.2
## 251 5.90 24.4
## 252 3.59 24.8
## 253 3.53 29.6
## 254 3.54 42.8
## 255 6.57 21.9
## 256 9.25 20.9
## 257 3.11 44.0
## 258 5.12 50.0
## 259 7.79 36.0
## 260 6.90 30.1
## 261 9.59 33.8
## 262 7.26 43.1
## 263 5.91 48.8
## 264 11.25 31.0
## 265 8.10 36.5
## 266 10.45 22.8
## 267 14.79 30.7
## 268 7.44 50.0
## 269 3.16 43.5
## 270 13.65 20.7
## 271 13.00 21.1
## 272 6.59 25.2
## 273 7.73 24.4
## 274 6.58 35.2
## 275 3.53 32.4
## 276 2.98 32.0
## 277 6.05 33.2
## 278 4.16 33.1
## 279 7.19 29.1
## 280 4.85 35.1
## 281 3.76 45.4
## 282 4.59 35.4
## 283 3.01 46.0
## 284 3.16 50.0
## 285 7.85 32.2
## 286 8.23 22.0
## 287 12.93 20.1
## 288 7.14 23.2
## 289 7.60 22.3
## 290 9.51 24.8
## 291 3.33 28.5
## 292 3.56 37.3
## 293 4.70 27.9
## 294 8.58 23.9
## 295 10.40 21.7
## 296 6.27 28.6
## 297 7.39 27.1
## 298 15.84 20.3
## 299 4.97 22.5
## 300 4.74 29.0
## 301 6.07 24.8
## 302 9.50 22.0
## 303 8.67 26.4
## 304 4.86 33.1
## 305 6.93 36.1
## 306 8.93 28.4
## 307 6.47 33.4
## 308 7.53 28.2
## 309 4.54 22.8
## 310 9.97 20.3
## 311 12.64 16.1
## 312 5.98 22.1
## 313 11.72 19.4
## 314 7.90 21.6
## 315 9.28 23.8
## 316 11.50 16.2
## 317 18.33 17.8
## 318 15.94 19.8
## 319 10.36 23.1
## 320 12.73 21.0
## 321 7.20 23.8
## 322 6.87 23.1
## 323 7.70 20.4
## 324 11.74 18.5
## 325 6.12 25.0
## 326 5.08 24.6
## 327 6.15 23.0
## 328 12.79 22.2
## 329 9.97 19.3
## 330 7.34 22.6
## 331 9.09 19.8
## 332 12.43 17.1
## 333 7.83 19.4
## 334 5.68 22.2
## 335 6.75 20.7
## 336 8.01 21.1
## 337 9.80 19.5
## 338 10.56 18.5
## 339 8.51 20.6
## 340 9.74 19.0
## 341 9.29 18.7
## 342 5.49 32.7
## 343 8.65 16.5
## 344 7.18 23.9
## 345 4.61 31.2
## 346 10.53 17.5
## 347 12.67 17.2
## 348 6.36 23.1
## 349 5.99 24.5
## 350 5.89 26.6
## 351 5.98 22.9
## 352 5.49 24.1
## 353 7.79 18.6
## 354 4.50 30.1
## 355 8.05 18.2
## 356 5.57 20.6
## 357 17.60 17.8
## 358 13.27 21.7
## 359 11.48 22.7
## 360 12.67 22.6
## 361 7.79 25.0
## 362 14.19 19.9
## 363 10.19 20.8
## 364 14.64 16.8
## 365 5.29 21.9
## 366 7.12 27.5
## 367 14.00 21.9
## 368 13.33 23.1
## 369 3.26 50.0
## 370 3.73 50.0
## 371 2.96 50.0
## 372 9.53 50.0
## 373 8.88 50.0
## 374 34.77 13.8
## 375 37.97 13.8
## 376 13.44 15.0
## 377 23.24 13.9
## 378 21.24 13.3
## 379 23.69 13.1
## 380 21.78 10.2
## 381 17.21 10.4
## 382 21.08 10.9
## 383 23.60 11.3
## 384 24.56 12.3
## 385 30.63 8.8
## 386 30.81 7.2
## 387 28.28 10.5
## 388 31.99 7.4
## 389 30.62 10.2
## 390 20.85 11.5
## 391 17.11 15.1
## 392 18.76 23.2
## 393 25.68 9.7
## 394 15.17 13.8
## 395 16.35 12.7
## 396 17.12 13.1
## 397 19.37 12.5
## 398 19.92 8.5
## 399 30.59 5.0
## 400 29.97 6.3
## 401 26.77 5.6
## 402 20.32 7.2
## 403 20.31 12.1
## 404 19.77 8.3
## 405 27.38 8.5
## 406 22.98 5.0
## 407 23.34 11.9
## 408 12.13 27.9
## 409 26.40 17.2
## 410 19.78 27.5
## 411 10.11 15.0
## 412 21.22 17.2
## 413 34.37 17.9
## 414 20.08 16.3
## 415 36.98 7.0
## 416 29.05 7.2
## 417 25.79 7.5
## 418 26.64 10.4
## 419 20.62 8.8
## 420 22.74 8.4
## 421 15.02 16.7
## 422 15.70 14.2
## 423 14.10 20.8
## 424 23.29 13.4
## 425 17.16 11.7
## 426 24.39 8.3
## 427 15.69 10.2
## 428 14.52 10.9
## 429 21.52 11.0
## 430 24.08 9.5
## 431 17.64 14.5
## 432 19.69 14.1
## 433 12.03 16.1
## 434 16.22 14.3
## 435 15.17 11.7
## 436 23.27 13.4
## 437 18.05 9.6
## 438 26.45 8.7
## 439 34.02 8.4
## 440 22.88 12.8
## 441 22.11 10.5
## 442 19.52 17.1
## 443 16.59 18.4
## 444 18.85 15.4
## 445 23.79 10.8
## 446 23.98 11.8
## 447 17.79 14.9
## 448 16.44 12.6
## 449 18.13 14.1
## 450 19.31 13.0
## 451 17.44 13.4
## 452 17.73 15.2
## 453 17.27 16.1
## 454 16.74 17.8
## 455 18.71 14.9
## 456 18.13 14.1
## 457 19.01 12.7
## 458 16.94 13.5
## 459 16.23 14.9
## 460 14.70 20.0
## 461 16.42 16.4
## 462 14.65 17.7
## 463 13.99 19.5
## 464 10.29 20.2
## 465 13.22 21.4
## 466 14.13 19.9
## 467 17.15 19.0
## 468 21.32 19.1
## 469 18.13 19.1
## 470 14.76 20.1
## 471 16.29 19.9
## 472 12.87 19.6
## 473 14.36 23.2
## 474 11.66 29.8
## 475 18.14 13.8
## 476 24.10 13.3
## 477 18.68 16.7
## 478 24.91 12.0
## 479 18.03 14.6
## 480 13.11 21.4
## 481 10.74 23.0
## 482 7.74 23.7
## 483 7.01 25.0
## 484 10.42 21.8
## 485 13.34 20.6
## 486 10.58 21.2
## 487 14.98 19.1
## 488 11.45 20.6
## 489 18.06 15.2
## 490 23.97 7.0
## 491 29.68 8.1
## 492 18.07 13.6
## 493 13.35 20.1
## 494 12.01 21.8
## 495 13.59 24.5
## 496 17.60 23.1
## 497 21.14 19.7
## 498 14.10 18.3
## 499 12.92 21.2
## 500 15.10 17.5
## 501 14.33 16.8
## 502 9.67 22.4
## 503 9.08 20.6
## 504 5.64 23.9
## 505 6.48 22.0
## 506 7.88 11.9
?Boston
## starting httpd help server ... done
#There are 506 rows and 14 columns.
#The rows represent a specific neighborhood or census tract (subdivision of a county)
#
#Each column represents the data specific to that subdivision of houses.
#
#I could paste the entire definition for each variable from the "Help" page in the bottom right of Rstudio here,
#but i don't think that's what you intend for me to do.
par(mfrow = c(2, 2))
plot(Boston$crim, Boston$medv,
main = "Crime Rate vs. MHV",
xlab = "Per Capita Crime Rate",
ylab = "Median Home Value in $1000s",
col = "blue", pch = 16, cex = 0.7)
abline(lm(medv ~ crim, data = Boston), col = "red", lwd = 2)
plot(Boston$age, Boston$medv,
main = "Built Pre-1940 vs. MHV",
xlab = "Proportion Built Pre-1940",
ylab = "Median Home Value in $1000s",
col = "blue", pch = 16, cex = 0.7)
abline(lm(medv ~ age, data = Boston), col = "red", lwd = 2)
plot(Boston$dis, Boston$medv,
main = "Dis2Employment vs. MHV",
xlab = "Avg Distance to Employment Center",
ylab = "Median Home Value in $1000s",
col = "blue", pch = 16, cex = 0.7)
abline(lm(medv ~ dis, data = Boston), col = "red", lwd = 2)
plot(Boston$nox, Boston$medv,
main = "Nitrogen Oxides Concentration vs. MHV",
xlab = "Nitrogen Oxides pp10m",
ylab = "Median Home Value in $1000s",
col = "blue", pch = 16, cex = 0.7)
abline(lm(medv ~ nox, data = Boston), col = "red", lwd = 2)
par(mfrow = c(1, 1))
#It seems crime rate and median home value have some correlation.
#With drastically higher crime rates in lower median value home areas.
#But it should be noted that it is not a perfect predictor as there are
#plenty of data points where there is virtually 0 crime rate regardless of the median value.
#
#It appears that pre-1940 houses may be worth less, or are coincidentally built
#in census tracts where the median value of homes is lower.
#This can be seen by the median value going down as the percentage of pre1940 houses goes up.
#
#It can be seen that there is pretty good correlation between
#lower median value areas being in closer proximity (on average) to employment centers.
#Although there are exceptions where extremely high value areas are also very close proximity.
#
#It can be seen that there is pretty good correlation between
#nitrogen oxide concentrations and median home value.
#The higher the median home value the lower the concentration is.
#There are some outliers however the average concentration
#generally increases as the median value goes down.
#correlation with crim
cor_with_crim <- cor(Boston)[,"crim"]
cor_with_crim <- sort(cor_with_crim[-1], decreasing = TRUE) # remove crim~crim
print(round(cor_with_crim, 3))
## rad tax lstat nox indus age ptratio chas zn rm
## 0.626 0.583 0.456 0.421 0.407 0.353 0.290 -0.056 -0.200 -0.219
## dis black medv
## -0.380 -0.385 -0.388
#The 3 highest positive correlations between crime rate and other indicators are
#rad (0.626), tax (0.583), and lstat (.456),
#as well as the highest negative correlation being medv (-0.388)
#
#This indicates that crime rate is correlated with accessibility to highways.
#I'm actually not sure what to think of this off the top of my head.
#This might indicate that due to high volume of traffic there is simply
#more crime that occurs relative to low traffic areas where
#criminals won't go out of there way to visit?
#
#There is a a correlation between crime rate and property tax rates.
#This can be explained by high density population areas having higher tax rates
#as opposed to wealthier low population areas.
#
#The correlation between crime rate and low socioeconomic status is well documented.
#Driven by factors like poverty and unemployment.
#
#Related to the previous correlation, it can be seen that crime rate is
#negatively correlated to median value of houses.
#This can thought of as people who live in high value areas
#are generally wealthier, leading to lower crime rates.
cat("Crime Rate\n")
## Crime Rate
cat("Mean: ", mean(Boston$crim), "\n")
## Mean: 3.613524
cat("Median: ", median(Boston$crim), "\n")
## Median: 0.25651
cat("Max: ", max(Boston$crim), "\n\n")
## Max: 88.9762
high_crime_threshold <- quantile(Boston$crim, 0.95)
cat("95% cut off:", high_crime_threshold, "\n")
## 95% cut off: 15.78915
cat("# of high crime census tracts:", sum(Boston$crim > high_crime_threshold), "\n\n")
## # of high crime census tracts: 26
cat("\n-----------------------------\n\n")
##
## -----------------------------
cat("Tax Rate\n")
## Tax Rate
cat("Mean: ", mean(Boston$tax), "\n")
## Mean: 408.2372
cat("Median: ", median(Boston$tax), "\n")
## Median: 330
cat("Max: ", max(Boston$tax), "\n\n")
## Max: 711
high_tax_threshold <- quantile(Boston$tax, 0.95)
cat("95% cut off:", high_tax_threshold, "\n")
## 95% cut off: 666
cat("# of high tax census tracts:", sum(Boston$tax > high_tax_threshold), "\n\n")
## # of high tax census tracts: 5
cat("\n-----------------------------\n\n")
##
## -----------------------------
sapply(Boston, function(x) c(Min = min(x), Max = max(x), Range = diff(range(x)), RangeProportion = diff(range(x))/max(x)))
## crim zn indus chas nox rm age
## Min 0.006320 0 0.4600000 0 0.3850000 3.5610000 2.900
## Max 88.976200 100 27.7400000 1 0.8710000 8.7800000 100.000
## Range 88.969880 100 27.2800000 1 0.4860000 5.2190000 97.100
## RangeProportion 0.999929 1 0.9834174 1 0.5579793 0.5944191 0.971
## dis rad tax ptratio black
## Min 1.1296000 1.0000000 187.0000000 12.6000000 0.3200000
## Max 12.1265000 24.0000000 711.0000000 22.0000000 396.9000000
## Range 10.9969000 23.0000000 524.0000000 9.4000000 396.5800000
## RangeProportion 0.9068486 0.9583333 0.7369902 0.4272727 0.9991938
## lstat medv
## Min 1.7300000 5.0
## Max 37.9700000 50.0
## Range 36.2400000 45.0
## RangeProportion 0.9544377 0.9
#It can be seen that there are 26 census tracts that are
#above the 95th percentile for all tracts in the data set
#
#There are 5 census tracts that are above the 95th percentile
#for all tax rates in the data set
#
#Unsure if you want me to comment on the range of all predictors or just crime and tax rates so:
#Crime has a very large range, with a minimum of virtually 0% (0.00632) to almost 89%.
#This makes the range very large at 88.96988
#
#Tax has a large range as well. With a minimum of 187 and a maximum of 711,
#that puts the range of values at 524.
#
#It can be seen from the other indicators that the ranges are also very large (relative to the max) with many indicators having a range of over 90% of the maximum value of the indicator.
#
table(Boston$chas)
##
## 0 1
## 471 35
#Out of 506 census tracts, 35 of them bound the Charles river.
median(Boston$ptratio)
## [1] 19.05
#The median pupil teacher ratio is 19.05
library(mlbench)
data(Soybean)
?Soybean
cat("Frequency Distributions\n\n")
## Frequency Distributions
for (var in names(Soybean)) {
cat("---------------------\n")
cat(var)
print(table(Soybean[[var]], useNA = "always"))
cat("\n")
}
## ---------------------
## Class
## 2-4-d-injury alternarialeaf-spot
## 16 91
## anthracnose bacterial-blight
## 44 20
## bacterial-pustule brown-spot
## 20 92
## brown-stem-rot charcoal-rot
## 44 20
## cyst-nematode diaporthe-pod-&-stem-blight
## 14 15
## diaporthe-stem-canker downy-mildew
## 20 20
## frog-eye-leaf-spot herbicide-injury
## 91 8
## phyllosticta-leaf-spot phytophthora-rot
## 20 88
## powdery-mildew purple-seed-stain
## 20 20
## rhizoctonia-root-rot <NA>
## 20 0
##
## ---------------------
## date
## 0 1 2 3 4 5 6 <NA>
## 26 75 93 118 131 149 90 1
##
## ---------------------
## plant.stand
## 0 1 <NA>
## 354 293 36
##
## ---------------------
## precip
## 0 1 2 <NA>
## 74 112 459 38
##
## ---------------------
## temp
## 0 1 2 <NA>
## 80 374 199 30
##
## ---------------------
## hail
## 0 1 <NA>
## 435 127 121
##
## ---------------------
## crop.hist
## 0 1 2 3 <NA>
## 65 165 219 218 16
##
## ---------------------
## area.dam
## 0 1 2 3 <NA>
## 123 227 145 187 1
##
## ---------------------
## sever
## 0 1 2 <NA>
## 195 322 45 121
##
## ---------------------
## seed.tmt
## 0 1 2 <NA>
## 305 222 35 121
##
## ---------------------
## germ
## 0 1 2 <NA>
## 165 213 193 112
##
## ---------------------
## plant.growth
## 0 1 <NA>
## 441 226 16
##
## ---------------------
## leaves
## 0 1 <NA>
## 77 606 0
##
## ---------------------
## leaf.halo
## 0 1 2 <NA>
## 221 36 342 84
##
## ---------------------
## leaf.marg
## 0 1 2 <NA>
## 357 21 221 84
##
## ---------------------
## leaf.size
## 0 1 2 <NA>
## 51 327 221 84
##
## ---------------------
## leaf.shread
## 0 1 <NA>
## 487 96 100
##
## ---------------------
## leaf.malf
## 0 1 <NA>
## 554 45 84
##
## ---------------------
## leaf.mild
## 0 1 2 <NA>
## 535 20 20 108
##
## ---------------------
## stem
## 0 1 <NA>
## 296 371 16
##
## ---------------------
## lodging
## 0 1 <NA>
## 520 42 121
##
## ---------------------
## stem.cankers
## 0 1 2 3 <NA>
## 379 39 36 191 38
##
## ---------------------
## canker.lesion
## 0 1 2 3 <NA>
## 320 83 177 65 38
##
## ---------------------
## fruiting.bodies
## 0 1 <NA>
## 473 104 106
##
## ---------------------
## ext.decay
## 0 1 2 <NA>
## 497 135 13 38
##
## ---------------------
## mycelium
## 0 1 <NA>
## 639 6 38
##
## ---------------------
## int.discolor
## 0 1 2 <NA>
## 581 44 20 38
##
## ---------------------
## sclerotia
## 0 1 <NA>
## 625 20 38
##
## ---------------------
## fruit.pods
## 0 1 2 3 <NA>
## 407 130 14 48 84
##
## ---------------------
## fruit.spots
## 0 1 2 4 <NA>
## 345 75 57 100 106
##
## ---------------------
## seed
## 0 1 <NA>
## 476 115 92
##
## ---------------------
## mold.growth
## 0 1 <NA>
## 524 67 92
##
## ---------------------
## seed.discolor
## 0 1 <NA>
## 513 64 106
##
## ---------------------
## seed.size
## 0 1 <NA>
## 532 59 92
##
## ---------------------
## shriveling
## 0 1 <NA>
## 539 38 106
##
## ---------------------
## roots
## 0 1 2 <NA>
## 551 86 15 31
#It can be seen from the tables that the predictors mycelium, leaf.malf, leaf.mild, sclerotia, and lodging are degenerate. With a majority of values in a single category.
na_values <- sapply(Soybean, function(x) mean(is.na(x)))
sorted <- sort(na_values, decreasing = TRUE)
print(sorted)
## hail sever seed.tmt lodging germ
## 0.177159590 0.177159590 0.177159590 0.177159590 0.163982430
## leaf.mild fruiting.bodies fruit.spots seed.discolor shriveling
## 0.158125915 0.155197657 0.155197657 0.155197657 0.155197657
## leaf.shread seed mold.growth seed.size leaf.halo
## 0.146412884 0.134699854 0.134699854 0.134699854 0.122986823
## leaf.marg leaf.size leaf.malf fruit.pods precip
## 0.122986823 0.122986823 0.122986823 0.122986823 0.055636896
## stem.cankers canker.lesion ext.decay mycelium int.discolor
## 0.055636896 0.055636896 0.055636896 0.055636896 0.055636896
## sclerotia plant.stand roots temp crop.hist
## 0.055636896 0.052708638 0.045387994 0.043923865 0.023426061
## plant.growth stem date area.dam Class
## 0.023426061 0.023426061 0.001464129 0.001464129 0.000000000
## leaves
## 0.000000000
#It appears that hail, sever, seed.tmt, and lodging have the highest percentage of missing values.
#Each of these have over 17.7. The predictors then drop off into around 15.5%, and steadily decrease from #there until it reaches precip, which drastically drops off to only has 5% missing values.
library(caret)
## Loading required package: ggplot2
## Loading required package: lattice
sum(is.na(Soybean))
## [1] 2337
Soybean_reduced <- Soybean[, na_values <= 0.06]
sum(is.na(Soybean_reduced))
## [1] 413
#By eliminating predictors with more than 6% missing values this eliminates
#over 75% of total missing values from the dataset.
data(BloodBrain)
?BloodBrain
str(logBBB)
## num [1:208] 1.08 -0.4 0.22 0.14 0.69 0.44 -0.43 1.38 0.75 0.88 ...
str(bbbDescr)
## 'data.frame': 208 obs. of 134 variables:
## $ tpsa : num 12 49.3 50.5 37.4 37.4 ...
## $ nbasic : int 1 0 1 0 1 1 1 1 1 1 ...
## $ negative : int 0 0 0 0 0 0 0 0 0 0 ...
## $ vsa_hyd : num 167.1 92.6 295.2 319.1 299.7 ...
## $ a_aro : int 0 6 15 15 12 11 6 12 12 6 ...
## $ weight : num 156 151 366 383 326 ...
## $ peoe_vsa.0 : num 76.9 38.2 58.1 62.2 74.8 ...
## $ peoe_vsa.1 : num 43.4 25.5 124.7 124.7 118 ...
## $ peoe_vsa.2 : num 0 0 21.7 13.2 33 ...
## $ peoe_vsa.3 : num 0 8.62 8.62 21.79 0 ...
## $ peoe_vsa.4 : num 0 23.3 17.4 0 0 ...
## $ peoe_vsa.5 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ peoe_vsa.6 : num 17.24 0 8.62 8.62 8.62 ...
## $ peoe_vsa.0.1 : num 18.7 49 83.8 83.8 83.8 ...
## $ peoe_vsa.1.1 : num 43.5 0 49 68.8 36.8 ...
## $ peoe_vsa.2.1 : num 0 0 0 0 0 ...
## $ peoe_vsa.3.1 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ peoe_vsa.4.1 : num 0 0 5.68 5.68 5.68 ...
## $ peoe_vsa.5.1 : num 0 13.567 2.504 0 0.137 ...
## $ peoe_vsa.6.1 : num 0 7.9 2.64 2.64 2.5 ...
## $ a_acc : int 0 2 2 2 2 2 2 2 0 2 ...
## $ a_acid : int 0 0 0 0 0 0 0 0 0 0 ...
## $ a_base : int 1 0 1 1 1 1 1 1 1 1 ...
## $ vsa_acc : num 0 13.57 8.19 8.19 8.19 ...
## $ vsa_acid : num 0 0 0 0 0 0 0 0 0 0 ...
## $ vsa_base : num 5.68 0 0 0 0 ...
## $ vsa_don : num 5.68 5.68 5.68 5.68 5.68 ...
## $ vsa_other : num 0 28.1 43.6 28.3 19.6 ...
## $ vsa_pol : num 0 13.6 0 0 0 ...
## $ slogp_vsa0 : num 18 25.4 14.1 14.1 14.1 ...
## $ slogp_vsa1 : num 0 23.3 34.8 34.8 34.8 ...
## $ slogp_vsa2 : num 3.98 23.86 0 0 0 ...
## $ slogp_vsa3 : num 0 0 76.2 76.2 76.2 ...
## $ slogp_vsa4 : num 4.41 0 3.19 3.19 3.19 ...
## $ slogp_vsa5 : num 32.9 0 9.51 0 0 ...
## $ slogp_vsa6 : num 0 0 0 0 0 0 0 0 0 0 ...
## $ slogp_vsa7 : num 0 70.6 148.1 144 140.7 ...
## $ slogp_vsa8 : num 113.2 0 75.5 75.5 75.5 ...
## $ slogp_vsa9 : num 33.3 41.3 28.3 55.5 26 ...
## $ smr_vsa0 : num 0 23.86 12.63 3.12 3.12 ...
## $ smr_vsa1 : num 18 25.4 27.8 27.8 27.8 ...
## $ smr_vsa2 : num 4.41 0 0 0 0 ...
## $ smr_vsa3 : num 3.98 5.24 8.43 8.43 8.43 ...
## $ smr_vsa4 : num 0 20.8 29.6 21.4 20.3 ...
## $ smr_vsa5 : num 113.2 70.6 235.1 235.1 234.6 ...
## $ smr_vsa6 : num 0 5.26 76.25 76.25 76.25 ...
## $ smr_vsa7 : num 66.2 33.3 0 31.3 0 ...
## $ tpsa.1 : num 16.6 49.3 51.7 38.6 38.6 ...
## $ logp.o.w. : num 2.948 0.889 4.439 5.254 3.8 ...
## $ frac.anion7. : num 0 0.001 0 0 0 0 0.001 0 0 0 ...
## $ frac.cation7. : num 0.999 0 0.986 0.986 0.986 0.986 0.996 0.946 0.999 0.976 ...
## $ andrewbind : num 3.4 -3.3 12.8 12.8 10.3 10 10.4 15.9 12.9 9.5 ...
## $ rotatablebonds : int 3 2 8 8 8 8 8 7 4 5 ...
## $ mlogp : num 2.5 1.06 4.66 3.82 3.27 ...
## $ clogp : num 2.97 0.494 5.137 5.878 4.367 ...
## $ mw : num 155 151 365 382 325 ...
## $ nocount : int 1 3 5 4 4 4 4 3 2 4 ...
## $ hbdnr : int 1 2 1 1 1 1 2 1 1 0 ...
## $ rule.of.5violations : int 0 0 1 1 0 0 0 0 1 0 ...
## $ alert : int 0 0 0 0 0 0 0 0 0 0 ...
## $ prx : int 0 1 6 2 2 2 1 0 0 4 ...
## $ ub : num 0 3 5.3 5.3 4.2 3.6 3 4.7 4.2 3 ...
## $ pol : int 0 2 3 3 2 2 2 3 4 1 ...
## $ inthb : int 0 0 0 0 0 0 1 0 0 0 ...
## $ adistm : num 0 395 1365 703 746 ...
## $ adistd : num 0 10.9 25.7 10 10.6 ...
## $ polar_area : num 21.1 117.4 82.1 65.1 66.2 ...
## $ nonpolar_area : num 379 248 638 668 602 ...
## $ psa_npsa : num 0.0557 0.4743 0.1287 0.0974 0.11 ...
## $ tcsa : num 0.0097 0.0134 0.0111 0.0108 0.0118 0.0111 0.0123 0.0099 0.0106 0.0115 ...
## $ tcpa : num 0.1842 0.0417 0.0972 0.1218 0.1186 ...
## $ tcnp : num 0.0103 0.0198 0.0125 0.0119 0.013 0.0125 0.0162 0.011 0.0109 0.0122 ...
## $ ovality : num 1.1 1.12 1.3 1.3 1.27 ...
## $ surface_area : num 400 365 720 733 668 ...
## $ volume : num 656 555 1224 1257 1133 ...
## $ most_negative_charge: num -0.617 -0.84 -0.801 -0.761 -0.857 ...
## $ most_positive_charge: num 0.307 0.497 0.541 0.48 0.455 ...
## $ sum_absolute_charge : num 3.89 4.89 7.98 7.93 7.85 ...
## $ dipole_moment : num 1.19 4.21 3.52 3.15 3.27 ...
## $ homo : num -9.67 -8.96 -8.63 -8.56 -8.67 ...
## $ lumo : num 3.4038 0.1942 0.0589 -0.2651 0.3149 ...
## $ hardness : num 6.54 4.58 4.34 4.15 4.49 ...
## $ ppsa1 : num 349 223 518 508 509 ...
## $ ppsa2 : num 679 546 2066 2013 1999 ...
## $ ppsa3 : num 31 42.3 64 61.7 61.6 ...
## $ pnsa1 : num 51.1 141.8 202 225.4 158.8 ...
## $ pnsa2 : num -99.3 -346.9 -805.9 -894 -623.3 ...
## $ pnsa3 : num -10.5 -44 -43.8 -42 -39.8 ...
## $ fpsa1 : num 0.872 0.611 0.719 0.692 0.762 ...
## $ fpsa2 : num 1.7 1.5 2.87 2.75 2.99 ...
## $ fpsa3 : num 0.0774 0.1159 0.0888 0.0842 0.0922 ...
## $ fnsa1 : num 0.128 0.389 0.281 0.307 0.238 ...
## $ fnsa2 : num -0.248 -0.951 -1.12 -1.22 -0.933 ...
## $ fnsa3 : num -0.0262 -0.1207 -0.0608 -0.0573 -0.0596 ...
## $ wpsa1 : num 139.7 81.4 372.7 372.1 340.1 ...
## $ wpsa2 : num 272 199 1487 1476 1335 ...
## $ wpsa3 : num 12.4 15.4 46 45.2 41.1 ...
## $ wnsa1 : num 20.4 51.8 145.4 165.3 106 ...
## $ wnsa2 : num -39.8 -126.6 -580.1 -655.3 -416.3 ...
## [list output truncated]
nzv_result <- nearZeroVar(bbbDescr, saveMetrics = TRUE)
print(nzv_result[nzv_result$nzv == TRUE, ])
## freqRatio percentUnique zeroVar nzv
## negative 207.00000 0.9615385 FALSE TRUE
## peoe_vsa.2.1 25.57143 5.7692308 FALSE TRUE
## peoe_vsa.3.1 21.00000 7.2115385 FALSE TRUE
## a_acid 33.50000 1.4423077 FALSE TRUE
## vsa_acid 33.50000 1.4423077 FALSE TRUE
## frac.anion7. 47.75000 5.7692308 FALSE TRUE
## alert 103.00000 0.9615385 FALSE TRUE
#negative, peoe_vsa.2.1, peoe_vsa.3.1, a_acid, vsa_acid, frac.anion7., and alert are near zero variance.
#This means that these predictors may not be useful for any kind of predictive modeling.
correlation_matrix <- cor(bbbDescr)
summary(correlation_matrix[upper.tri(correlation_matrix)])
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -1.00000 -0.14213 0.04727 0.06536 0.26261 1.00000
#We can clearly see that there are some predictors that
#have either extremely high (positive or negative) correlations.
hist(correlation_matrix[upper.tri(correlation_matrix)],
main = "Predictor Correlations",
xlab = "Correlation",
col = "blue")
dim(bbbDescr)
## [1] 208 134
highCorrelation <- findCorrelation(correlation_matrix, cutoff = 0.80)
bbbDescr_reduced <- bbbDescr[, -highCorrelation]
dim(bbbDescr_reduced)
## [1] 208 77
#We can see that by removing predictors with over 80% correlation
#we cut down predictors by a little under half. 134->77
data(oil)
str(oilType)
## Factor w/ 7 levels "A","B","C","D",..: 1 1 1 1 1 1 1 1 1 1 ...
table(oilType)
## oilType
## A B C D E F G
## 37 26 3 7 11 10 2
cat("------------------------\n\n")
## ------------------------
set.seed(67)
sample_repeats <- replicate(10, table(oilType[sample(length(oilType), 60)]), simplify = FALSE)
print(sample_repeats)
## [[1]]
##
## A B C D E F G
## 21 18 2 4 6 7 2
##
## [[2]]
##
## A B C D E F G
## 26 16 1 4 5 7 1
##
## [[3]]
##
## A B C D E F G
## 18 20 3 2 7 8 2
##
## [[4]]
##
## A B C D E F G
## 25 15 2 2 9 6 1
##
## [[5]]
##
## A B C D E F G
## 23 17 2 6 5 6 1
##
## [[6]]
##
## A B C D E F G
## 23 17 2 4 7 6 1
##
## [[7]]
##
## A B C D E F G
## 22 11 3 6 7 9 2
##
## [[8]]
##
## A B C D E F G
## 24 17 0 5 6 7 1
##
## [[9]]
##
## A B C D E F G
## 22 17 3 6 4 7 1
##
## [[10]]
##
## A B C D E F G
## 23 13 3 6 7 7 1
#It appears that for oil types of low quantity in the original, the random samples
#closely match the original frequency (C, G). However if the original frequency has a
#a high amount of an oil type then the variation in the samples increases significantly.
#Especially with the low sample size of 60, the variation is too large to accurately
#replicate the original distribution.
strat <- createDataPartition(oilType, p = 60/length(oilType), list = FALSE)
strat_sample <- oilType[strat]
print(table(oilType))
## oilType
## A B C D E F G
## 37 26 3 7 11 10 2
print(table(strat_sample))
## strat_sample
## A B C D E F G
## 24 17 2 5 7 7 2
#Without creating 20 stratified samples its hard to tell, but the stratified
#sample should be more closely represent the original as opposed
#to random sampling, which can over/under represent some oil types.
#I think the test set should not be used when the sample size is too small.
#A test set would create an even smaller sample size, further amplifying
#the problem of over/underpresenting when the sample size is already so low.
#
#Using 10 fold cross validation or LOOCV should be more reliable than splitting up small sample sizes.
binom.test(4, 5)
##
## Exact binomial test
##
## data: 4 and 5
## number of successes = 4, number of trials = 5, p-value = 0.375
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
## 0.2835821 0.9949492
## sample estimates:
## probability of success
## 0.8
binom.test(16, 20)
##
## Exact binomial test
##
## data: 16 and 20
## number of successes = 16, number of trials = 20, p-value = 0.01182
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
## 0.563386 0.942666
## sample estimates:
## probability of success
## 0.8
binom.test(80, 100)
##
## Exact binomial test
##
## data: 80 and 100
## number of successes = 80, number of trials = 100, p-value = 1.116e-09
## alternative hypothesis: true probability of success is not equal to 0.5
## 95 percent confidence interval:
## 0.7081573 0.8733444
## sample estimates:
## probability of success
## 0.8
#With all tests having an 80% probability we can see the differences between trial amounts.
#
#The precision of the estimate increases as the sample size increases. With 5 trials
#the confidence interval (0.2835821-0.9949492) is essentially the entire range. This is basically useless
#and doesn't tell us anything. The more we increase it, the more confident we can be.
#at 100 trials the interval is now at (0.7081573-0.8733444). This is much more useful.
#
#Statistical significance also changes with the trials. We can see that the p value
#shrinks exponentially as we increase the trials. At 5 we have a p value of 0.375, however at 100 trials
#we have a p value virtually zero (8 repeating zeros from the decimal)
#this shows us that despite both having success rates of 80%, its very likely at small sample sizes
#to be purely the result of luck, and the inverse true at large sample sizes.
#
#Basically the trade off is that small sample sizes are cheap to evaluate but you cannot truly be sure
#the models performance unless you put effort (time, money, etc depending on the situation)
#to create a large sample size to evaluate
#Bias is the error introduced by modeling real world problem (complex data)
#into a simpler problem (introducing error)
#
#The trade off is that the more flexible and complex the model gets,
#the less bias we will have, however the variance will
#increase (the models sensitivity to the data)
#
#The more complex the model is the less error it will have, as it can more
#more accuretly model the problem without simplifying it.
#
#However when the model becomes too complex
#(more complex than the actual problem its trying to model)
#the error will instead start to increase as the error is now
#dominated by the variance in the data set.
#
#Im unsure if you wanted me to use R code to make
#a fake bias variance plot (not that I would even know how)
#so I drew one with Chapter 5 as reference.
