REGRESIÓN POLINÓMICA ENTRE EL SiO2 Y EL Al2O3

ANÁLISIS MULTIVARIABLE

CARGA DE DATOS Y LIBRERÍAS

# CARGA DE DATOS

library(readr)
library(knitr)

datos <- read_csv("D:/modelo_regresion_polinomica_2500.csv")

TABLA PARES DE VALORES

# Extraer variables numéricas

sio2  <- as.numeric(datos$SIO2_WT_PERCENT_X)

al2o3 <- as.numeric(datos$AL2O3_WT_PERCENT_Y)

TPV <- data.frame(sio2,al2o3)

#TABLA DE PARES DE VALORES

TPV <- na.omit(TPV) #OMITIR NA

TPV <- TPV[TPV$sio2 >= 0 & TPV$al2o3 >= 0, ] #OMITIR VALORES NEGATIVOS

TPV

##        sio2 al2o3
## 1    30.618 5.179
## 2    96.134 6.449
## 3    76.600 4.590
## 4    89.161 5.009
## 5    90.422 6.962
## 6    95.057 5.039
## 7    71.746 6.848
## 8    72.805 5.858
## 9    22.458 4.864
## 10   76.866 4.610
## 11   57.420 4.982
## 12   49.253 5.998
## 13   19.314 4.154
## 14   21.981 3.857
## 15   13.141 1.662
## 16   96.901 4.579
## 17   49.721 4.549
## 18   46.058 6.584
## 19   48.654 6.271
## 20   55.069 5.649
## 21   37.998 4.668
## 22   61.968 4.494
## 23   14.376 2.422
## 24   60.398 3.242
## 25   44.313 5.532
## 26   62.498 5.332
## 27   67.597 6.046
## 28   38.787 4.867
## 29   67.762 5.021
## 30   83.641 5.643
## 31   80.289 5.017
## 32   19.020 3.745
## 33   17.061 3.776
## 34   20.705 3.692
## 35   38.980 4.864
## 36   53.355 3.908
## 37   60.493 5.718
## 38   39.692 6.012
## 39   36.727 4.911
## 40   63.592 4.107
## 41    8.490 1.837
## 42   51.270 7.315
## 43   66.961 3.871
## 44   89.120 5.739
## 45   88.076 4.224
## 46    5.743 3.928
## 47   93.730 5.970
## 48   82.080 6.356
## 49   35.389 4.011
## 50   47.463 5.624
## 51   23.415 3.373
## 52   34.627 4.842
## 53   82.765 5.593
## 54   23.400 4.809
## 55   72.672 4.566
## 56   84.423 6.347
## 57   78.415 6.113
## 58   68.567 6.763
## 59   91.898 4.437
## 60   70.757 4.793
## 61   95.948 4.596
## 62   69.982 5.558
## 63   43.654 4.082
## 64   61.485 4.780
## 65   59.138 6.295
## 66   73.563 5.950
## 67   68.122 5.947
## 68    7.191 2.619
## 69   20.992 5.343
## 70    5.238 2.653
## 71   78.996 5.628
## 72   85.238 3.868
## 73   32.310 4.512
## 74   21.256 3.868
## 75   97.576 5.860
## 76   88.320 3.145
## 77   14.238 3.504
## 78   58.655 4.436
## 79   54.322 4.443
## 80   21.347 4.963
## 81   81.353 5.647
## 82   84.889 5.411
## 83   17.661 1.880
## 84   86.529 5.545
## 85   73.589 5.048
## 86   63.451 5.018
## 87   17.678 3.996
## 88   33.264 4.629
## 89   60.067 5.878
## 90   70.271 6.463
## 91   34.348 5.563
## 92   22.585 3.843
## 93   35.827 5.377
## 94   71.808 4.333
## 95   34.526 4.487
## 96   25.700 3.025
## 97   59.358 5.513
## 98   56.550 5.354
## 99   79.641 4.530
## 100  58.017 5.179
## 101  63.817 5.623
## 102  85.945 5.736
## 103   6.273 2.818
## 104  12.611 3.921
## 105  74.800 3.146
## 106  38.886 4.741
## 107  86.346 6.198
## 108  94.933 7.094
## 109  64.097 3.701
## 110  12.788 2.452
## 111  18.188 2.492
## 112  49.597 4.891
## 113  53.400 6.278
## 114  18.644 3.446
## 115  75.060 3.664
## 116  89.746 6.504
## 117  20.913 4.988
## 118  67.285 3.690
## 119  67.409 5.578
## 120  34.734 4.301
## 121  78.581 5.979
## 122  47.181 6.358
## 123  59.946 4.914
## 124  16.868 3.804
## 125  44.311 4.526
## 126  18.663 3.770
## 127  55.262 5.681
## 128  90.384 5.803
## 129  60.817 5.779
## 130  93.624 5.265
## 131  66.254 4.915
## 132  35.444 5.549
## 133  95.353 4.478
## 134  16.946 3.673
## 135  40.136 4.307
## 136  63.770 5.824
## 137  70.592 5.355
## 138   7.880 4.383
## 139  93.857 4.315
## 140  19.469 2.204
## 141  15.286 3.888
## 142  52.243 4.538
## 143  49.024 4.337
## 144   6.544 2.044
## 145  38.958 5.493
## 146  43.255 5.173
## 147  26.618 2.726
## 148  65.565 6.503
## 149  32.548 4.510
## 150  52.708 5.019
## 151  60.098 5.835
## 152  38.479 5.413
## 153  39.739 7.206
## 154  36.005 5.689
## 155  57.635 6.570
## 156   7.038 1.968
## 157  74.878 6.010
## 158  74.260 6.246
## 159  89.573 4.134
## 160  78.171 5.971
## 161  12.932 2.125
## 162  17.566 4.711
## 163  70.624 3.869
## 164  25.107 5.575
## 165  80.089 6.485
## 166  93.340 5.457
## 167  19.061 2.588
## 168  22.990 2.606
## 169  32.784 4.129
## 170  66.390 4.151
## 171  35.522 5.379
## 172  41.210 3.921
## 173  88.240 5.436
## 174  49.143 5.818
## 175  33.866 4.655
## 176  17.544 2.035
## 177  19.552 4.054
## 178  97.930 4.671
## 179   8.151 2.046
## 180  32.996 4.777
## 181  19.061 3.236
## 182  67.976 4.322
## 183  46.706 6.414
## 184  49.520 3.537
## 185  54.327 3.882
## 186  52.713 4.833
## 187  10.340 2.120
## 188  74.630 5.855
## 189   7.319 3.191
## 190   8.236 3.442
## 191  88.037 5.972
## 192  90.553 4.441
## 193  32.022 4.824
## 194  31.707 4.374
## 195  44.513 8.137
## 196  53.362 4.188
## 197   9.840 4.296
## 198  22.306 3.982
## 199  57.417 5.969
## 200  23.685 6.692
## 201  93.462 5.375
## 202  65.835 1.803
## 203  55.824 4.896
## 204  14.379 4.527
## 205   5.936 1.990
## 206  56.325 5.567
## 207  21.351 4.653
## 208  77.235 5.898
## 209  64.186 6.391
## 210  35.992 3.561
## 211  79.984 3.442
## 212  18.395 3.117
## 213  27.112 4.464
## 214  11.770 2.964
## 215  95.590 3.519
## 216  66.511 4.621
## 217  33.757 4.451
## 218  19.393 4.108
## 219  83.127 5.145
## 220  47.326 5.361
## 221  27.840 3.863
## 222  10.407 4.064
## 223  41.561 4.379
## 224  28.407 5.117
## 225  50.783 5.530
## 226  91.945 3.342
## 227  97.853 7.542
## 228  69.998 7.122
## 229  73.178 4.141
## 230  91.485 6.343
## 231  36.214 3.163
## 232  65.504 3.665
## 233  97.850 4.154
## 234  15.044 3.205
## 235  92.187 5.790
## 236  82.804 5.186
## 237  76.899 2.349
## 238  80.957 6.119
## 239  62.396 4.906
## 240  47.239 5.187
## 241  35.894 5.499
## 242  28.693 2.563
## 243  83.025 6.474
## 244  65.408 4.952
## 245  16.468 6.168
## 246  70.984 5.712
## 247   7.251 1.852
## 248  89.749 4.880
## 249  78.359 3.614
## 250  63.838 6.243
## 251  23.290 2.904
## 252  24.024 3.278
## 253  31.614 5.557
## 254  58.402 3.799
## 255  33.650 8.009
## 256  19.496 4.094
## 257  94.682 4.257
## 258  35.114 3.964
## 259   8.782 2.646
## 260  11.709 2.716
## 261  94.630 4.233
## 262  82.622 6.999
## 263  53.688 5.089
## 264  34.110 4.971
## 265   6.645 1.283
## 266   9.313 1.580
## 267  37.751 5.872
## 268  78.029 5.066
## 269  30.000 4.678
## 270  47.694 4.907
## 271  52.905 4.507
## 272  35.158 3.327
## 273  19.857 2.538
## 274  52.672 4.460
## 275  64.839 2.338
## 276  78.869 5.741
## 277  80.826 4.608
## 278  86.544 6.906
## 279   9.448 2.571
## 280  13.004 3.820
## 281  46.994 6.120
## 282  87.974 4.357
## 283  76.560 4.451
## 284  63.450 4.600
## 285  30.506 3.748
## 286  12.629 3.314
## 287  83.424 5.062
## 288  73.407 5.839
## 289  11.901 1.361
## 290  15.841 2.222
## 291  16.529 2.864
## 292  89.218 3.675
## 293  51.760 6.219
## 294  70.473 5.841
## 295  55.679 4.655
## 296  68.258 6.523
## 297  71.314 5.768
## 298  12.893 4.108
## 299  74.946 5.493
## 300  48.505 5.634
## 301  17.419 3.801
## 302   9.183 5.411
## 303  33.110 3.548
## 304  24.467 5.426
## 305  46.352 6.374
## 306  10.510 5.304
## 307   8.249 2.267
## 308  43.381 4.706
## 309  16.240 3.074
## 310  42.147 4.612
## 311  47.101 7.112
## 312  80.904 7.107
## 313   6.829 2.856
## 314  97.428 5.087
## 315  55.087 3.393
## 316  44.141 4.575
## 317  77.378 5.654
## 318  59.074 6.040
## 319   7.122 2.820
## 320  79.729 4.685
## 321  54.155 5.259
## 322  14.014 4.416
## 323  87.483 4.572
## 324  84.726 3.536
## 325  46.883 4.101
## 326   5.904 4.552
## 327  62.288 4.434
## 328  35.278 4.624
## 329  61.673 5.612
## 330  23.766 3.597
## 331  51.711 6.064
## 332  84.019 3.450
## 333  63.212 6.489
## 334  18.090 3.088
## 335  96.742 5.327
## 336   8.604 3.178
## 337  51.120 6.575
## 338  80.529 5.981
## 339  39.104 3.292
## 340  74.054 6.923
## 341  23.200 3.458
## 342  40.249 4.835
## 343  36.665 5.221
## 344  84.720 5.878
## 345  94.120 3.752
## 346  32.534 5.473
## 347  83.644 4.506
## 348  29.381 6.138
## 349  54.799 6.453
## 350  23.918 3.644
## 351  40.211 3.215
## 352  53.808 3.992
## 353  74.133 5.368
## 354  61.139 5.994
## 355  86.477 3.125
## 356  80.900 5.547
## 357  54.832 5.320
## 358  72.155 4.854
## 359  65.039 5.753
## 360  24.031 4.489
## 361  74.755 5.293
## 362  90.022 5.002
## 363  14.572 1.447
## 364  77.165 5.739
## 365  50.366 3.270
## 366  13.938 3.711
## 367  25.575 3.455
## 368  59.344 5.687
## 369  65.070 7.029
## 370  96.517 4.174
## 371  32.558 5.111
## 372  88.256 4.590
## 373  83.633 5.927
## 374  70.626 1.146
## 375  44.797 4.544
## 376  43.535 6.280
## 377  18.786 3.759
## 378  93.070 5.031
## 379  31.381 3.876
## 380   6.315 2.163
## 381  48.622 4.174
## 382   8.745 2.431
## 383  54.191 3.339
## 384  10.856 3.940
## 385  21.694 3.738
## 386  37.339 3.373
## 387  83.961 4.125
## 388  84.921 4.481
## 389  86.912 4.099
## 390  55.953 5.193
## 391  96.943 6.125
## 392  97.228 4.959
## 393  59.270 5.443
## 394  60.913 4.588
## 395  39.117 4.663
## 396  96.746 5.579
## 397  63.706 7.306
## 398  16.397 4.686
## 399  89.048 7.141
## 400   5.729 4.394
## 401  55.447 2.672
## 402  49.340 3.962
## 403  49.828 5.111
## 404   6.834 2.322
## 405  41.907 5.557
## 406  15.115 2.475
## 407  64.873 5.425
## 408  93.405 5.265
## 409  17.715 3.470
## 410   9.856 4.363
## 411  64.029 4.713
## 412  69.949 5.192
## 413  85.792 5.163
## 414  90.767 4.176
## 415  52.491 6.495
## 416  57.007 6.012
## 417  21.365 4.253
## 418  88.728 5.813
## 419   5.543 1.782
## 420  83.122 4.576
## 421  64.139 5.124
## 422  27.677 5.399
## 423  14.371 3.384
## 424  50.584 4.742
## 425  86.226 5.065
## 426  41.633 5.403
## 427  46.796 6.051
## 428   5.670 2.987
## 429  41.368 3.972
## 430  78.678 5.619
## 431  30.650 5.117
## 432  10.336 3.835
## 433  71.312 6.075
## 434  57.607 4.869
## 435  24.442 5.425
## 436  68.561 6.325
## 437  49.290 6.105
## 438  40.181 4.178
## 439  71.382 5.187
## 440  75.045 7.053
## 441  28.387 4.540
## 442  84.388 6.142
## 443  54.178 4.861
## 444  65.084 5.290
## 445  41.179 4.553
## 446  35.831 4.529
## 447  18.560 2.403
## 448  68.198 5.226
## 449  54.398 7.319
## 450  53.470 7.604
## 451  54.955 6.694
## 452  26.492 4.482
## 453  44.169 4.787
## 454  40.284 5.228
## 455  12.506 2.635
## 456  33.117 2.603
## 457  46.460 4.670
## 458  89.949 3.481
## 459  28.934 4.820
## 460   8.351 3.818
## 461  21.871 1.778
## 462  91.773 4.834
## 463  30.043 4.570
## 464  23.024 5.490
## 465  57.357 3.486
## 466  34.192 5.049
## 467  17.178 3.237
## 468  64.121 4.034
## 469  10.513 1.527
## 470   5.854 3.983
## 471  62.077 4.699
## 472  61.413 5.413
## 473  53.506 5.386
## 474  64.295 5.483
## 475  56.653 5.283
## 476  26.417 5.793
## 477  74.046 6.263
## 478  16.876 2.625
## 479  34.392 5.553
## 480   9.517 2.701
## 481  26.731 2.958
## 482  18.590 4.307
## 483  87.087 5.084
## 484  65.045 3.686
## 485  86.408 6.239
## 486  73.631 6.179
## 487  38.234 5.321
## 488  51.274 6.969
## 489  76.768 5.447
## 490  66.079 4.978
## 491  79.448 4.538
## 492  26.610 3.054
## 493  75.632 6.134
## 494  57.603 6.366
## 495  59.519 4.989
## 496  64.028 6.195
## 497   9.515 1.152
## 498  72.688 5.877
## 499  22.698 3.637
## 500  39.822 5.871
## 501  79.233 5.928
## 502  85.193 6.612
## 503  92.383 7.169
## 504  88.353 5.805
## 505  46.222 5.401
## 506  77.501 4.436
## 507  61.236 5.512
## 508   8.656 2.058
## 509  44.126 4.500
## 510  37.057 4.181
## 511  94.252 5.214
## 512  77.297 4.785
## 513   8.678 3.154
## 514  43.644 6.112
## 515  40.441 4.398
## 516  30.231 4.448
## 517  90.888 5.896
## 518  46.735 5.699
## 519  83.731 5.699
## 520  19.235 1.608
## 521  71.953 5.153
## 522   7.956 3.043
## 523  45.436 4.937
## 524  41.662 5.770
## 525  85.769 4.212
## 526  88.980 5.938
## 527  47.379 4.587
## 528  29.472 3.624
## 529  85.434 3.059
## 530  20.982 3.128
## 531  75.366 4.117
## 532  48.695 3.608
## 533  55.257 5.860
## 534  71.679 5.682
## 535  31.868 7.139
## 536  57.904 4.726
## 537  24.251 4.102
## 538  13.624 2.825
## 539  74.507 5.977
## 540   6.754 5.651
## 541  30.940 5.261
## 542  68.130 4.410
## 543  87.525 7.008
## 544  28.430 4.421
## 545   6.169 3.903
## 546  10.749 3.365
## 547  59.522 4.663
## 548  87.608 5.787
## 549  27.495 3.952
## 550  95.136 4.953
## 551  86.037 6.365
## 552  56.133 6.713
## 553  81.710 4.582
## 554  15.011 4.109
## 555  86.227 5.525
## 556  18.944 2.646
## 557  26.208 4.283
## 558  14.137 3.098
## 559  54.184 3.818
## 560  27.726 4.611
## 561  93.312 4.042
## 562  81.420 4.599
## 563  23.422 3.717
## 564  63.864 6.801
## 565  78.467 7.468
## 566  71.363 5.240
## 567  66.615 6.740
## 568  42.482 4.710
## 569  75.429 6.542
## 570  52.293 5.789
## 571  47.697 6.031
## 572  81.821 5.452
## 573  49.207 5.523
## 574  58.107 5.062
## 575  44.986 6.219
## 576  43.259 4.164
## 577  36.260 5.584
## 578  24.116 4.649
## 579  31.876 4.618
## 580  71.334 8.032
## 581  24.732 4.431
## 582  38.879 3.920
## 583  50.814 4.888
## 584  66.725 4.561
## 585  66.876 4.340
## 586  61.186 6.289
## 587  47.056 4.351
## 588  39.687 4.624
## 589  26.477 2.554
## 590  30.239 5.834
## 591  13.794 4.318
## 592  15.264 4.488
## 593  56.407 2.471
## 594  25.562 5.997
## 595  63.179 4.182
## 596  34.998 5.945
## 597  81.090 3.595
## 598  55.497 5.155
## 599  51.814 3.562
## 600  49.997 5.818
## 601  47.233 4.784
## 602  17.733 5.001
## 603  56.604 6.009
## 604  79.938 4.853
## 605  58.576 4.434
## 606  27.214 4.617
## 607  45.543 5.694
## 608  90.600 4.150
## 609  12.827 4.081
## 610  69.488 5.512
## 611  63.293 6.342
## 612  71.135 5.201
## 613  52.126 4.268
## 614  21.176 1.091
## 615  58.042 4.214
## 616   6.767 3.789
## 617  91.955 5.381
## 618  68.945 5.351
## 619  87.932 4.298
## 620  70.163 3.912
## 621  69.788 4.404
## 622   7.300 1.923
## 623  33.614 4.995
## 624  75.685 4.396
## 625  26.170 1.929
## 626  86.083 5.987
## 627  61.749 7.757
## 628  57.263 5.007
## 629  85.798 4.089
## 630  46.956 4.745
## 631  70.700 6.051
## 632  23.990 0.848
## 633  88.049 2.830
## 634  11.487 3.432
## 635   9.027 2.610
## 636  26.866 4.774
## 637  50.271 5.088
## 638  47.854 5.401
## 639  61.760 4.312
## 640  11.453 4.523
## 641  11.917 4.036
## 642  38.570 5.939
## 643  43.281 5.095
## 644  70.200 5.350
## 645  10.261 2.536
## 646  97.275 5.544
## 647  41.533 5.243
## 648  27.293 6.149
## 649  72.834 3.190
## 650  43.220 7.260
## 651  75.289 5.468
## 652  50.097 5.062
## 653  12.448 2.451
## 654  27.243 2.990
## 655  41.726 4.355
## 656  34.064 3.481
## 657  59.185 5.717
## 658  12.888 2.226
## 659  97.924 4.907
## 660  13.908 2.925
## 661  14.249 3.797
## 662  83.453 5.019
## 663  33.964 3.197
## 664  16.395 4.030
## 665   9.406 3.639
## 666  93.718 5.551
## 667  56.944 3.466
## 668  35.137 3.359
## 669  12.669 3.887
## 670  15.502 3.203
## 671  62.928 5.399
## 672  58.472 6.274
## 673  64.903 8.184
## 674  60.216 5.336
## 675  42.219 6.989
## 676  24.886 2.953
## 677  52.943 5.165
## 678  87.197 5.332
## 679  56.996 4.927
## 680  41.250 4.155
## 681  94.181 4.968
## 682  53.911 4.121
## 683  61.008 1.450
## 684  40.781 4.397
## 685  59.839 5.733
## 686  16.501 2.506
## 687  38.020 5.474
## 688  72.078 5.365
## 689  25.748 3.258
## 690  52.995 4.125
## 691  71.054 4.917
## 692  36.506 3.739
## 693  39.637 3.913
## 694  51.800 3.143
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## 1599 12.347 2.826
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## 1611 33.476 4.829
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## 1631 24.018 3.912
## 1632 44.270 2.454
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## 1635  7.588 3.586
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## 1637 12.856 5.220
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## 1704 15.099 3.494
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## 1716 11.304 3.983
## 1717 64.932 6.838
## 1718  9.973 2.928
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## 1726 78.612 6.540
## 1727 88.438 3.992
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## 1729 87.320 7.774
## 1730 74.670 4.727
## 1731 78.393 5.123
## 1732 35.045 2.087
## 1733 64.691 4.928
## 1734 38.706 4.306
## 1735 88.456 7.139
## 1736  8.286 1.384
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## 1740 50.394 5.823
## 1741 41.969 2.198
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## 1746 26.112 3.388
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## 1778 65.780 4.088
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## 1780 38.453 3.233
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## 1786 42.395 4.450
## 1787 19.997 4.027
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## 1791 19.498 2.803
## 1792  8.826 2.848
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## 1794 25.278 4.133
## 1795 75.348 4.337
## 1796 42.989 5.450
## 1797 21.412 5.304
## 1798  9.261 3.608
## 1799 72.371 6.614
## 1800 78.880 6.151
## 1801 86.980 7.108
## 1802 36.641 5.247
## 1803 77.395 4.489
## 1804 82.818 7.401
## 1805  6.492 2.530
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## 1808 95.974 4.725
## 1809 67.483 4.875
## 1810 94.353 6.845
## 1811 83.394 7.147
## 1812 45.508 4.217
## 1813 42.403 5.819
## 1814 44.283 2.595
## 1815 36.642 6.448
## 1816 69.636 5.689
## 1817 80.210 7.059
## 1818 37.532 5.094
## 1819 95.208 4.687
## 1820 84.195 5.195
## 1821 80.641 4.776
## 1822 92.218 5.424
## 1823 47.696 4.643
## 1824 38.212 3.702
## 1825 24.401 3.741
## 1826 79.085 3.876
## 1827 34.202 7.076
## 1828 45.070 6.751
## 1829 22.546 2.555
## 1830 58.681 6.452
## 1831 33.650 4.906
## 1832 90.157 5.602
## 1833 87.926 3.647
## 1834 13.229 3.572
## 1835 64.650 5.297
## 1836 73.115 5.588
## 1837 65.404 3.510
## 1838 42.807 4.872
## 1839 15.272 4.308
## 1840 67.781 5.655
## 1841 38.882 4.549
## 1842 49.313 6.237
## 1843 96.483 4.892
## 1844 76.575 4.659
## 1845 82.634 5.228
## 1846 27.888 3.310
## 1847 33.322 4.838
## 1848 36.104 4.100
## 1849 79.089 5.624
## 1850 41.317 5.180
## 1851 42.260 4.783
## 1852 17.427 4.970
## 1853 19.042 2.523
## 1854 15.940 3.395
## 1855 45.529 4.216
## 1856 40.747 5.426
## 1857 96.514 6.226
## 1858 53.300 4.371
## 1859 44.471 5.652
## 1860 54.854 5.127
## 1861 80.304 6.390
## 1862 89.167 5.890
## 1863 27.426 3.961
## 1864 72.711 3.510
## 1865 89.251 5.049
## 1866  5.784 4.087
## 1867 85.355 4.561
## 1868 66.351 7.432
## 1869 17.791 2.676
## 1870 20.403 4.155
## 1871 40.479 5.534
## 1872 13.385 2.336
## 1873 83.230 5.966
## 1874 88.530 4.679
## 1875 81.143 6.626
## 1876 60.783 5.565
## 1877 92.262 4.759
## 1878 14.425 2.999
## 1879 89.624 6.323
## 1880 17.569 7.150
## 1881 61.450 6.463
## 1882  6.131 3.153
## 1883 20.768 4.134
## 1884 91.703 5.285
## 1885  7.469 1.342
## 1886  6.809 2.158
## 1887 91.463 5.031
## 1888 79.716 4.628
## 1889 21.385 4.018
## 1890 50.892 5.630
## 1891 57.207 6.351
## 1892 46.793 6.877
## 1893 86.438 5.596
## 1894 18.459 3.334
## 1895 93.869 5.205
## 1896 20.995 4.796
## 1897 67.728 6.497
## 1898 70.730 5.123
## 1899 74.246 6.287
## 1900 78.472 5.126
## 1901 62.609 5.907
## 1902 68.841 3.765
## 1903 46.128 5.144
## 1904 73.554 4.277
## 1905 32.683 4.195
## 1906 96.482 6.150
## 1907 38.491 6.024
## 1908 43.722 3.372
## 1909 45.221 4.752
## 1910 69.093 5.779
## 1911 63.644 4.592
## 1912 88.015 5.827
## 1913 22.703 4.960
## 1914 11.522 2.104
## 1915 32.558 5.327
## 1916 85.370 6.646
## 1917 14.635 3.706
## 1918 43.997 5.655
## 1919 52.877 4.846
## 1920 57.614 7.952
## 1921 92.232 5.706
## 1922 10.578 3.901
## 1923 59.032 4.597
## 1924  9.141 4.021
## 1925  5.449 5.075
## 1926 97.652 5.346
## 1927 97.308 3.966
## 1928 90.712 5.981
## 1929 44.231 5.554
## 1930 89.631 4.222
## 1931 73.987 5.440
## 1932 25.968 3.622
## 1933 92.546 4.786
## 1934 94.413 2.860
## 1935  6.772 3.481
## 1936 65.402 5.964
## 1937 40.915 4.047
## 1938 69.374 5.180
## 1939 30.154 5.726
## 1940 59.941 3.428
## 1941 91.619 5.422
## 1942 19.413 3.048
## 1943 22.942 3.294
## 1944 60.075 4.098
## 1945 94.175 4.388
## 1946 24.189 5.881
## 1947 58.425 3.978
## 1948 61.083 4.144
## 1949 90.129 4.290
## 1950 44.053 5.852
## 1951 37.540 4.618
## 1952 37.687 4.440
## 1953 22.868 3.407
## 1954 54.205 4.856
## 1955 88.970 5.799
## 1956 86.893 5.435
## 1957 62.037 5.032
## 1958 53.697 5.903
## 1959 16.419 3.035
## 1960 71.584 6.223
## 1961 97.321 4.947
## 1962 47.592 4.684
## 1963 36.566 3.827
## 1964 64.243 5.399
## 1965 97.141 4.517
## 1966 33.443 4.125
## 1967 91.384 5.052
## 1968 12.047 3.028
## 1969 82.408 6.559
## 1970 96.260 4.341
## 1971 42.010 6.422
## 1972 92.566 5.187
## 1973 64.528 6.455
## 1974 86.613 4.631
## 1975 35.783 4.414
## 1976 61.511 5.924
## 1977 66.635 5.575
## 1978 25.632 4.884
## 1979 53.246 6.814
## 1980 59.259 4.490
## 1981 60.011 8.052
## 1982 12.348 3.979
## 1983 26.919 3.748
## 1984 71.780 6.081
## 1985 57.929 5.132
## 1986 80.479 5.353
## 1987  5.216 3.003
## 1988 84.104 5.019
## 1989 95.784 4.008
## 1990 70.025 4.756
## 1991 34.219 5.735
## 1992 74.574 4.963
## 1993 27.746 3.463
## 1994 76.451 5.035
## 1995 89.265 6.288
## 1996 20.255 8.754
## 1997 51.291 5.161
## 1998 16.396 3.861
## 1999 88.426 4.092
## 2000 88.885 4.890
## 2001 15.672 3.199
## 2002 39.249 4.576
## 2003  6.957 1.157
## 2004 80.650 6.527
## 2005 62.676 6.039
## 2006 52.366 5.377
## 2007 25.781 4.613
## 2008 90.933 4.140
## 2009  5.592 0.979
## 2010 22.727 2.747
## 2011 18.767 2.933
## 2012 54.739 4.649
## 2013 93.982 4.393
## 2014 24.989 4.312
## 2015 87.114 4.507
## 2016 75.254 5.693
## 2017 62.519 5.176
## 2018 15.372 4.661
## 2019 27.166 6.578
## 2020 31.966 4.358
## 2021 46.295 5.512
## 2022  7.527 1.500
## 2023 32.823 6.405
## 2024 63.637 4.623
## 2025 53.179 5.146
## 2026 85.024 3.262
## 2027 13.266 3.521
## 2028 49.511 4.659
## 2029 78.139 4.230
## 2030 60.602 5.103
## 2031 45.622 4.065
## 2032 81.832 5.884
## 2033 94.833 5.462
## 2034 96.091 5.156
## 2035 19.916 3.492
## 2036 42.897 4.693
## 2037 30.587 3.675
## 2038 43.333 5.780
## 2039  5.893 2.615
## 2040 92.848 5.763
## 2041 96.765 4.386
## 2042 14.177 4.398
## 2043 40.600 5.427
## 2044 15.730 3.171
## 2045 23.441 2.470
## 2046 19.256 3.642
## 2047 42.382 3.804
## 2048  6.508 4.119
## 2049 81.058 5.351
## 2050 63.304 4.131
## 2051 13.124 2.487
## 2052 65.610 5.152
## 2053 51.861 5.809
## 2054 89.767 4.911
## 2055 32.591 4.598
## 2056 93.061 3.975
## 2057 42.639 6.361
## 2058 73.782 3.819
## 2059 58.045 5.215
## 2060 54.562 5.961
## 2061 32.601 3.928
## 2062 53.935 5.103
## 2063 95.433 5.205
## 2064 36.559 5.288
## 2065 91.941 3.550
## 2066 21.972 2.741
## 2067 36.130 3.813
## 2068 72.195 3.468
## 2069 49.669 4.158
## 2070 53.685 5.036
## 2071 83.025 5.791
## 2072  7.868 3.353
## 2073 70.575 6.000
## 2074 64.377 4.950
## 2075 37.165 3.349
## 2076 82.617 5.379
## 2077 65.037 5.372
## 2078 33.122 4.427
## 2079 88.219 3.734
## 2080 49.883 6.343
## 2081 27.637 4.271
## 2082 87.859 5.093
## 2083 88.981 7.088
## 2084 93.679 5.334
## 2085 38.363 5.693
## 2086  7.297 3.843
## 2087 59.181 5.625
## 2088 55.486 5.786
## 2089 13.991 3.621
## 2090 50.615 5.867
## 2091 68.267 5.791
## 2092 63.823 7.316
## 2093 58.738 5.968
## 2094 75.216 5.373
## 2095 38.952 4.792
## 2096 66.541 5.404
## 2097 12.770 1.789
## 2098 34.157 5.833
## 2099  5.700 1.124
## 2100 13.164 3.590
## 2101 47.847 7.198
## 2102 33.261 1.825
## 2103 88.962 6.436
## 2104 56.640 5.216
## 2105 42.410 4.530
## 2106 87.428 4.770
## 2107 42.500 7.557
## 2108 94.196 5.339
## 2109 29.058 4.272
## 2110 75.163 6.869
## 2111 91.114 4.372
## 2112 37.721 5.189
## 2113 83.148 4.173
## 2114 32.832 5.193
## 2115 57.125 4.090
## 2116 40.397 3.849
## 2117 13.218 2.938
## 2118  6.384 4.470
## 2119 35.497 4.822
## 2120 41.838 4.032
## 2121 48.035 6.151
## 2122 90.808 6.324
## 2123 74.577 6.042
## 2124  6.210 3.091
## 2125 33.137 4.109
## 2126 88.719 3.254
## 2127 50.224 5.068
## 2128 54.973 7.079
## 2129 72.300 5.326
## 2130 49.409 4.898
## 2131 81.496 4.808
## 2132 91.838 4.534
## 2133 86.903 3.522
## 2134  7.593 4.376
## 2135 31.267 5.567
## 2136 48.517 2.503
## 2137 38.049 3.864
## 2138 68.532 5.738
## 2139 66.228 5.060
## 2140 83.246 4.259
## 2141 59.862 4.807
## 2142 37.578 3.886
## 2143 66.241 5.999
## 2144 22.944 5.174
## 2145 53.618 4.105
## 2146 94.298 5.012
## 2147 68.885 5.028
## 2148 49.313 5.547
## 2149 78.742 5.552
## 2150 11.705 4.607
## 2151  6.663 3.234
## 2152 48.972 3.759
## 2153  8.730 2.353
## 2154 46.881 5.809
## 2155 79.029 5.466
## 2156 41.716 5.102
## 2157 82.554 5.682
## 2158 11.736 1.394
## 2159 92.433 5.127
## 2160  8.229 1.398
## 2161 57.585 3.797
## 2162 82.551 5.297
## 2163 49.341 4.526
## 2164 35.394 3.857
## 2165 58.237 4.376
## 2166 97.218 5.817
## 2167 16.718 5.567
## 2168 37.539 4.364
## 2169 94.344 4.023
## 2170 84.417 4.689
## 2171 40.126 5.063
## 2172 73.589 5.353
## 2173 94.393 6.156
## 2174 58.926 5.112
## 2175 71.094 6.158
## 2176 71.190 6.093
## 2177 62.189 5.365
## 2178 29.886 3.709
## 2179 45.676 4.793
## 2180 67.846 6.592
## 2181 77.119 5.570
## 2182 13.679 4.073
## 2183 72.152 4.376
## 2184  7.218 0.933
## 2185 33.753 4.785
## 2186 84.207 5.464
## 2187 55.228 5.504
## 2188 64.380 5.561
## 2189 14.252 3.994
## 2190 43.570 6.012
## 2191 56.972 5.020
## 2192 68.444 5.250
## 2193 82.135 7.048
## 2194 43.620 3.906
## 2195 53.842 6.450
## 2196 18.832 4.649
## 2197 60.002 4.220
## 2198 85.403 6.570
## 2199 54.602 4.627
## 2200 94.181 7.265
## 2201 91.807 6.035
## 2202 71.910 4.906
## 2203 92.175 6.929
## 2204 96.682 4.921
## 2205 85.319 5.136
## 2206 81.535 5.233
## 2207 79.407 4.984
## 2208 65.447 6.624
## 2209 31.143 4.045
## 2210 63.838 5.625
## 2211 20.273 3.036
## 2212 32.749 3.546
## 2213 75.314 4.653
## 2214 92.111 4.134
## 2215 27.135 2.796
## 2216 79.483 5.784
## 2217 89.160 6.013
## 2218 90.780 5.264
## 2219 47.107 2.578
## 2220 97.129 5.219
## 2221 20.240 3.455
## 2222 17.870 3.422
## 2223  5.388 2.309
## 2224 64.827 6.004
## 2225 20.304 4.101
## 2226 37.159 5.006
## 2227 76.255 6.328
## 2228 38.869 5.052
## 2229 95.136 5.393
## 2230 18.516 4.713
## 2231 56.653 5.185
## 2232 60.868 5.884
## 2233 93.750 4.832
## 2234 74.225 4.019
## 2235 47.393 7.505
## 2236 75.835 5.155
## 2237 27.236 4.423
## 2238 17.692 3.443
## 2239 43.495 4.510
## 2240 21.790 2.936
## 2241 75.520 6.249
## 2242 51.278 5.217
## 2243 80.691 3.154
## 2244 94.661 7.688
## 2245 51.641 4.428
## 2246 20.029 4.819
## 2247 20.932 2.979
## 2248 17.940 3.579
## 2249 38.844 4.280
## 2250 47.752 3.034
## 2251 13.305 2.041
## 2252 88.539 4.849
## 2253 38.936 6.278
## 2254 80.341 4.799
## 2255 92.657 6.118
## 2256  8.275 1.349
## 2257 64.154 6.521
## 2258 26.452 2.610
## 2259 11.557 4.467
## 2260 78.735 7.462
## 2261 80.426 3.897
## 2262 45.141 3.553
## 2263  8.768 2.901
## 2264 46.783 3.253
## 2265 52.314 4.261
## 2266 81.568 4.586
## 2267 76.344 5.550
## 2268 62.374 5.717
## 2269 48.105 5.197
## 2270 23.494 4.493
## 2271  8.257 3.969
## 2272 91.564 5.651
## 2273  5.518 2.724
## 2274 21.565 4.151
## 2275 38.190 5.202
## 2276 18.980 3.163
## 2277 18.985 3.973
## 2278 35.116 5.631
## 2279 71.992 4.478
## 2280 75.639 6.386
## 2281 76.768 6.782
## 2282 35.241 3.776
## 2283 77.155 7.057
## 2284 88.127 6.233
## 2285 29.429 3.835
## 2286 28.060 3.596
## 2287 78.640 4.033
## 2288  5.456 3.298
## 2289 62.838 4.829
## 2290 82.500 4.957
## 2291 37.419 5.160
## 2292 48.792 5.536
## 2293 10.922 1.598
## 2294 97.121 4.911
## 2295 70.092 3.922
## 2296 16.225 4.113
## 2297 27.709 4.051
## 2298 27.567 2.424
## 2299 43.639 5.591
## 2300 19.801 5.106
## 2301 77.275 4.779
## 2302 81.116 3.919
## 2303 95.556 5.803
## 2304 63.216 3.308
## 2305 82.291 4.643
## 2306 41.122 3.272
## 2307 60.407 6.831
## 2308 29.385 5.440
## 2309 84.871 5.349
## 2310  6.054 2.762
## 2311 40.465 5.483
## 2312 94.955 4.846
## 2313 27.482 4.446
## 2314 21.730 4.196
## 2315  6.248 3.287
## 2316 35.077 5.424
## 2317 85.751 6.963
## 2318 29.167 3.780
## 2319 55.646 5.362
## 2320 44.989 4.398
## 2321 26.570 4.020
## 2322 53.028 5.503
## 2323 54.470 5.830
## 2324 89.997 4.003
## 2325 86.118 3.672
## 2326 75.546 5.119
## 2327 54.903 4.352
## 2328 58.268 5.466
## 2329 69.719 3.299
## 2330 70.520 5.649
## 2331 60.962 4.624
## 2332 44.612 4.283
## 2333 13.216 4.821
## 2334 32.761 5.202
## 2335 93.389 5.573
## 2336 63.826 4.809
## 2337 17.275 3.961
## 2338 16.341 1.538
## 2339 93.697 4.569
## 2340 66.984 4.595
## 2341  5.814 2.538
## 2342 28.164 3.378
## 2343 76.622 5.267
## 2344 79.123 5.691
## 2345 78.554 3.435
## 2346 70.504 4.140
## 2347 57.696 5.249
## 2348 14.639 2.771
## 2349 49.352 5.981
## 2350 59.843 7.889
## 2351 55.274 5.148
## 2352 38.865 4.005
## 2353 13.542 3.308
## 2354 34.843 5.556
## 2355 86.695 6.023
## 2356 93.808 4.406
## 2357 30.705 3.216
## 2358 44.982 4.192
## 2359 31.241 4.618
## 2360 74.648 7.296
## 2361 29.106 4.380
## 2362 20.724 5.876
## 2363 45.357 5.040
## 2364 83.351 6.073
## 2365 76.441 5.267
## 2366 73.746 5.599
## 2367 69.688 5.363
## 2368 21.977 3.633
## 2369 89.182 6.522
## 2370 78.628 6.279
## 2371 64.932 3.048
## 2372 47.715 5.639
## 2373 50.939 6.051
## 2374 51.209 3.609
## 2375 28.371 3.884
## 2376 22.375 1.644
## 2377 51.038 6.830
## 2378 76.900 5.157
## 2379 70.490 4.487
## 2380 89.177 5.039
## 2381 52.883 6.258
## 2382 21.838 3.923
## 2383 95.707 4.141
## 2384 96.597 4.261
## 2385 54.549 4.345
## 2386 27.041 4.711
## 2387 10.324 2.455
## 2388 34.825 5.200
## 2389 58.199 5.858
## 2390 28.930 2.504
## 2391 88.774 5.192
## 2392 45.663 5.355
## 2393 36.052 3.469
## 2394 60.127 4.769
## 2395 48.184 4.735
## 2396 94.668 4.767
## 2397 89.219 5.328
## 2398 89.619 5.866
## 2399 97.538 4.192
## 2400 83.335 5.404
## 2401 61.235 5.338
## 2402 44.897 3.168
## 2403 89.317 5.578
## 2404 51.090 5.862
## 2405 79.937 4.993
## 2406 60.217 6.078
## 2407 16.412 4.200
## 2408 94.984 4.676
## 2409 47.124 4.512
## 2410 78.425 4.881
## 2411 19.381 4.668
## 2412 47.040 4.728
## 2413 66.439 5.296
## 2414 83.212 5.657
## 2415 64.068 5.966
## 2416 69.771 4.970
## 2417 61.005 7.025
## 2418 70.281 6.386
## 2419 20.521 4.594
## 2420 77.682 4.531
## 2421 87.618 6.035
## 2422 22.352 4.282
## 2423 47.837 5.323
## 2424  6.127 3.624
## 2425 37.686 5.959
## 2426 33.731 4.072
## 2427 32.226 4.481
## 2428 83.836 6.346
## 2429 45.572 6.427
## 2430 94.986 5.322
## 2431 72.331 6.161
## 2432 36.217 5.474
## 2433 65.891 7.250
## 2434 87.012 4.859
## 2435 67.201 5.862
## 2436 66.541 6.115
## 2437 17.476 4.066
## 2438 69.677 4.528
## 2439 47.541 4.141
## 2440 97.720 4.854
## 2441 97.768 5.673
## 2442  7.074 2.030
## 2443 61.002 5.846
## 2444 75.170 6.178
## 2445  5.297 2.918
## 2446 31.685 5.420
## 2447 89.546 5.410
## 2448 42.840 3.710
## 2449 73.212 5.991
## 2450 81.370 5.865
## 2451 76.204 4.509
## 2452 79.017 5.513
## 2453 65.447 6.093
## 2454  6.397 2.374
## 2455 29.923 5.524
## 2456 72.300 4.421
## 2457 53.435 4.896
## 2458 23.675 3.184
## 2459 61.038 4.659
## 2460  9.882 4.244
## 2461  8.547 2.743
## 2462 13.754 5.874
## 2463 61.199 6.468
## 2464 82.215 3.710
## 2465 97.722 5.198
## 2466 31.386 4.567
## 2467 27.582 4.733
## 2468 81.834 5.339
## 2469 78.681 2.598
## 2470  7.647 2.015
## 2471 61.050 5.173
## 2472 29.996 5.648
## 2473 41.094 5.732
## 2474 89.209 4.768
## 2475 38.715 5.110
## 2476 40.922 3.783
## 2477 32.632 4.684
## 2478 66.919 3.051
## 2479 43.014 5.136
## 2480 52.336 2.942
## 2481 63.630 5.684
## 2482 83.484 6.595
## 2483 82.242 5.134
## 2484 85.205 5.582
## 2485 91.484 4.071
## 2486 79.398 6.228
## 2487 17.596 2.787
## 2488 87.163 3.869
## 2489 11.283 4.874
## 2490 48.303 5.342
## 2491 83.849 4.318
## 2492 10.825 2.203
## 2493 25.709 4.251
## 2494 45.143 4.739
## 2495 97.969 6.836
## 2496 18.636 2.640
## 2497 50.117 5.564
## 2498 38.128 4.792
## 2499 67.133 5.395
## 2500 54.097 3.362

TPV <- TPV[order(TPV$sio2), ] #DAR ORDEN A LA TABLA

TPV

##        sio2 al2o3
## 1124  5.114 1.815
## 1987  5.216 3.003
## 70    5.238 2.653
## 1451  5.272 2.450
## 1005  5.278 4.053
## 2445  5.297 2.918
## 2223  5.388 2.309
## 1925  5.449 5.075
## 2288  5.456 3.298
## 1581  5.501 4.017
## 2273  5.518 2.724
## 419   5.543 1.782
## 2009  5.592 0.979
## 428   5.670 2.987
## 2099  5.700 1.124
## 400   5.729 4.394
## 1525  5.733 4.771
## 46    5.743 3.928
## 1866  5.784 4.087
## 2341  5.814 2.538
## 1252  5.848 0.483
## 470   5.854 3.983
## 2039  5.893 2.615
## 326   5.904 4.552
## 205   5.936 1.990
## 1684  5.973 2.925
## 816   5.976 5.537
## 2310  6.054 2.762
## 2424  6.127 3.624
## 1882  6.131 3.153
## 1248  6.167 1.874
## 545   6.169 3.903
## 1492  6.171 1.593
## 2124  6.210 3.091
## 2315  6.248 3.287
## 103   6.273 2.818
## 380   6.315 2.163
## 2118  6.384 4.470
## 2454  6.397 2.374
## 1805  6.492 2.530
## 2048  6.508 4.119
## 1213  6.518 2.646
## 144   6.544 2.044
## 1302  6.579 1.450
## 265   6.645 1.283
## 2151  6.663 3.234
## 1337  6.670 3.625
## 1035  6.717 4.594
## 540   6.754 5.651
## 616   6.767 3.789
## 1935  6.772 3.481
## 1886  6.809 2.158
## 313   6.829 2.856
## 404   6.834 2.322
## 774   6.900 2.682
## 889   6.924 3.171
## 2003  6.957 1.157
## 1249  6.966 2.828
## 156   7.038 1.968
## 915   7.065 2.841
## 2442  7.074 2.030
## 319   7.122 2.820
## 68    7.191 2.619
## 983   7.192 3.728
## 2184  7.218 0.933
## 247   7.251 1.852
## 2086  7.297 3.843
## 622   7.300 1.923
## 189   7.319 3.191
## 1156  7.366 3.520
## 1328  7.384 3.220
## 1613  7.426 4.322
## 1885  7.469 1.342
## 2022  7.527 1.500
## 1635  7.588 3.586
## 1428  7.590 2.209
## 2134  7.593 4.376
## 1344  7.606 3.969
## 2470  7.647 2.015
## 2072  7.868 3.353
## 952   7.870 2.614
## 138   7.880 4.383
## 1513  7.941 2.677
## 522   7.956 3.043
## 1288  7.960 3.006
## 1280  7.988 3.914
## 1304  7.988 2.097
## 1719  7.995 3.615
## 179   8.151 2.046
## 2160  8.229 1.398
## 190   8.236 3.442
## 307   8.249 2.267
## 2271  8.257 3.969
## 2256  8.275 1.349
## 1736  8.286 1.384
## 1369  8.325 1.138
## 460   8.351 3.818
## 717   8.388 2.761
## 1056  8.466 1.880
## 41    8.490 1.837
## 2461  8.547 2.743
## 336   8.604 3.178
## 1068  8.634 3.207
## 508   8.656 2.058
## 1191  8.660 1.824
## 513   8.678 3.154
## 1447  8.695 3.731
## 741   8.729 4.503
## 2153  8.730 2.353
## 382   8.745 2.431
## 2263  8.768 2.901
## 1385  8.770 3.479
## 259   8.782 2.646
## 1203  8.815 2.469
## 1176  8.824 2.481
## 1792  8.826 2.848
## 1027  8.833 4.173
## 1652  8.885 1.509
## 949   8.916 3.815
## 635   9.027 2.610
## 1125  9.054 3.406
## 1503  9.072 3.256
## 984   9.131 4.186
## 1924  9.141 4.021
## 302   9.183 5.411
## 1798  9.261 3.608
## 266   9.313 1.580
## 1461  9.327 2.717
## 1055  9.396 2.553
## 665   9.406 3.639
## 279   9.448 2.571
## 778   9.502 2.876
## 497   9.515 1.152
## 480   9.517 2.701
## 1493  9.627 4.286
## 1347  9.653 4.969
## 991   9.791 3.028
## 197   9.840 4.296
## 410   9.856 4.363
## 2460  9.882 4.244
## 1718  9.973 2.928
## 1715 10.050 3.868
## 963  10.136 2.937
## 801  10.206 2.825
## 645  10.261 2.536
## 1520 10.287 3.610
## 2387 10.324 2.455
## 432  10.336 3.835
## 187  10.340 2.120
## 1612 10.358 5.138
## 1091 10.393 3.402
## 222  10.407 4.064
## 1414 10.470 1.500
## 306  10.510 5.304
## 469  10.513 1.527
## 1043 10.518 2.305
## 922  10.575 3.190
## 1922 10.578 3.901
## 1208 10.686 3.118
## 546  10.749 3.365
## 957  10.775 3.092
## 1185 10.796 3.475
## 1164 10.802 4.218
## 2492 10.825 2.203
## 384  10.856 3.940
## 825  10.860 2.171
## 920  10.892 4.616
## 2293 10.922 1.598
## 1030 10.948 2.847
## 975  10.957 3.960
## 1230 11.155 3.520
## 1578 11.277 3.805
## 2489 11.283 4.874
## 1146 11.304 3.361
## 1716 11.304 3.983
## 1572 11.425 2.702
## 971  11.438 2.148
## 640  11.453 4.523
## 819  11.478 3.820
## 634  11.487 3.432
## 1367 11.498 2.887
## 1914 11.522 2.104
## 1186 11.531 2.720
## 2259 11.557 4.467
## 1681 11.600 4.076
## 2150 11.705 4.607
## 260  11.709 2.716
## 1244 11.714 2.834
## 2158 11.736 1.394
## 214  11.770 2.964
## 1247 11.777 3.901
## 1464 11.814 3.296
## 1793 11.869 3.321
## 1628 11.895 3.182
## 289  11.901 1.361
## 641  11.917 4.036
## 1297 11.992 3.372
## 1968 12.047 3.028
## 877  12.099 2.694
## 903  12.255 2.257
## 994  12.295 3.397
## 1599 12.347 2.826
## 1982 12.348 3.979
## 966  12.400 3.256
## 653  12.448 2.451
## 455  12.506 2.635
## 1790 12.528 3.994
## 104  12.611 3.921
## 286  12.629 3.314
## 1751 12.630 4.525
## 669  12.669 3.887
## 2097 12.770 1.789
## 110  12.788 2.452
## 1774 12.802 3.288
## 609  12.827 4.081
## 1637 12.856 5.220
## 658  12.888 2.226
## 298  12.893 4.108
## 161  12.932 2.125
## 280  13.004 3.820
## 1526 13.014 4.375
## 1465 13.020 2.425
## 1107 13.046 4.432
## 703  13.054 3.557
## 1040 13.117 1.479
## 2051 13.124 2.487
## 15   13.141 1.662
## 2100 13.164 3.590
## 2333 13.216 4.821
## 2117 13.218 2.938
## 1834 13.229 3.572
## 1108 13.243 3.892
## 1178 13.252 3.983
## 932  13.254 4.408
## 2027 13.266 3.521
## 2251 13.305 2.041
## 1872 13.385 2.336
## 2353 13.542 3.308
## 538  13.624 2.825
## 2182 13.679 4.073
## 2462 13.754 5.874
## 1467 13.767 3.842
## 591  13.794 4.318
## 904  13.877 3.146
## 660  13.908 2.925
## 366  13.938 3.711
## 2089 13.991 3.621
## 322  14.014 4.416
## 1029 14.019 3.917
## 558  14.137 3.098
## 1661 14.137 2.748
## 2042 14.177 4.398
## 1079 14.223 2.578
## 77   14.238 3.504
## 661  14.249 3.797
## 2189 14.252 3.994
## 1325 14.287 3.682
## 1528 14.333 4.367
## 423  14.371 3.384
## 1031 14.373 3.312
## 23   14.376 2.422
## 204  14.379 4.527
## 1878 14.425 2.999
## 898  14.429 2.154
## 1459 14.530 1.704
## 363  14.572 1.447
## 1917 14.635 3.706
## 2348 14.639 2.771
## 760  14.765 3.505
## 554  15.011 4.109
## 234  15.044 3.205
## 1704 15.099 3.494
## 406  15.115 2.475
## 718  15.206 4.965
## 592  15.264 4.488
## 1839 15.272 4.308
## 787  15.281 5.061
## 141  15.286 3.888
## 1340 15.359 4.248
## 2018 15.372 4.661
## 800  15.430 3.658
## 670  15.502 3.203
## 1225 15.519 4.034
## 716  15.592 3.402
## 2001 15.672 3.199
## 2044 15.730 3.171
## 869  15.769 2.605
## 1395 15.829 3.013
## 290  15.841 2.222
## 1173 15.884 3.175
## 1854 15.940 3.395
## 767  16.204 3.548
## 2296 16.225 4.113
## 309  16.240 3.074
## 1254 16.261 2.846
## 2338 16.341 1.538
## 664  16.395 4.030
## 1998 16.396 3.861
## 398  16.397 4.686
## 2407 16.412 4.200
## 1959 16.419 3.035
## 245  16.468 6.168
## 1025 16.485 3.738
## 686  16.501 2.506
## 291  16.529 2.864
## 1001 16.712 4.148
## 2167 16.718 5.567
## 1569 16.737 3.030
## 1180 16.755 4.915
## 799  16.845 4.442
## 124  16.868 3.804
## 478  16.876 2.625
## 1319 16.924 1.728
## 134  16.946 3.673
## 917  17.006 2.103
## 33   17.061 3.776
## 1650 17.174 4.816
## 467  17.178 3.237
## 1678 17.184 4.326
## 2337 17.275 3.961
## 802  17.299 3.758
## 1140 17.339 3.888
## 1523 17.373 5.754
## 301  17.419 3.801
## 1852 17.427 4.970
## 1162 17.433 3.887
## 2437 17.476 4.066
## 176  17.544 2.035
## 162  17.566 4.711
## 1880 17.569 7.150
## 1420 17.573 3.640
## 2487 17.596 2.787
## 83   17.661 1.880
## 87   17.678 3.996
## 2238 17.692 3.443
## 813  17.704 4.798
## 409  17.715 3.470
## 602  17.733 5.001
## 1869 17.791 2.676
## 1453 17.814 5.097
## 2222 17.870 3.422
## 1495 17.928 5.423
## 2248 17.940 3.579
## 1133 18.010 5.082
## 334  18.090 3.088
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## 649  72.834 3.190
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## 1549 72.994 5.794
## 1278 73.076 7.006
## 1836 73.115 5.588
## 1629 73.157 4.685
## 1462 73.176 4.304
## 229  73.178 4.141
## 2449 73.212 5.991
## 1708 73.273 5.465
## 1460 73.355 7.553
## 288  73.407 5.839
## 1904 73.554 4.277
## 66   73.563 5.950
## 85   73.589 5.048
## 2172 73.589 5.353
## 1323 73.590 4.797
## 486  73.631 6.179
## 733  73.657 3.627
## 886  73.710 5.359
## 2366 73.746 5.599
## 1646 73.756 4.702
## 1105 73.781 6.946
## 2058 73.782 3.819
## 1038 73.897 5.588
## 1207 73.918 6.206
## 1065 73.962 5.012
## 1931 73.987 5.440
## 1299 73.991 5.348
## 477  74.046 6.263
## 340  74.054 6.923
## 353  74.133 5.368
## 2234 74.225 4.019
## 1899 74.246 6.287
## 1560 74.249 5.832
## 158  74.260 6.246
## 1085 74.293 7.017
## 1531 74.307 6.247
## 1049 74.311 5.521
## 1052 74.347 3.224
## 1279 74.408 5.767
## 1171 74.423 6.390
## 1382 74.472 5.594
## 539  74.507 5.977
## 1992 74.574 4.963
## 2123 74.577 6.042
## 188  74.630 5.855
## 2360 74.648 7.296
## 1730 74.670 4.727
## 1320 74.747 5.532
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## 1018 74.772 4.455
## 105  74.800 3.146
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## 157  74.878 6.010
## 870  74.923 6.181
## 299  74.946 5.493
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## 2110 75.163 6.869
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## 1291 75.495 5.258
## 2241 75.520 6.249
## 2326 75.546 5.119
## 947  75.585 5.966
## 1013 75.605 5.433
## 1242 75.607 6.382
## 493  75.632 6.134
## 2280 75.639 6.386
## 624  75.685 4.396
## 1111 75.726 5.413
## 2236 75.835 5.155
## 1350 75.846 6.733
## 1398 75.846 4.068
## 1626 75.877 4.266
## 1042 75.892 5.195
## 1788 76.018 6.001
## 1630 76.172 6.297
## 2451 76.204 4.509
## 2227 76.255 6.328
## 1114 76.310 5.946
## 2267 76.344 5.550
## 1004 76.412 5.442
## 2365 76.441 5.267
## 1994 76.451 5.035
## 1292 76.469 6.232
## 874  76.478 3.976
## 1212 76.478 8.103
## 283  76.560 4.451
## 1844 76.575 4.659
## 3    76.600 4.590
## 2343 76.622 5.267
## 1506 76.689 4.572
## 1663 76.700 4.385
## 489  76.768 5.447
## 2281 76.768 6.782
## 1519 76.769 4.351
## 10   76.866 4.610
## 237  76.899 2.349
## 2378 76.900 5.157
## 1000 76.914 7.081
## 754  77.035 5.240
## 1126 77.038 4.777
## 2181 77.119 5.570
## 2283 77.155 7.057
## 364  77.165 5.739
## 978  77.210 5.595
## 1658 77.231 6.845
## 208  77.235 5.898
## 2301 77.275 4.779
## 1634 77.281 5.287
## 512  77.297 4.785
## 317  77.378 5.654
## 1803 77.395 4.489
## 506  77.501 4.436
## 1250 77.585 4.604
## 761  77.635 5.729
## 1505 77.660 6.236
## 1416 77.673 5.723
## 2420 77.682 4.531
## 1371 77.712 5.214
## 1417 77.737 5.485
## 1062 77.773 6.713
## 793  77.992 5.226
## 890  78.022 6.629
## 268  78.029 5.066
## 950  78.109 5.774
## 2029 78.139 4.230
## 160  78.171 5.971
## 1785 78.290 4.914
## 1643 78.307 4.447
## 249  78.359 3.614
## 1731 78.393 5.123
## 871  78.398 5.699
## 1377 78.408 4.021
## 57   78.415 6.113
## 1672 78.422 5.287
## 2410 78.425 4.881
## 565  78.467 7.468
## 1900 78.472 5.126
## 1284 78.523 5.321
## 2345 78.554 3.435
## 1050 78.555 5.688
## 121  78.581 5.979
## 1243 78.606 4.806
## 1726 78.612 6.540
## 2370 78.628 6.279
## 2287 78.640 4.033
## 866  78.677 5.447
## 430  78.678 5.619
## 2469 78.681 2.598
## 2260 78.735 7.462
## 2149 78.742 5.552
## 276  78.869 5.741
## 1800 78.880 6.151
## 1565 78.913 5.278
## 817  78.956 4.286
## 755  78.962 4.369
## 71   78.996 5.628
## 2452 79.017 5.513
## 2155 79.029 5.466
## 1826 79.085 3.876
## 1849 79.089 5.624
## 2344 79.123 5.691
## 1222 79.188 4.156
## 501  79.233 5.928
## 1233 79.239 4.764
## 1089 79.288 4.329
## 2486 79.398 6.228
## 2207 79.407 4.984
## 491  79.448 4.538
## 2216 79.483 5.784
## 1555 79.494 5.519
## 1101 79.599 4.992
## 99   79.641 4.530
## 1888 79.716 4.628
## 320  79.729 4.685
## 855  79.753 5.210
## 1081 79.807 7.180
## 2405 79.937 4.993
## 604  79.938 4.853
## 765  79.960 4.389
## 1669 79.964 6.587
## 1182 79.966 6.210
## 211  79.984 3.442
## 165  80.089 6.485
## 1556 80.133 3.758
## 1701 80.190 7.182
## 1817 80.210 7.059
## 31   80.289 5.017
## 1538 80.297 5.294
## 1861 80.304 6.390
## 896  80.338 4.873
## 2254 80.341 4.799
## 2261 80.426 3.897
## 1986 80.479 5.353
## 1363 80.508 5.053
## 338  80.529 5.981
## 1821 80.641 4.776
## 1566 80.647 6.443
## 2004 80.650 6.527
## 853  80.663 5.814
## 2243 80.691 3.154
## 1134 80.747 4.872
## 1437 80.752 5.094
## 277  80.826 4.608
## 356  80.900 5.547
## 312  80.904 7.107
## 238  80.957 6.119
## 933  80.980 5.714
## 1540 80.982 6.230
## 1536 81.017 4.757
## 960  81.043 5.632
## 2049 81.058 5.351
## 597  81.090 3.595
## 1449 81.106 4.235
## 2302 81.116 3.919
## 1875 81.143 6.626
## 995  81.151 5.223
## 944  81.327 4.466
## 1071 81.340 4.941
## 81   81.353 5.647
## 2450 81.370 5.865
## 925  81.396 5.966
## 562  81.420 4.599
## 2131 81.496 4.808
## 2206 81.535 5.233
## 2266 81.568 4.586
## 1585 81.635 4.401
## 1324 81.707 6.305
## 553  81.710 4.582
## 1486 81.711 7.221
## 911  81.741 7.129
## 742  81.804 5.611
## 572  81.821 5.452
## 2032 81.832 5.884
## 2468 81.834 5.339
## 1600 81.858 5.618
## 1771 81.899 6.384
## 1535 82.076 5.009
## 48   82.080 6.356
## 1314 82.133 6.235
## 2193 82.135 7.048
## 2464 82.215 3.710
## 2483 82.242 5.134
## 1287 82.288 4.886
## 2305 82.291 4.643
## 1559 82.307 6.716
## 737  82.327 4.763
## 1969 82.408 6.559
## 1689 82.463 6.450
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## 1265 82.470 6.692
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## 2290 82.500 4.957
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## 1537 82.794 6.125
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## 1804 82.818 7.401
## 1575 82.839 5.333
## 243  83.025 6.474
## 2071 83.025 5.791
## 420  83.122 4.576
## 219  83.127 5.145
## 2113 83.148 4.173
## 1083 83.179 4.870
## 1011 83.203 4.031
## 2414 83.212 5.657
## 1873 83.230 5.966
## 2140 83.246 4.259
## 1172 83.289 7.320
## 2400 83.335 5.404
## 2364 83.351 6.073
## 1202 83.356 4.081
## 1267 83.387 4.747
## 1361 83.387 4.689
## 1811 83.394 7.147
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## 1586 83.443 6.619
## 662  83.453 5.019
## 2482 83.484 6.595
## 1691 83.522 5.191
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## 30   83.641 5.643
## 347  83.644 4.506
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## 519  83.731 5.699
## 1654 83.748 6.423
## 1470 83.762 5.847
## 2428 83.836 6.346
## 1232 83.837 5.501
## 1391 83.845 3.972
## 2491 83.849 4.318
## 902  83.862 5.252
## 1157 83.955 6.368
## 387  83.961 4.125
## 332  84.019 3.450
## 711  84.062 5.018
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## 2186 84.207 5.464
## 442  84.388 6.142
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## 56   84.423 6.347
## 938  84.531 3.079
## 837  84.611 4.133
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## 1169 86.247 5.060
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## 1974 86.613 4.631
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## 2133 86.903 3.522
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## 1159 86.961 5.571
## 1801 86.980 7.108
## 2434 87.012 4.859
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## 2015 87.114 4.507
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## 1078 87.184 4.302
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## 937  87.600 6.198
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## 2421 87.618 6.035
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## 1143 87.893 5.042
## 1677 87.925 5.588
## 1833 87.926 3.647
## 619  87.932 4.298
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## 1196 87.968 6.467
## 282  87.974 4.357
## 1433 87.989 4.403
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## 191  88.037 5.972
## 633  88.049 2.830
## 45   88.076 4.224
## 1527 88.109 7.301
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## 2079 88.219 3.734
## 1017 88.227 5.270
## 173  88.240 5.436
## 372  88.256 4.590
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## 1755 88.348 5.461
## 504  88.353 5.805
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## 833  88.401 5.131
## 1999 88.426 4.092
## 1727 88.438 3.992
## 1735 88.456 7.139
## 1874 88.530 4.679
## 2252 88.539 4.849
## 1311 88.573 5.728
## 1554 88.575 4.617
## 1679 88.600 5.135
## 2126 88.719 3.254
## 418  88.728 5.813
## 2391 88.774 5.192
## 2000 88.885 4.890
## 1275 88.910 5.695
## 958  88.959 3.865
## 2103 88.962 6.436
## 1955 88.970 5.799
## 526  88.980 5.938
## 2083 88.981 7.088
## 399  89.048 7.141
## 44   89.120 5.739
## 1552 89.124 6.036
## 1386 89.127 5.139
## 2217 89.160 6.013
## 4    89.161 5.009
## 1862 89.167 5.890
## 2380 89.177 5.039
## 2369 89.182 6.522
## 2474 89.209 4.768
## 292  89.218 3.675
## 2397 89.219 5.328
## 1865 89.251 5.049
## 1466 89.257 5.475
## 1995 89.265 6.288
## 2403 89.317 5.578
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## 1308 89.463 4.102
## 1087 89.510 4.835
## 2447 89.546 5.410
## 159  89.573 4.134
## 2398 89.619 5.866
## 1879 89.624 6.323
## 1930 89.631 4.222
## 1664 89.716 5.759
## 1352 89.719 6.118
## 1408 89.719 4.188
## 1640 89.728 7.005
## 116  89.746 6.504
## 1700 89.748 6.497
## 248  89.749 4.880
## 2054 89.767 4.911
## 873  89.769 5.260
## 458  89.949 3.481
## 1606 89.983 4.613
## 2324 89.997 4.003
## 362  90.022 5.002
## 1184 90.110 4.153
## 1949 90.129 4.290
## 1832 90.157 5.602
## 842  90.171 5.147
## 1516 90.259 3.977
## 1695 90.282 6.622
## 1028 90.303 4.013
## 1045 90.352 5.796
## 128  90.384 5.803
## 1713 90.415 6.021
## 5    90.422 6.962
## 1760 90.470 6.192
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## 1426 90.698 4.993
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## 2218 90.780 5.264
## 2122 90.808 6.324
## 749  90.818 5.151
## 1149 90.818 6.737
## 517  90.888 5.896
## 1614 90.927 5.105
## 2008 90.933 4.140
## 1702 91.073 6.039
## 2111 91.114 4.372
## 1220 91.206 4.837
## 1738 91.367 5.870
## 1967 91.384 5.052
## 909  91.392 4.874
## 1418 91.427 5.193
## 1887 91.463 5.031
## 1696 91.466 4.509
## 2485 91.484 4.071
## 230  91.485 6.343
## 2272 91.564 5.651
## 1295 91.596 4.877
## 1941 91.619 5.422
## 1647 91.661 4.962
## 743  91.691 4.194
## 1884 91.703 5.285
## 1742 91.749 4.455
## 1722 91.756 6.186
## 462  91.773 4.834
## 2201 91.807 6.035
## 2132 91.838 4.534
## 59   91.898 4.437
## 2065 91.941 3.550
## 226  91.945 3.342
## 617  91.955 5.381
## 785  91.980 5.515
## 1388 92.033 6.188
## 2214 92.111 4.134
## 2203 92.175 6.929
## 235  92.187 5.790
## 1822 92.218 5.424
## 1921 92.232 5.706
## 1877 92.262 4.759
## 1660 92.304 3.639
## 503  92.383 7.169
## 1148 92.398 3.545
## 2159 92.433 5.127
## 1060 92.444 5.147
## 982  92.509 4.737
## 1933 92.546 4.786
## 1972 92.566 5.187
## 2255 92.657 6.118
## 1561 92.765 7.740
## 1776 92.787 3.024
## 1636 92.788 5.216
## 2040 92.848 5.763
## 2056 93.061 3.975
## 378  93.070 5.031
## 1425 93.084 6.629
## 1648 93.101 6.602
## 1415 93.301 5.309
## 561  93.312 4.042
## 166  93.340 5.457
## 2335 93.389 5.573
## 408  93.405 5.265
## 201  93.462 5.375
## 1749 93.532 6.681
## 130  93.624 5.265
## 2084 93.679 5.334
## 1310 93.688 5.375
## 2339 93.697 4.569
## 666  93.718 5.551
## 1256 93.729 5.080
## 47   93.730 5.970
## 1737 93.750 4.038
## 2233 93.750 4.832
## 1529 93.756 5.822
## 2356 93.808 4.406
## 139  93.857 4.315
## 1070 93.863 5.459
## 1895 93.869 5.205
## 2013 93.982 4.393
## 345  94.120 3.752
## 835  94.121 5.295
## 1945 94.175 4.388
## 681  94.181 4.968
## 2200 94.181 7.265
## 2108 94.196 5.339
## 912  94.200 4.902
## 511  94.252 5.214
## 2146 94.298 5.012
## 1448 94.313 4.870
## 2169 94.344 4.023
## 1810 94.353 6.845
## 1277 94.390 6.247
## 2173 94.393 6.156
## 1934 94.413 2.860
## 1580 94.441 4.470
## 836  94.455 4.322
## 1498 94.466 6.531
## 1683 94.626 4.395
## 261  94.630 4.233
## 2244 94.661 7.688
## 2396 94.668 4.767
## 257  94.682 4.257
## 1758 94.733 5.732
## 892  94.761 2.041
## 2033 94.833 5.462
## 108  94.933 7.094
## 2312 94.955 4.846
## 2408 94.984 4.676
## 2430 94.986 5.322
## 1373 95.031 6.449
## 829  95.040 4.055
## 6    95.057 5.039
## 550  95.136 4.953
## 2229 95.136 5.393
## 1349 95.208 5.585
## 1819 95.208 4.687
## 781  95.257 4.527
## 133  95.353 4.478
## 700  95.390 5.841
## 2063 95.433 5.205
## 1750 95.541 6.001
## 2303 95.556 5.803
## 215  95.590 3.519
## 2383 95.707 4.141
## 1989 95.784 4.008
## 1298 95.832 4.294
## 1015 95.901 4.462
## 61   95.948 4.596
## 1808 95.974 4.725
## 964  96.014 5.784
## 1281 96.021 5.683
## 1227 96.038 6.691
## 2034 96.091 5.156
## 2    96.134 6.449
## 745  96.161 4.881
## 1318 96.197 4.331
## 1970 96.260 4.341
## 935  96.350 3.322
## 1290 96.391 3.440
## 1210 96.471 6.053
## 1906 96.482 6.150
## 1843 96.483 4.892
## 1857 96.514 6.226
## 370  96.517 4.174
## 2384 96.597 4.261
## 986  96.615 5.553
## 1217 96.677 4.945
## 2204 96.682 4.921
## 335  96.742 5.327
## 396  96.746 5.579
## 2041 96.765 4.386
## 1183 96.852 4.329
## 724  96.875 5.712
## 16   96.901 4.579
## 863  96.932 5.445
## 391  96.943 6.125
## 1144 96.998 5.925
## 1393 97.016 6.810
## 1431 97.111 5.625
## 2294 97.121 4.911
## 2220 97.129 5.219
## 1965 97.141 4.517
## 2166 97.218 5.817
## 392  97.228 4.959
## 646  97.275 5.544
## 1927 97.308 3.966
## 1961 97.321 4.947
## 1440 97.421 6.038
## 314  97.428 5.087
## 810  97.437 4.920
## 1201 97.473 5.849
## 1356 97.498 4.574
## 1622 97.501 3.264
## 1283 97.511 4.275
## 934  97.523 4.847
## 2399 97.538 4.192
## 1223 97.561 6.980
## 75   97.576 5.860
## 1508 97.577 5.977
## 1439 97.589 5.473
## 1547 97.592 4.911
## 1926 97.652 5.346
## 1757 97.691 7.444
## 2440 97.720 4.854
## 2465 97.722 5.198
## 1610 97.732 4.306
## 1192 97.750 3.662
## 2441 97.768 5.673
## 1728 97.790 6.532
## 233  97.850 4.154
## 227  97.853 7.542
## 1199 97.872 4.459
## 1080 97.900 5.244
## 659  97.924 4.907
## 178  97.930 4.671
## 2495 97.969 6.836
## 1272 97.986 4.726

DIAGRAMA DE DISPERSIÓN

#Extraer Variables de la tabla

x<-TPV$sio2 #Variable independiente

y<-TPV$al2o3 #Variable dependiente

#Diagrama de dispersión para el modelo

plot(x,y,
     pch = 16,
     col = "blue",
     xlim = c(0, max(x)),
     ylim = c(0, max(y)),
     main = "Grafica N°1 : Comparación de la realidad con el modelo polinómico
     entre el contenido de SiO2 y el porcentaje de Al2O3
     en muestras geoquímicas",
     xlab = "SiO2 (%)",
     ylab = "Al2O3 (%)")

# Parámetros polinómicos

regresion_polinomica <- lm(y ~ x + I(x^2))

regresion_polinomica

## 
## Call:
## lm(formula = y ~ x + I(x^2))
## 
## Coefficients:
## (Intercept)            x       I(x^2)  
##   2.4278460    0.0828962   -0.0005763

CONJETURA DEL MODELO

# Crear curva polinómica

curva <- predict(regresion_polinomica)

# Gráfico base

plot(x,y,
     pch = 16,
     col = "blue",
     xlim = c(0,max(x)),
     ylim = c(0,max(y)),
     main = "Grafica N°2 : Comparación de la realidad con el modelo polinómico",
     xlab = "SiO2 (%)",
     ylab = "Al2O3 (%)")

# Ordenar para dibujar la curva correctamente

orden <- order(x)

lines(x[orden],
      curva[orden],
      col = "red",
      lwd = 3)

legend("topright",
       legend = c("Datos reales","Modelo polinómico"),
       col = c("blue","red"),
       pch = c(16,NA),
       lty = c(NA,1),
       lwd = c(NA,3))

# Coeficientes del modelo

coeficientes <- coef(regresion_polinomica)

coeficientes

##   (Intercept)             x        I(x^2) 
##  2.4278460068  0.0828961775 -0.0005763194

# Extraer coeficientes

c <- coeficientes[1]   # intercepto
b <- coeficientes[2]   # coeficiente lineal
a <- coeficientes[3]   # coeficiente cuadrático

# Formamos la ecuación

plot(1,
     type = "n",
     axes = FALSE,
     xlab = "",
     ylab = "")

text(x = 1,
     y = 1,
     labels = paste(
       "Ecuación polinómica general\n",
       "Y = ax² + bx + c\n\n",
       "Modelo ajustado:\n",
       "Y =",
       round(a,5),"x² +",
       round(b,5),"x +",
       round(c,5)
     ),
     cex = 1.4,
     col = "blue",
     font = 2)

TEST DE APROBACION Y RESTRICCIONES

#TEST DE PEARSON

r<-cor(x,y)

r*100

## [1] 50.47436

#Coeficiente de determinación

modelo_resumen <- summary(regresion_polinomica)

r2<-modelo_resumen$r.squared

r2*100

## [1] 34.62916

#RESTRICCIONES DEL MODELO

plot(1,
     type = "n",
     axes = FALSE,
     xlab = "",
     ylab = "")

text(x = 1,
     y = 1,
     labels = "Consideraciones del modelo:
     
     - El modelo presenta un ajuste lineal adecuado
       para los datos analizados.
     
     - No se identifican observaciones que contradigan
       el comportamiento general de la tendencia.
     
     - Las predicciones deben interpretarse dentro del
       rango de concentraciones utilizado para construir
       el modelo.
     
     - La relación estadística observada describe la
       asociación entre las variables estudiadas y
       puede emplearse para realizar estimaciones
       dentro del dominio analizado.
     ",
     
     
     cex = 1.2,
     col = 'darkred',
     font = 2)

CÁLCULO DE PRONOSTICOS

# Cálculo de pronósticos

coeficientes <- coef(regresion_polinomica)

c <- coeficientes[1]
b <- coeficientes[2]
a <- coeficientes[3]

Al_Esp <- c +
          b*(50) +
          a*(50^2)

Al_Esp

## (Intercept) 
##    5.131856

plot(1, type = "n", axes = FALSE, xlab = "", ylab = "")

text(x = 1, y = 1,
     labels = paste(
     "¿Que porcentaje de Al2O3 se espera
     cuando el contenido de SiO2 es de 50 % ?
     
     R = ", round(Al_Esp,2)," % "),
     
     cex = 1.6,
     col = "blue",
     font = 6)

CONCLUSIÓN

"Entre el contenido de SiO2 y el porcentaje de Al2O3 existe una relación
de tipo polinómica donde el modelo ajustado sigue la forma
f(x)=ax²+bx+c siendo “x” el contenido de SiO2 y “y” el porcentaje
de Al2O3. Esto indica que el comportamiento geoquímico entre ambas
variables no es estrictamente lineal y presenta variaciones de curvatura
a medida que aumenta el contenido de sílice.

Ejemplo: Cuando el contenido de SiO2 es de 50 % se espera un porcentaje
aproximado de Al2O3 calculado mediante el modelo polinómico ajusta."

## [1] "Entre el contenido de SiO2 y el porcentaje de Al2O3 existe una relación\nde tipo polinómica donde el modelo ajustado sigue la forma\nf(x)=ax²+bx+c siendo “x” el contenido de SiO2 y “y” el porcentaje\nde Al2O3. Esto indica que el comportamiento geoquímico entre ambas\nvariables no es estrictamente lineal y presenta variaciones de curvatura\na medida que aumenta el contenido de sílice.\n\nEjemplo: Cuando el contenido de SiO2 es de 50 % se espera un porcentaje\naproximado de Al2O3 calculado mediante el modelo polinómico ajusta."