Análisis Multivariable de Sedimentos Marinos
Grupo 3
CARGA DE DATOS Y LIBRERÍAS
# CARGA DE DATOS
datos <- read.csv("C:\\Users\\Grace\\OneDrive - Universidad Central del Ecuador\\Proyecto Estadistica\\Original\\texture.csv",
header = TRUE,
sep = ",",
dec = ".")
# CARGA DE LIBRERÍAS
library(dplyr)##
## Adjuntando el paquete: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(knitr)
library(gt)TABLA DE PARES DE VALORES
MEAN <- as.numeric(datos$MEAN)
MEDIAN <- as.numeric(datos$MEDIAN)
TPV <- data.frame(MEAN, MEDIAN)
TPV <- na.omit(TPV)
TPV <- TPV[TPV$MEAN > 0 & TPV$MEDIAN > 0, ]
Q1_MEAN <- quantile(TPV$MEAN, 0.25)
Q3_MEAN <- quantile(TPV$MEAN, 0.75)
IQR_MEAN <- Q3_MEAN - Q1_MEAN
lim_inf_MEAN <- Q1_MEAN - 1.5 * IQR_MEAN
lim_sup_MEAN <- Q3_MEAN + 1.5 * IQR_MEAN
Q1_MEDIAN <- quantile(TPV$MEDIAN, 0.25)
Q3_MEDIAN <- quantile(TPV$MEDIAN, 0.75)
IQR_MEDIAN <- Q3_MEDIAN - Q1_MEDIAN
lim_inf_MEDIAN <- Q1_MEDIAN - 1.5 * IQR_MEDIAN
lim_sup_MEDIAN <- Q3_MEDIAN + 1.5 * IQR_MEDIAN
TPV_limpio <- TPV[
TPV$MEAN >= lim_inf_MEAN & TPV$MEAN <= lim_sup_MEAN &
TPV$MEDIAN >= lim_inf_MEDIAN & TPV$MEDIAN <= lim_sup_MEDIAN,
]
TPV_FILTRADO <- TPV_limpio[TPV_limpio$MEAN < 20 & TPV_limpio$MEDIAN < 80, ]
tabla_media <- aggregate(MEDIAN ~ MEAN,
data = TPV_FILTRADO,
FUN = mean)
tabla_media## MEAN MEDIAN
## 1 0.01 0.2683333
## 2 0.02 0.1220000
## 3 0.03 0.3400000
## 4 0.04 0.4900000
## 5 0.05 0.4409091
## 6 0.06 0.4087500
## 7 0.07 0.2171429
## 8 0.08 0.2600000
## 9 0.09 0.3421429
## 10 0.10 0.2173333
## 11 0.11 0.2400000
## 12 0.12 0.4381818
## 13 0.13 0.3269231
## 14 0.14 0.3892308
## 15 0.15 0.3210000
## 16 0.16 0.3518182
## 17 0.17 0.3012500
## 18 0.18 0.2372727
## 19 0.19 0.4400000
## 20 0.20 0.4211111
## 21 0.21 0.3161538
## 22 0.22 0.3484615
## 23 0.23 0.4325000
## 24 0.24 0.4017391
## 25 0.25 0.3433333
## 26 0.26 0.4644444
## 27 0.27 0.6024138
## 28 0.28 0.4369565
## 29 0.29 0.4265517
## 30 0.30 0.2800000
## 31 0.31 0.5181818
## 32 0.32 0.4647368
## 33 0.33 0.4570588
## 34 0.34 0.4100000
## 35 0.35 0.3877273
## 36 0.36 0.5481818
## 37 0.37 0.4781818
## 38 0.38 0.5059091
## 39 0.39 0.6045455
## 40 0.40 0.4607692
## 41 0.41 0.4505882
## 42 0.42 0.5442857
## 43 0.43 0.5531579
## 44 0.44 0.5223529
## 45 0.45 0.5855556
## 46 0.46 0.5352000
## 47 0.47 0.4547619
## 48 0.48 0.4345455
## 49 0.49 0.5640909
## 50 0.50 0.5970370
## 51 0.51 0.5207143
## 52 0.52 0.5667742
## 53 0.53 0.5274074
## 54 0.54 0.5908000
## 55 0.55 0.6682143
## 56 0.56 0.6700000
## 57 0.57 0.6181250
## 58 0.58 0.5950000
## 59 0.59 0.6426087
## 60 0.60 0.5813043
## 61 0.61 0.6200000
## 62 0.62 0.6550000
## 63 0.63 0.7511765
## 64 0.64 0.6796429
## 65 0.65 0.6792857
## 66 0.66 0.6540000
## 67 0.67 0.6720690
## 68 0.68 0.7558824
## 69 0.69 0.7742857
## 70 0.70 0.7456522
## 71 0.71 0.7659259
## 72 0.72 0.7602857
## 73 0.73 0.7391429
## 74 0.74 0.7841176
## 75 0.75 0.7487879
## 76 0.76 0.7263333
## 77 0.77 0.8622222
## 78 0.78 0.7708333
## 79 0.79 0.8356667
## 80 0.80 0.8043243
## 81 0.81 0.7667742
## 82 0.82 0.8284615
## 83 0.83 0.7800000
## 84 0.84 0.8416129
## 85 0.85 0.7985714
## 86 0.86 0.8627273
## 87 0.87 0.8418182
## 88 0.88 0.8703125
## 89 0.89 0.8695000
## 90 0.90 0.8928571
## 91 0.91 0.8507500
## 92 0.92 0.9145946
## 93 0.93 0.8217500
## 94 0.94 0.9277778
## 95 0.95 0.9327027
## 96 0.96 1.0058333
## 97 0.97 0.9469767
## 98 0.98 0.9662500
## 99 0.99 0.9387500
## 100 1.00 0.9550000
## 101 1.01 0.9709302
## 102 1.02 1.0100000
## 103 1.03 1.0278261
## 104 1.04 1.0590000
## 105 1.05 0.9960870
## 106 1.06 1.0181633
## 107 1.07 0.9792857
## 108 1.08 1.0785294
## 109 1.09 1.0278947
## 110 1.10 1.1318919
## 111 1.11 1.1910000
## 112 1.12 1.0935556
## 113 1.13 1.1248148
## 114 1.14 1.1380645
## 115 1.15 1.1612500
## 116 1.16 1.1562500
## 117 1.17 1.1736364
## 118 1.18 1.1251111
## 119 1.19 1.2038095
## 120 1.20 1.2195918
## 121 1.21 1.2002857
## 122 1.22 1.2532075
## 123 1.23 1.1797059
## 124 1.24 1.1873684
## 125 1.25 1.2782353
## 126 1.26 1.2857143
## 127 1.27 1.2109756
## 128 1.28 1.2961702
## 129 1.29 1.3247368
## 130 1.30 1.3082609
## 131 1.31 1.3137778
## 132 1.32 1.2800000
## 133 1.33 1.3260465
## 134 1.34 1.3341176
## 135 1.35 1.3553488
## 136 1.36 1.3546939
## 137 1.37 1.4446875
## 138 1.38 1.3724390
## 139 1.39 1.3728571
## 140 1.40 1.3692453
## 141 1.41 1.3334211
## 142 1.42 1.4448718
## 143 1.43 1.3968293
## 144 1.44 1.3551852
## 145 1.45 1.4091429
## 146 1.46 1.4533333
## 147 1.47 1.4750000
## 148 1.48 1.4351429
## 149 1.49 1.5285294
## 150 1.50 1.4871429
## 151 1.51 1.4661111
## 152 1.52 1.5056410
## 153 1.53 1.5258333
## 154 1.54 1.5466667
## 155 1.55 1.5680000
## 156 1.56 1.5897143
## 157 1.57 1.4960714
## 158 1.58 1.5850000
## 159 1.59 1.5648649
## 160 1.60 1.5669565
## 161 1.61 1.5015385
## 162 1.62 1.6139474
## 163 1.63 1.6270000
## 164 1.64 1.6196970
## 165 1.65 1.5487500
## 166 1.66 1.6278571
## 167 1.67 1.6552500
## 168 1.68 1.5732258
## 169 1.69 1.6344898
## 170 1.70 1.6797297
## 171 1.71 1.6344828
## 172 1.72 1.6086047
## 173 1.73 1.6946875
## 174 1.74 1.6556757
## 175 1.75 1.6743243
## 176 1.76 1.6940625
## 177 1.77 1.7230952
## 178 1.78 1.7390000
## 179 1.79 1.7492105
## 180 1.80 1.7745946
## 181 1.81 1.7803448
## 182 1.82 1.7417073
## 183 1.83 1.7368750
## 184 1.84 1.7910870
## 185 1.85 1.7352632
## 186 1.86 1.7744737
## 187 1.87 1.8179545
## 188 1.88 1.8317073
## 189 1.89 1.8160526
## 190 1.90 1.8679412
## 191 1.91 1.7441935
## 192 1.92 1.9006977
## 193 1.93 1.7850000
## 194 1.94 1.8524138
## 195 1.95 1.9100000
## 196 1.96 1.8007500
## 197 1.97 1.8965000
## 198 1.98 1.9128205
## 199 1.99 1.8502857
## 200 2.00 1.8629032
## 201 2.01 1.9153191
## 202 2.02 1.9095556
## 203 2.03 1.8814894
## 204 2.04 2.0293478
## 205 2.05 2.0193023
## 206 2.06 2.0147368
## 207 2.07 1.9474359
## 208 2.08 2.0193878
## 209 2.09 2.0381818
## 210 2.10 2.0143478
## 211 2.11 2.0532727
## 212 2.12 2.0384444
## 213 2.13 2.0905263
## 214 2.14 2.0793023
## 215 2.15 2.1190909
## 216 2.16 2.0984000
## 217 2.17 2.0593182
## 218 2.18 2.1076471
## 219 2.19 2.1718605
## 220 2.20 2.1044186
## 221 2.21 2.1570588
## 222 2.22 2.0762162
## 223 2.23 2.1527273
## 224 2.24 2.2069048
## 225 2.25 2.2089744
## 226 2.26 2.2109302
## 227 2.27 2.2678947
## 228 2.28 2.2715556
## 229 2.29 2.2514894
## 230 2.30 2.1988571
## 231 2.31 2.2700000
## 232 2.32 2.2542424
## 233 2.33 2.2289286
## 234 2.34 2.2051163
## 235 2.35 2.2997727
## 236 2.36 2.2919565
## 237 2.37 2.3029412
## 238 2.38 2.2819231
## 239 2.39 2.3465217
## 240 2.40 2.3515000
## 241 2.41 2.3262500
## 242 2.42 2.3268750
## 243 2.43 2.3730435
## 244 2.44 2.3880488
## 245 2.45 2.3993750
## 246 2.46 2.4270732
## 247 2.47 2.3619512
## 248 2.48 2.4251282
## 249 2.49 2.3823636
## 250 2.50 2.4101724
## 251 2.51 2.4183784
## 252 2.52 2.4240385
## 253 2.53 2.4419048
## 254 2.54 2.4178049
## 255 2.55 2.5002128
## 256 2.56 2.4620000
## 257 2.57 2.4500000
## 258 2.58 2.4819048
## 259 2.59 2.4835417
## 260 2.60 2.4530508
## 261 2.61 2.5015556
## 262 2.62 2.5102041
## 263 2.63 2.4680488
## 264 2.64 2.4883721
## 265 2.65 2.5653704
## 266 2.66 2.4550000
## 267 2.67 2.5188095
## 268 2.68 2.4952941
## 269 2.69 2.5337778
## 270 2.70 2.4637778
## 271 2.71 2.6228205
## 272 2.72 2.5307500
## 273 2.73 2.5880952
## 274 2.74 2.5281395
## 275 2.75 2.5315385
## 276 2.76 2.5719565
## 277 2.77 2.6341176
## 278 2.78 2.5725000
## 279 2.79 2.6439474
## 280 2.80 2.6110714
## 281 2.81 2.5865625
## 282 2.82 2.6000000
## 283 2.83 2.7107500
## 284 2.84 2.5933333
## 285 2.85 2.7055263
## 286 2.86 2.6938095
## 287 2.87 2.6863636
## 288 2.88 2.7777500
## 289 2.89 2.7334783
## 290 2.90 2.7520000
## 291 2.91 2.6956000
## 292 2.92 2.7206818
## 293 2.93 2.7447619
## 294 2.94 2.7737500
## 295 2.95 2.6809375
## 296 2.96 2.7596552
## 297 2.97 2.7967742
## 298 2.98 2.8428947
## 299 2.99 2.7921212
## 300 3.00 2.7815152
## 301 3.01 2.7692500
## 302 3.02 2.7672000
## 303 3.03 2.8579310
## 304 3.04 2.8323529
## 305 3.05 2.8534375
## 306 3.06 2.8940000
## 307 3.07 2.7978378
## 308 3.08 2.9017021
## 309 3.09 2.9336364
## 310 3.10 2.9750000
## 311 3.11 2.8940000
## 312 3.12 2.7968182
## 313 3.13 2.9746667
## 314 3.14 3.0347619
## 315 3.15 2.9161765
## 316 3.16 2.9430556
## 317 3.17 2.9650000
## 318 3.18 3.0307895
## 319 3.19 2.9896154
## 320 3.20 3.0075000
## 321 3.21 2.9755556
## 322 3.22 2.9754167
## 323 3.23 3.0827027
## 324 3.24 2.9972727
## 325 3.25 2.9725641
## 326 3.26 3.0770732
## 327 3.27 3.0665854
## 328 3.28 2.9628205
## 329 3.29 3.0447500
## 330 3.30 3.1450000
## 331 3.31 3.1905714
## 332 3.32 3.1877778
## 333 3.33 3.0816667
## 334 3.34 3.0576667
## 335 3.35 3.1800000
## 336 3.36 3.2096429
## 337 3.37 3.2617143
## 338 3.38 3.1344828
## 339 3.39 3.1769444
## 340 3.40 3.2762791
## 341 3.41 3.1534694
## 342 3.42 3.1468750
## 343 3.43 3.1771875
## 344 3.44 3.1552000
## 345 3.45 3.1768571
## 346 3.46 3.0939394
## 347 3.47 3.1155172
## 348 3.48 3.1866667
## 349 3.49 3.0195238
## 350 3.50 3.2600000
## 351 3.51 3.1761538
## 352 3.52 3.1875758
## 353 3.53 3.1806250
## 354 3.54 3.2453125
## 355 3.55 3.2600000
## 356 3.56 3.1336000
## 357 3.57 3.1945833
## 358 3.58 3.1945946
## 359 3.59 3.2006250
## 360 3.60 3.2815385
## 361 3.61 3.2853125
## 362 3.62 3.1664865
## 363 3.63 3.2844000
## 364 3.64 3.2442857
## 365 3.65 3.3066667
## 366 3.66 3.2235294
## 367 3.67 3.3078571
## 368 3.68 3.1440000
## 369 3.69 3.2790476
## 370 3.70 3.2513043
## 371 3.71 3.3005882
## 372 3.72 3.3262500
## 373 3.73 3.3605882
## 374 3.74 3.1904348
## 375 3.75 3.3876000
## 376 3.76 3.3012500
## 377 3.77 3.2990000
## 378 3.78 3.3295455
## 379 3.79 3.3441667
## 380 3.80 3.3123077
## 381 3.81 3.2815000
## 382 3.82 3.2706250
## 383 3.83 3.4540000
## 384 3.84 3.3430435
## 385 3.85 3.4869231
## 386 3.86 3.4506667
## 387 3.87 3.2792000
## 388 3.88 3.3277778
## 389 3.89 3.4363636
## 390 3.90 3.3786364
## 391 3.91 3.4671429
## 392 3.92 3.4127273
## 393 3.93 3.6900000
## 394 3.94 3.6016667
## 395 3.95 3.5742105
## 396 3.96 3.5007143
## 397 3.97 3.3825000
## 398 3.98 3.4378947
## 399 3.99 3.4652381
## 400 4.00 3.6955556
## 401 4.01 3.4869565
## 402 4.02 3.6369565
## 403 4.03 3.4733333
## 404 4.04 3.7100000
## 405 4.05 3.5821739
## 406 4.06 3.5100000
## 407 4.07 3.5191667
## 408 4.08 3.5483333
## 409 4.09 3.5690909
## 410 4.10 3.5990909
## 411 4.11 3.7341667
## 412 4.12 3.5150000
## 413 4.13 3.4364286
## 414 4.14 3.5150000
## 415 4.15 3.5007692
## 416 4.16 3.5753571
## 417 4.17 3.6353846
## 418 4.18 3.6331034
## 419 4.19 3.5806061
## 420 4.20 3.6995238
## 421 4.21 3.6229412
## 422 4.22 3.6252941
## 423 4.23 3.5770588
## 424 4.24 3.6011765
## 425 4.25 3.6289474
## 426 4.26 3.5468182
## 427 4.27 3.5912000
## 428 4.28 3.6961111
## 429 4.29 3.5658824
## 430 4.30 3.8094444
## 431 4.31 3.8013333
## 432 4.32 3.7331250
## 433 4.33 3.7647619
## 434 4.34 3.6975000
## 435 4.35 3.8094737
## 436 4.36 3.7988462
## 437 4.37 3.9200000
## 438 4.38 3.6911111
## 439 4.39 3.8252000
## 440 4.40 3.8613333
## 441 4.41 3.8550000
## 442 4.42 3.8394444
## 443 4.43 3.7355000
## 444 4.44 3.9271429
## 445 4.45 3.8616667
## 446 4.46 3.8638095
## 447 4.47 3.9440000
## 448 4.48 3.8700000
## 449 4.49 3.8590000
## 450 4.50 3.8037500
## 451 4.51 3.7570588
## 452 4.52 3.8152941
## 453 4.53 4.0990000
## 454 4.54 4.0040909
## 455 4.55 3.9445833
## 456 4.56 3.9750000
## 457 4.57 3.9617647
## 458 4.58 4.0214286
## 459 4.59 4.1175000
## 460 4.60 3.8911111
## 461 4.61 3.9400000
## 462 4.62 4.2135000
## 463 4.63 4.2928571
## 464 4.64 3.9931250
## 465 4.65 4.0255000
## 466 4.66 4.2170588
## 467 4.67 4.0134615
## 468 4.68 3.9357895
## 469 4.69 4.0265000
## 470 4.70 4.2892857
## 471 4.71 4.0478947
## 472 4.72 4.0815000
## 473 4.73 4.2483333
## 474 4.74 4.2294444
## 475 4.75 4.0526667
## 476 4.76 4.2652000
## 477 4.77 4.2642105
## 478 4.78 4.1164706
## 479 4.79 4.4000000
## 480 4.80 4.2866667
## 481 4.81 4.2178947
## 482 4.82 4.2300000
## 483 4.83 4.2982609
## 484 4.84 4.3950000
## 485 4.85 4.0823810
## 486 4.86 4.4670588
## 487 4.87 4.5189474
## 488 4.88 4.1353333
## 489 4.89 4.2395238
## 490 4.90 4.4269565
## 491 4.91 4.1850000
## 492 4.92 4.3338462
## 493 4.93 4.4288000
## 494 4.94 4.4342105
## 495 4.95 4.6086957
## 496 4.96 4.4874074
## 497 4.97 4.2712500
## 498 4.98 4.5216667
## 499 4.99 4.3621053
## 500 5.00 4.4056522
## 501 5.01 4.6878947
## 502 5.02 4.2346667
## 503 5.03 4.4983333
## 504 5.04 4.3510000
## 505 5.05 4.3915385
## 506 5.06 4.5180000
## 507 5.07 4.4105000
## 508 5.08 4.7451724
## 509 5.09 4.4485714
## 510 5.10 4.5433333
## 511 5.11 4.3560714
## 512 5.12 4.5472222
## 513 5.13 4.6080769
## 514 5.14 4.6714286
## 515 5.15 4.6394737
## 516 5.16 4.7325000
## 517 5.17 4.4566667
## 518 5.18 4.7855556
## 519 5.19 4.7594444
## 520 5.20 4.7428000
## 521 5.21 4.8650000
## 522 5.22 4.7118182
## 523 5.23 4.7162500
## 524 5.24 4.8025000
## 525 5.25 4.9821429
## 526 5.26 5.0466667
## 527 5.27 4.6609091
## 528 5.28 4.9089474
## 529 5.29 4.8073333
## 530 5.30 4.8052000
## 531 5.31 4.7540000
## 532 5.32 5.0065000
## 533 5.33 4.9400000
## 534 5.34 4.8007692
## 535 5.35 5.0321739
## 536 5.36 4.8881818
## 537 5.37 5.0817391
## 538 5.38 5.1108333
## 539 5.39 5.2843750
## 540 5.40 4.9426923
## 541 5.41 5.0325000
## 542 5.42 5.0663158
## 543 5.43 5.3593333
## 544 5.44 5.0866667
## 545 5.45 4.9950000
## 546 5.46 5.2593750
## 547 5.47 5.0386364
## 548 5.48 5.1161111
## 549 5.49 5.0717647
## 550 5.50 5.1322222
## 551 5.51 5.1975000
## 552 5.52 5.2595000
## 553 5.53 5.2842105
## 554 5.54 5.3223810
## 555 5.55 5.1785714
## 556 5.56 5.3930000
## 557 5.57 5.4188235
## 558 5.58 5.2800000
## 559 5.59 5.3990476
## 560 5.60 5.4261905
## 561 5.61 5.4995833
## 562 5.62 5.3700000
## 563 5.63 5.3394118
## 564 5.64 5.3731579
## 565 5.65 5.4038889
## 566 5.66 5.2900000
## 567 5.67 5.4620833
## 568 5.68 5.3283333
## 569 5.69 5.5605882
## 570 5.70 5.4808000
## 571 5.71 5.5742308
## 572 5.72 5.6017647
## 573 5.73 5.5352000
## 574 5.74 5.4818182
## 575 5.75 5.5210714
## 576 5.76 5.5226316
## 577 5.77 5.5560000
## 578 5.78 5.4857143
## 579 5.79 5.7176667
## 580 5.80 5.6270588
## 581 5.81 5.7068182
## 582 5.82 5.6733333
## 583 5.83 5.8243750
## 584 5.84 5.8084000
## 585 5.85 5.7690000
## 586 5.86 5.7837500
## 587 5.87 5.8200000
## 588 5.88 5.7282609
## 589 5.89 5.7795833
## 590 5.90 5.7011111
## 591 5.91 5.6542105
## 592 5.92 6.1610526
## 593 5.93 5.8064000
## 594 5.94 5.6940909
## 595 5.95 5.8665385
## 596 5.96 5.7452632
## 597 5.97 5.9900000
## 598 5.98 5.9454167
## 599 5.99 5.8283333
## 600 6.00 5.7604167
## 601 6.01 6.1873333
## 602 6.02 6.0056250
## 603 6.03 6.0600000
## 604 6.04 5.9585714
## 605 6.05 6.0090476
## 606 6.06 6.0652941
## 607 6.07 5.9741935
## 608 6.08 5.9658621
## 609 6.09 5.9858333
## 610 6.10 5.9444000
## 611 6.11 5.9422222
## 612 6.12 6.0025000
## 613 6.13 6.0228571
## 614 6.14 6.0826923
## 615 6.15 5.9446429
## 616 6.16 6.1816667
## 617 6.17 5.9820000
## 618 6.18 6.2375000
## 619 6.19 6.0469565
## 620 6.20 6.0304000
## 621 6.21 6.1137500
## 622 6.22 6.2778947
## 623 6.23 6.2176190
## 624 6.24 6.1677273
## 625 6.25 6.1685000
## 626 6.26 6.2705263
## 627 6.27 6.1311538
## 628 6.28 6.3664706
## 629 6.29 6.2557143
## 630 6.30 6.2823333
## 631 6.31 6.4061905
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## 944 9.66 9.4500000
## 945 9.69 9.6500000
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## 947 9.72 9.7500000
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## 949 9.78 9.7400000
## 950 9.80 10.1000000
## 951 9.84 9.3400000
## 952 9.89 9.9200000
## 953 9.92 9.8800000
## 954 9.99 10.3100000
## 955 10.06 10.0300000
## 956 10.14 10.4300000
## 957 10.15 10.2000000
## 958 10.62 10.7400000DIAGRAMA DE DISPERSIÓN
x <- tabla_media$MEAN
y <- tabla_media$MEDIAN
plot(x, y,
pch = 16,
col = "lightblue",
main = "Grafica N°1: Diagrama de dispersión entre el Promedio y la Mediana
de Sedimentos Marinos",
xlab = "PROMEDIO (φ)",
ylab = "MEDIANA (φ)")
CONJETURA DEL MODELO POTENCIAL
Debido a la similitud de la nube de puntos conjeturamos a un modelo lineal
# Diagrama de dispersión
regresion_lineal <- lm(y ~ x)
regresion_lineal##
## Call:
## lm(formula = y ~ x)
##
## Coefficients:
## (Intercept) x
## -0.2099 1.0256summary(regresion_lineal)##
## Call:
## lm(formula = y ~ x)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.70408 -0.14074 0.05995 0.18003 0.65891
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.209933 0.016774 -12.52 <2e-16 ***
## x 1.025633 0.003022 339.37 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.2601 on 956 degrees of freedom
## Multiple R-squared: 0.9918, Adjusted R-squared: 0.9918
## F-statistic: 1.152e+05 on 1 and 956 DF, p-value: < 2.2e-16a <- regresion_lineal$coefficients[1]
b <- regresion_lineal$coefficients[2]
a## (Intercept)
## -0.2099327b## x
## 1.025633plot(x, y,
pch = 16,
col = "lightblue",
main = "Grafica N°2: Comparación de la realidad con el modelo lineal
entre el Promedio y la Mediana de Sedimentos Marinos",
xlab = "PROMEDIO (φ)",
ylab = "MEDIANA (φ)")
abline(a, b,
col = "red",
lwd = 2)
ECUACIÓN DEL MODELO a
plot(1, type = "n", axes = FALSE, xlab = "", ylab = "")
ecuacion <- paste("Ecuación lineal\n",
"Y = a + bX\n",
"Y =", round(a, 4), "+", round(b, 4), "X")
text(x = 1, y = 1,
labels = ecuacion,
cex = 2,
col = "black",
font = 2)
TEST DE APROBACIÓN Y RESTRICCIONES
TEST DE PEARSON
# TEST DE PEARSON
r <- cor(x, y)
r * 100## [1] 99.58754Coeficiente de determinación
r2 <- r^2
r2 * 100## [1] 99.17677RESTRICCIONES
min(x)## [1] 0.01max(x)## [1] 10.62“Sí existe restricción, ya que el modelo lineal es confiable únicamente dentro del rango de valores observados del promedio (MEAN), el cual varía entre 0.01 y 10.62. Al utilizar valores fuera de este intervalo, la predicción de la mediana (MEDIAN) puede no representar adecuadamente el comportamiento real de los sedimentos marinos.”
CALCULOS DE PRONOSTICOS
Si el tamaño promedio del sedimento es 12, ¿cuál sería aproximadamente el tamaño central de las partículas?
# Cálculo de pronósticos
Y_Esp <- a + b * 12
Y_Esp## (Intercept)
## 12.09766plot(1, type = "n", axes = FALSE, xlab = "", ylab = "")
text(x = 1, y = 1,
labels = paste("¿Cuál sería la mediana
si el promedio es 12?\n",
"R =", round(Y_Esp, 4)),
cex = 2,
col = "black",
font = 2)
CONCLUSIÓN
Entre el promedio y la mediana existe una relación de tipo lineal donde el modelo f(x)=-0,2099+1.0256x, siendo “x” el promedio (MEAN) y “y” la mediana (MEDIAN), donde sí existe restricción, ya que el modelo solo es confiable dentro del rango de valores observados del promedio, el cual varía entre 0.01 y 10.62. Además, la mediana está influenciada en un 99.17% por el promedio, mientras que el resto se debe a otros factores.
Ejemplo: Cuando el promedio es 12 se espera una mediana de 12.09766.