# Import BD
bd<- read.csv("/Users/Mariana/Documents/5to/Econometrics/real_estate_data.csv")
bd
##     medv cmedv     crim    zn indus chas    nox    rm   age     dis rad tax
## 1   24.0  24.0  0.00632  18.0  2.31    0 0.5380 6.575  65.2  4.0900   1 296
## 2   21.6  21.6  0.02731   0.0  7.07    0 0.4690 6.421  78.9  4.9671   2 242
## 3   34.7  34.7  0.02729   0.0  7.07    0 0.4690 7.185  61.1  4.9671   2 242
## 4   33.4  33.4  0.03237   0.0  2.18    0 0.4580 6.998  45.8  6.0622   3 222
## 5   36.2  36.2  0.06905   0.0  2.18    0 0.4580 7.147  54.2  6.0622   3 222
## 6   28.7  28.7  0.02985   0.0  2.18    0 0.4580 6.430  58.7  6.0622   3 222
## 7   22.9  22.9  0.08829  12.5  7.87    0 0.5240 6.012  66.6  5.5605   5 311
## 8   27.1  22.1  0.14455  12.5  7.87    0 0.5240 6.172  96.1  5.9505   5 311
## 9   16.5  16.5  0.21124  12.5  7.87    0 0.5240 5.631 100.0  6.0821   5 311
## 10  18.9  18.9  0.17004  12.5  7.87    0 0.5240 6.004  85.9  6.5921   5 311
## 11  15.0  15.0  0.22489  12.5  7.87    0 0.5240 6.377  94.3  6.3467   5 311
## 12  18.9  18.9  0.11747  12.5  7.87    0 0.5240 6.009  82.9  6.2267   5 311
## 13  21.7  21.7  0.09378  12.5  7.87    0 0.5240 5.889  39.0  5.4509   5 311
## 14  20.4  20.4  0.62976   0.0  8.14    0 0.5380 5.949  61.8  4.7075   4 307
## 15  18.2  18.2  0.63796   0.0  8.14    0 0.5380 6.096  84.5  4.4619   4 307
## 16  19.9  19.9  0.62739   0.0  8.14    0 0.5380 5.834  56.5  4.4986   4 307
## 17  23.1  23.1  1.05393   0.0  8.14    0 0.5380 5.935  29.3  4.4986   4 307
## 18  17.5  17.5  0.78420   0.0  8.14    0 0.5380 5.990  81.7  4.2579   4 307
## 19  20.2  20.2  0.80271   0.0  8.14    0 0.5380 5.456  36.6  3.7965   4 307
## 20  18.2  18.2  0.72580   0.0  8.14    0 0.5380 5.727  69.5  3.7965   4 307
## 21  13.6  13.6  1.25179   0.0  8.14    0 0.5380 5.570  98.1  3.7979   4 307
## 22  19.6  19.6  0.85204   0.0  8.14    0 0.5380 5.965  89.2  4.0123   4 307
## 23  15.2  15.2  1.23247   0.0  8.14    0 0.5380 6.142  91.7  3.9769   4 307
## 24  14.5  14.5  0.98843   0.0  8.14    0 0.5380 5.813 100.0  4.0952   4 307
## 25  15.6  15.6  0.75026   0.0  8.14    0 0.5380 5.924  94.1  4.3996   4 307
## 26  13.9  13.9  0.84054   0.0  8.14    0 0.5380 5.599  85.7  4.4546   4 307
## 27  16.6  16.6  0.67191   0.0  8.14    0 0.5380 5.813  90.3  4.6820   4 307
## 28  14.8  14.8  0.95577   0.0  8.14    0 0.5380 6.047  88.8  4.4534   4 307
## 29  18.4  18.4  0.77299   0.0  8.14    0 0.5380 6.495  94.4  4.4547   4 307
## 30  21.0  21.0  1.00245   0.0  8.14    0 0.5380 6.674  87.3  4.2390   4 307
## 31  12.7  12.7  1.13081   0.0  8.14    0 0.5380 5.713  94.1  4.2330   4 307
## 32  14.5  14.5  1.35472   0.0  8.14    0 0.5380 6.072 100.0  4.1750   4 307
## 33  13.2  13.2  1.38799   0.0  8.14    0 0.5380 5.950  82.0  3.9900   4 307
## 34  13.1  13.1  1.15172   0.0  8.14    0 0.5380 5.701  95.0  3.7872   4 307
## 35  13.5  13.5  1.61282   0.0  8.14    0 0.5380 6.096  96.9  3.7598   4 307
## 36  18.9  18.9  0.06417   0.0  5.96    0 0.4990 5.933  68.2  3.3603   5 279
## 37  20.0  20.0  0.09744   0.0  5.96    0 0.4990 5.841  61.4  3.3779   5 279
## 38  21.0  21.0  0.08014   0.0  5.96    0 0.4990 5.850  41.5  3.9342   5 279
## 39  24.7  24.2  0.17505   0.0  5.96    0 0.4990 5.966  30.2  3.8473   5 279
## 40  30.8  30.8  0.02763  75.0  2.95    0 0.4280 6.595  21.8  5.4011   3 252
## 41  34.9  34.9  0.03359  75.0  2.95    0 0.4280 7.024  15.8  5.4011   3 252
## 42  26.6  26.6  0.12744   0.0  6.91    0 0.4480 6.770   2.9  5.7209   3 233
## 43  25.3  25.3  0.14150   0.0  6.91    0 0.4480 6.169   6.6  5.7209   3 233
## 44  24.7  24.7  0.15936   0.0  6.91    0 0.4480 6.211   6.5  5.7209   3 233
## 45  21.2  21.2  0.12269   0.0  6.91    0 0.4480 6.069  40.0  5.7209   3 233
## 46  19.3  19.3  0.17142   0.0  6.91    0 0.4480 5.682  33.8  5.1004   3 233
## 47  20.0  20.0  0.18836   0.0  6.91    0 0.4480 5.786  33.3  5.1004   3 233
## 48  16.6  16.6  0.22927   0.0  6.91    0 0.4480 6.030  85.5  5.6894   3 233
## 49  14.4  14.4  0.25387   0.0  6.91    0 0.4480 5.399  95.3  5.8700   3 233
## 50  19.4  19.4  0.21977   0.0  6.91    0 0.4480 5.602  62.0  6.0877   3 233
## 51  19.7  19.7  0.08873  21.0  5.64    0 0.4390 5.963  45.7  6.8147   4 243
## 52  20.5  20.5  0.04337  21.0  5.64    0 0.4390 6.115  63.0  6.8147   4 243
## 53  25.0  25.0  0.05360  21.0  5.64    0 0.4390 6.511  21.1  6.8147   4 243
## 54  23.4  23.4  0.04981  21.0  5.64    0 0.4390 5.998  21.4  6.8147   4 243
## 55  18.9  18.9  0.01360  75.0  4.00    0 0.4100 5.888  47.6  7.3197   3 469
## 56  35.4  35.4  0.01311  90.0  1.22    0 0.4030 7.249  21.9  8.6966   5 226
## 57  24.7  24.7  0.02055  85.0  0.74    0 0.4100 6.383  35.7  9.1876   2 313
## 58  31.6  31.6  0.01432 100.0  1.32    0 0.4110 6.816  40.5  8.3248   5 256
## 59  23.3  23.3  0.15445  25.0  5.13    0 0.4530 6.145  29.2  7.8148   8 284
## 60  19.6  19.6  0.10328  25.0  5.13    0 0.4530 5.927  47.2  6.9320   8 284
## 61  18.7  18.7  0.14932  25.0  5.13    0 0.4530 5.741  66.2  7.2254   8 284
## 62  16.0  16.0  0.17171  25.0  5.13    0 0.4530 5.966  93.4  6.8185   8 284
## 63  22.2  22.2  0.11027  25.0  5.13    0 0.4530 6.456  67.8  7.2255   8 284
## 64  25.0  25.0  0.12650  25.0  5.13    0 0.4530 6.762  43.4  7.9809   8 284
## 65  33.0  33.0  0.01951  17.5  1.38    0 0.4161 7.104  59.5  9.2229   3 216
## 66  23.5  23.5  0.03584  80.0  3.37    0 0.3980 6.290  17.8  6.6115   4 337
## 67  19.4  19.4  0.04379  80.0  3.37    0 0.3980 5.787  31.1  6.6115   4 337
## 68  22.0  22.0  0.05789  12.5  6.07    0 0.4090 5.878  21.4  6.4980   4 345
## 69  17.4  17.4  0.13554  12.5  6.07    0 0.4090 5.594  36.8  6.4980   4 345
## 70  20.9  20.9  0.12816  12.5  6.07    0 0.4090 5.885  33.0  6.4980   4 345
## 71  24.2  24.2  0.08826   0.0 10.81    0 0.4130 6.417   6.6  5.2873   4 305
## 72  21.7  21.7  0.15876   0.0 10.81    0 0.4130 5.961  17.5  5.2873   4 305
## 73  22.8  22.8  0.09164   0.0 10.81    0 0.4130 6.065   7.8  5.2873   4 305
## 74  23.4  23.4  0.19539   0.0 10.81    0 0.4130 6.245   6.2  5.2873   4 305
## 75  24.1  24.1  0.07896   0.0 12.83    0 0.4370 6.273   6.0  4.2515   5 398
## 76  21.4  21.4  0.09512   0.0 12.83    0 0.4370 6.286  45.0  4.5026   5 398
## 77  20.0  20.0  0.10153   0.0 12.83    0 0.4370 6.279  74.5  4.0522   5 398
## 78  20.8  20.8  0.08707   0.0 12.83    0 0.4370 6.140  45.8  4.0905   5 398
## 79  21.2  21.2  0.05646   0.0 12.83    0 0.4370 6.232  53.7  5.0141   5 398
## 80  20.3  20.3  0.08387   0.0 12.83    0 0.4370 5.874  36.6  4.5026   5 398
## 81  28.0  28.0  0.04113  25.0  4.86    0 0.4260 6.727  33.5  5.4007   4 281
## 82  23.9  23.9  0.04462  25.0  4.86    0 0.4260 6.619  70.4  5.4007   4 281
## 83  24.8  24.8  0.03659  25.0  4.86    0 0.4260 6.302  32.2  5.4007   4 281
## 84  22.9  22.9  0.03551  25.0  4.86    0 0.4260 6.167  46.7  5.4007   4 281
## 85  23.9  23.9  0.05059   0.0  4.49    0 0.4490 6.389  48.0  4.7794   3 247
## 86  26.6  26.6  0.05735   0.0  4.49    0 0.4490 6.630  56.1  4.4377   3 247
## 87  22.5  22.5  0.05188   0.0  4.49    0 0.4490 6.015  45.1  4.4272   3 247
## 88  22.2  22.2  0.07151   0.0  4.49    0 0.4490 6.121  56.8  3.7476   3 247
## 89  23.6  23.6  0.05660   0.0  3.41    0 0.4890 7.007  86.3  3.4217   2 270
## 90  28.7  28.7  0.05302   0.0  3.41    0 0.4890 7.079  63.1  3.4145   2 270
## 91  22.6  22.6  0.04684   0.0  3.41    0 0.4890 6.417  66.1  3.0923   2 270
## 92  22.0  22.0  0.03932   0.0  3.41    0 0.4890 6.405  73.9  3.0921   2 270
## 93  22.9  22.9  0.04203  28.0 15.04    0 0.4640 6.442  53.6  3.6659   4 270
## 94  25.0  25.0  0.02875  28.0 15.04    0 0.4640 6.211  28.9  3.6659   4 270
## 95  20.6  20.6  0.04294  28.0 15.04    0 0.4640 6.249  77.3  3.6150   4 270
## 96  28.4  28.4  0.12204   0.0  2.89    0 0.4450 6.625  57.8  3.4952   2 276
## 97  21.4  21.4  0.11504   0.0  2.89    0 0.4450 6.163  69.6  3.4952   2 276
## 98  38.7  38.7  0.12083   0.0  2.89    0 0.4450 8.069  76.0  3.4952   2 276
## 99  43.8  43.8  0.08187   0.0  2.89    0 0.4450 7.820  36.9  3.4952   2 276
## 100 33.2  33.2  0.06860   0.0  2.89    0 0.4450 7.416  62.5  3.4952   2 276
## 101 27.5  27.5  0.14866   0.0  8.56    0 0.5200 6.727  79.9  2.7778   5 384
## 102 26.5  26.5  0.11432   0.0  8.56    0 0.5200 6.781  71.3  2.8561   5 384
## 103 18.6  18.6  0.22876   0.0  8.56    0 0.5200 6.405  85.4  2.7147   5 384
## 104 19.3  19.3  0.21161   0.0  8.56    0 0.5200 6.137  87.4  2.7147   5 384
## 105 20.1  20.1  0.13960   0.0  8.56    0 0.5200 6.167  90.0  2.4210   5 384
## 106 19.5  19.5  0.13262   0.0  8.56    0 0.5200 5.851  96.7  2.1069   5 384
## 107 19.5  19.5  0.17120   0.0  8.56    0 0.5200 5.836  91.9  2.2110   5 384
## 108 20.4  20.4  0.13117   0.0  8.56    0 0.5200 6.127  85.2  2.1224   5 384
## 109 19.8  19.8  0.12802   0.0  8.56    0 0.5200 6.474  97.1  2.4329   5 384
## 110 19.4  19.4  0.26363   0.0  8.56    0 0.5200 6.229  91.2  2.5451   5 384
## 111 21.7  21.7  0.10793   0.0  8.56    0 0.5200 6.195  54.4  2.7778   5 384
## 112 22.8  22.8  0.10084   0.0 10.01    0 0.5470 6.715  81.6  2.6775   6 432
## 113 18.8  18.8  0.12329   0.0 10.01    0 0.5470 5.913  92.9  2.3534   6 432
## 114 18.7  18.7  0.22212   0.0 10.01    0 0.5470 6.092  95.4  2.5480   6 432
## 115 18.5  18.5  0.14231   0.0 10.01    0 0.5470 6.254  84.2  2.2565   6 432
## 116 18.3  18.3  0.17134   0.0 10.01    0 0.5470 5.928  88.2  2.4631   6 432
## 117 21.2  21.2  0.13158   0.0 10.01    0 0.5470 6.176  72.5  2.7301   6 432
## 118 19.2  19.2  0.15098   0.0 10.01    0 0.5470 6.021  82.6  2.7474   6 432
## 119 20.4  20.4  0.13058   0.0 10.01    0 0.5470 5.872  73.1  2.4775   6 432
## 120 19.3  19.3  0.14476   0.0 10.01    0 0.5470 5.731  65.2  2.7592   6 432
## 121 22.0  22.0  0.06899   0.0 25.65    0 0.5810 5.870  69.7  2.2577   2 188
## 122 20.3  20.3  0.07165   0.0 25.65    0 0.5810 6.004  84.1  2.1974   2 188
## 123 20.5  20.5  0.09299   0.0 25.65    0 0.5810 5.961  92.9  2.0869   2 188
## 124 17.3  17.3  0.15038   0.0 25.65    0 0.5810 5.856  97.0  1.9444   2 188
## 125 18.8  18.8  0.09849   0.0 25.65    0 0.5810 5.879  95.8  2.0063   2 188
## 126 21.4  21.4  0.16902   0.0 25.65    0 0.5810 5.986  88.4  1.9929   2 188
## 127 15.7  15.7  0.38735   0.0 25.65    0 0.5810 5.613  95.6  1.7572   2 188
## 128 16.2  16.2  0.25915   0.0 21.89    0 0.6240 5.693  96.0  1.7883   4 437
## 129 18.0  18.0  0.32543   0.0 21.89    0 0.6240 6.431  98.8  1.8125   4 437
## 130 14.3  14.3  0.88125   0.0 21.89    0 0.6240 5.637  94.7  1.9799   4 437
## 131 19.2  19.2  0.34006   0.0 21.89    0 0.6240 6.458  98.9  2.1185   4 437
## 132 19.6  19.6  1.19294   0.0 21.89    0 0.6240 6.326  97.7  2.2710   4 437
## 133 23.0  23.0  0.59005   0.0 21.89    0 0.6240 6.372  97.9  2.3274   4 437
## 134 18.4  18.4  0.32982   0.0 21.89    0 0.6240 5.822  95.4  2.4699   4 437
## 135 15.6  15.6  0.97617   0.0 21.89    0 0.6240 5.757  98.4  2.3460   4 437
## 136 18.1  18.1  0.55778   0.0 21.89    0 0.6240 6.335  98.2  2.1107   4 437
## 137 17.4  17.4  0.32264   0.0 21.89    0 0.6240 5.942  93.5  1.9669   4 437
## 138 17.1  17.1  0.35233   0.0 21.89    0 0.6240 6.454  98.4  1.8498   4 437
## 139 13.3  13.3  0.24980   0.0 21.89    0 0.6240 5.857  98.2  1.6686   4 437
## 140 17.8  17.8  0.54452   0.0 21.89    0 0.6240 6.151  97.9  1.6687   4 437
## 141 14.0  14.0  0.29090   0.0 21.89    0 0.6240 6.174  93.6  1.6119   4 437
## 142 14.4  14.4  1.62864   0.0 21.89    0 0.6240 5.019 100.0  1.4394   4 437
## 143 13.4  13.4  3.32105   0.0 19.58    1 0.8710 5.403 100.0  1.3216   5 403
## 144 15.6  15.6  4.09740   0.0 19.58    0 0.8710 5.468 100.0  1.4118   5 403
## 145 11.8  11.8  2.77974   0.0 19.58    0 0.8710 4.903  97.8  1.3459   5 403
## 146 13.8  13.8  2.37934   0.0 19.58    0 0.8710 6.130 100.0  1.4191   5 403
## 147 15.6  15.6  2.15505   0.0 19.58    0 0.8710 5.628 100.0  1.5166   5 403
## 148 14.6  14.6  2.36862   0.0 19.58    0 0.8710 4.926  95.7  1.4608   5 403
## 149 17.8  17.8  2.33099   0.0 19.58    0 0.8710 5.186  93.8  1.5296   5 403
## 150 15.4  15.4  2.73397   0.0 19.58    0 0.8710 5.597  94.9  1.5257   5 403
## 151 21.5  21.5  1.65660   0.0 19.58    0 0.8710 6.122  97.3  1.6180   5 403
## 152 19.6  19.6  1.49632   0.0 19.58    0 0.8710 5.404 100.0  1.5916   5 403
## 153 15.3  15.3  1.12658   0.0 19.58    1 0.8710 5.012  88.0  1.6102   5 403
## 154 19.4  19.4  2.14918   0.0 19.58    0 0.8710 5.709  98.5  1.6232   5 403
## 155 17.0  17.0  1.41385   0.0 19.58    1 0.8710 6.129  96.0  1.7494   5 403
## 156 15.6  15.6  3.53501   0.0 19.58    1 0.8710 6.152  82.6  1.7455   5 403
## 157 13.1  13.1  2.44668   0.0 19.58    0 0.8710 5.272  94.0  1.7364   5 403
## 158 41.3  41.3  1.22358   0.0 19.58    0 0.6050 6.943  97.4  1.8773   5 403
## 159 24.3  24.3  1.34284   0.0 19.58    0 0.6050 6.066 100.0  1.7573   5 403
## 160 23.3  23.3  1.42502   0.0 19.58    0 0.8710 6.510 100.0  1.7659   5 403
## 161 27.0  27.0  1.27346   0.0 19.58    1 0.6050 6.250  92.6  1.7984   5 403
## 162 50.0  50.0  1.46336   0.0 19.58    0 0.6050 7.489  90.8  1.9709   5 403
## 163 50.0  50.0  1.83377   0.0 19.58    1 0.6050 7.802  98.2  2.0407   5 403
## 164 50.0  50.0  1.51902   0.0 19.58    1 0.6050 8.375  93.9  2.1620   5 403
## 165 22.7  22.7  2.24236   0.0 19.58    0 0.6050 5.854  91.8  2.4220   5 403
## 166 25.0  25.0  2.92400   0.0 19.58    0 0.6050 6.101  93.0  2.2834   5 403
## 167 50.0  50.0  2.01019   0.0 19.58    0 0.6050 7.929  96.2  2.0459   5 403
## 168 23.8  23.8  1.80028   0.0 19.58    0 0.6050 5.877  79.2  2.4259   5 403
## 169 23.8  23.8  2.30040   0.0 19.58    0 0.6050 6.319  96.1  2.1000   5 403
## 170 22.3  22.3  2.44953   0.0 19.58    0 0.6050 6.402  95.2  2.2625   5 403
## 171 17.4  17.4  1.20742   0.0 19.58    0 0.6050 5.875  94.6  2.4259   5 403
## 172 19.1  19.1  2.31390   0.0 19.58    0 0.6050 5.880  97.3  2.3887   5 403
## 173 23.1  23.1  0.13914   0.0  4.05    0 0.5100 5.572  88.5  2.5961   5 296
## 174 23.6  23.6  0.09178   0.0  4.05    0 0.5100 6.416  84.1  2.6463   5 296
## 175 22.6  22.6  0.08447   0.0  4.05    0 0.5100 5.859  68.7  2.7019   5 296
## 176 29.4  29.4  0.06664   0.0  4.05    0 0.5100 6.546  33.1  3.1323   5 296
## 177 23.2  23.2  0.07022   0.0  4.05    0 0.5100 6.020  47.2  3.5549   5 296
## 178 24.6  24.6  0.05425   0.0  4.05    0 0.5100 6.315  73.4  3.3175   5 296
## 179 29.9  29.9  0.06642   0.0  4.05    0 0.5100 6.860  74.4  2.9153   5 296
## 180 37.2  37.2  0.05780   0.0  2.46    0 0.4880 6.980  58.4  2.8290   3 193
## 181 39.8  39.8  0.06588   0.0  2.46    0 0.4880 7.765  83.3  2.7410   3 193
## 182 36.2  36.2  0.06888   0.0  2.46    0 0.4880 6.144  62.2  2.5979   3 193
## 183 37.9  37.9  0.09103   0.0  2.46    0 0.4880 7.155  92.2  2.7006   3 193
## 184 32.5  32.5  0.10008   0.0  2.46    0 0.4880 6.563  95.6  2.8470   3 193
## 185 26.4  26.4  0.08308   0.0  2.46    0 0.4880 5.604  89.8  2.9879   3 193
## 186 29.6  29.6  0.06047   0.0  2.46    0 0.4880 6.153  68.8  3.2797   3 193
## 187 50.0  50.0  0.05602   0.0  2.46    0 0.4880 7.831  53.6  3.1992   3 193
## 188 32.0  32.0  0.07875  45.0  3.44    0 0.4370 6.782  41.1  3.7886   5 398
## 189 29.8  29.8  0.12579  45.0  3.44    0 0.4370 6.556  29.1  4.5667   5 398
## 190 34.9  34.9  0.08370  45.0  3.44    0 0.4370 7.185  38.9  4.5667   5 398
## 191 37.0  33.0  0.09068  45.0  3.44    0 0.4370 6.951  21.5  6.4798   5 398
## 192 30.5  30.5  0.06911  45.0  3.44    0 0.4370 6.739  30.8  6.4798   5 398
## 193 36.4  36.4  0.08664  45.0  3.44    0 0.4370 7.178  26.3  6.4798   5 398
## 194 31.1  31.1  0.02187  60.0  2.93    0 0.4010 6.800   9.9  6.2196   1 265
## 195 29.1  29.1  0.01439  60.0  2.93    0 0.4010 6.604  18.8  6.2196   1 265
## 196 50.0  50.0  0.01381  80.0  0.46    0 0.4220 7.875  32.0  5.6484   4 255
## 197 33.3  33.3  0.04011  80.0  1.52    0 0.4040 7.287  34.1  7.3090   2 329
## 198 30.3  30.3  0.04666  80.0  1.52    0 0.4040 7.107  36.6  7.3090   2 329
## 199 34.6  34.6  0.03768  80.0  1.52    0 0.4040 7.274  38.3  7.3090   2 329
## 200 34.9  34.9  0.03150  95.0  1.47    0 0.4030 6.975  15.3  7.6534   3 402
## 201 32.9  32.9  0.01778  95.0  1.47    0 0.4030 7.135  13.9  7.6534   3 402
## 202 24.1  24.1  0.03445  82.5  2.03    0 0.4150 6.162  38.4  6.2700   2 348
## 203 42.3  42.3  0.02177  82.5  2.03    0 0.4150 7.610  15.7  6.2700   2 348
## 204 48.5  48.5  0.03510  95.0  2.68    0 0.4161 7.853  33.2  5.1180   4 224
## 205 50.0  50.0  0.02009  95.0  2.68    0 0.4161 8.034  31.9  5.1180   4 224
## 206 22.6  22.6  0.13642   0.0 10.59    0 0.4890 5.891  22.3  3.9454   4 277
## 207 24.4  24.4  0.22969   0.0 10.59    0 0.4890 6.326  52.5  4.3549   4 277
## 208 22.5  22.5  0.25199   0.0 10.59    0 0.4890 5.783  72.7  4.3549   4 277
## 209 24.4  24.4  0.13587   0.0 10.59    1 0.4890 6.064  59.1  4.2392   4 277
## 210 20.0  20.0  0.43571   0.0 10.59    1 0.4890 5.344 100.0  3.8750   4 277
## 211 21.7  21.7  0.17446   0.0 10.59    1 0.4890 5.960  92.1  3.8771   4 277
## 212 19.3  19.3  0.37578   0.0 10.59    1 0.4890 5.404  88.6  3.6650   4 277
## 213 22.4  22.4  0.21719   0.0 10.59    1 0.4890 5.807  53.8  3.6526   4 277
## 214 28.1  28.1  0.14052   0.0 10.59    0 0.4890 6.375  32.3  3.9454   4 277
## 215 23.7  23.7  0.28955   0.0 10.59    0 0.4890 5.412   9.8  3.5875   4 277
## 216 25.0  25.0  0.19802   0.0 10.59    0 0.4890 6.182  42.4  3.9454   4 277
## 217 23.3  23.3  0.04560   0.0 13.89    1 0.5500 5.888  56.0  3.1121   5 276
## 218 28.7  28.7  0.07013   0.0 13.89    0 0.5500 6.642  85.1  3.4211   5 276
## 219 21.5  21.5  0.11069   0.0 13.89    1 0.5500 5.951  93.8  2.8893   5 276
## 220 23.0  23.0  0.11425   0.0 13.89    1 0.5500 6.373  92.4  3.3633   5 276
## 221 26.7  26.7  0.35809   0.0  6.20    1 0.5070 6.951  88.5  2.8617   8 307
## 222 21.7  21.7  0.40771   0.0  6.20    1 0.5070 6.164  91.3  3.0480   8 307
## 223 27.5  27.5  0.62356   0.0  6.20    1 0.5070 6.879  77.7  3.2721   8 307
## 224 30.1  30.1  0.61470   0.0  6.20    0 0.5070 6.618  80.8  3.2721   8 307
## 225 44.8  44.8  0.31533   0.0  6.20    0 0.5040 8.266  78.3  2.8944   8 307
## 226 50.0  50.0  0.52693   0.0  6.20    0 0.5040 8.725  83.0  2.8944   8 307
## 227 37.6  37.6  0.38214   0.0  6.20    0 0.5040 8.040  86.5  3.2157   8 307
## 228 31.6  31.6  0.41238   0.0  6.20    0 0.5040 7.163  79.9  3.2157   8 307
## 229 46.7  46.7  0.29819   0.0  6.20    0 0.5040 7.686  17.0  3.3751   8 307
## 230 31.5  31.5  0.44178   0.0  6.20    0 0.5040 6.552  21.4  3.3751   8 307
## 231 24.3  24.3  0.53700   0.0  6.20    0 0.5040 5.981  68.1  3.6715   8 307
## 232 31.7  31.7  0.46296   0.0  6.20    0 0.5040 7.412  76.9  3.6715   8 307
## 233 41.7  41.7  0.57529   0.0  6.20    0 0.5070 8.337  73.3  3.8384   8 307
## 234 48.3  48.3  0.33147   0.0  6.20    0 0.5070 8.247  70.4  3.6519   8 307
## 235 29.0  29.0  0.44791   0.0  6.20    1 0.5070 6.726  66.5  3.6519   8 307
## 236 24.0  24.0  0.33045   0.0  6.20    0 0.5070 6.086  61.5  3.6519   8 307
## 237 25.1  25.1  0.52058   0.0  6.20    1 0.5070 6.631  76.5  4.1480   8 307
## 238 31.5  31.5  0.51183   0.0  6.20    0 0.5070 7.358  71.6  4.1480   8 307
## 239 23.7  23.7  0.08244  30.0  4.93    0 0.4280 6.481  18.5  6.1899   6 300
## 240 23.3  23.3  0.09252  30.0  4.93    0 0.4280 6.606  42.2  6.1899   6 300
## 241 22.0  27.0  0.11329  30.0  4.93    0 0.4280 6.897  54.3  6.3361   6 300
## 242 20.1  20.1  0.10612  30.0  4.93    0 0.4280 6.095  65.1  6.3361   6 300
## 243 22.2  22.2  0.10290  30.0  4.93    0 0.4280 6.358  52.9  7.0355   6 300
## 244 23.7  23.7  0.12757  30.0  4.93    0 0.4280 6.393   7.8  7.0355   6 300
## 245 17.6  17.6  0.20608  22.0  5.86    0 0.4310 5.593  76.5  7.9549   7 330
## 246 18.5  18.5  0.19133  22.0  5.86    0 0.4310 5.605  70.2  7.9549   7 330
## 247 24.3  24.3  0.33983  22.0  5.86    0 0.4310 6.108  34.9  8.0555   7 330
## 248 20.5  20.5  0.19657  22.0  5.86    0 0.4310 6.226  79.2  8.0555   7 330
## 249 24.5  24.5  0.16439  22.0  5.86    0 0.4310 6.433  49.1  7.8265   7 330
## 250 26.2  26.2  0.19073  22.0  5.86    0 0.4310 6.718  17.5  7.8265   7 330
## 251 24.4  24.4  0.14030  22.0  5.86    0 0.4310 6.487  13.0  7.3967   7 330
## 252 24.8  24.8  0.21409  22.0  5.86    0 0.4310 6.438   8.9  7.3967   7 330
## 253 29.6  29.6  0.08221  22.0  5.86    0 0.4310 6.957   6.8  8.9067   7 330
## 254 42.8  42.8  0.36894  22.0  5.86    0 0.4310 8.259   8.4  8.9067   7 330
## 255 21.9  21.9  0.04819  80.0  3.64    0 0.3920 6.108  32.0  9.2203   1 315
## 256 20.9  20.9  0.03548  80.0  3.64    0 0.3920 5.876  19.1  9.2203   1 315
## 257 44.0  44.0  0.01538  90.0  3.75    0 0.3940 7.454  34.2  6.3361   3 244
## 258 50.0  50.0  0.61154  20.0  3.97    0 0.6470 8.704  86.9  1.8010   5 264
## 259 36.0  36.0  0.66351  20.0  3.97    0 0.6470 7.333 100.0  1.8946   5 264
## 260 30.1  30.1  0.65665  20.0  3.97    0 0.6470 6.842 100.0  2.0107   5 264
## 261 33.8  33.8  0.54011  20.0  3.97    0 0.6470 7.203  81.8  2.1121   5 264
## 262 43.1  43.1  0.53412  20.0  3.97    0 0.6470 7.520  89.4  2.1398   5 264
## 263 48.8  48.8  0.52014  20.0  3.97    0 0.6470 8.398  91.5  2.2885   5 264
## 264 31.0  31.0  0.82526  20.0  3.97    0 0.6470 7.327  94.5  2.0788   5 264
## 265 36.5  36.5  0.55007  20.0  3.97    0 0.6470 7.206  91.6  1.9301   5 264
## 266 22.8  22.8  0.76162  20.0  3.97    0 0.6470 5.560  62.8  1.9865   5 264
## 267 30.7  30.7  0.78570  20.0  3.97    0 0.6470 7.014  84.6  2.1329   5 264
## 268 50.0  50.0  0.57834  20.0  3.97    0 0.5750 8.297  67.0  2.4216   5 264
## 269 43.5  43.5  0.54050  20.0  3.97    0 0.5750 7.470  52.6  2.8720   5 264
## 270 20.7  20.7  0.09065  20.0  6.96    1 0.4640 5.920  61.5  3.9175   3 223
## 271 21.1  21.1  0.29916  20.0  6.96    0 0.4640 5.856  42.1  4.4290   3 223
## 272 25.2  25.2  0.16211  20.0  6.96    0 0.4640 6.240  16.3  4.4290   3 223
## 273 24.4  24.4  0.11460  20.0  6.96    0 0.4640 6.538  58.7  3.9175   3 223
## 274 35.2  35.2  0.22188  20.0  6.96    1 0.4640 7.691  51.8  4.3665   3 223
## 275 32.4  32.4  0.05644  40.0  6.41    1 0.4470 6.758  32.9  4.0776   4 254
## 276 32.0  32.0  0.09604  40.0  6.41    0 0.4470 6.854  42.8  4.2673   4 254
## 277 33.2  33.2  0.10469  40.0  6.41    1 0.4470 7.267  49.0  4.7872   4 254
## 278 33.1  33.1  0.06127  40.0  6.41    1 0.4470 6.826  27.6  4.8628   4 254
## 279 29.1  29.1  0.07978  40.0  6.41    0 0.4470 6.482  32.1  4.1403   4 254
## 280 35.1  35.1  0.21038  20.0  3.33    0 0.4429 6.812  32.2  4.1007   5 216
## 281 45.4  45.4  0.03578  20.0  3.33    0 0.4429 7.820  64.5  4.6947   5 216
## 282 35.4  35.4  0.03705  20.0  3.33    0 0.4429 6.968  37.2  5.2447   5 216
## 283 46.0  46.0  0.06129  20.0  3.33    1 0.4429 7.645  49.7  5.2119   5 216
## 284 50.0  50.0  0.01501  90.0  1.21    1 0.4010 7.923  24.8  5.8850   1 198
## 285 32.2  32.2  0.00906  90.0  2.97    0 0.4000 7.088  20.8  7.3073   1 285
## 286 22.0  22.0  0.01096  55.0  2.25    0 0.3890 6.453  31.9  7.3073   1 300
## 287 20.1  20.1  0.01965  80.0  1.76    0 0.3850 6.230  31.5  9.0892   1 241
## 288 23.2  23.2  0.03871  52.5  5.32    0 0.4050 6.209  31.3  7.3172   6 293
## 289 22.3  22.3  0.04590  52.5  5.32    0 0.4050 6.315  45.6  7.3172   6 293
## 290 24.8  24.8  0.04297  52.5  5.32    0 0.4050 6.565  22.9  7.3172   6 293
## 291 28.5  28.5  0.03502  80.0  4.95    0 0.4110 6.861  27.9  5.1167   4 245
## 292 37.3  37.3  0.07886  80.0  4.95    0 0.4110 7.148  27.7  5.1167   4 245
## 293 27.9  27.9  0.03615  80.0  4.95    0 0.4110 6.630  23.4  5.1167   4 245
## 294 23.9  23.9  0.08265   0.0 13.92    0 0.4370 6.127  18.4  5.5027   4 289
## 295 21.7  21.7  0.08199   0.0 13.92    0 0.4370 6.009  42.3  5.5027   4 289
## 296 28.6  28.6  0.12932   0.0 13.92    0 0.4370 6.678  31.1  5.9604   4 289
## 297 27.1  27.1  0.05372   0.0 13.92    0 0.4370 6.549  51.0  5.9604   4 289
## 298 20.3  20.3  0.14103   0.0 13.92    0 0.4370 5.790  58.0  6.3200   4 289
## 299 22.5  22.5  0.06466  70.0  2.24    0 0.4000 6.345  20.1  7.8278   5 358
## 300 29.0  29.0  0.05561  70.0  2.24    0 0.4000 7.041  10.0  7.8278   5 358
## 301 24.8  24.8  0.04417  70.0  2.24    0 0.4000 6.871  47.4  7.8278   5 358
## 302 22.0  22.0  0.03537  34.0  6.09    0 0.4330 6.590  40.4  5.4917   7 329
## 303 26.4  26.4  0.09266  34.0  6.09    0 0.4330 6.495  18.4  5.4917   7 329
## 304 33.1  33.1  0.10000  34.0  6.09    0 0.4330 6.982  17.7  5.4917   7 329
## 305 36.1  36.1  0.05515  33.0  2.18    0 0.4720 7.236  41.1  4.0220   7 222
## 306 28.4  28.4  0.05479  33.0  2.18    0 0.4720 6.616  58.1  3.3700   7 222
## 307 33.4  33.4  0.07503  33.0  2.18    0 0.4720 7.420  71.9  3.0992   7 222
## 308 28.2  28.2  0.04932  33.0  2.18    0 0.4720 6.849  70.3  3.1827   7 222
## 309 22.8  22.8  0.49298   0.0  9.90    0 0.5440 6.635  82.5  3.3175   4 304
## 310 20.3  20.3  0.34940   0.0  9.90    0 0.5440 5.972  76.7  3.1025   4 304
## 311 16.1  16.1  2.63548   0.0  9.90    0 0.5440 4.973  37.8  2.5194   4 304
## 312 22.1  22.1  0.79041   0.0  9.90    0 0.5440 6.122  52.8  2.6403   4 304
## 313 19.4  19.4  0.26169   0.0  9.90    0 0.5440 6.023  90.4  2.8340   4 304
## 314 21.6  21.6  0.26938   0.0  9.90    0 0.5440 6.266  82.8  3.2628   4 304
## 315 23.8  23.8  0.36920   0.0  9.90    0 0.5440 6.567  87.3  3.6023   4 304
## 316 16.2  16.2  0.25356   0.0  9.90    0 0.5440 5.705  77.7  3.9450   4 304
## 317 17.8  17.8  0.31827   0.0  9.90    0 0.5440 5.914  83.2  3.9986   4 304
## 318 19.8  19.8  0.24522   0.0  9.90    0 0.5440 5.782  71.7  4.0317   4 304
## 319 23.1  23.1  0.40202   0.0  9.90    0 0.5440 6.382  67.2  3.5325   4 304
## 320 21.0  21.0  0.47547   0.0  9.90    0 0.5440 6.113  58.8  4.0019   4 304
## 321 23.8  23.8  0.16760   0.0  7.38    0 0.4930 6.426  52.3  4.5404   5 287
## 322 23.1  23.1  0.18159   0.0  7.38    0 0.4930 6.376  54.3  4.5404   5 287
## 323 20.4  20.4  0.35114   0.0  7.38    0 0.4930 6.041  49.9  4.7211   5 287
## 324 18.5  18.5  0.28392   0.0  7.38    0 0.4930 5.708  74.3  4.7211   5 287
## 325 25.0  25.0  0.34109   0.0  7.38    0 0.4930 6.415  40.1  4.7211   5 287
## 326 24.6  24.6  0.19186   0.0  7.38    0 0.4930 6.431  14.7  5.4159   5 287
## 327 23.0  23.0  0.30347   0.0  7.38    0 0.4930 6.312  28.9  5.4159   5 287
## 328 22.2  22.2  0.24103   0.0  7.38    0 0.4930 6.083  43.7  5.4159   5 287
## 329 19.3  19.3  0.06617   0.0  3.24    0 0.4600 5.868  25.8  5.2146   4 430
## 330 22.6  22.6  0.06724   0.0  3.24    0 0.4600 6.333  17.2  5.2146   4 430
## 331 19.8  19.8  0.04544   0.0  3.24    0 0.4600 6.144  32.2  5.8736   4 430
## 332 17.1  17.1  0.05023  35.0  6.06    0 0.4379 5.706  28.4  6.6407   1 304
## 333 19.4  19.4  0.03466  35.0  6.06    0 0.4379 6.031  23.3  6.6407   1 304
## 334 22.2  22.2  0.05083   0.0  5.19    0 0.5150 6.316  38.1  6.4584   5 224
## 335 20.7  20.7  0.03738   0.0  5.19    0 0.5150 6.310  38.5  6.4584   5 224
## 336 21.1  21.1  0.03961   0.0  5.19    0 0.5150 6.037  34.5  5.9853   5 224
## 337 19.5  19.5  0.03427   0.0  5.19    0 0.5150 5.869  46.3  5.2311   5 224
## 338 18.5  18.5  0.03041   0.0  5.19    0 0.5150 5.895  59.6  5.6150   5 224
## 339 20.6  20.6  0.03306   0.0  5.19    0 0.5150 6.059  37.3  4.8122   5 224
## 340 19.0  19.0  0.05497   0.0  5.19    0 0.5150 5.985  45.4  4.8122   5 224
## 341 18.7  18.7  0.06151   0.0  5.19    0 0.5150 5.968  58.5  4.8122   5 224
## 342 32.7  32.7  0.01301  35.0  1.52    0 0.4420 7.241  49.3  7.0379   1 284
## 343 16.5  16.5  0.02498   0.0  1.89    0 0.5180 6.540  59.7  6.2669   1 422
## 344 23.9  23.9  0.02543  55.0  3.78    0 0.4840 6.696  56.4  5.7321   5 370
## 345 31.2  31.2  0.03049  55.0  3.78    0 0.4840 6.874  28.1  6.4654   5 370
## 346 17.5  17.5  0.03113   0.0  4.39    0 0.4420 6.014  48.5  8.0136   3 352
## 347 17.2  17.2  0.06162   0.0  4.39    0 0.4420 5.898  52.3  8.0136   3 352
## 348 23.1  23.1  0.01870  85.0  4.15    0 0.4290 6.516  27.7  8.5353   4 351
## 349 24.5  24.5  0.01501  80.0  2.01    0 0.4350 6.635  29.7  8.3440   4 280
## 350 26.6  26.6  0.02899  40.0  1.25    0 0.4290 6.939  34.5  8.7921   1 335
## 351 22.9  22.9  0.06211  40.0  1.25    0 0.4290 6.490  44.4  8.7921   1 335
## 352 24.1  24.1  0.07950  60.0  1.69    0 0.4110 6.579  35.9 10.7103   4 411
## 353 18.6  18.6  0.07244  60.0  1.69    0 0.4110 5.884  18.5 10.7103   4 411
## 354 30.1  30.1  0.01709  90.0  2.02    0 0.4100 6.728  36.1 12.1265   5 187
## 355 18.2  18.2  0.04301  80.0  1.91    0 0.4130 5.663  21.9 10.5857   4 334
## 356 20.6  20.6  0.10659  80.0  1.91    0 0.4130 5.936  19.5 10.5857   4 334
## 357 17.8  17.8  8.98296   0.0 18.10    1 0.7700 6.212  97.4  2.1222  24 666
## 358 21.7  21.7  3.84970   0.0 18.10    1 0.7700 6.395  91.0  2.5052  24 666
## 359 22.7  22.7  5.20177   0.0 18.10    1 0.7700 6.127  83.4  2.7227  24 666
## 360 22.6  22.6  4.26131   0.0 18.10    0 0.7700 6.112  81.3  2.5091  24 666
## 361 25.0  25.0  4.54192   0.0 18.10    0 0.7700 6.398  88.0  2.5182  24 666
## 362 19.9  19.9  3.83684   0.0 18.10    0 0.7700 6.251  91.1  2.2955  24 666
## 363 20.8  20.8  3.67822   0.0 18.10    0 0.7700 5.362  96.2  2.1036  24 666
## 364 16.8  16.8  4.22239   0.0 18.10    1 0.7700 5.803  89.0  1.9047  24 666
## 365 21.9  21.9  3.47428   0.0 18.10    1 0.7180 8.780  82.9  1.9047  24 666
## 366 27.5  27.5  4.55587   0.0 18.10    0 0.7180 3.561  87.9  1.6132  24 666
## 367 21.9  21.9  3.69695   0.0 18.10    0 0.7180 4.963  91.4  1.7523  24 666
## 368 23.1  23.1 13.52220   0.0 18.10    0 0.6310 3.863 100.0  1.5106  24 666
## 369 50.0  50.0  4.89822   0.0 18.10    0 0.6310 4.970 100.0  1.3325  24 666
## 370 50.0  50.0  5.66998   0.0 18.10    1 0.6310 6.683  96.8  1.3567  24 666
## 371 50.0  50.0  6.53876   0.0 18.10    1 0.6310 7.016  97.5  1.2024  24 666
## 372 50.0  50.0  9.23230   0.0 18.10    0 0.6310 6.216 100.0  1.1691  24 666
## 373 50.0  50.0  8.26725   0.0 18.10    1 0.6680 5.875  89.6  1.1296  24 666
## 374 13.8  13.8 11.10810   0.0 18.10    0 0.6680 4.906 100.0  1.1742  24 666
## 375 13.8  13.8 18.49820   0.0 18.10    0 0.6680 4.138 100.0  1.1370  24 666
## 376 15.0  15.0 19.60910   0.0 18.10    0 0.6710 7.313  97.9  1.3163  24 666
## 377 13.9  13.9 15.28800   0.0 18.10    0 0.6710 6.649  93.3  1.3449  24 666
## 378 13.3  13.3  9.82349   0.0 18.10    0 0.6710 6.794  98.8  1.3580  24 666
## 379 13.1  13.1 23.64820   0.0 18.10    0 0.6710 6.380  96.2  1.3861  24 666
## 380 10.2  10.2 17.86670   0.0 18.10    0 0.6710 6.223 100.0  1.3861  24 666
## 381 10.4  10.4 88.97620   0.0 18.10    0 0.6710 6.968  91.9  1.4165  24 666
## 382 10.9  10.9 15.87440   0.0 18.10    0 0.6710 6.545  99.1  1.5192  24 666
## 383 11.3  11.3  9.18702   0.0 18.10    0 0.7000 5.536 100.0  1.5804  24 666
## 384 12.3  12.3  7.99248   0.0 18.10    0 0.7000 5.520 100.0  1.5331  24 666
## 385  8.8   8.8 20.08490   0.0 18.10    0 0.7000 4.368  91.2  1.4395  24 666
## 386  7.2   7.2 16.81180   0.0 18.10    0 0.7000 5.277  98.1  1.4261  24 666
## 387 10.5  10.5 24.39380   0.0 18.10    0 0.7000 4.652 100.0  1.4672  24 666
## 388  7.4   7.4 22.59710   0.0 18.10    0 0.7000 5.000  89.5  1.5184  24 666
## 389 10.2  10.2 14.33370   0.0 18.10    0 0.7000 4.880 100.0  1.5895  24 666
## 390 11.5  11.5  8.15174   0.0 18.10    0 0.7000 5.390  98.9  1.7281  24 666
## 391 15.1  15.1  6.96215   0.0 18.10    0 0.7000 5.713  97.0  1.9265  24 666
## 392 23.2  23.2  5.29305   0.0 18.10    0 0.7000 6.051  82.5  2.1678  24 666
## 393  9.7   9.7 11.57790   0.0 18.10    0 0.7000 5.036  97.0  1.7700  24 666
## 394 13.8  13.8  8.64476   0.0 18.10    0 0.6930 6.193  92.6  1.7912  24 666
## 395 12.7  12.7 13.35980   0.0 18.10    0 0.6930 5.887  94.7  1.7821  24 666
## 396 13.1  13.1  8.71675   0.0 18.10    0 0.6930 6.471  98.8  1.7257  24 666
## 397 12.5  12.5  5.87205   0.0 18.10    0 0.6930 6.405  96.0  1.6768  24 666
## 398  8.5   8.5  7.67202   0.0 18.10    0 0.6930 5.747  98.9  1.6334  24 666
## 399  5.0   5.0 38.35180   0.0 18.10    0 0.6930 5.453 100.0  1.4896  24 666
## 400  6.3   6.3  9.91655   0.0 18.10    0 0.6930 5.852  77.8  1.5004  24 666
## 401  5.6   5.6 25.04610   0.0 18.10    0 0.6930 5.987 100.0  1.5888  24 666
## 402  7.2   7.2 14.23620   0.0 18.10    0 0.6930 6.343 100.0  1.5741  24 666
## 403 12.1  12.1  9.59571   0.0 18.10    0 0.6930 6.404 100.0  1.6390  24 666
## 404  8.3   8.3 24.80170   0.0 18.10    0 0.6930 5.349  96.0  1.7028  24 666
## 405  8.5   8.5 41.52920   0.0 18.10    0 0.6930 5.531  85.4  1.6074  24 666
## 406  5.0   5.0 67.92080   0.0 18.10    0 0.6930 5.683 100.0  1.4254  24 666
## 407 11.9  11.9 20.71620   0.0 18.10    0 0.6590 4.138 100.0  1.1781  24 666
## 408 27.9  27.9 11.95110   0.0 18.10    0 0.6590 5.608 100.0  1.2852  24 666
## 409 17.2  17.2  7.40389   0.0 18.10    0 0.5970 5.617  97.9  1.4547  24 666
## 410 27.5  27.5 14.43830   0.0 18.10    0 0.5970 6.852 100.0  1.4655  24 666
## 411 15.0  15.0 51.13580   0.0 18.10    0 0.5970 5.757 100.0  1.4130  24 666
## 412 17.2  17.2 14.05070   0.0 18.10    0 0.5970 6.657 100.0  1.5275  24 666
## 413 17.9  17.9 18.81100   0.0 18.10    0 0.5970 4.628 100.0  1.5539  24 666
## 414 16.3  16.3 28.65580   0.0 18.10    0 0.5970 5.155 100.0  1.5894  24 666
## 415  7.0   7.0 45.74610   0.0 18.10    0 0.6930 4.519 100.0  1.6582  24 666
## 416  7.2   7.2 18.08460   0.0 18.10    0 0.6790 6.434 100.0  1.8347  24 666
## 417  7.5   7.5 10.83420   0.0 18.10    0 0.6790 6.782  90.8  1.8195  24 666
## 418 10.4  10.4 25.94060   0.0 18.10    0 0.6790 5.304  89.1  1.6475  24 666
## 419  8.8   8.8 73.53410   0.0 18.10    0 0.6790 5.957 100.0  1.8026  24 666
## 420  8.4   8.4 11.81230   0.0 18.10    0 0.7180 6.824  76.5  1.7940  24 666
## 421 16.7  16.7 11.08740   0.0 18.10    0 0.7180 6.411 100.0  1.8589  24 666
## 422 14.2  14.2  7.02259   0.0 18.10    0 0.7180 6.006  95.3  1.8746  24 666
## 423 20.8  20.8 12.04820   0.0 18.10    0 0.6140 5.648  87.6  1.9512  24 666
## 424 13.4  13.4  7.05042   0.0 18.10    0 0.6140 6.103  85.1  2.0218  24 666
## 425 11.7  11.7  8.79212   0.0 18.10    0 0.5840 5.565  70.6  2.0635  24 666
## 426  8.3   8.3 15.86030   0.0 18.10    0 0.6790 5.896  95.4  1.9096  24 666
## 427 10.2  10.2 12.24720   0.0 18.10    0 0.5840 5.837  59.7  1.9976  24 666
## 428 10.9  10.9 37.66190   0.0 18.10    0 0.6790 6.202  78.7  1.8629  24 666
## 429 11.0  11.0  7.36711   0.0 18.10    0 0.6790 6.193  78.1  1.9356  24 666
## 430  9.5   9.5  9.33889   0.0 18.10    0 0.6790 6.380  95.6  1.9682  24 666
## 431 14.5  14.5  8.49213   0.0 18.10    0 0.5840 6.348  86.1  2.0527  24 666
## 432 14.1  14.1 10.06230   0.0 18.10    0 0.5840 6.833  94.3  2.0882  24 666
## 433 16.1  16.1  6.44405   0.0 18.10    0 0.5840 6.425  74.8  2.2004  24 666
## 434 14.3  14.3  5.58107   0.0 18.10    0 0.7130 6.436  87.9  2.3158  24 666
## 435 11.7  11.7 13.91340   0.0 18.10    0 0.7130 6.208  95.0  2.2222  24 666
## 436 13.4  13.4 11.16040   0.0 18.10    0 0.7400 6.629  94.6  2.1247  24 666
## 437  9.6   9.6 14.42080   0.0 18.10    0 0.7400 6.461  93.3  2.0026  24 666
## 438  8.7   8.2 15.17720   0.0 18.10    0 0.7400 6.152 100.0  1.9142  24 666
## 439  8.4   8.4 13.67810   0.0 18.10    0 0.7400 5.935  87.9  1.8206  24 666
## 440 12.8  12.8  9.39063   0.0 18.10    0 0.7400 5.627  93.9  1.8172  24 666
## 441 10.5  10.5 22.05110   0.0 18.10    0 0.7400 5.818  92.4  1.8662  24 666
## 442 17.1  17.1  9.72418   0.0 18.10    0 0.7400 6.406  97.2  2.0651  24 666
## 443 18.4  14.8  5.66637   0.0 18.10    0 0.7400 6.219 100.0  2.0048  24 666
## 444 15.4  15.4  9.96654   0.0 18.10    0 0.7400 6.485 100.0  1.9784  24 666
## 445 10.8  10.8 12.80230   0.0 18.10    0 0.7400 5.854  96.6  1.8956  24 666
## 446 11.8  11.8 10.67180   0.0 18.10    0 0.7400 6.459  94.8  1.9879  24 666
## 447 14.9  14.9  6.28807   0.0 18.10    0 0.7400 6.341  96.4  2.0720  24 666
## 448 12.6  12.6  9.92485   0.0 18.10    0 0.7400 6.251  96.6  2.1980  24 666
## 449 14.1  14.1  9.32909   0.0 18.10    0 0.7130 6.185  98.7  2.2616  24 666
## 450 13.0  13.0  7.52601   0.0 18.10    0 0.7130 6.417  98.3  2.1850  24 666
## 451 13.4  13.4  6.71772   0.0 18.10    0 0.7130 6.749  92.6  2.3236  24 666
## 452 15.2  15.2  5.44114   0.0 18.10    0 0.7130 6.655  98.2  2.3552  24 666
## 453 16.1  16.1  5.09017   0.0 18.10    0 0.7130 6.297  91.8  2.3682  24 666
## 454 17.8  17.8  8.24809   0.0 18.10    0 0.7130 7.393  99.3  2.4527  24 666
## 455 14.9  14.4  9.51363   0.0 18.10    0 0.7130 6.728  94.1  2.4961  24 666
## 456 14.1  14.1  4.75237   0.0 18.10    0 0.7130 6.525  86.5  2.4358  24 666
## 457 12.7  12.7  4.66883   0.0 18.10    0 0.7130 5.976  87.9  2.5806  24 666
## 458 13.5  13.5  8.20058   0.0 18.10    0 0.7130 5.936  80.3  2.7792  24 666
## 459 14.9  14.9  7.75223   0.0 18.10    0 0.7130 6.301  83.7  2.7831  24 666
## 460 20.0  20.0  6.80117   0.0 18.10    0 0.7130 6.081  84.4  2.7175  24 666
## 461 16.4  16.4  4.81213   0.0 18.10    0 0.7130 6.701  90.0  2.5975  24 666
## 462 17.7  17.7  3.69311   0.0 18.10    0 0.7130 6.376  88.4  2.5671  24 666
## 463 19.5  19.5  6.65492   0.0 18.10    0 0.7130 6.317  83.0  2.7344  24 666
## 464 20.2  20.2  5.82115   0.0 18.10    0 0.7130 6.513  89.9  2.8016  24 666
## 465 21.4  21.4  7.83932   0.0 18.10    0 0.6550 6.209  65.4  2.9634  24 666
## 466 19.9  19.9  3.16360   0.0 18.10    0 0.6550 5.759  48.2  3.0665  24 666
## 467 19.0  19.0  3.77498   0.0 18.10    0 0.6550 5.952  84.7  2.8715  24 666
## 468 19.1  19.1  4.42228   0.0 18.10    0 0.5840 6.003  94.5  2.5403  24 666
## 469 19.1  19.1 15.57570   0.0 18.10    0 0.5800 5.926  71.0  2.9084  24 666
## 470 20.1  20.1 13.07510   0.0 18.10    0 0.5800 5.713  56.7  2.8237  24 666
## 471 19.9  19.9  4.34879   0.0 18.10    0 0.5800 6.167  84.0  3.0334  24 666
## 472 19.6  19.6  4.03841   0.0 18.10    0 0.5320 6.229  90.7  3.0993  24 666
## 473 23.2  23.2  3.56868   0.0 18.10    0 0.5800 6.437  75.0  2.8965  24 666
## 474 29.8  29.8  4.64689   0.0 18.10    0 0.6140 6.980  67.6  2.5329  24 666
## 475 13.8  13.8  8.05579   0.0 18.10    0 0.5840 5.427  95.4  2.4298  24 666
## 476 13.3  13.3  6.39312   0.0 18.10    0 0.5840 6.162  97.4  2.2060  24 666
## 477 16.7  16.7  4.87141   0.0 18.10    0 0.6140 6.484  93.6  2.3053  24 666
## 478 12.0  12.0 15.02340   0.0 18.10    0 0.6140 5.304  97.3  2.1007  24 666
## 479 14.6  14.6 10.23300   0.0 18.10    0 0.6140 6.185  96.7  2.1705  24 666
## 480 21.4  21.4 14.33370   0.0 18.10    0 0.6140 6.229  88.0  1.9512  24 666
## 481 23.0  23.0  5.82401   0.0 18.10    0 0.5320 6.242  64.7  3.4242  24 666
## 482 23.7  23.7  5.70818   0.0 18.10    0 0.5320 6.750  74.9  3.3317  24 666
## 483 25.0  25.0  5.73116   0.0 18.10    0 0.5320 7.061  77.0  3.4106  24 666
## 484 21.8  21.8  2.81838   0.0 18.10    0 0.5320 5.762  40.3  4.0983  24 666
## 485 20.6  20.6  2.37857   0.0 18.10    0 0.5830 5.871  41.9  3.7240  24 666
## 486 21.2  21.2  3.67367   0.0 18.10    0 0.5830 6.312  51.9  3.9917  24 666
## 487 19.1  19.1  5.69175   0.0 18.10    0 0.5830 6.114  79.8  3.5459  24 666
## 488 20.6  20.6  4.83567   0.0 18.10    0 0.5830 5.905  53.2  3.1523  24 666
## 489 15.2  15.2  0.15086   0.0 27.74    0 0.6090 5.454  92.7  1.8209   4 711
## 490  7.0   7.0  0.18337   0.0 27.74    0 0.6090 5.414  98.3  1.7554   4 711
## 491  8.1   8.1  0.20746   0.0 27.74    0 0.6090 5.093  98.0  1.8226   4 711
## 492 13.6  13.6  0.10574   0.0 27.74    0 0.6090 5.983  98.8  1.8681   4 711
## 493 20.1  20.1  0.11132   0.0 27.74    0 0.6090 5.983  83.5  2.1099   4 711
## 494 21.8  21.8  0.17331   0.0  9.69    0 0.5850 5.707  54.0  2.3817   6 391
## 495 24.5  24.5  0.27957   0.0  9.69    0 0.5850 5.926  42.6  2.3817   6 391
## 496 23.1  23.1  0.17899   0.0  9.69    0 0.5850 5.670  28.8  2.7986   6 391
## 497 19.7  19.7  0.28960   0.0  9.69    0 0.5850 5.390  72.9  2.7986   6 391
## 498 18.3  18.3  0.26838   0.0  9.69    0 0.5850 5.794  70.6  2.8927   6 391
## 499 21.2  21.2  0.23912   0.0  9.69    0 0.5850 6.019  65.3  2.4091   6 391
## 500 17.5  17.5  0.17783   0.0  9.69    0 0.5850 5.569  73.5  2.3999   6 391
## 501 16.8  16.8  0.22438   0.0  9.69    0 0.5850 6.027  79.7  2.4982   6 391
## 502 22.4  22.4  0.06263   0.0 11.93    0 0.5730 6.593  69.1  2.4786   1 273
## 503 20.6  20.6  0.04527   0.0 11.93    0 0.5730 6.120  76.7  2.2875   1 273
## 504 23.9  23.9  0.06076   0.0 11.93    0 0.5730 6.976  91.0  2.1675   1 273
## 505 22.0  22.0  0.10959   0.0 11.93    0 0.5730 6.794  89.3  2.3889   1 273
## 506 11.9  19.0  0.04741   0.0 11.93    0 0.5730 6.030  80.8  2.5050   1 273
##     ptratio      b lstat
## 1      15.3 396.90  4.98
## 2      17.8 396.90  9.14
## 3      17.8 392.83  4.03
## 4      18.7 394.63  2.94
## 5      18.7 396.90  5.33
## 6      18.7 394.12  5.21
## 7      15.2 395.60 12.43
## 8      15.2 396.90 19.15
## 9      15.2 386.63 29.93
## 10     15.2 386.71 17.10
## 11     15.2 392.52 20.45
## 12     15.2 396.90 13.27
## 13     15.2 390.50 15.71
## 14     21.0 396.90  8.26
## 15     21.0 380.02 10.26
## 16     21.0 395.62  8.47
## 17     21.0 386.85  6.58
## 18     21.0 386.75 14.67
## 19     21.0 288.99 11.69
## 20     21.0 390.95 11.28
## 21     21.0 376.57 21.02
## 22     21.0 392.53 13.83
## 23     21.0 396.90 18.72
## 24     21.0 394.54 19.88
## 25     21.0 394.33 16.30
## 26     21.0 303.42 16.51
## 27     21.0 376.88 14.81
## 28     21.0 306.38 17.28
## 29     21.0 387.94 12.80
## 30     21.0 380.23 11.98
## 31     21.0 360.17 22.60
## 32     21.0 376.73 13.04
## 33     21.0 232.60 27.71
## 34     21.0 358.77 18.35
## 35     21.0 248.31 20.34
## 36     19.2 396.90  9.68
## 37     19.2 377.56 11.41
## 38     19.2 396.90  8.77
## 39     19.2 393.43 10.13
## 40     18.3 395.63  4.32
## 41     18.3 395.62  1.98
## 42     17.9 385.41  4.84
## 43     17.9 383.37  5.81
## 44     17.9 394.46  7.44
## 45     17.9 389.39  9.55
## 46     17.9 396.90 10.21
## 47     17.9 396.90 14.15
## 48     17.9 392.74 18.80
## 49     17.9 396.90 30.81
## 50     17.9 396.90 16.20
## 51     16.8 395.56 13.45
## 52     16.8 393.97  9.43
## 53     16.8 396.90  5.28
## 54     16.8 396.90  8.43
## 55     21.1 396.90 14.80
## 56     17.9 395.93  4.81
## 57     17.3 396.90  5.77
## 58     15.1 392.90  3.95
## 59     19.7 390.68  6.86
## 60     19.7 396.90  9.22
## 61     19.7 395.11 13.15
## 62     19.7 378.08 14.44
## 63     19.7 396.90  6.73
## 64     19.7 395.58  9.50
## 65     18.6 393.24  8.05
## 66     16.1 396.90  4.67
## 67     16.1 396.90 10.24
## 68     18.9 396.21  8.10
## 69     18.9 396.90 13.09
## 70     18.9 396.90  8.79
## 71     19.2 383.73  6.72
## 72     19.2 376.94  9.88
## 73     19.2 390.91  5.52
## 74     19.2 377.17  7.54
## 75     18.7 394.92  6.78
## 76     18.7 383.23  8.94
## 77     18.7 373.66 11.97
## 78     18.7 386.96 10.27
## 79     18.7 386.40 12.34
## 80     18.7 396.06  9.10
## 81     19.0 396.90  5.29
## 82     19.0 395.63  7.22
## 83     19.0 396.90  6.72
## 84     19.0 390.64  7.51
## 85     18.5 396.90  9.62
## 86     18.5 392.30  6.53
## 87     18.5 395.99 12.86
## 88     18.5 395.15  8.44
## 89     17.8 396.90  5.50
## 90     17.8 396.06  5.70
## 91     17.8 392.18  8.81
## 92     17.8 393.55  8.20
## 93     18.2 395.01  8.16
## 94     18.2 396.33  6.21
## 95     18.2 396.90 10.59
## 96     18.0 357.98  6.65
## 97     18.0 391.83 11.34
## 98     18.0 396.90  4.21
## 99     18.0 393.53  3.57
## 100    18.0 396.90  6.19
## 101    20.9 394.76  9.42
## 102    20.9 395.58  7.67
## 103    20.9  70.80 10.63
## 104    20.9 394.47 13.44
## 105    20.9 392.69 12.33
## 106    20.9 394.05 16.47
## 107    20.9 395.67 18.66
## 108    20.9 387.69 14.09
## 109    20.9 395.24 12.27
## 110    20.9 391.23 15.55
## 111    20.9 393.49 13.00
## 112    17.8 395.59 10.16
## 113    17.8 394.95 16.21
## 114    17.8 396.90 17.09
## 115    17.8 388.74 10.45
## 116    17.8 344.91 15.76
## 117    17.8 393.30 12.04
## 118    17.8 394.51 10.30
## 119    17.8 338.63 15.37
## 120    17.8 391.50 13.61
## 121    19.1 389.15 14.37
## 122    19.1 377.67 14.27
## 123    19.1 378.09 17.93
## 124    19.1 370.31 25.41
## 125    19.1 379.38 17.58
## 126    19.1 385.02 14.81
## 127    19.1 359.29 27.26
## 128    21.2 392.11 17.19
## 129    21.2 396.90 15.39
## 130    21.2 396.90 18.34
## 131    21.2 395.04 12.60
## 132    21.2 396.90 12.26
## 133    21.2 385.76 11.12
## 134    21.2 388.69 15.03
## 135    21.2 262.76 17.31
## 136    21.2 394.67 16.96
## 137    21.2 378.25 16.90
## 138    21.2 394.08 14.59
## 139    21.2 392.04 21.32
## 140    21.2 396.90 18.46
## 141    21.2 388.08 24.16
## 142    21.2 396.90 34.41
## 143    14.7 396.90 26.82
## 144    14.7 396.90 26.42
## 145    14.7 396.90 29.29
## 146    14.7 172.91 27.80
## 147    14.7 169.27 16.65
## 148    14.7 391.71 29.53
## 149    14.7 356.99 28.32
## 150    14.7 351.85 21.45
## 151    14.7 372.80 14.10
## 152    14.7 341.60 13.28
## 153    14.7 343.28 12.12
## 154    14.7 261.95 15.79
## 155    14.7 321.02 15.12
## 156    14.7  88.01 15.02
## 157    14.7  88.63 16.14
## 158    14.7 363.43  4.59
## 159    14.7 353.89  6.43
## 160    14.7 364.31  7.39
## 161    14.7 338.92  5.50
## 162    14.7 374.43  1.73
## 163    14.7 389.61  1.92
## 164    14.7 388.45  3.32
## 165    14.7 395.11 11.64
## 166    14.7 240.16  9.81
## 167    14.7 369.30  3.70
## 168    14.7 227.61 12.14
## 169    14.7 297.09 11.10
## 170    14.7 330.04 11.32
## 171    14.7 292.29 14.43
## 172    14.7 348.13 12.03
## 173    16.6 396.90 14.69
## 174    16.6 395.50  9.04
## 175    16.6 393.23  9.64
## 176    16.6 390.96  5.33
## 177    16.6 393.23 10.11
## 178    16.6 395.60  6.29
## 179    16.6 391.27  6.92
## 180    17.8 396.90  5.04
## 181    17.8 395.56  7.56
## 182    17.8 396.90  9.45
## 183    17.8 394.12  4.82
## 184    17.8 396.90  5.68
## 185    17.8 391.00 13.98
## 186    17.8 387.11 13.15
## 187    17.8 392.63  4.45
## 188    15.2 393.87  6.68
## 189    15.2 382.84  4.56
## 190    15.2 396.90  5.39
## 191    15.2 377.68  5.10
## 192    15.2 389.71  4.69
## 193    15.2 390.49  2.87
## 194    15.6 393.37  5.03
## 195    15.6 376.70  4.38
## 196    14.4 394.23  2.97
## 197    12.6 396.90  4.08
## 198    12.6 354.31  8.61
## 199    12.6 392.20  6.62
## 200    17.0 396.90  4.56
## 201    17.0 384.30  4.45
## 202    14.7 393.77  7.43
## 203    14.7 395.38  3.11
## 204    14.7 392.78  3.81
## 205    14.7 390.55  2.88
## 206    18.6 396.90 10.87
## 207    18.6 394.87 10.97
## 208    18.6 389.43 18.06
## 209    18.6 381.32 14.66
## 210    18.6 396.90 23.09
## 211    18.6 393.25 17.27
## 212    18.6 395.24 23.98
## 213    18.6 390.94 16.03
## 214    18.6 385.81  9.38
## 215    18.6 348.93 29.55
## 216    18.6 393.63  9.47
## 217    16.4 392.80 13.51
## 218    16.4 392.78  9.69
## 219    16.4 396.90 17.92
## 220    16.4 393.74 10.50
## 221    17.4 391.70  9.71
## 222    17.4 395.24 21.46
## 223    17.4 390.39  9.93
## 224    17.4 396.90  7.60
## 225    17.4 385.05  4.14
## 226    17.4 382.00  4.63
## 227    17.4 387.38  3.13
## 228    17.4 372.08  6.36
## 229    17.4 377.51  3.92
## 230    17.4 380.34  3.76
## 231    17.4 378.35 11.65
## 232    17.4 376.14  5.25
## 233    17.4 385.91  2.47
## 234    17.4 378.95  3.95
## 235    17.4 360.20  8.05
## 236    17.4 376.75 10.88
## 237    17.4 388.45  9.54
## 238    17.4 390.07  4.73
## 239    16.6 379.41  6.36
## 240    16.6 383.78  7.37
## 241    16.6 391.25 11.38
## 242    16.6 394.62 12.40
## 243    16.6 372.75 11.22
## 244    16.6 374.71  5.19
## 245    19.1 372.49 12.50
## 246    19.1 389.13 18.46
## 247    19.1 390.18  9.16
## 248    19.1 376.14 10.15
## 249    19.1 374.71  9.52
## 250    19.1 393.74  6.56
## 251    19.1 396.28  5.90
## 252    19.1 377.07  3.59
## 253    19.1 386.09  3.53
## 254    19.1 396.90  3.54
## 255    16.4 392.89  6.57
## 256    16.4 395.18  9.25
## 257    15.9 386.34  3.11
## 258    13.0 389.70  5.12
## 259    13.0 383.29  7.79
## 260    13.0 391.93  6.90
## 261    13.0 392.80  9.59
## 262    13.0 388.37  7.26
## 263    13.0 386.86  5.91
## 264    13.0 393.42 11.25
## 265    13.0 387.89  8.10
## 266    13.0 392.40 10.45
## 267    13.0 384.07 14.79
## 268    13.0 384.54  7.44
## 269    13.0 390.30  3.16
## 270    18.6 391.34 13.65
## 271    18.6 388.65 13.00
## 272    18.6 396.90  6.59
## 273    18.6 394.96  7.73
## 274    18.6 390.77  6.58
## 275    17.6 396.90  3.53
## 276    17.6 396.90  2.98
## 277    17.6 389.25  6.05
## 278    17.6 393.45  4.16
## 279    17.6 396.90  7.19
## 280    14.9 396.90  4.85
## 281    14.9 387.31  3.76
## 282    14.9 392.23  4.59
## 283    14.9 377.07  3.01
## 284    13.6 395.52  3.16
## 285    15.3 394.72  7.85
## 286    15.3 394.72  8.23
## 287    18.2 341.60 12.93
## 288    16.6 396.90  7.14
## 289    16.6 396.90  7.60
## 290    16.6 371.72  9.51
## 291    19.2 396.90  3.33
## 292    19.2 396.90  3.56
## 293    19.2 396.90  4.70
## 294    16.0 396.90  8.58
## 295    16.0 396.90 10.40
## 296    16.0 396.90  6.27
## 297    16.0 392.85  7.39
## 298    16.0 396.90 15.84
## 299    14.8 368.24  4.97
## 300    14.8 371.58  4.74
## 301    14.8 390.86  6.07
## 302    16.1 395.75  9.50
## 303    16.1 383.61  8.67
## 304    16.1 390.43  4.86
## 305    18.4 393.68  6.93
## 306    18.4 393.36  8.93
## 307    18.4 396.90  6.47
## 308    18.4 396.90  7.53
## 309    18.4 396.90  4.54
## 310    18.4 396.24  9.97
## 311    18.4 350.45 12.64
## 312    18.4 396.90  5.98
## 313    18.4 396.30 11.72
## 314    18.4 393.39  7.90
## 315    18.4 395.69  9.28
## 316    18.4 396.42 11.50
## 317    18.4 390.70 18.33
## 318    18.4 396.90 15.94
## 319    18.4 395.21 10.36
## 320    18.4 396.23 12.73
## 321    19.6 396.90  7.20
## 322    19.6 396.90  6.87
## 323    19.6 396.90  7.70
## 324    19.6 391.13 11.74
## 325    19.6 396.90  6.12
## 326    19.6 393.68  5.08
## 327    19.6 396.90  6.15
## 328    19.6 396.90 12.79
## 329    16.9 382.44  9.97
## 330    16.9 375.21  7.34
## 331    16.9 368.57  9.09
## 332    16.9 394.02 12.43
## 333    16.9 362.25  7.83
## 334    20.2 389.71  5.68
## 335    20.2 389.40  6.75
## 336    20.2 396.90  8.01
## 337    20.2 396.90  9.80
## 338    20.2 394.81 10.56
## 339    20.2 396.14  8.51
## 340    20.2 396.90  9.74
## 341    20.2 396.90  9.29
## 342    15.5 394.74  5.49
## 343    15.9 389.96  8.65
## 344    17.6 396.90  7.18
## 345    17.6 387.97  4.61
## 346    18.8 385.64 10.53
## 347    18.8 364.61 12.67
## 348    17.9 392.43  6.36
## 349    17.0 390.94  5.99
## 350    19.7 389.85  5.89
## 351    19.7 396.90  5.98
## 352    18.3 370.78  5.49
## 353    18.3 392.33  7.79
## 354    17.0 384.46  4.50
## 355    22.0 382.80  8.05
## 356    22.0 376.04  5.57
## 357    20.2 377.73 17.60
## 358    20.2 391.34 13.27
## 359    20.2 395.43 11.48
## 360    20.2 390.74 12.67
## 361    20.2 374.56  7.79
## 362    20.2 350.65 14.19
## 363    20.2 380.79 10.19
## 364    20.2 353.04 14.64
## 365    20.2 354.55  5.29
## 366    20.2 354.70  7.12
## 367    20.2 316.03 14.00
## 368    20.2 131.42 13.33
## 369    20.2 375.52  3.26
## 370    20.2 375.33  3.73
## 371    20.2 392.05  2.96
## 372    20.2 366.15  9.53
## 373    20.2 347.88  8.88
## 374    20.2 396.90 34.77
## 375    20.2 396.90 37.97
## 376    20.2 396.90 13.44
## 377    20.2 363.02 23.24
## 378    20.2 396.90 21.24
## 379    20.2 396.90 23.69
## 380    20.2 393.74 21.78
## 381    20.2 396.90 17.21
## 382    20.2 396.90 21.08
## 383    20.2 396.90 23.60
## 384    20.2 396.90 24.56
## 385    20.2 285.83 30.63
## 386    20.2 396.90 30.81
## 387    20.2 396.90 28.28
## 388    20.2 396.90 31.99
## 389    20.2 372.92 30.62
## 390    20.2 396.90 20.85
## 391    20.2 394.43 17.11
## 392    20.2 378.38 18.76
## 393    20.2 396.90 25.68
## 394    20.2 396.90 15.17
## 395    20.2 396.90 16.35
## 396    20.2 391.98 17.12
## 397    20.2 396.90 19.37
## 398    20.2 393.10 19.92
## 399    20.2 396.90 30.59
## 400    20.2 338.16 29.97
## 401    20.2 396.90 26.77
## 402    20.2 396.90 20.32
## 403    20.2 376.11 20.31
## 404    20.2 396.90 19.77
## 405    20.2 329.46 27.38
## 406    20.2 384.97 22.98
## 407    20.2 370.22 23.34
## 408    20.2 332.09 12.13
## 409    20.2 314.64 26.40
## 410    20.2 179.36 19.78
## 411    20.2   2.60 10.11
## 412    20.2  35.05 21.22
## 413    20.2  28.79 34.37
## 414    20.2 210.97 20.08
## 415    20.2  88.27 36.98
## 416    20.2  27.25 29.05
## 417    20.2  21.57 25.79
## 418    20.2 127.36 26.64
## 419    20.2  16.45 20.62
## 420    20.2  48.45 22.74
## 421    20.2 318.75 15.02
## 422    20.2 319.98 15.70
## 423    20.2 291.55 14.10
## 424    20.2   2.52 23.29
## 425    20.2   3.65 17.16
## 426    20.2   7.68 24.39
## 427    20.2  24.65 15.69
## 428    20.2  18.82 14.52
## 429    20.2  96.73 21.52
## 430    20.2  60.72 24.08
## 431    20.2  83.45 17.64
## 432    20.2  81.33 19.69
## 433    20.2  97.95 12.03
## 434    20.2 100.19 16.22
## 435    20.2 100.63 15.17
## 436    20.2 109.85 23.27
## 437    20.2  27.49 18.05
## 438    20.2   9.32 26.45
## 439    20.2  68.95 34.02
## 440    20.2 396.90 22.88
## 441    20.2 391.45 22.11
## 442    20.2 385.96 19.52
## 443    20.2 395.69 16.59
## 444    20.2 386.73 18.85
## 445    20.2 240.52 23.79
## 446    20.2  43.06 23.98
## 447    20.2 318.01 17.79
## 448    20.2 388.52 16.44
## 449    20.2 396.90 18.13
## 450    20.2 304.21 19.31
## 451    20.2   0.32 17.44
## 452    20.2 355.29 17.73
## 453    20.2 385.09 17.27
## 454    20.2 375.87 16.74
## 455    20.2   6.68 18.71
## 456    20.2  50.92 18.13
## 457    20.2  10.48 19.01
## 458    20.2   3.50 16.94
## 459    20.2 272.21 16.23
## 460    20.2 396.90 14.70
## 461    20.2 255.23 16.42
## 462    20.2 391.43 14.65
## 463    20.2 396.90 13.99
## 464    20.2 393.82 10.29
## 465    20.2 396.90 13.22
## 466    20.2 334.40 14.13
## 467    20.2  22.01 17.15
## 468    20.2 331.29 21.32
## 469    20.2 368.74 18.13
## 470    20.2 396.90 14.76
## 471    20.2 396.90 16.29
## 472    20.2 395.33 12.87
## 473    20.2 393.37 14.36
## 474    20.2 374.68 11.66
## 475    20.2 352.58 18.14
## 476    20.2 302.76 24.10
## 477    20.2 396.21 18.68
## 478    20.2 349.48 24.91
## 479    20.2 379.70 18.03
## 480    20.2 383.32 13.11
## 481    20.2 396.90 10.74
## 482    20.2 393.07  7.74
## 483    20.2 395.28  7.01
## 484    20.2 392.92 10.42
## 485    20.2 370.73 13.34
## 486    20.2 388.62 10.58
## 487    20.2 392.68 14.98
## 488    20.2 388.22 11.45
## 489    20.1 395.09 18.06
## 490    20.1 344.05 23.97
## 491    20.1 318.43 29.68
## 492    20.1 390.11 18.07
## 493    20.1 396.90 13.35
## 494    19.2 396.90 12.01
## 495    19.2 396.90 13.59
## 496    19.2 393.29 17.60
## 497    19.2 396.90 21.14
## 498    19.2 396.90 14.10
## 499    19.2 396.90 12.92
## 500    19.2 395.77 15.10
## 501    19.2 396.90 14.33
## 502    21.0 391.99  9.67
## 503    21.0 396.90  9.08
## 504    21.0 396.90  5.64
## 505    21.0 393.45  6.48
## 506    21.0 396.90  7.88

Exploratory data analysis

#Identify missing values
missing_values<-is.na(bd)
missing_values
##         medv cmedv  crim    zn indus  chas   nox    rm   age   dis   rad   tax
##   [1,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [2,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [3,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [4,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [5,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [6,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [7,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [8,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##   [9,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [10,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [11,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [12,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [13,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [14,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [15,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [16,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [17,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [18,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [19,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [20,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [21,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [22,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [23,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [24,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [25,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [26,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [27,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [28,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [29,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [30,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [31,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [32,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [33,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [34,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [35,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [36,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [37,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [38,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [39,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [40,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [41,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [42,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [43,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [44,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [45,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [46,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [47,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [48,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [49,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [50,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [51,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [52,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [53,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [54,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [55,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [56,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [57,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [58,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [59,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [60,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [61,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [62,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [63,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [64,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [65,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [66,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [67,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [68,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [69,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [70,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [71,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [72,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [73,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [74,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [75,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [76,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [77,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [78,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [79,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [80,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [81,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [82,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [83,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [84,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [85,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [86,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [87,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [88,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [89,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [90,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [91,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [92,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [93,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [94,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [95,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [96,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [97,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [98,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [99,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [100,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [101,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [102,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [103,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [104,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [105,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [106,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [107,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [108,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [109,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [110,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [111,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [112,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [113,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [114,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [115,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [116,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [117,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [118,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [119,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [120,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [121,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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## [485,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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## [490,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
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## [504,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [505,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [506,] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##        ptratio     b lstat
##   [1,]   FALSE FALSE FALSE
##   [2,]   FALSE FALSE FALSE
##   [3,]   FALSE FALSE FALSE
##   [4,]   FALSE FALSE FALSE
##   [5,]   FALSE FALSE FALSE
##   [6,]   FALSE FALSE FALSE
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#Display data set structure
str(bd)
## 'data.frame':    506 obs. of  15 variables:
##  $ medv   : num  24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...
##  $ cmedv  : num  24 21.6 34.7 33.4 36.2 28.7 22.9 22.1 16.5 18.9 ...
##  $ crim   : num  0.00632 0.02731 0.02729 0.03237 0.06905 ...
##  $ zn     : num  18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
##  $ indus  : num  2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ...
##  $ chas   : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ nox    : num  0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ...
##  $ rm     : num  6.58 6.42 7.18 7 7.15 ...
##  $ age    : num  65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ...
##  $ dis    : num  4.09 4.97 4.97 6.06 6.06 ...
##  $ rad    : int  1 2 2 3 3 3 5 5 5 5 ...
##  $ tax    : int  296 242 242 222 222 222 311 311 311 311 ...
##  $ ptratio: num  15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ...
##  $ b      : num  397 397 393 395 397 ...
##  $ lstat  : num  4.98 9.14 4.03 2.94 5.33 ...
# Include descriptive statistics (mean, median, standard deviation, minimum, maximum)
summary(bd)
##       medv           cmedv            crim                zn        
##  Min.   : 5.00   Min.   : 5.00   Min.   : 0.00632   Min.   :  0.00  
##  1st Qu.:17.02   1st Qu.:17.02   1st Qu.: 0.08205   1st Qu.:  0.00  
##  Median :21.20   Median :21.20   Median : 0.25651   Median :  0.00  
##  Mean   :22.53   Mean   :22.53   Mean   : 3.61352   Mean   : 11.36  
##  3rd Qu.:25.00   3rd Qu.:25.00   3rd Qu.: 3.67708   3rd Qu.: 12.50  
##  Max.   :50.00   Max.   :50.00   Max.   :88.97620   Max.   :100.00  
##      indus            chas              nox               rm       
##  Min.   : 0.46   Min.   :0.00000   Min.   :0.3850   Min.   :3.561  
##  1st Qu.: 5.19   1st Qu.:0.00000   1st Qu.:0.4490   1st Qu.:5.886  
##  Median : 9.69   Median :0.00000   Median :0.5380   Median :6.208  
##  Mean   :11.14   Mean   :0.06917   Mean   :0.5547   Mean   :6.285  
##  3rd Qu.:18.10   3rd Qu.:0.00000   3rd Qu.:0.6240   3rd Qu.:6.623  
##  Max.   :27.74   Max.   :1.00000   Max.   :0.8710   Max.   :8.780  
##       age              dis              rad              tax       
##  Min.   :  2.90   Min.   : 1.130   Min.   : 1.000   Min.   :187.0  
##  1st Qu.: 45.02   1st Qu.: 2.100   1st Qu.: 4.000   1st Qu.:279.0  
##  Median : 77.50   Median : 3.207   Median : 5.000   Median :330.0  
##  Mean   : 68.57   Mean   : 3.795   Mean   : 9.549   Mean   :408.2  
##  3rd Qu.: 94.08   3rd Qu.: 5.188   3rd Qu.:24.000   3rd Qu.:666.0  
##  Max.   :100.00   Max.   :12.127   Max.   :24.000   Max.   :711.0  
##     ptratio            b              lstat      
##  Min.   :12.60   Min.   :  0.32   Min.   : 1.73  
##  1st Qu.:17.40   1st Qu.:375.38   1st Qu.: 6.95  
##  Median :19.05   Median :391.44   Median :11.36  
##  Mean   :18.46   Mean   :356.67   Mean   :12.65  
##  3rd Qu.:20.20   3rd Qu.:396.23   3rd Qu.:16.95  
##  Max.   :22.00   Max.   :396.90   Max.   :37.97
# Transform variables if required
str(bd)
## 'data.frame':    506 obs. of  15 variables:
##  $ medv   : num  24 21.6 34.7 33.4 36.2 28.7 22.9 27.1 16.5 18.9 ...
##  $ cmedv  : num  24 21.6 34.7 33.4 36.2 28.7 22.9 22.1 16.5 18.9 ...
##  $ crim   : num  0.00632 0.02731 0.02729 0.03237 0.06905 ...
##  $ zn     : num  18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
##  $ indus  : num  2.31 7.07 7.07 2.18 2.18 2.18 7.87 7.87 7.87 7.87 ...
##  $ chas   : int  0 0 0 0 0 0 0 0 0 0 ...
##  $ nox    : num  0.538 0.469 0.469 0.458 0.458 0.458 0.524 0.524 0.524 0.524 ...
##  $ rm     : num  6.58 6.42 7.18 7 7.15 ...
##  $ age    : num  65.2 78.9 61.1 45.8 54.2 58.7 66.6 96.1 100 85.9 ...
##  $ dis    : num  4.09 4.97 4.97 6.06 6.06 ...
##  $ rad    : int  1 2 2 3 3 3 5 5 5 5 ...
##  $ tax    : int  296 242 242 222 222 222 311 311 311 311 ...
##  $ ptratio: num  15.3 17.8 17.8 18.7 18.7 18.7 15.2 15.2 15.2 15.2 ...
##  $ b      : num  397 397 393 395 397 ...
##  $ lstat  : num  4.98 9.14 4.03 2.94 5.33 ...

Data Visualization

# Build at least 2 pair-wised graphs between the dependent variable and independent variables


# Display a histogram of dependent variable
# Display a correlation plot

Hypotheses Statement

# Briefly describe at least 3 hypotheses which you would like to explore through regression analysis

Regression Analysis

# Estimate 3 different linear regression models by using:

#multiple linear regression
# polynomial – multiple linear regression
# lasso regression model
# ridge regression model


# Show the level of accuracy for each linear regression model
# Select the regression model that better fits the data
# Interpret the main results of the selected regression model

Results Discussion (how linear regression analysis can contribute to improve predictive analytics)

# With linear regression analysis we can model the relationship between a dependent variable(y)  and independent variables (x) by adjusting a linear equation to the observed data.

# When a linear regression model is built and validated, it can be helpful to make predictions. Given new values of the independent variables, the model can provide predictions of the dependent variable. This technique can help us in the forecasting of sales, predicting customer behavior, or estimating housing prices. It uses linear relationships between a dependent variable (target) and one or more independent variables (predictors) to predict the future of the target.

# An advantage of using linear regression for predictive analytics is that it is flexible and adaptable. You can use linear regression to model different types of relationships, such as linear, polynomial, logarithmic, exponential, or inverse.

#(IBM 2022)

# IBM Documentation. (2022, November 3). Ibm.com. https://www.ibm.com/docs/en/db2-warehouse?topic=procedures-linear-regression#:~:text=Linear%20regression%20is%20the%20most,the%20future%20of%20the%20target

# What are the advantages and disadvantages of using linear regression for predictive analytics? (2023). Linkedin.com. https://www.linkedin.com/advice/1/what-advantages-disadvantages-using-linear-1e#:~:text=It%20is%20a%20statistical%20technique,expectancy%20based%20on%20health%20factors
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