Regresion Lineal
Enunciado
En el dataset encontrarán valores de materia seca obtenidos mediante tres metodologías diferentes que actualmente empleamos en el programa de yuca:
DM_raw: Materia seca usando la metodología de horno convencional.
DM_gravity: Materia seca por el método gravimétrico.
Para más detalles, pueden ver el siguiente video: Metodo Gravimétrico DM_nirs: Materia seca usando espectroscopía NIR (Near-infrared). Más información en el video desde el minuto 2:27: Espectroscopía NIR
Tarea:
Seleccionen dos variables y apliquen el mismo pipeline de regresión lineal que revisamos en clase. Recuerden que este es un conjunto de datos reales y contiene valores faltantes, por lo que deben utilizar el argumento de observaciones completas dentro de la función cor. Deben entregarlo en formato informe usando Rmarkdown.
Además, cuando necesiten unir el dataset crudo con las predicciones y las bandas de confianza, asegúrense de eliminar primero todas las filas que contengan valores faltantes. Pueden utilizar los siguientes códigos:
data_cruda %>% filter(!is.na()) %>% bind_cols(predict(…)) data_cruda %>% drop_na() %>% bind_cols(predict(…))
Cargando los datos
# Cargando las librerías necesarias
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.5.1 ✔ tibble 3.2.1
## ✔ lubridate 1.9.3 ✔ tidyr 1.3.1
## ✔ purrr 1.0.2
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(ggpubr)
library(readr)
Materia_seca <- read.csv("dm_data.csv")
print(head(Materia_seca))## plot_name accession_name DM_raw DM_gravity DM_nirs
## 1 202109DVGN6_momi_rep1_ARG55_83 ARG55 39.41 35.6 38.9
## 2 202109DVGN6_momi_rep1_ARG65_42 ARG65 37.92 34.3 38.8
## 3 202109DVGN6_momi_rep1_ARG67_107 ARG67 35.26 34.2 34.1
## 4 202109DVGN6_momi_rep1_BOL1_135 BOL1 30.72 30.1 30.8
## 5 202109DVGN6_momi_rep1_BRA1001_71 BRA1001 37.28 34.1 36.3
## 6 202109DVGN6_momi_rep1_BRA1081_11 BRA1081 32.30 32.4 33.6print(tail(Materia_seca))## plot_name accession_name DM_raw DM_gravity
## 1281 202101DVGN6_ciat_rep2_USA2_233 USA2 32.94349 36.70857
## 1282 202101DVGN6_ciat_rep2_USA5_236 USA5 37.44100 35.11073
## 1283 202101DVGN6_ciat_rep2_VEN128_239 VEN128 36.35951 36.69617
## 1284 202101DVGN6_ciat_rep2_VEN208_150 VEN208 36.97320 34.72979
## 1285 202101DVGN6_ciat_rep2_VEN25_211 VEN25 35.23612 38.35291
## 1286 202101DVGN6_ciat_rep2_VEN312_192 VEN312 33.55062 35.38164
## DM_nirs
## 1281 33.45413
## 1282 35.89616
## 1283 37.10273
## 1284 36.29892
## 1285 34.84373
## 1286 34.72980Grafico multivariado
A continuación presentamos un gráfico, en el que se puede ver la tendencia de los datos
# Gráfico multivariado
ggplot(Materia_seca, aes(x = DM_raw, y = DM_gravity, z = DM_nirs)) +
geom_point(color = "blue", size = 3) +
labs(x = "DM_raw", y = "DM_gravity", z = "DM_nirs", title = "Gráfico Multivariado") +
theme_minimal()
Análisis de correlación
Vamos a hacer la matriz de correlación entre dos columnas, DM_raw y DM_gravity
# Calcular la matriz de correlación entre DM_raw y DM_gravity
correlacion <- cor(Materia_seca$DM_raw, Materia_seca$DM_gravity,use = "complete.obs")
# Imprimir la matriz de correlación
print(correlacion)## [1] 0.6568777Un valor de correlación de aproximadamente \(0.657\) indica una correlación positiva moderada entre las variables DM_raw y DM_gravity. Lo que significa que, en general, cuando una variable aumenta, la otra también tiende a aumentar, y viceversa. Sin embargo, como la correlación no es tan cercana a 1, se puede apreciar que la relación entre estas dos variables no es exacta y seguro hay cierta variabilidad no explicada por la relación lineal entre ellas.
#Vamos a sacar las dos columnas
# Seleccionar las columnas DM_raw y DM_gravity
datos_seleccionados <- Materia_seca %>% select(DM_raw, DM_gravity)
# Ver las primeras filas de los datos seleccionados
head(datos_seleccionados)## DM_raw DM_gravity
## 1 39.41 35.6
## 2 37.92 34.3
## 3 35.26 34.2
## 4 30.72 30.1
## 5 37.28 34.1
## 6 32.30 32.4# Gráfico de scatter
ggplot(data = datos_seleccionados, aes(x = DM_raw, y = DM_gravity)) +
geom_point(size = 3, colour = "red", shape = 10) +
geom_text(aes(label = paste("r =", round(cor(DM_raw, DM_gravity), 3)), x = 90, y = 30)) +
geom_text(aes(label = "Author: JJLG"), x = 60, y = 20, size = 3) +
labs(x = "DM_raw", y = "DM_gravity", title = "Materia Seca") +
theme_bw()
Modelo lineal
Ahora vamos a determinar el modelo
modelo <- lm(DM_raw ~ DM_gravity, data = datos_seleccionados)
summary(modelo)##
## Call:
## lm(formula = DM_raw ~ DM_gravity, data = datos_seleccionados)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.1974 -2.5194 0.1161 2.3385 18.4420
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.75407 1.00178 11.73 <2e-16 ***
## DM_gravity 0.73243 0.02894 25.31 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.709 on 844 degrees of freedom
## (440 observations deleted due to missingness)
## Multiple R-squared: 0.4315, Adjusted R-squared: 0.4308
## F-statistic: 640.6 on 1 and 844 DF, p-value: < 2.2e-16anova(modelo)## Analysis of Variance Table
##
## Response: DM_raw
## Df Sum Sq Mean Sq F value Pr(>F)
## DM_gravity 1 8814.5 8814.5 640.58 < 2.2e-16 ***
## Residuals 844 11613.7 13.8
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Valores ajustados
# fitted values
modelo$fitted.values## 1 2 3 4 5 6 7 8
## 37.82851 36.87635 36.80311 33.80015 36.72986 35.48474 39.73282 34.89879
## 9 10 11 12 13 14 15 16
## 32.92124 34.89879 37.38905 36.43689 38.12148 32.77475 36.58338 38.85390
## 17 18 19 20 21 22 23 24
## 36.21716 36.65662 38.85390 33.72691 37.16932 39.51309 40.24552 34.60582
## 25 26 27 28 29 30 31 33
## 36.65662 36.58338 40.61173 36.36365 35.26501 31.60287 36.58338 37.68202
## 34 35 36 37 38 39 40 41
## 35.77771 36.80311 37.16932 34.75231 37.82851 39.07363 32.48178 35.55798
## 42 43 44 45 46 47 48 49
## 35.11852 34.09312 38.19472 36.72986 35.11852 31.74935 34.31285 38.48769
## 50 51 52 53 54 55 56 57
## 37.68202 38.41445 38.41445 34.53258 34.89879 30.72395 34.09312 35.04528
## 58 59 60 61 62 63 64 65
## 35.04528 38.70742 29.55207 37.53553 35.55798 41.34416 36.58338 32.18881
## 66 67 68 69 70 71 72 73
## 38.70742 29.84504 35.41149 33.28745 33.36069 34.45934 35.33825 29.69856
## 74 75 76 77 78 79 80 81
## 35.92419 29.03937 35.92419 35.41149 39.14688 37.46229 28.38019 38.85390
## 82 83 85 86 87 88 89 90
## 31.38314 37.75526 38.04823 37.46229 34.67907 38.34120 37.31581 40.31876
## 91 92 93 94 95 96 97 98
## 28.74640 35.11852 39.14688 33.14097 38.12148 34.82555 38.78066 30.43098
## 99 100 101 102 103 104 105 106
## 36.29041 34.82555 36.21716 38.04823 37.82851 37.09608 34.82555 34.89879
## 107 108 109 110 111 112 113 114
## 36.07068 31.82260 37.46229 35.11852 36.87635 34.89879 34.16637 32.48178
## 115 116 117 118 119 120 121 122
## 31.09017 31.60287 37.53553 35.77771 28.23370 30.57747 38.26796 33.14097
## 123 124 125 126 127 128 129 130
## 34.01988 31.16341 36.29041 30.50423 28.45343 42.00334 40.24552 39.65957
## 131 132 133 134 135 136 137 138
## 34.16637 34.75231 34.60582 35.26501 38.70742 38.85390 35.33825 37.75526
## 139 140 141 142 143 144 145 146
## 36.14392 32.18881 34.16637 34.45934 39.36660 38.04823 36.51013 34.60582
## 147 148 149 150 151 152 153 154
## 40.24552 37.60878 38.85390 30.94368 38.41445 37.75526 33.80015 36.43689
## 155 156 157 158 159 160 161 162
## 38.34120 34.97204 36.72986 38.34120 39.65957 33.65367 34.09312 38.70742
## 163 164 165 166 167 168 169 170
## 40.17227 38.41445 37.60878 32.33530 33.36069 31.01693 35.33825 35.85095
## 171 172 173 174 175 177 178 179
## 35.41149 36.07068 31.67611 39.29336 39.22012 33.28745 35.92419 29.18586
## 180 181 182 183 184 185 186 187
## 38.34120 35.92419 34.16637 33.72691 33.87339 38.85390 35.99744 36.72986
## 188 189 190 191 192 193 194 195
## 39.80606 24.71805 34.97204 31.52963 34.23961 34.97204 32.84800 38.85390
## 196 197 198 199 200 201 202 203
## 29.33234 38.19472 37.60878 41.27092 34.31285 33.65367 38.34120 34.82555
## 204 205 206 207 208 209 210 211
## 34.38609 36.21716 32.99448 35.99744 34.23961 31.60287 29.84504 32.40854
## 212 213 214 215 216 217 219 220
## 37.60878 36.14392 38.26796 38.19472 29.25910 39.14688 35.41149 27.35479
## 221 222 223 224 225 226 227 228
## 38.26796 35.77771 30.50423 39.29336 36.94959 41.19767 29.77180 33.06772
## 229 230 231 232 233 234 235 236
## 40.02579 33.43394 38.56093 31.89584 39.07363 33.58042 36.80311 37.75526
## 237 238 239 240 241 242 243 244
## 34.60582 35.55798 37.53553 39.58633 33.87339 34.23961 37.53553 32.62827
## 245 246 247 248 249 250 251 252
## 37.75526 34.89879 37.31581 36.29041 35.41149 33.58042 28.08721 32.92124
## 253 254 255 256 257 258 259 260
## 37.31581 35.77771 25.88993 30.21126 37.53553 32.70151 33.87339 33.80015
## 261 262 263 264 265 266 267 268
## 35.99744 31.30990 28.52667 40.68497 41.19767 38.92715 34.31285 36.58338
## 269 270 271 272 273 274 275 276
## 33.58042 36.94959 37.53553 39.07363 43.30776 39.65127 41.21604 40.60159
## 277 278 279 280 281 283 284 285
## 39.31589 38.91007 38.65621 41.30156 40.25154 42.62903 38.49077 40.38026
## 286 287 288 290 292 293 294 295
## 40.33050 38.43977 40.37645 38.34874 39.97036 37.10013 41.00895 43.05741
## 296 297 299 300 301 303 304 305
## 35.77324 41.37010 40.73463 37.66637 39.12175 35.30799 51.79189 37.16486
## 306 307 308 309 310 311 312 313
## 35.40968 40.92035 37.93350 40.47179 30.01631 39.51919 32.57944 40.54733
## 314 315 316 317 319 320 321 322
## 41.18275 40.40251 36.79101 39.28041 39.16160 33.16763 39.70904 40.04374
## 323 324 325 326 327 328 329 330
## 40.54664 37.65275 38.06075 37.75476 34.09871 40.32252 35.50960 39.45553
## 331 332 333 334 335 336 337 338
## 34.60272 37.27304 32.69591 41.72037 37.51819 37.43169 35.35450 37.85497
## 339 341 342 343 345 347 348 349
## 37.95318 41.12168 42.90112 41.17047 36.18311 36.20785 40.29411 37.09890
## 350 351 352 354 355 356 357 358
## 41.82811 39.35170 40.82437 38.29892 41.95475 39.67432 45.46920 42.58798
## 359 360 361 362 363 364 365 367
## 32.21295 36.43763 35.46741 41.45966 34.75971 38.19184 38.12557 38.65352
## 368 369 370 371 372 373 374 375
## 38.83411 36.85929 39.27157 40.34284 35.60770 41.67737 31.44385 37.76259
## 376 377 378 379 380 382 383 384
## 40.23095 39.67636 31.95944 41.77507 37.05385 38.01874 34.25007 38.79065
## 386 387 388 389 390 391 392 393
## 40.27736 38.93613 42.38460 43.37234 42.87365 31.59029 38.96748 37.46009
## 394 395 396 397 398 400 401 402
## 40.89483 36.94265 40.21769 34.41752 35.16691 40.70880 32.61061 38.47414
## 405 406 407 409 410 411 413 414
## 37.67532 38.53192 44.56841 35.44495 33.57110 39.15496 39.50839 35.79450
## 415 416 417 418 419 420 421 422
## 38.50427 38.68138 34.63407 39.14065 40.72880 39.98835 36.45386 37.25054
## 423 424 425 426 427 428 429 430
## 32.70755 32.69664 39.79991 47.93128 35.06889 39.57820 35.79770 37.84260
## 431 432 433 434 435 436 437 438
## 35.53884 37.42602 34.76257 40.66532 42.78867 36.21468 38.56470 34.79111
## 439 441 443 444 446 447 448 449
## 37.77822 36.84933 39.39028 37.27531 43.90412 41.42266 43.16009 40.87905
## 450 451 452 453 454 455 456 457
## 35.28740 37.53641 36.27442 41.00540 40.03013 41.52783 40.67954 40.23380
## 458 459 460 461 462 463 464 465
## 41.98523 41.09530 38.25788 41.05801 41.63279 39.29725 39.86804 41.77080
## 466 467 469 470 471 472 474 475
## 36.37842 38.81972 39.82482 32.76518 35.38745 37.08436 35.45469 38.40607
## 477 478 479 480 481 482 483 484
## 35.83009 40.35703 36.31618 32.06252 41.74290 38.88078 32.50499 39.81733
## 486 488 490 491 492 493 494 495
## 39.13450 37.27290 44.17513 38.74595 34.34147 30.92369 34.70002 38.93613
## 496 497 498 500 501 502 503 504
## 37.47699 31.37954 41.29838 38.55211 40.00961 39.31111 34.08977 33.36740
## 506 507 508 509 510 511 512 513
## 37.08104 33.93387 37.09978 38.52071 39.70102 35.82099 32.19654 39.05025
## 514 515 516 517 518 519 520 521
## 31.35433 36.27787 35.73020 38.57655 27.91037 39.56737 31.32897 39.68615
## 522 523 524 525 526 528 529 530
## 31.79517 39.13293 34.94646 36.65276 37.38065 40.63342 41.44129 39.36930
## 532 534 535 536 537 538 539 540
## 34.55254 35.42830 41.19468 34.29892 35.51535 37.84931 44.32566 36.11696
## 541 542 543 544 545 547 550 551
## 38.24652 41.47589 38.72119 44.40377 36.29203 34.59373 29.33889 36.92525
## 552 553 554 556 557 558 559 560
## 34.48674 35.61784 39.18419 35.45469 32.41739 41.59365 37.68843 38.03350
## 561 562 563 564 565 566 567 569
## 31.62080 36.63669 38.64549 35.54312 31.57751 39.32636 37.42189 37.69105
## 570 571 573 575 576 577 578 579
## 35.42490 41.44383 39.26657 40.64854 39.83283 35.23308 27.95547 34.64489
## 580 581 582 583 584 586 587 588
## 39.53305 40.00589 35.85333 40.63429 31.20252 37.84260 34.19348 30.56047
## 589 590 591 592 593 597 598 600
## 33.81336 37.53965 37.00142 38.41995 38.59819 35.38612 36.61457 40.35728
## 601 602 603 604 605 606 607 608
## 37.89307 36.46323 36.33924 33.53271 33.71531 37.75071 34.72293 34.98317
## 609 610 611 613 614 615 617 618
## 31.95205 25.39537 31.12756 36.20138 49.26156 33.53064 35.18849 31.85913
## 620 621 622 623 624 625 626 628
## 31.37034 39.05896 41.08366 30.98079 37.34717 34.17357 35.97466 35.63376
## 629 630 631 633 634 635 636 637
## 39.74141 38.63030 40.05409 41.75320 41.41884 43.26594 37.42209 38.71803
## 638 639 640 641 642 643 644 645
## 34.85619 27.66354 39.28833 40.41567 39.03639 39.02011 38.83717 39.79548
## 646 1015 1017 1018 1019 1020 1021 1022
## 38.99546 37.64902 36.92481 37.67139 40.26013 38.81546 39.47856 35.40441
## 1023 1024 1025 1026 1027 1028 1030 1031
## 37.07894 37.18250 40.17551 36.36660 38.56279 34.78718 39.61487 37.26816
## 1032 1033 1034 1035 1036 1037 1039 1040
## 34.81350 38.87157 34.46761 38.91138 36.00590 35.51431 37.60091 38.90419
## 1041 1042 1043 1044 1045 1046 1047 1048
## 39.52002 38.89113 37.73034 34.30823 39.16160 34.04565 39.91072 38.00366
## 1049 1050 1051 1054 1055 1056 1057 1058
## 39.18419 39.70385 36.99392 31.39391 37.02425 39.10140 34.64440 37.32002
## 1059 1060 1061 1062 1063 1064 1065 1066
## 37.06695 37.95318 34.71581 38.94533 37.32213 39.43319 33.10490 40.89938
## 1067 1068 1069 1070 1071 1072 1073 1074
## 40.18588 36.39014 35.83685 35.57052 38.12133 31.74995 39.94974 41.29741
## 1076 1078 1079 1080 1081 1082 1083 1084
## 36.73362 37.14524 35.18849 39.86743 36.87815 36.72660 38.54444 35.28192
## 1085 1086 1087 1088 1089 1090 1091 1092
## 35.68573 36.33107 36.83779 37.52420 31.16748 38.00740 37.95318 38.56803
## 1093 1094 1095 1096 1097 1098 1099 1100
## 38.59657 34.06730 31.53778 34.13810 37.72976 39.66387 36.30196 38.40501
## 1101 1102 1103 1104 1105 1106 1107 1108
## 36.60154 38.21194 42.29453 41.57802 34.98803 37.71241 38.56803 38.62058
## 1109 1110 1111 1112 1113 1114 1115 1116
## 40.28689 37.20794 35.53539 38.11598 36.89400 36.91044 38.00740 39.88267
## 1117 1119 1120 1121 1122 1123 1124 1125
## 36.31232 37.55870 33.60846 36.72326 31.58033 39.78389 36.36312 33.99350
## 1126 1127 1128 1129 1130 1131 1132 1133
## 36.01449 36.98485 34.42666 37.95318 35.59770 38.32006 37.08104 35.84804
## 1134 1135 1136 1137 1138 1139 1140 1141
## 32.78527 38.64549 36.23590 37.09173 34.39470 38.28148 33.60294 34.14795
## 1145 1146 1147 1148 1149 1150 1151 1152
## 36.68804 34.57009 38.27167 37.86840 40.23321 37.60091 33.56507 37.03047
## 1153 1154 1155 1156 1157 1158 1159 1160
## 38.20275 36.87830 39.64737 39.86743 40.76729 38.53542 35.55906 36.96197
## 1161 1162 1163 1164 1165 1166 1167 1168
## 36.93743 36.56699 37.18189 35.14775 36.62849 39.50394 38.72591 34.92344
## 1169 1170 1171 1172 1173 1174 1175 1176
## 39.97759 35.71300 40.02152 36.81962 35.84607 35.94365 37.75088 39.75577
## 1177 1178 1179 1180 1181 1182 1183 1184
## 41.39201 40.11022 38.26566 36.76030 39.91819 33.00332 38.22331 38.13342
## 1185 1186 1187 1191 1192 1193 1194 1195
## 39.98486 39.17463 37.15142 35.41460 39.62894 31.35433 35.94852 38.73304
## 1196 1197 1198 1199 1200 1201 1202 1203
## 39.30363 33.94658 36.85989 39.48764 39.52319 40.08226 39.81066 40.74776
## 1204 1205 1206 1207 1208 1209 1210 1212
## 35.68940 35.80610 36.41440 38.24198 33.81021 39.93578 41.42099 35.41460
## 1214 1215 1216 1217 1218 1219 1220 1221
## 33.62398 33.27005 40.04374 35.75727 38.29617 34.17960 31.12847 35.44691
## 1222 1223 1224 1225 1226 1227 1228 1229
## 34.26139 35.95962 38.55211 33.12122 41.31423 39.92234 40.01662 38.71143
## 1230 1231 1232 1233 1234 1235 1236 1237
## 29.12604 39.31490 34.71188 38.76398 37.60018 36.63008 40.14205 36.78727
## 1238 1239 1240 1241 1242 1243 1244 1245
## 37.70974 40.94722 40.62087 34.10544 39.23391 39.89105 37.02962 41.40495
## 1246 1247 1248 1249 1250 1251 1252 1253
## 37.56992 37.04983 38.07399 37.89570 38.11598 36.57838 39.67851 38.71453
## 1254 1255 1256 1257 1258 1259 1260 1261
## 37.18817 37.14196 33.28623 38.09762 28.90967 37.29250 37.34753 37.45447
## 1262 1263 1264 1265 1266 1267 1268 1269
## 35.99549 37.64248 37.07229 37.30135 33.47617 40.56431 38.26150 34.44986
## 1270 1271 1272 1273 1274 1275 1276 1277
## 34.23581 41.39395 39.20194 38.33292 36.93558 38.57684 33.62716 33.77588
## 1281 1282 1283 1284 1285 1286
## 38.64045 37.47015 38.63137 37.19114 39.84481 37.66857# errores
modelo$residuals## 1 2 3 4 5
## 1.581494930 1.043651184 -1.543106027 -3.080151690 0.550136761
## 6 7 8 9 10
## -3.184735830 -0.742817577 -0.078793521 -1.901238225 3.391206479
## 11 12 13 14 15
## 0.060951663 4.103107916 3.288523775 -6.644752647 -5.843377661
## 16 17 18 19 20
## 1.926095888 -0.627163718 0.363379550 1.486095888 1.873091099
## 21 22 23 24 25
## 4.210680029 0.376910790 1.444482902 -4.175822366 -2.056620450
## 26 27 28 29 30
## 3.226622339 -1.001731041 -3.483649295 0.594992536 -2.872868028
## 31 33 34 35 36
## 0.776622339 -0.502019492 -4.917706985 1.906893973 1.610680029
## 37 38 39 40 41
## -4.022307943 0.091494930 0.106367522 -2.671781492 0.492021381
## 42 43 44 45 46
## 2.071478113 -2.753122845 3.745280987 0.520136761 -0.748521887
## 47 48 49 50 51
## 0.390646395 -2.502851211 1.282309832 0.827980508 2.545552621
## 52 53 54 55 56
## 2.785552621 8.787420423 0.741206479 -3.803954563 -4.033122845
## 57 58 59 60 61
## 5.364720902 -2.165279098 2.202581466 3.497930057 1.294466085
## 62 63 64 65 66
## 3.622021381 2.725841071 -3.753377661 -4.658810338 -0.427418534
## 67 68 69 70 71
## -3.675041098 -2.101493042 0.822547832 -4.670694957 1.460663212
## 72 73 74 75 76
## -5.288250253 -5.398555521 -3.254192563 -2.519370422 4.315807437
## 77 78 79 80 81
## -2.541493042 5.713124733 1.637708874 -9.490185324 1.756095888
## 82 83 85 86 87
## -2.923139662 -1.295262281 -0.388233436 1.157708874 1.640934846
## 88 89 90 91 92
## 2.208795409 1.834194451 0.941240114 -5.526399267 3.351478113
## 93 94 95 96 97
## 2.323124733 -0.070966591 1.398523775 -0.225550732 0.319338677
## 98 99 100 101 102
## -1.960983408 -1.500406506 -1.805550732 2.992836282 -0.738233436
## 103 104 105 106 107
## -0.358505070 -0.906077182 1.494449268 -0.458793521 -2.340678140
## 108 109 110 111 112
## -4.992596394 -0.582291126 1.081478113 3.273651184 -0.088793521
## 113 114 115 116 117
## 2.843634367 1.598218508 3.169831493 4.397131972 3.004466085
## 118 119 120 121 122
## 2.582293015 -3.163699746 0.792531014 2.142038198 -0.600966591
## 123 124 125 126 127
## 3.950119944 -2.733411295 3.689593494 -0.554226197 -5.983428112
## 128 129 130 131 132
## 3.936655973 3.434482902 2.260425212 -4.706365633 2.427692057
## 133 134 135 136 137
## 1.354177634 2.574992536 -1.177418534 2.206095888 0.171749747
## 138 139 140 141 142
## 0.004737719 -0.013920929 -6.908810338 -1.406365633 -10.049336788
## 143 144 145 146 147
## -3.166603633 0.161766564 -2.850134873 2.814177634 2.004482902
## 148 149 150 151 152
## 2.311223297 2.096095888 -8.203682929 -1.694447379 1.024737719
## 153 154 155 156 157
## 0.509848310 2.553107916 1.728795409 -0.802036309 3.470136761
## 158 159 160 161 162
## 0.078795409 -0.569574788 -4.613666112 -5.793122845 1.362581466
## 163 164 165 166 167
## 2.427725691 -0.994447379 -0.758776703 -4.845295915 -0.170694957
## 168 169 170 171 172
## -9.696925718 -4.618250253 -4.000949774 -1.991493042 0.529321860
## 173 174 175 177 178
## -2.206110816 1.646639156 -1.070118055 -0.487452168 3.165807437
## 179 180 181 182 183
## -10.775856000 2.278795409 -0.874192563 2.343634367 -2.696908901
## 184 185 186 187 188
## -5.793394478 0.456095888 -1.817435351 3.800136761 3.573939635
## 189 190 191 192 193
## 18.441954113 0.217963691 -6.659625239 -5.989608422 1.167963691
## 194 195 196 197 198
## -2.537995436 2.366095888 -0.582341577 -1.394719013 3.541223297
## 199 200 201 202 203
## 3.609083860 -3.802851211 -7.673666112 -2.231204591 -4.185550732
## 204 205 206 207 208
## -3.296093999 0.832836282 -4.474481014 -3.337435351 -2.269608422
## 209 210 211 212 213
## -4.382868028 2.534958902 -3.688538704 2.831223297 -2.923920929
## 214 215 216 217 219
## 4.462038198 0.535280987 -8.539098788 2.693124733 -3.231493042
## 220 221 222 223 224
## 5.385213718 -0.297961802 1.082293015 0.885773803 1.826639156
## 225 226 227 228 229
## -0.279591605 0.442326649 -2.681798310 -0.277723802 3.084211269
## 230 231 232 233 234
## 1.186062254 3.169067043 4.174160817 -0.523632478 -2.550423323
## 235 236 237 238 239
## 0.226893973 -1.085262281 -3.585822366 -3.257978619 -0.705533915
## 240 241 242 243 244
## 3.013668001 0.796605522 -1.429608422 -2.845533915 -2.448267070
## 245 246 247 248 249
## 1.074737719 0.771206479 3.174194451 1.659593494 2.768506958
## 250 251 252 253 254
## 1.679576677 -6.207214169 3.688761775 4.594194451 2.082293015
## 255 256 257 258 259
## -6.639930507 -6.811255042 4.664466085 -2.411509859 3.576605522
## 260 261 262 263 264
## -1.640151690 4.732564649 -5.119896873 -5.576670901 2.565026170
## 265 266 267 268 269
## 3.092326649 3.282853099 -2.972851211 2.306622339 -0.920423323
## 270 271 272 273 274
## 1.940408395 -2.685533915 4.036367522 -1.212739802 2.594981391
## 275 276 277 278 279
## -6.339805706 0.764763704 3.036585149 1.779801788 -5.155026566
## 280 281 283 284 285
## 0.996121600 -0.244035872 -3.567717319 -0.081042205 -2.045613653
## 286 287 288 290 292
## 2.432123228 6.488214916 0.111032176 4.844493867 4.147664048
## 293 294 295 296 297
## -7.392079605 0.813572029 -1.694749063 0.621092434 0.388160990
## 299 300 301 303 304
## -0.280275768 3.778993175 0.982184033 -0.417978032 -11.197440026
## 305 306 307 308 309
## -1.162653222 -4.801667998 -2.948003311 4.520285208 0.525817720
## 310 311 312 313 314
## -7.820894251 -2.704483138 3.563590678 0.544944815 -1.907559428
## 315 316 317 319 320
## -1.962393836 0.939113583 4.284112282 -2.815229050 -6.471456578
## 321 322 323 324 325
## -3.462912413 -3.402576232 1.003051081 -0.183420102 1.834432000
## 326 327 328 329 330
## -1.339094760 6.291851043 -3.290375812 -0.865289660 -4.181140217
## 331 332 333 334 335
## 1.551167422 4.559339060 -7.781199408 -2.609510775 2.032240728
## 336 337 338 339 341
## 2.091909095 -0.593930869 -4.381959768 -2.519435852 0.090878749
## 342 343 345 347 348
## -1.373855455 0.152208491 3.177076657 -3.409676000 4.311035922
## 349 350 351 352 354
## -4.134056629 -0.949518144 2.845987288 1.085269578 2.954655233
## 355 356 357 358 359
## 2.601272259 1.595056162 1.059147419 -0.792912243 6.234218511
## 360 361 362 363 364
## -0.123641434 -0.953015412 -4.403749534 0.560262181 -3.050372909
## 365 367 368 369 370
## -6.097056156 -2.791105792 -2.460839650 4.061788421 -2.596358745
## 371 372 373 374 375
## 4.490550001 5.116284444 4.988076386 -0.028570711 1.309200830
## 376 377 378 379 380
## -4.497849927 -3.629432061 -2.989914206 0.830632401 -0.315347421
## 382 383 384 386 387
## -0.144864503 -1.011645347 3.313109927 -0.157231526 1.884859304
## 388 389 390 391 392
## 4.339447955 -0.665342197 1.104163068 -2.472850921 1.542306234
## 393 394 395 396 397
## 1.154651585 1.670518871 1.127833417 1.451323197 -2.686097261
## 398 400 401 402 405
## -2.114716707 1.025590906 7.620513606 0.121191081 -3.314902913
## 406 407 409 410 411
## -2.800102169 -0.873656083 5.450921547 1.895228958 1.272283730
## 413 414 415 416 417
## 6.151274691 7.122741116 3.218874481 6.928199488 3.940680151
## 418 419 420 421 422
## -1.337411766 0.867254764 0.719302290 4.717446756 1.553292986
## 423 424 425 426 427
## 5.313604454 6.559281926 -1.271200040 -5.865695185 4.706584982
## 428 429 430 431 432
## -1.970538806 8.244636773 2.172318521 0.176687833 -2.932851206
## 433 434 435 436 437
## -1.114511539 2.093969345 1.027114588 3.111240491 1.122199444
## 438 439 441 443 444
## 1.733587851 3.518576487 -0.492113506 0.096677533 5.115292003
## 446 447 448 449 450
## 2.236095205 1.731870948 2.666275148 -0.498070024 -2.349449087
## 451 452 453 454 455
## 2.817378992 3.629642641 1.714607559 1.738140031 3.761564567
## 456 457 458 459 460
## 0.203181512 -2.085012559 -1.907178309 -1.916125463 7.097337479
## 461 462 463 464 465
## 4.032098849 -2.758541124 3.344223347 5.227884867 -0.478039497
## 466 467 469 470 471
## 2.163747198 2.746131089 -0.423860560 8.332262681 5.392394912
## 472 474 475 477 478
## -1.025525786 7.081677102 2.910664144 0.345879662 0.560848465
## 479 480 481 482 483
## 5.793387386 3.775018485 -0.965063852 3.261640975 8.973813144
## 484 486 488 490 491
## 2.752828739 3.154691095 3.364724072 -3.732960423 2.105720467
## 492 493 494 495 496
## 0.552128028 -1.946225956 5.468154139 8.424360564 2.671619660
## 497 498 500 501 502
## -7.104570866 0.186581466 3.353612200 1.494288884 0.682829483
## 503 504 506 507 508
## -6.417123964 8.732982962 -0.030736526 0.909772565 4.481884495
## 509 510 511 512 513
## 0.421471479 1.817431184 -0.399272562 10.051236945 1.496937319
## 514 515 516 517 518
## 13.048293346 0.520558648 0.452521037 -0.995772488 6.972844396
## 519 520 521 522 523
## 2.175762280 5.892318804 4.418971769 7.602314881 0.443413184
## 524 525 526 528 529
## 1.282022432 0.247452232 0.644292127 3.885982462 3.492781089
## 530 532 534 535 536
## 0.615901124 4.928603005 2.307685517 5.669346011 2.202469813
## 537 538 539 540 541
## 5.196595001 2.398317062 -3.519383916 6.321449030 3.366286399
## 542 543 544 545 547
## 3.992230007 5.483452120 3.148994938 6.495825731 1.404793278
## 550 551 552 553 554
## 3.396137401 1.441237764 -1.886539167 -3.884299408 2.200391393
## 556 557 558 559 560
## 5.140679782 2.768457870 -0.266589388 3.839451031 8.829717109
## 561 562 563 564 565
## -2.875649124 1.889850804 -0.030939548 -2.756601211 0.949358904
## 566 567 569 570 571
## 2.720865677 -0.898673893 1.124076254 -2.789512386 3.045846456
## 573 575 576 577 578
## -0.150387973 -1.452343991 2.662500916 5.618143779 1.747442578
## 579 580 581 582 583
## 6.419481097 4.256986561 1.052497368 4.302647526 3.464071186
## 584 586 587 588 589
## 2.203774037 2.804028111 6.494634339 3.354522901 1.892576608
## 590 591 592 593 597
## 2.814549116 4.300190807 0.900954319 1.678396403 0.318146861
## 598 600 601 602 603
## 3.238912058 -0.687293797 3.358937682 5.809107596 6.225407785
## 604 605 606 607 608
## 7.643858274 7.613905986 4.720471095 5.169129666 -1.428074541
## 609 610 611 613 614
## 2.625194950 9.860900057 7.166629585 7.327027781 -8.651322677
## 615 617 618 620 621
## 5.036118372 5.402382202 3.469984425 -0.655956234 2.726701026
## 622 623 624 625 626
## 1.323133245 8.721994838 4.995527147 1.603339290 9.213755601
## 628 629 630 631 633
## 1.855697185 0.709069936 6.806956354 2.771819951 4.377237041
## 634 635 636 637 638
## 3.042142924 0.425364629 2.745903262 -0.521101135 8.555219798
## 639 640 641 642 643
## 11.982555890 2.283571061 5.359600025 6.355712242 2.872204913
## 644 645 646 1015 1017
## 3.387611713 0.843537192 2.811118726 1.139285091 -2.612698191
## 1018 1019 1020 1021 1022
## -5.478832254 -0.570149003 -4.926251545 -1.476556568 1.409400232
## 1023 1024 1025 1026 1027
## -5.297262860 0.885909968 -2.260948734 4.621148436 2.884191174
## 1028 1030 1031 1032 1033
## -6.997866941 1.239677967 -2.502963418 -0.168651892 -0.060068021
## 1034 1035 1036 1037 1039
## 2.283621628 5.415561180 -1.436679774 5.369917135 -5.465871674
## 1040 1041 1042 1043 1044
## 1.877280407 -2.354990103 0.205842159 -3.303259752 -2.737491638
## 1045 1046 1047 1048 1049
## 0.183581190 -8.115986481 -3.161869120 -4.999927844 -0.052958627
## 1050 1051 1054 1055 1056
## -4.324353925 -4.073086275 -4.001846060 0.185096148 2.377135679
## 1057 1058 1059 1060 1061
## -4.070091929 -0.101664584 -0.708781164 -2.905349392 -1.222016453
## 1062 1063 1064 1065 1066
## -5.430071753 -2.087625469 -3.639031396 6.998400061 -2.434557140
## 1067 1068 1069 1070 1071
## 0.141946838 2.648252469 -3.187688474 -2.976380159 3.749280400
## 1072 1073 1074 1076 1078
## -4.903877161 -3.318318527 -1.813221215 1.853106012 -0.199717717
## 1079 1080 1081 1082 1083
## -6.321261958 -3.525041164 -4.011518238 0.438480897 -0.974658503
## 1084 1085 1086 1087 1088
## -6.764944750 -1.591043994 -5.299521178 0.594658664 -1.856017802
## 1089 1090 1091 1092 1093
## 9.131664848 1.139841001 -3.655524142 1.243210254 -4.873143158
## 1094 1095 1096 1097 1098
## -6.933031285 8.701465826 -2.867435967 -7.118684083 -3.414753159
## 1099 1100 1101 1102 1103
## -4.649963843 -1.624691218 -5.120600863 -1.118569202 -0.815993386
## 1104 1105 1106 1107 1108
## -0.764695223 -8.141955983 -1.881279672 1.704443524 -0.144781578
## 1109 1110 1111 1112 1113
## -0.209682672 2.693651815 -6.188554475 -2.947198525 -4.691664294
## 1114 1115 1116 1117 1119
## -4.742309452 -1.710383469 0.019538765 -0.948373092 -0.143909163
## 1120 1121 1122 1123 1124
## 1.464324286 -2.656582183 1.069284053 -1.380713080 -1.413577377
## 1125 1126 1127 1128 1129
## 1.577409618 -0.674802400 -0.910960376 3.381403098 0.718150248
## 1130 1131 1132 1133 1134
## -2.210725298 5.535482655 1.930916944 -3.230353896 0.803934932
## 1135 1136 1137 1138 1139
## -0.715083918 -4.453049290 2.229586146 -0.269545924 1.250602799
## 1140 1141 1145 1146 1147
## -0.073284962 -2.025588563 -1.886433356 2.583838175 -1.341230665
## 1148 1149 1150 1151 1152
## -2.441192201 -3.006095510 -3.671618944 1.134202994 -2.085611909
## 1153 1154 1155 1156 1157
## -0.950481687 -5.708130165 -0.720429354 -6.154303874 -2.934285215
## 1158 1159 1160 1161 1162
## -4.949764849 0.688512800 1.633697823 -4.454806420 -0.009884414
## 1163 1164 1165 1166 1167
## 2.225460344 -10.107275461 -7.504077933 0.633007592 -0.672953484
## 1168 1169 1170 1171 1172
## -1.164057136 -2.036856037 -2.987633148 1.943089333 -2.640514190
## 1173 1174 1175 1176 1177
## -0.681657143 -5.994246331 -5.447465227 1.179835072 -5.857711596
## 1178 1179 1180 1181 1182
## -3.684126146 -2.076365153 -8.172547211 -2.772095059 -7.661214041
## 1183 1184 1185 1186 1187
## -5.025075420 -5.563612465 0.492417866 -1.846706099 -1.873046736
## 1191 1192 1193 1194 1195
## -1.023206641 -4.913650995 0.169912206 -1.212458309 -4.509600912
## 1196 1197 1198 1199 1200
## -4.541474969 -1.692026296 -2.469758054 -3.132463107 -3.743295577
## 1201 1202 1203 1204 1205
## -0.193855678 -0.794924911 1.281279847 -1.248604137 -2.370947767
## 1206 1207 1208 1209 1210
## -3.363504259 2.195707605 -2.009401438 -1.950296370 -3.601303084
## 1212 1214 1215 1216 1217
## 2.296130449 2.254741540 -2.523025651 -7.638001912 -6.474937475
## 1218 1219 1220 1221 1222
## -4.891909992 3.333672767 -2.638270255 -1.425230953 -4.485499778
## 1223 1224 1225 1226 1227
## -5.814670205 -6.675972640 2.590328527 -3.819294040 -5.962792784
## 1228 1229 1230 1231 1232
## -1.213027009 -6.087073616 -10.214717037 -1.141108840 -2.033696825
## 1233 1234 1235 1236 1237
## -8.430646062 0.549259904 -6.879315635 -2.053273627 -8.030134851
## 1238 1239 1240 1241 1242
## -1.214919612 0.992012389 0.366658633 -2.037347279 -2.951313918
## 1243 1244 1245 1246 1247
## 0.732006302 0.300660086 -0.428408553 0.149484030 -6.074042605
## 1248 1249 1250 1251 1252
## -2.342419526 -4.633399764 -1.244093635 0.896784279 -2.327721483
## 1253 1254 1255 1256 1257
## -4.456029033 2.090196791 -1.425817787 -1.318400973 -3.137666269
## 1258 1259 1260 1261 1262
## 3.674368940 -1.670936479 -2.618043000 -1.649021049 -1.184836543
## 1263 1264 1265 1266 1267
## -1.063438379 -0.146635307 1.987136486 -3.694270212 2.289679110
## 1268 1269 1270 1271 1272
## -0.101532563 -3.475931072 4.198800671 -3.392694392 -5.858343303
## 1273 1274 1275 1276 1277
## 3.736727092 -1.960008087 1.372943608 -3.474051464 0.652973652
## 1281 1282 1283 1284 1285
## -5.696966110 -0.029152595 -2.271859295 -0.217939339 -4.608691388
## 1286
## -4.117950527hist(modelo$residuals)
Se aprecia que los residuos siguen una distribución aproximadamente normal.
# Coeficientes
b0 = modelo$coefficients[1]###intercepto en y
b1 = modelo$coefficients[2]#Pendiente
#inpresion de los coeficientes
print(b0)## (Intercept)
## 11.75407print(b1)## DM_gravity
## 0.7324279Coeficientes y predicciones
Con los valores de \(b_0\) y \(b_1\), se puede hacer el ajuste de la recta
# Generar las predicciones del modelo para datos_seleccionados
predicciones <- predict(modelo, newdata = datos_seleccionados, interval = "prediction", level = 0.9)
# Agregar las predicciones al conjunto de datos
datos_seleccionados <- cbind(datos_seleccionados, predicciones)
# Verificar las primeras filas de los datos con las predicciones
head(datos_seleccionados)## DM_raw DM_gravity fit lwr upr
## 1 39.41 35.6 37.82851 31.71634 43.94067
## 2 37.92 34.3 36.87635 30.76448 42.98822
## 3 35.26 34.2 36.80311 30.69123 42.91498
## 4 30.72 30.1 33.80015 27.68495 39.91535
## 5 37.28 34.1 36.72986 30.61798 42.84174
## 6 32.30 32.4 35.48474 29.37217 41.59730Gráfica
# Plot with predictions and confidence intervals
datos_seleccionados %>%
ggplot(aes(x = DM_raw, y = DM_gravity)) +
geom_point(size = 3) +
geom_line(aes(y = fit), color = "blue") +
geom_point(aes(y = fit), size = 2, color = 'red') +
geom_segment(aes(xend = DM_raw, yend = fit), color = 'blue') +
geom_line(aes(y = lwr), color = 'red') +
geom_line(aes(y = upr), color = 'red') +
geom_text(aes(label = paste("R^2=", round(cor(DM_raw, DM_gravity)^2, 3))),
x = 80, y = 30) +
geom_text(aes(label = "Author: JJLG"), x = 60, y = 20, size = 3) +
labs(x = "DM_raw", y = "DM_gravity", title = "Materia Seca") +
theme_minimal()
Gráfico con bandas
st <- ggscatter(Materia_seca, x = "DM_raw", y = "DM_gravity",
add = "reg.line", conf.int = TRUE,
shape = 21, add.params = list(color = "blue", fill = "lightgray")) +
stat_cor(method = "pearson", label.x = 60, label.y = 35)
st
Predict DM_gravity at 80% coverage
predicted_DM <- coef(modelo)[1] + coef(modelo)[2] * 80
predicted_DM## (Intercept)
## 70.3483