REGRESIÓN POLINÓMICA ENTRE EL SiO2 Y EL Al2O3
# CARGA DE DATOS
library(readr)
library(knitr)
datos <- read_csv("D:/modelo_regresion_polinomica_2500.csv")## Rows: 2500 Columns: 3
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (3): SIO2_WT_PERCENT_X, SIO2_WT_PERCENT_X2, AL2O3_WT_PERCENT_Y
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.# 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
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## 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
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## 538 13.624 2.825
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## 540 6.754 5.651
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## 544 28.430 4.421
## 545 6.169 3.903
## 546 10.749 3.365
## 547 59.522 4.663
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## 549 27.495 3.952
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## 552 56.133 6.713
## 553 81.710 4.582
## 554 15.011 4.109
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## 556 18.944 2.646
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## 563 23.422 3.717
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## 569 75.429 6.542
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## 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
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## 584 66.725 4.561
## 585 66.876 4.340
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## 587 47.056 4.351
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## 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
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## 605 58.576 4.434
## 606 27.214 4.617
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## 608 90.600 4.150
## 609 12.827 4.081
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## 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
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## 627 61.749 7.757
## 628 57.263 5.007
## 629 85.798 4.089
## 630 46.956 4.745
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## 635 9.027 2.610
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## 645 10.261 2.536
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## 652 50.097 5.062
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## 655 41.726 4.355
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## 668 35.137 3.359
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## 670 15.502 3.203
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## 673 64.903 8.184
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## 678 87.197 5.332
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## 680 41.250 4.155
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## 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
## 695 37.657 5.272
## 696 23.595 4.646
## 697 28.090 3.080
## 698 54.703 5.891
## 699 65.625 5.477
## 700 95.390 5.841
## 701 47.254 2.319
## 702 28.205 2.704
## 703 13.054 3.557
## 704 40.639 4.622
## 705 22.341 3.743
## 706 38.135 6.150
## 707 58.907 5.549
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## 710 72.813 5.590
## 711 84.062 5.018
## 712 34.197 4.599
## 713 64.240 5.891
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## 715 75.099 4.258
## 716 15.592 3.402
## 717 8.388 2.761
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## 719 57.080 4.484
## 720 37.294 5.331
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## 722 61.806 7.076
## 723 29.184 4.349
## 724 96.875 5.712
## 725 54.895 4.650
## 726 43.128 4.671
## 727 42.156 5.646
## 728 55.640 4.402
## 729 61.172 5.910
## 730 72.664 5.688
## 731 53.929 3.687
## 732 62.167 6.090
## 733 73.657 3.627
## 734 72.036 6.626
## 735 27.558 3.513
## 736 67.512 5.507
## 737 82.327 4.763
## 738 44.366 4.845
## 739 57.691 5.061
## 740 46.932 5.056
## 741 8.729 4.503
## 742 81.804 5.611
## 743 91.691 4.194
## 744 88.328 3.219
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## 746 71.602 5.895
## 747 51.395 5.390
## 748 50.762 5.393
## 749 90.818 5.151
## 750 40.129 5.997
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## 1637 12.856 5.220
## 1638 67.994 4.984
## 1639 55.340 4.374
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## 1641 20.510 3.619
## 1642 18.563 3.778
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## 1646 73.756 4.702
## 1647 91.661 4.962
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## 1651 36.674 5.059
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## 1656 20.928 5.543
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## 1671 65.013 4.995
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## 1673 82.787 5.843
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## 1702 91.073 6.039
## 1703 55.548 3.917
## 1704 15.099 3.494
## 1705 46.387 6.551
## 1706 38.737 3.855
## 1707 62.623 4.528
## 1708 73.273 5.465
## 1709 26.450 4.600
## 1710 46.061 5.413
## 1711 24.856 6.477
## 1712 46.246 4.577
## 1713 90.415 6.021
## 1714 68.698 5.214
## 1715 10.050 3.868
## 1716 11.304 3.983
## 1717 64.932 6.838
## 1718 9.973 2.928
## 1719 7.995 3.615
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## 1721 36.149 3.577
## 1722 91.756 6.186
## 1723 38.544 3.904
## 1724 49.569 5.078
## 1725 34.431 3.854
## 1726 78.612 6.540
## 1727 88.438 3.992
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## 1730 74.670 4.727
## 1731 78.393 5.123
## 1732 35.045 2.087
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## 1734 38.706 4.306
## 1735 88.456 7.139
## 1736 8.286 1.384
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## 1739 68.642 6.265
## 1740 50.394 5.823
## 1741 41.969 2.198
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## 1744 31.924 5.921
## 1745 40.607 3.594
## 1746 26.112 3.388
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## 1748 21.692 4.257
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## 1750 95.541 6.001
## 1751 12.630 4.525
## 1752 68.558 3.940
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## 1755 88.348 5.461
## 1756 66.069 6.467
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## 1778 65.780 4.088
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## 1780 38.453 3.233
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## 1782 64.320 6.050
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## 1786 42.395 4.450
## 1787 19.997 4.027
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## 1794 25.278 4.133
## 1795 75.348 4.337
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## 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
## 1806 37.507 4.291
## 1807 21.333 5.268
## 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
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## 2013 93.982 4.393
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## 1934 94.413 2.860
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## 261 94.630 4.233
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## 2396 94.668 4.767
## 257 94.682 4.257
## 1758 94.733 5.732
## 892 94.761 2.041
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## 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
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## 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#Extraer Variables de la tabla
x<-TPV$sio2 #Variable independiente
y<-TPV$al2o3 #Variable dependiente
#Diagrama de dispersión
plot(x,y,
pch = 16,
col = "blue",
xlim = c(0, max(x)),
ylim = c(0, max(y)),
main = "Grafica N°1 : Diagrama de dispersión entre el contenido de SiO2
y el porcentaje de Al2O3 en muestras geoquímicas",
xlab = "SiO2 (%)",
ylab = "Al2O3 (%)")
#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°2 : 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)-1)
regresion_polinomica##
## Call:
## lm(formula = y ~ x + I(x^2) - 1)
##
## Coefficients:
## x I(x^2)
## 0.17991 -0.00139#Crear la curva polinómica
curva <- predict(regresion_polinomica)
lines(x,curva,
col = "red",
lwd = 3)
## x I(x^2)
## 0.17990642 -0.00139033#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 \n Modelo ajustado: Y = ",
round(coeficientes[2],5),"x² + ",
round(coeficientes[1],5),"x"),
cex = 1.4,
col = "blue",
font = 6)
## [1] 50.47436#Coeficiente de determinación
modelo_resumen <- summary(regresion_polinomica)
r2<-modelo_resumen$r.squared
r2*100## [1] 94.01378#RESTRICCIONES DEL MODELO
plot(1, type = "n", axes = FALSE, xlab = "", ylab = "")
text(x = 1, y = 1,
labels = "Restricciones del modelo:
- El contenido de SiO2 debe ser mayor o igual a 0 %
- El porcentaje de Al2O3 debe ser mayor o igual a 0 %
- El modelo es válido únicamente dentro del rango
de datos analizados
- La relación entre las variables debe mantener
comportamiento polinómico
- El modelo no debe extrapolarse fuera del rango
geoquímico estudiado",
cex = 1.2,
col = "darkred",
font = 2)
## x
## 5.519497plot(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)
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.
El coeficiente de determinación obtenido demuestra que parte de la variabilidad del porcentaje de Al2O3 puede ser explicada por el contenido de SiO2, mientras que el resto puede estar asociado a otros factores geoquímicos, mineralógicos y procesos de alteración presentes en las muestras analizadas.
Ejemplo: Cuando el contenido de SiO2 es de 50 % se espera un porcentaje aproximado de Al2O3 calculado mediante el modelo polinómico ajustado.