Nonlinear Regression Part 1
#install.packages("MultiKink")
library(MultiKink)
library(MatrixModels)
library(tidyverse)## -- Attaching packages --------------------------------------- tidyverse 1.3.2 --
## v ggplot2 3.3.6 v purrr 0.3.4
## v tibble 3.1.8 v dplyr 1.0.10
## v tidyr 1.2.1 v stringr 1.4.1
## v readr 2.1.2 v forcats 0.5.2
## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()library(ggplot2)
library(dplyr)
library(purrr)
library(rsample)
library(mlr3measures)## In order to avoid name clashes, do not attach 'mlr3measures'. Instead, only load the namespace with `requireNamespace("mlrmeasures")` and access the measures directly via `::`, e.g. `mlr3measures::auc()`.set.seed(123)
data.x <- rnorm(1000,1,1)
err <- rnorm(1000)
y <- 5+2*data.x+3*data.x^2+err
plot(data.x,y,xlim=c(-2,5), ylim=c(-10,70))
#Regresi Linier
lin.mod <-lm( y~data.x)
plot( data.x,y,xlim=c( -2,5), ylim=c( -10,70))
lines(data.x,lin.mod$fitted.values,col="red")
summary(lin.mod)##
## Call:
## lm(formula = y ~ data.x)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.686 -2.574 -1.428 1.195 27.185
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.6056 0.1902 24.22 <2e-16 ***
## data.x 8.3790 0.1340 62.54 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.2 on 998 degrees of freedom
## Multiple R-squared: 0.7967, Adjusted R-squared: 0.7965
## F-statistic: 3911 on 1 and 998 DF, p-value: < 2.2e-16#Polynomial
pol.mod <- lm( y~data.x+I(data.x^2)) #ordo 2
ix <- sort( data.x,index.return=T)$ix #ix=observasi keberapa
plot(data.x,y,xlim=c(-2,5), ylim=c(-10,70))
lines(data.x[ix], pol.mod$fitted.values[ix],col="blue", cex=2)
summary(pol.mod)##
## Call:
## lm(formula = y ~ data.x + I(data.x^2))
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.0319 -0.6942 0.0049 0.7116 3.2855
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.95193 0.04568 108.41 <2e-16 ***
## data.x 2.10732 0.05861 35.95 <2e-16 ***
## I(data.x^2) 2.99081 0.02338 127.93 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.007 on 997 degrees of freedom
## Multiple R-squared: 0.9883, Adjusted R-squared: 0.9883
## F-statistic: 4.221e+04 on 2 and 997 DF, p-value: < 2.2e-16#Fungsi Tangga
#regresi fungsi tangga
range( data.x) #nilai min dan max## [1] -1.809775 4.241040c1 <- as.factor(ifelse(data.x<=0,1,0))
c2 <- as.factor(ifelse(data.x<=2 & data.x>0,1,0))
c3 <- as.factor(ifelse(data.x>2,1,0))
data.frame(y,c1,c2,c3)## y c1 c2 c3
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## 985 30.009010 0 0 1
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## 990 33.009783 0 0 1
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## 993 14.503345 0 1 0
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## 996 9.381129 0 1 0
## 997 22.257307 0 0 1
## 998 4.945060 1 0 0
## 999 7.175307 0 1 0
## 1000 7.732277 0 1 0step.mod <- lm(y~c1+c2+c3)
plot(data.x,y,xlim=c(-2,5), ylim=c(-10,70))
lines(data.x,lin.mod$fitted.values,col="red")
lines(data.x[ix], step.mod$fitted.values[ix],col="green")
summary(step.mod)##
## Call:
## lm(formula = y ~ c1 + c2 + c3)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.395 -3.534 -0.530 2.527 36.876
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 30.4499 0.4087 74.50 <2e-16 ***
## c11 -25.2395 0.5710 -44.21 <2e-16 ***
## c21 -19.4184 0.4536 -42.81 <2e-16 ***
## c31 NA NA NA NA
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.121 on 997 degrees of freedom
## Multiple R-squared: 0.698, Adjusted R-squared: 0.6974
## F-statistic: 1152 on 2 and 997 DF, p-value: < 2.2e-16#Komparasi Model
nilai_AIC <- rbind(AIC(lin.mod),
AIC(pol.mod),
AIC(step.mod))
nama_model <- c("Linear","Poly (ordo=2)","Tangga (breaks=3)")
data.frame(nama_model,nilai_AIC) #AIS, MRSE, MSE terkecil yang terbaik## nama_model nilai_AIC
## 1 Linear 5711.836
## 2 Poly (ordo=2) 2856.470
## 3 Tangga (breaks=3) 6109.609MSE=function(pred,actual){
mean((pred-actual)^2)
}MSE(predict(lin.mod), y)## [1] 17.60106MSE(predict(pol.mod), y)## [1] 1.010649MSE(predict(step.mod), y)## [1] 26.14693#Contoh data TRICEPS Data yang digunakan untuk ilustrasi berasal dari studi antropometri terhadap 892 perempuan di bawah 50 tahun di tiga desa Gambia di Afrika Barat. Data terdiri dari 3 Kolom yaitu Age, Intriceps dan tricepts. Berikut adalah penjelasannya pada masing-masing kolom:
age : umur responden(x) Intriceps : logaritma dari ketebalan lipatan kulit triceps triceps: ketebalan lipatan kulit triceps (y) Lipatan kulit trisep diperlukan untuk menghitung lingkar otot lengan atas. Ketebalannya memberikan informasi tentang cadangan lemak tubuh, sedangkan massa otot yang dihitung memberikan informasi tentang cadangan protein
data("triceps", package="MultiKink")Jika kita gambarkan dalam bentuk scatterplot
ggplot(triceps,aes(x=age, y=triceps)) +
geom_point(alpha=0.55, color="black") +
theme_bw() 
Berdasarkan pola hubungan yang terlihat pada scatterplot, kita akan
mencoba untuk mencari model yang bisa merepresentasikan pola hubungan
tersebut dengan baik.
#Regresi Linear
mod_linear = lm(triceps~age,data=triceps)
summary(mod_linear)##
## Call:
## lm(formula = triceps ~ age, data = triceps)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.9512 -2.3965 -0.5154 1.5822 25.1233
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.19717 0.21244 29.17 <2e-16 ***
## age 0.21584 0.01014 21.28 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.007 on 890 degrees of freedom
## Multiple R-squared: 0.3372, Adjusted R-squared: 0.3365
## F-statistic: 452.8 on 1 and 890 DF, p-value: < 2.2e-16ringkasan_liniar <- summary(mod_linear)
ringkasan_liniar$r.squared## [1] 0.3372092AIC(mod_linear)## [1] 5011.515predict(mod_linear) #y duga## 1 2 3 4 5 6 7 8
## 8.798074 8.336171 8.364231 8.677202 8.381498 8.759222 8.552014 8.362072
## 9 10 11 12 13 14 15 16
## 8.575756 8.355597 8.649143 8.653460 8.573598 8.353439 8.346963 8.772173
## 17 18 19 20 21 22 23 24
## 8.627558 8.372864 8.353439 8.806708 8.441934 8.355597 8.573598 8.754906
## 25 26 27 28 29 30 31 32
## 8.580073 8.441934 8.657776 8.716054 8.703103 8.364231 8.340488 8.495894
## 33 34 35 36 37 38 39 40
## 8.817500 8.465677 8.478627 8.463518 8.830450 8.782965 8.493736 8.700945
## 41 42 43 44 45 46 47 48
## 8.422508 8.485103 8.638351 8.435459 8.703103 8.653460 8.450568 8.614608
## 49 50 51 52 53 54 55 56
## 8.785123 8.666410 8.383657 8.459201 8.666410 8.657776 8.670727 8.763539
## 57 58 59 60 61 62 63 64
## 8.644826 8.830450 8.495894 8.463518 8.467835 8.651301 8.605974 8.782965
## 65 66 67 68 69 70 71 72
## 8.599499 8.504528 8.461360 8.731163 8.815341 8.413875 8.316745 8.787282
## 73 74 75 76 77 78 79 80
## 8.651301 8.683678 8.789440 8.336171 8.754906 8.828292 8.834767 8.694469
## 81 82 83 84 85 86 87 88
## 8.623242 8.642667 8.547697 8.474310 8.452726 8.631875 14.077578 6.840384
## 89 90 91 92 93 94 95 96
## 13.043693 7.116662 11.457252 10.406100 14.986275 10.026217 10.065069 10.097445
## 97 98 99 100 101 102 103 104
## 9.352789 7.876427 10.108237 7.382148 11.560856 11.850085 11.191766 15.633802
## 105 106 107 108 109 110 111 112
## 7.766347 10.123346 7.013057 10.932755 12.139314 6.682819 6.531729 9.149897
## 113 114 115 116 117 118 119 120
## 7.133929 14.915047 7.371356 7.248326 8.959956 12.860228 14.120747 8.182923
## 121 122 123 124 125 126 127 128
## 6.421649 6.892186 7.403732 12.048660 7.054067 11.297528 8.867143 8.131121
## 129 130 131 132 133 134 135 136
## 10.414734 17.151174 7.677852 10.552872 8.107378 9.106728 13.037218 10.395308
## 137 138 139 140 141 142 143 144
## 10.473011 6.501511 11.161548 11.068736 6.570581 8.012408 12.609850 13.943756
## 145 146 147 148 149 150 151 152
## 6.365530 6.365530 6.510145 7.669218 11.146439 7.496544 7.129612 8.267102
## 153 154 155 156 157 158 159 160
## 6.678502 10.453585 10.978082 6.454026 11.105429 12.579632 7.844051 7.310920
## 161 162 163 164 165 166 167 168
## 9.283719 13.691221 7.295811 9.303145 7.073493 9.307462 9.244868 6.777789
## 169 170 171 172 173 174 175 176
## 7.969239 17.367016 14.122906 8.992332 7.082127 7.338979 9.020392 7.798724
## 177 178 179 180 181 182 183 184
## 6.833908 9.326888 8.858510 7.721020 13.995559 17.367016 12.109096 7.772823
## 185 186 187 188 189 190 191 192
## 13.693379 14.241619 9.020392 9.119679 9.132630 9.430492 6.404382 13.330764
## 193 194 195 196 197 198 199 200
## 9.093778 6.941829 9.074352 8.148388 8.938371 8.269260 9.708929 9.197382
## 201 202 203 204 205 206 207 208
## 7.302286 6.954780 9.255660 8.247676 6.546838 12.773890 7.686486 6.831750
## 209 210 211 212 213 214 215 216
## 7.246167 9.272927 6.963414 6.516620 9.698136 6.590006 9.756414 9.596691
## 217 218 219 220 221 222 223 224
## 9.683028 13.546606 6.980681 9.706770 15.849645 14.409976 9.639859 12.270978
## 225 226 227 228 229 230 231 232
## 14.772591 8.118170 7.453376 6.339629 7.347613 9.836276 7.733971 13.848786
## 233 234 235 236 237 238 239 240
## 6.715195 9.434809 9.432650 12.914188 6.766997 15.849645 6.421649 14.483362
## 241 242 243 244 245 246 247 248
## 8.157022 6.497194 15.849645 10.278753 9.654968 13.652369 11.539272 10.600358
## 249 250 251 252 253 254 255 256
## 11.776699 8.085794 10.090970 9.542730 7.936863 7.278544 9.572948 9.156372
## 257 258 259 260 261 262 263 264
## 9.566473 8.970748 6.466976 11.373073 14.552432 7.995140 7.060543 7.528921
## 265 266 267 268 269 270 271 272
## 9.182273 6.309411 10.026217 10.729863 10.276594 7.166305 13.853103 9.037659
## 273 274 275 276 277 278 279 280
## 7.205157 9.777998 12.074561 7.867793 12.473870 14.768274 14.125064 10.738497
## 281 282 283 284 285 286 287 288
## 8.893044 14.770433 14.768274 14.768274 9.691661 10.280911 12.184641 13.907063
## 289 290 291 292 293 294 295 296
## 6.387115 9.223283 13.963182 8.888728 12.398325 9.711087 13.395516 7.114503
## 297 298 299 300 301 302 303 304
## 13.786191 14.392709 7.300128 15.202118 7.207316 14.321480 15.417960 9.175798
## 305 306 307 308 309 310 311 312
## 7.153355 9.639859 6.797215 9.182273 15.847486 8.912470 11.081686 6.943988
## 313 314 315 316 317 318 319 320
## 7.205157 15.199959 16.065487 16.274854 6.413016 16.495013 15.851803 15.849645
## 321 322 323 324 325 326 327 328
## 6.855492 12.180324 6.859809 6.803690 7.518129 14.701363 9.171481 6.883552
## 329 330 331 332 333 334 335 336
## 12.031393 6.341788 9.708929 10.529130 7.151197 9.965781 16.935332 16.931015
## 337 338 339 340 341 342 343 344
## 16.926698 15.204276 14.511422 6.572739 13.958865 7.129612 6.486402 9.331205
## 345 346 347 348 349 350 351 352
## 8.191557 6.438917 7.218108 7.390782 12.402642 7.712387 7.824625 7.077810
## 353 354 355 356 357 358 359 360
## 6.898661 15.847486 15.847486 7.518129 9.346314 9.799583 12.180324 8.923263
## 361 362 363 364 365 366 367 368
## 15.417960 16.497172 10.900379 8.286528 9.393799 10.166514 6.479927 9.136946
## 369 370 371 372 373 374 375 376
## 11.204717 6.788581 13.697696 13.475379 11.955848 16.065487 17.142540 9.534096
## 377 378 379 380 381 382 383 384
## 13.978291 11.964481 13.598409 12.173849 6.760522 6.823116 6.883552 6.270560
## 385 386 387 388 389 390 391 392
## 7.187890 7.321712 14.552432 15.208593 13.296229 12.098304 12.070244 7.503020
## 393 394 395 396 397 398 399 400
## 6.462659 9.911820 6.633175 9.510354 9.415383 7.295811 6.691452 11.355806
## 401 402 403 404 405 406 407 408
## 8.157022 6.831750 15.417960 6.704403 7.138246 6.413016 14.856769 10.460060
## 409 410 411 412 413 414 415 416
## 6.721670 7.807357 11.770223 12.262344 9.713246 11.563015 11.595391 11.647193
## 417 418 419 420 421 422 423 424
## 8.264943 9.244868 9.838434 9.335521 7.556980 13.261694 13.261694 7.779298
## 425 426 427 428 429 430 431 432
## 7.921754 6.372006 9.283719 7.015216 6.417332 6.725987 8.163497 7.090761
## 433 434 435 436 437 438 439 440
## 9.262135 9.631225 8.847718 7.921754 6.902978 13.661003 14.125064 10.993191
## 441 442 443 444 445 446 447 448
## 13.477537 7.608782 13.557398 7.153355 6.555472 13.477537 6.946146 7.418841
## 449 450 451 452 453 454 455 456
## 7.684327 13.473220 7.932546 9.713246 13.261694 10.665111 12.219176 8.146230
## 457 458 459 460 461 462 463 464
## 7.092919 8.297319 7.675694 6.741096 9.430492 8.023200 13.693379 6.626700
## 465 466 467 468 469 470 471 472
## 12.232126 6.477768 12.542939 13.475379 11.431351 12.396166 14.086212 6.857651
## 473 474 475 476 477 478 479 480
## 9.883761 16.719489 8.893044 6.926720 7.997299 6.717353 7.572089 7.779298
## 481 482 483 484 485 486 487 488
## 9.549205 9.115362 9.976573 7.000107 12.314146 6.972047 6.993632 6.393590
## 489 490 491 492 493 494 495 496
## 14.768274 9.035500 7.233217 13.641577 7.060543 14.804968 16.928857 7.440425
## 497 498 499 500 501 502 503 504
## 11.398975 8.100903 7.852684 10.902537 8.133279 6.499353 12.044343 8.299478
## 505 506 507 508 509 510 511 512
## 6.648284 15.847486 10.801091 6.758363 7.334663 7.513812 11.966640 6.454026
## 513 514 515 516 517 518 519 520
## 6.400065 12.609850 10.039167 6.931037 7.967081 6.410857 11.893253 9.581582
## 521 522 523 524 525 526 527 528
## 8.154864 15.631643 13.924330 10.293861 6.922404 6.525254 9.044134 13.477537
## 529 530 531 532 533 534 535 536
## 7.272068 15.849645 7.341138 12.178165 16.067645 11.496103 12.594741 6.833908
## 537 538 539 540 541 542 543 544
## 6.898661 15.199959 6.479927 14.984116 7.397257 7.395098 13.259536 8.910312
## 545 546 547 548 549 550 551 552
## 7.032483 10.062910 7.423158 11.720580 16.065487 12.583949 12.374582 6.516620
## 553 554 555 556 557 558 559 560
## 9.398116 14.986275 10.065069 7.334663 11.003983 11.601867 15.202118 10.496753
## 561 562 563 564 565 566 567 568
## 6.890027 8.979382 7.136088 9.145580 7.287177 10.688853 7.882902 8.215300
## 569 570 571 572 573 574 575 576
## 11.476678 7.198682 15.417960 6.786423 6.404382 6.989315 10.116871 10.179465
## 577 578 579 580 581 582 583 584
## 8.003774 14.986275 6.443234 7.071335 14.986275 11.155073 6.853334 10.291703
## 585 586 587 588 589 590 591 592
## 6.419491 6.417332 8.087953 6.432441 6.384956 15.415801 6.313728 14.094846
## 593 594 595 596 597 598 599 600
## 14.584808 6.570581 6.512303 9.970098 9.037659 7.710228 6.441075 12.247235
## 601 602 603 604 605 606 607 608
## 7.552663 10.062910 7.589357 7.630367 7.157672 7.004424 6.445392 11.964481
## 609 610 611 612 613 614 615 616
## 6.372006 14.213559 8.046942 6.982840 6.333154 7.639000 9.903187 10.375882
## 617 618 619 620 621 622 623 624
## 6.415174 6.413016 6.410857 16.067645 9.417542 16.713014 7.343296 8.210983
## 625 626 627 628 629 630 631 632
## 9.983049 12.024917 7.941180 7.615258 9.262135 10.714754 7.533238 6.754047
## 633 634 635 636 637 638 639 640
## 6.374164 7.274227 8.994490 13.015634 9.139105 11.664461 9.616117 12.603375
## 641 642 643 644 645 646 647 648
## 6.721670 12.055135 6.808007 9.141263 7.520287 6.766997 6.529570 7.585040
## 649 650 651 652 653 654 655 656
## 6.775631 6.782106 7.345455 7.764189 6.792898 7.794407 11.273786 6.525254
## 657 658 659 660 661 662 663 664
## 6.553313 15.204276 6.546838 7.187890 6.566264 11.405450 8.139755 7.507337
## 665 666 667 668 669 670 671 672
## 16.065487 7.960605 8.232567 6.529570 12.719930 7.326029 9.829800 9.311779
## 673 674 675 676 677 678 679 680
## 9.898870 10.447110 15.130889 6.732462 10.021900 11.970957 9.413225 11.299687
## 681 682 683 684 685 686 687 688
## 8.234725 7.185731 10.887428 9.719721 6.905136 9.115362 8.929738 7.537554
## 689 690 691 692 693 694 695 696
## 7.228900 13.332923 14.125064 14.554590 11.103270 9.199541 9.350630 6.326679
## 697 698 699 700 701 702 703 704
## 7.546188 13.725756 11.206875 10.701804 7.658426 7.865635 7.187890 9.754256
## 705 706 707 708 709 710 711 712
## 7.526762 6.348263 17.360541 12.186799 8.940530 10.280911 13.475379 7.382148
## 713 714 715 716 717 718 719 720
## 15.847486 6.810166 9.093778 8.159180 7.064860 10.436317 11.813392 9.184432
## 721 722 723 724 725 726 727 728
## 8.174289 7.444742 11.401133 7.477119 13.693379 15.417960 7.496544 13.907063
## 729 730 731 732 733 734 735 736
## 7.142563 8.888728 14.455302 7.392940 9.935563 8.299478 7.768506 14.915047
## 737 738 739 740 741 742 743 744
## 6.676343 14.986275 10.507545 7.923912 16.281329 8.103061 14.543798 14.472570
## 745 746 747 748 749 750 751 752
## 7.522445 6.611591 8.871460 6.527412 8.992332 16.065487 7.332504 15.204276
## 753 754 755 756 757 758 759 760
## 9.816850 13.924330 7.202999 6.333154 12.825692 13.689062 7.466326 7.669218
## 761 762 763 764 765 766 767 768
## 7.067018 14.770433 7.330346 6.669868 7.423158 6.590006 11.314796 8.113854
## 769 770 771 772 773 774 775 776
## 11.066577 12.063769 15.202118 10.673744 16.706538 8.005932 9.801741 8.882252
## 777 778 779 780 781 782 783 784
## 7.224583 16.713014 7.835417 9.864335 6.641809 14.768274 12.137156 14.697046
## 785 786 787 788 789 790 791 792
## 6.993632 7.967081 7.155513 9.937722 7.524604 9.348472 11.621292 7.518129
## 793 794 795 796 797 798 799 800
## 6.922404 8.157022 10.496753 14.554590 6.507986 7.582881 7.561297 17.144699
## 801 802 803 804 805 806 807 808
## 8.295161 11.925630 9.497403 12.035709 11.491787 9.419700 11.707629 6.434600
## 809 810 811 812 813 814 815 816
## 10.401783 7.701595 9.855702 9.424017 7.362722 7.308762 7.483594 10.239901
## 817 818 819 820 821 822 823 824
## 7.030325 6.486402 13.259536 11.010458 10.578773 7.425316 7.464168 13.697696
## 825 826 827 828 829 830 831 832
## 7.440425 7.088602 9.989524 15.849645 9.387324 11.170182 6.853334 8.979382
## 833 834 835 836 837 838 839 840
## 7.505178 6.533887 12.454444 14.986275 12.050819 12.374582 6.372006 15.202118
## 841 842 843 844 845 846 847 848
## 13.186150 17.360541 14.498471 9.048451 9.721879 7.328187 7.541871 7.967081
## 849 850 851 852 853 854 855 856
## 9.527621 12.394008 6.680660 9.264293 10.934914 9.212491 7.787932 9.521146
## 857 858 859 860 861 862 863 864
## 8.152705 6.253292 8.072843 11.532797 9.657127 6.898661 11.316954 9.370056
## 865 866 867 868 869 870 871 872
## 14.261045 14.986275 7.852684 6.510145 6.393590 13.963182 6.449709 7.846209
## 873 874 875 876 877 878 879 880
## 8.947005 12.635751 15.199959 7.995140 7.459851 7.077810 8.273577 7.421000
## 881 882 883 884 885 886 887 888
## 7.764189 7.906645 6.516620 10.147089 6.905136 8.981540 15.204276 12.057294
## 889 890 891 892
## 7.904486 7.921754 9.354947 12.702662tabel_data <- rbind(data.frame("y_aktual"=triceps$triceps,
"y_pred"=predict(mod_linear),
"residual"=residuals(mod_linear)))
tabel_data## y_aktual y_pred residual
## 1 3.4 8.798074 -5.398073843
## 2 4.0 8.336171 -4.336171174
## 3 4.2 8.364231 -4.164230898
## 4 4.2 8.677202 -4.477202306
## 5 4.4 8.381498 -3.981497986
## 6 4.4 8.759222 -4.359222149
## 7 4.8 8.552014 -3.752013362
## 8 4.8 8.362072 -3.562072044
## 9 4.8 8.575756 -3.775756155
## 10 5.0 8.355597 -3.355597021
## 11 5.0 8.649143 -3.649142581
## 12 5.0 8.653460 -3.653459528
## 13 5.2 8.573598 -3.373598063
## 14 5.2 8.353439 -3.153438738
## 15 5.2 8.346963 -3.146963525
## 16 5.2 8.772173 -3.572173068
## 17 5.2 8.627558 -3.427558658
## 18 5.2 8.372864 -3.172864585
## 19 5.4 8.353439 -2.953438452
## 20 5.4 8.806708 -3.406707529
## 21 5.4 8.441934 -3.041933794
## 22 5.4 8.355597 -2.955596925
## 23 5.4 8.573598 -3.173597777
## 24 5.4 8.754906 -3.354905408
## 25 5.4 8.580073 -3.180072991
## 26 5.4 8.441934 -3.041933794
## 27 5.5 8.657776 -3.157776268
## 28 5.6 8.716054 -3.116053905
## 29 5.6 8.703103 -3.103103271
## 30 5.6 8.364231 -2.764230803
## 31 5.6 8.340488 -2.740488216
## 32 5.6 8.495894 -2.895894580
## 33 5.8 8.817500 -3.017499594
## 34 5.8 8.465677 -2.665676493
## 35 5.8 8.478627 -2.678626920
## 36 5.8 8.463518 -2.663518019
## 37 5.8 8.830450 -3.030450022
## 38 6.0 8.782965 -2.782964831
## 39 6.0 8.493736 -2.493736217
## 40 6.0 8.700945 -2.700944909
## 41 6.0 8.422508 -2.422508249
## 42 6.0 8.485103 -2.485102530
## 43 6.0 8.638351 -2.638350627
## 44 6.0 8.435459 -2.435458676
## 45 6.2 8.703103 -2.503103367
## 46 6.2 8.653460 -2.453459719
## 47 6.2 8.450568 -2.250567768
## 48 6.2 8.614608 -2.414608025
## 49 6.4 8.785123 -2.385123209
## 50 6.4 8.666410 -2.266409860
## 51 6.4 8.383657 -1.983656459
## 52 6.6 8.459201 -1.859201359
## 53 6.6 8.666410 -2.066410051
## 54 6.6 8.657776 -2.057776364
## 55 6.6 8.670727 -2.070726997
## 56 6.8 8.763539 -1.963539000
## 57 6.8 8.644826 -1.844825650
## 58 6.8 8.830450 -2.030450022
## 59 7.0 8.495894 -1.495894484
## 60 7.0 8.463518 -1.463518210
## 61 7.0 8.467835 -1.467835156
## 62 7.0 8.651301 -1.651301055
## 63 7.0 8.605974 -1.605974147
## 64 7.0 8.782965 -1.782964831
## 65 7.0 8.599499 -1.599498933
## 66 7.0 8.504528 -1.504528171
## 67 7.2 8.461360 -1.261359928
## 68 7.2 8.731163 -1.531162901
## 69 7.4 8.815341 -1.415341216
## 70 7.4 8.413875 -1.013874466
## 71 8.0 8.316745 -0.316745327
## 72 8.0 8.787282 -0.787281778
## 73 8.4 8.651301 -0.251301436
## 74 8.6 8.683678 -0.083677153
## 75 8.8 8.789440 0.010559940
## 76 8.8 8.336171 0.463829017
## 77 9.0 8.754906 0.245094497
## 78 9.0 8.828292 0.171708261
## 79 9.8 8.834767 0.965233032
## 80 9.8 8.694469 1.105530702
## 81 10.0 8.623242 1.376758479
## 82 10.2 8.642667 1.557332442
## 83 10.2 8.547697 1.652302997
## 84 13.0 8.474310 4.525689630
## 85 14.2 8.452726 5.747273759
## 86 16.0 8.631875 7.368124792
## 87 9.4 14.077578 -4.677578494
## 88 8.2 6.840384 1.359616282
## 89 21.2 13.043693 8.156307429
## 90 9.6 7.116662 2.483338564
## 91 10.2 11.457252 -1.257252372
## 92 13.2 10.406100 2.793900193
## 93 13.6 14.986275 -1.386274771
## 94 12.2 10.026217 2.173782828
## 95 6.8 10.065069 -3.265068484
## 96 6.4 10.097445 -3.697444854
## 97 14.0 9.352789 4.647211215
## 98 6.0 7.876427 -1.876426986
## 99 11.2 10.108237 1.091762494
## 100 7.4 7.382148 0.017852251
## 101 8.2 11.560856 -3.360856615
## 102 13.4 11.850085 1.549914374
## 103 17.6 11.191766 6.408234639
## 104 15.6 15.633802 -0.033801906
## 105 4.2 7.766347 -3.566347514
## 106 14.0 10.123346 3.876653784
## 107 8.2 7.013057 1.186942389
## 108 8.2 10.932755 -2.732755326
## 109 21.8 12.139314 9.660685173
## 110 7.8 6.682819 1.117181603
## 111 6.0 6.531729 -0.531728912
## 112 9.2 9.149897 0.050102770
## 113 6.4 7.133929 -0.733929096
## 114 17.4 14.915047 2.484952846
## 115 8.6 7.371356 1.228644594
## 116 5.8 7.248326 -1.448325404
## 117 8.0 8.959956 -0.959955722
## 118 10.0 12.860228 -2.860227641
## 119 13.6 14.120747 -0.520746372
## 120 7.6 8.182923 -0.582923172
## 121 8.2 6.421649 1.778350508
## 122 8.0 6.892186 1.107814299
## 123 9.0 7.403732 1.596267836
## 124 23.4 12.048660 11.351339370
## 125 6.4 7.054067 -0.654067389
## 126 9.0 11.297528 -2.297528459
## 127 5.2 8.867143 -3.667143624
## 128 5.8 8.131121 -2.331120765
## 129 8.2 10.414734 -2.214733700
## 130 4.2 17.151174 -12.951174136
## 131 4.2 7.677852 -3.477852172
## 132 22.6 10.552872 12.047127882
## 133 6.8 8.107378 -1.307378177
## 134 9.4 9.106728 0.293271219
## 135 8.0 13.037218 -5.037218326
## 136 11.0 10.395308 0.604692338
## 137 11.8 10.473011 1.326989552
## 138 8.4 6.501511 1.898488636
## 139 15.8 11.161548 4.638452249
## 140 17.4 11.068736 6.331263966
## 141 6.0 6.570581 -0.570580555
## 142 4.4 8.012408 -3.612407511
## 143 12.6 12.609850 -0.009849722
## 144 10.6 13.943756 -3.343755687
## 145 9.2 6.365530 2.834469525
## 146 7.8 6.365530 1.434469906
## 147 6.0 6.510145 -0.510144695
## 148 7.2 7.669218 -0.469218485
## 149 16.2 11.146439 5.053561722
## 150 5.2 7.496544 -2.296544541
## 151 6.6 7.129612 -0.529612443
## 152 6.0 8.267102 -2.267101679
## 153 6.2 6.678502 -0.478501935
## 154 13.6 10.453585 3.146415590
## 155 8.0 10.978082 -2.978081837
## 156 9.0 6.454026 2.545974322
## 157 11.2 11.105429 0.094570936
## 158 10.2 12.579632 -2.379632493
## 159 6.2 7.844051 -1.644050799
## 160 5.8 7.310920 -1.510919685
## 161 8.4 9.283719 -0.883719671
## 162 14.6 13.691221 0.908779500
## 163 6.6 7.295811 -0.695811071
## 164 9.6 9.303145 0.296855245
## 165 5.2 7.073493 -1.873493471
## 166 10.4 9.307462 1.092537741
## 167 7.4 9.244868 -1.844867500
## 168 10.2 6.777789 3.422210563
## 169 6.8 7.969239 -1.169238981
## 170 24.8 17.367016 7.432982913
## 171 19.0 14.122906 4.877094362
## 172 3.6 8.992332 -5.392332092
## 173 8.2 7.082127 1.117872842
## 174 7.0 7.338979 -0.338979410
## 175 6.2 9.020392 -2.820391721
## 176 4.6 7.798724 -3.198723796
## 177 9.4 6.833908 2.566091356
## 178 6.6 9.326888 -2.726887819
## 179 5.6 8.858510 -3.258509842
## 180 6.4 7.721020 -1.321020320
## 181 21.6 13.995559 7.604441780
## 182 15.2 17.367016 -2.167016514
## 183 12.4 12.109096 0.290903767
## 184 5.8 7.772823 -1.972822449
## 185 13.6 13.693379 -0.093378561
## 186 19.4 14.241619 5.158380837
## 187 7.0 9.020392 -2.020391530
## 188 6.8 9.119679 -2.319678842
## 189 7.0 9.132630 -2.132629666
## 190 10.4 9.430492 0.969507652
## 191 7.0 6.404382 0.595618086
## 192 14.2 13.330764 0.869236128
## 193 8.8 9.093778 -0.293777781
## 194 9.2 6.941829 2.258170357
## 195 6.4 9.074352 -2.674352029
## 196 6.8 8.148388 -1.348388138
## 197 5.0 8.938371 -3.938371402
## 198 7.2 8.269260 -1.069260342
## 199 7.6 9.708929 -2.108928928
## 200 8.2 9.197382 -0.997382405
## 201 8.6 7.302286 1.297714193
## 202 5.4 6.954780 -1.554779887
## 203 6.8 9.255660 -2.455659565
## 204 5.0 8.247676 -3.247675832
## 205 8.4 6.546838 1.853161729
## 206 24.8 12.773890 12.026108876
## 207 5.4 7.686486 -2.286485573
## 208 6.8 6.831750 -0.031749650
## 209 8.0 7.246167 0.753832776
## 210 6.2 9.272927 -3.072927320
## 211 6.4 6.963414 -0.563413574
## 212 7.0 6.516620 0.483380040
## 213 6.6 9.698136 -3.098136562
## 214 7.2 6.590006 0.609993433
## 215 9.0 9.756414 -0.756414008
## 216 7.0 9.596691 -2.596690697
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## 667 5.2 8.232567 -3.032567122
## 668 9.8 6.529570 3.270429700
## 669 14.0 12.719930 1.280070234
## 670 8.0 7.326029 0.673971121
## 671 16.8 9.829800 6.970198787
## 672 9.2 9.311779 -0.111779014
## 673 8.0 9.898870 -1.898869945
## 674 17.6 10.447110 7.152890598
## 675 13.6 15.130889 -1.530888769
## 676 6.8 6.732462 0.067537852
## 677 9.0 10.021900 -1.021900035
## 678 11.0 11.970957 -0.970956861
## 679 9.0 9.413225 -0.413224593
## 680 14.0 11.299687 2.700313068
## 681 6.0 8.234725 -2.234725198
## 682 9.6 7.185731 2.414269069
## 683 9.2 10.887428 -1.687428213
## 684 7.2 9.719721 -2.519720978
## 685 11.6 6.905136 4.694864150
## 686 6.4 9.115362 -2.715362197
## 687 5.6 8.929738 -3.329737810
## 688 4.0 7.537554 -3.537554414
## 689 5.8 7.228900 -1.428899660
## 690 20.4 13.332923 7.067077053
## 691 19.8 14.125064 5.674935537
## 692 14.0 14.554590 -0.554590395
## 693 14.6 11.103270 3.496729981
## 694 10.2 9.199541 1.000459121
## 695 12.0 9.350630 2.649369688
## 696 7.0 6.326679 0.673321332
## 697 6.2 7.546188 -1.346188292
## 698 13.6 13.725756 -0.125755247
## 699 18.0 11.206875 6.793125357
## 700 11.0 10.701804 0.298196144
## 701 6.2 7.658426 -1.458426325
## 702 5.0 7.865635 -2.865634826
## 703 10.4 7.187890 3.212109833
## 704 9.2 9.754256 -0.554255725
## 705 7.0 7.526762 -0.526762254
## 706 5.6 6.348263 -0.748262993
## 707 15.2 17.360541 -2.160541507
## 708 14.4 12.186799 2.213200379
## 709 6.0 8.940530 -2.940529875
## 710 18.0 10.280911 7.719088946
## 711 17.0 13.475379 3.524621497
## 712 7.5 7.382148 0.117852156
## 713 12.8 15.847486 -3.047485591
## 714 7.0 6.810166 0.189834428
## 715 5.4 9.093778 -3.693777876
## 716 4.6 8.159180 -3.559180585
## 717 9.2 7.064860 2.135140216
## 718 12.0 10.436317 1.563682582
## 719 19.2 11.813392 7.386608740
## 720 11.0 9.184432 1.815568213
## 721 10.2 8.174289 2.025710419
## 722 6.0 7.444742 -1.444742229
## 723 9.0 11.401133 -2.401133113
## 724 7.8 7.477119 0.322881688
## 725 13.8 13.693379 0.106621248
## 726 8.2 15.417960 -7.217960100
## 727 8.6 7.496544 1.103456031
## 728 11.2 13.907063 -2.707063450
## 729 8.0 7.142563 0.857437122
## 730 13.0 8.888728 4.111272247
## 731 18.6 14.455302 4.144698106
## 732 8.2 7.392940 0.807059805
## 733 17.0 9.935563 7.064436834
## 734 8.2 8.299478 -0.099478144
## 735 6.4 7.768506 -1.368505701
## 736 12.4 14.915047 -2.515047154
## 737 6.6 6.676343 -0.076343418
## 738 15.0 14.986275 0.013724848
## 739 9.0 10.507545 -1.507545386
## 740 5.4 7.923912 -2.523912168
## 741 7.0 16.281329 -9.281329423
## 742 6.8 8.103061 -1.303061231
## 743 14.5 14.543798 -0.043797618
## 744 8.8 14.472570 -5.672569870
## 745 7.0 7.522445 -0.522445411
## 746 6.2 6.611591 -0.411590784
## 747 10.6 8.871460 1.728540002
## 748 6.8 6.527412 0.272588122
## 749 6.8 8.992332 -2.192331806
## 750 16.0 16.065487 -0.065487045
## 751 7.2 7.332504 -0.132504387
## 752 7.6 15.204276 -7.604275688
## 753 11.6 9.816850 1.783150359
## 754 11.0 13.924330 -2.924330222
## 755 8.0 7.202999 0.797001313
## 756 5.4 6.333154 -0.933153838
## 757 11.6 12.825692 -1.225692101
## 758 11.2 13.689062 -2.489062187
## 759 7.4 7.466326 -0.066326351
## 760 6.4 7.669218 -1.269218199
## 761 7.0 7.067018 -0.067018066
## 762 4.2 14.770433 -10.570432964
## 763 8.8 7.330346 1.469654468
## 764 6.2 6.669868 -0.469868248
## 765 6.6 7.423158 -0.823158004
## 766 8.4 6.590006 1.809993243
## 767 4.0 11.314796 -7.314795833
## 768 7.0 8.113854 -1.113853582
## 769 8.0 11.066577 -3.066577180
## 770 20.0 12.063769 7.936230850
## 771 19.0 15.202118 3.797882469
## 772 5.4 10.673744 -5.273744021
## 773 24.6 16.706538 7.893462032
## 774 5.0 8.005932 -3.005932392
## 775 11.0 9.801741 1.198258878
## 776 5.0 8.882252 -3.882252334
## 777 8.6 7.224583 1.375417375
## 778 12.3 16.713014 -4.413013990
## 779 6.0 7.835417 -1.835416922
## 780 10.6 9.864335 0.735665184
## 781 7.0 6.641809 0.358191477
## 782 13.6 14.768274 -1.168273507
## 783 7.6 12.137156 -4.537155686
## 784 13.6 14.697046 -1.097045951
## 785 7.8 6.993632 0.806368566
## 786 6.8 7.967081 -1.167080508
## 787 5.4 7.155513 -1.755513313
## 788 10.0 9.937722 0.062278361
## 789 5.6 7.524604 -1.924603979
## 790 5.6 9.348472 -3.748472140
## 791 28.0 11.621292 16.378707973
## 792 10.0 7.518129 2.481871433
## 793 9.4 6.922404 2.477596014
## 794 5.2 8.157022 -2.957022207
## 795 14.0 10.496753 3.503246568
## 796 9.8 14.554590 -4.754590204
## 797 6.4 6.507986 -0.107986178
## 798 7.4 7.582881 -0.182881227
## 799 6.0 7.561297 -1.561297105
## 800 5.0 17.144699 -12.144698937
## 801 8.4 8.295161 0.104838406
## 802 17.4 11.925630 5.474369460
## 803 9.4 9.497403 -0.097403576
## 804 9.2 12.035709 -2.835709600
## 805 17.8 11.491787 6.308212308
## 806 7.0 9.419700 -2.419700013
## 807 11.0 11.707629 -0.707629307
## 808 6.4 6.434600 -0.034599762
## 809 11.0 10.401783 0.598217330
## 810 7.0 7.701595 -0.701594569
## 811 10.2 9.855702 0.344298093
## 812 9.2 9.424017 -0.224016944
## 813 6.2 7.362722 -1.162722291
## 814 8.0 7.308762 0.691238494
## 815 5.8 7.483594 -1.683593629
## 816 24.0 10.239901 13.760099114
## 817 8.0 7.030325 0.969675206
## 818 7.8 6.486402 1.313598161
## 819 20.8 13.259536 7.540463113
## 820 8.6 11.010458 -2.410457730
## 821 11.6 10.578773 1.021227027
## 822 6.6 7.425316 -0.825316477
## 823 8.6 7.464168 1.135832409
## 824 12.0 13.697696 -1.697695889
## 825 5.8 7.440425 -1.640425195
## 826 7.8 7.088602 0.711397907
## 827 10.4 9.989524 0.410475858
## 828 14.2 15.849645 -1.649644857
## 829 5.0 9.387324 -4.387323532
## 830 7.8 11.170182 -3.370181643
## 831 7.0 6.853334 0.146665942
## 832 7.0 8.979382 -1.979381569
## 833 8.0 7.505178 0.494821963
## 834 6.8 6.533887 0.266112857
## 835 19.6 12.454444 7.145556642
## 836 18.0 14.986275 3.013724848
## 837 14.2 12.050819 2.149181087
## 838 15.2 12.374582 2.825417519
## 839 5.0 6.372006 -1.372005563
## 840 17.6 15.202118 2.397882851
## 841 15.2 13.186150 2.013850127
## 842 24.8 17.360541 7.439457921
## 843 8.8 14.498471 -5.698470725
## 844 6.0 9.048451 -3.048451064
## 845 8.0 9.721879 -1.721879260
## 846 6.0 7.328187 -1.328187250
## 847 9.0 7.541871 1.458128742
## 848 5.6 7.967081 -2.367080794
## 849 9.4 9.527621 -0.127621583
## 850 7.0 12.394008 -5.394007725
## 851 8.0 6.680660 1.319339834
## 852 7.4 9.264293 -1.864293347
## 853 16.4 10.934914 5.465086010
## 854 12.0 9.212491 2.787508679
## 855 5.8 7.787932 -1.987931350
## 856 14.8 9.521146 5.278854408
## 857 4.0 8.152705 -4.152705276
## 858 8.0 6.253292 1.746707748
## 859 4.4 8.072843 -3.672843319
## 860 29.6 11.532797 18.067203697
## 861 11.2 9.657127 1.542873098
## 862 11.0 6.898661 4.101339034
## 863 4.2 11.316954 -7.116954497
## 864 6.8 9.370056 -2.570055968
## 865 13.8 14.261045 -0.461044438
## 866 14.0 14.986275 -0.986275152
## 867 5.2 7.852684 -2.652684486
## 868 5.4 6.510145 -1.110144599
## 869 7.4 6.393590 1.006410290
## 870 14.4 13.963182 0.436817703
## 871 8.2 6.449709 1.750291000
## 872 6.2 7.846209 -1.646209169
## 873 7.0 8.947005 -1.947005089
## 874 22.6 12.635751 9.964249011
## 875 12.8 15.199959 -2.399958455
## 876 7.7 7.995140 -0.295140423
## 877 6.6 7.459851 -0.859851225
## 878 7.0 7.077810 -0.077810124
## 879 5.2 8.273577 -3.073577083
## 880 5.8 7.421000 -1.620999348
## 881 7.0 7.764189 -0.764188953
## 882 5.9 7.906645 -2.006644795
## 883 9.8 6.516620 3.283380231
## 884 7.0 10.147089 -3.147088598
## 885 8.4 6.905136 1.494863388
## 886 4.4 8.981540 -4.581539741
## 887 22.0 15.204276 6.795724408
## 888 5.2 12.057294 -6.857293921
## 889 6.8 7.904486 -1.104486226
## 890 4.2 7.921754 -3.721753981
## 891 9.0 9.354947 -0.354947258
## 892 8.2 12.702662 -4.502662583ggplot(triceps,aes(x=age, y=triceps)) +
geom_point(alpha=0.55, color="black") +
stat_smooth(method = "lm",
formula = y~x,lty = 1,
col = "blue",se = F)+
theme_bw()
#Regresi Polinomial Derajat 2 (ordo 2)
mod_polinomial2 = lm(triceps ~ poly(age,2,raw = T),
data=triceps)
summary(mod_polinomial2)##
## Call:
## lm(formula = triceps ~ poly(age, 2, raw = T), data = triceps)
##
## Residuals:
## Min 1Q Median 3Q Max
## -12.5677 -2.4401 -0.4587 1.6368 24.9961
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.0229191 0.3063806 19.658 < 2e-16 ***
## poly(age, 2, raw = T)1 0.2434733 0.0364403 6.681 4.17e-11 ***
## poly(age, 2, raw = T)2 -0.0006257 0.0007926 -0.789 0.43
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 4.008 on 889 degrees of freedom
## Multiple R-squared: 0.3377, Adjusted R-squared: 0.3362
## F-statistic: 226.6 on 2 and 889 DF, p-value: < 2.2e-16ggplot(triceps,aes(x=age, y=triceps)) +
geom_point(alpha=0.55, color="black") +
stat_smooth(method = "lm",
formula = y~poly(x,2,raw=T),
lty = 1, col = "blue",se = F)+
theme_bw()
ggplot(triceps,aes(x=age, y=triceps)) +
geom_point(alpha=0.55, color="black") +
stat_smooth(method = "lm",
formula = y~poly(x,2,raw=T),
lty = 1, col = "blue",se = T)+
theme_bw()
#Regresi Polinomial Derajat 3 (ordo 3)
mod_polinomial3 = lm(triceps ~ poly(age,3,raw = T),data=triceps)
summary(mod_polinomial3)##
## Call:
## lm(formula = triceps ~ poly(age, 3, raw = T), data = triceps)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.5832 -1.9284 -0.5415 1.3283 24.4440
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 8.004e+00 3.831e-01 20.893 < 2e-16 ***
## poly(age, 3, raw = T)1 -3.157e-01 7.721e-02 -4.089 4.73e-05 ***
## poly(age, 3, raw = T)2 3.101e-02 3.964e-03 7.824 1.45e-14 ***
## poly(age, 3, raw = T)3 -4.566e-04 5.612e-05 -8.135 1.38e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.868 on 888 degrees of freedom
## Multiple R-squared: 0.3836, Adjusted R-squared: 0.3815
## F-statistic: 184.2 on 3 and 888 DF, p-value: < 2.2e-16ggplot(triceps,aes(x=age, y=triceps)) +
geom_point(alpha=0.55, color="black") +
stat_smooth(method = "lm",
formula = y~poly(x,3,raw=T),
lty = 1, col = "blue",se = T)+
theme_bw()
AIC(mod_linear)## [1] 5011.515AIC(mod_polinomial2)## [1] 5012.89AIC(mod_polinomial3)## [1] 4950.774MSE(predict(mod_linear), triceps$triceps)## [1] 16.01758MSE(predict(mod_polinomial2), triceps$triceps)## [1] 16.00636MSE(predict(mod_polinomial3), triceps$triceps)## [1] 14.89621#Regresi Fungsi Tangga (5)
mod_tangga5 = lm(triceps ~ cut(age,5),data=triceps)
summary(mod_tangga5)##
## Call:
## lm(formula = triceps ~ cut(age, 5), data = triceps)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.5474 -2.0318 -0.4465 1.3682 23.3759
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.2318 0.1994 36.260 < 2e-16 ***
## cut(age, 5)(10.6,20.9] 1.6294 0.3244 5.023 6.16e-07 ***
## cut(age, 5)(20.9,31.2] 5.9923 0.4222 14.192 < 2e-16 ***
## cut(age, 5)(31.2,41.5] 7.5156 0.4506 16.678 < 2e-16 ***
## cut(age, 5)(41.5,51.8] 7.4561 0.5543 13.452 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.939 on 887 degrees of freedom
## Multiple R-squared: 0.3617, Adjusted R-squared: 0.3588
## F-statistic: 125.7 on 4 and 887 DF, p-value: < 2.2e-16ggplot(triceps,aes(x=age, y=triceps)) +
geom_point(alpha=0.55, color="black") +
stat_smooth(method = "lm",
formula = y~cut(x,5),
lty = 1, col = "blue",se = F)+
theme_bw()
#Regresi Fungsi Tangga (7)
mod_tangga7 = lm(triceps ~ cut(age,7),data=triceps)
summary(mod_tangga7)##
## Call:
## lm(formula = triceps ~ cut(age, 7), data = triceps)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.8063 -1.7592 -0.4366 1.2894 23.1461
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 7.5592 0.2219 34.060 < 2e-16 ***
## cut(age, 7)(7.62,15] -0.6486 0.3326 -1.950 0.0515 .
## cut(age, 7)(15,22.3] 3.4534 0.4239 8.146 1.27e-15 ***
## cut(age, 7)(22.3,29.7] 5.8947 0.4604 12.804 < 2e-16 ***
## cut(age, 7)(29.7,37] 7.8471 0.5249 14.949 < 2e-16 ***
## cut(age, 7)(37,44.4] 6.9191 0.5391 12.835 < 2e-16 ***
## cut(age, 7)(44.4,51.8] 6.3013 0.6560 9.606 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.805 on 885 degrees of freedom
## Multiple R-squared: 0.4055, Adjusted R-squared: 0.4014
## F-statistic: 100.6 on 6 and 885 DF, p-value: < 2.2e-16ggplot(triceps,aes(x=age, y=triceps)) +
geom_point(alpha=0.55, color="black") +
stat_smooth(method = "lm",
formula = y~cut(x,7),
lty = 1, col = "blue",se = F)+
theme_bw()
#Perbandingan Model
MSE = function(pred,actual){
mean((pred-actual)^2)
}#membandingkan model (breaks 7 paling baik karena mse-nya paling kecil)
nilai_MSE <- rbind(MSE(predict(mod_linear),triceps$triceps),
MSE(predict(mod_polinomial2),triceps$triceps),
MSE(predict(mod_polinomial3),triceps$triceps),
MSE(predict(mod_tangga5),triceps$triceps),
MSE(predict(mod_tangga7),triceps$triceps))
nama_model <- c("Linear","Poly (ordo=2)", "Poly (ordo=3)",
"Tangga (breaks=5)", "Tangga (breaks=7)")
data.frame(nama_model,nilai_MSE)## nama_model nilai_MSE
## 1 Linear 16.01758
## 2 Poly (ordo=2) 16.00636
## 3 Poly (ordo=3) 14.89621
## 4 Tangga (breaks=5) 15.42602
## 5 Tangga (breaks=7) 14.36779#Evaluasi Model Menggunakan Cross Validation
#Regresi Linear
set.seed(123)
cross_val <- vfold_cv(triceps,v=10,strata = "triceps")
metric_linear <- map_dfr(cross_val$splits,
function(x){
mod <- lm(triceps ~ age,data=triceps[x$in_id,])
pred <- predict(mod,newdata=triceps[-x$in_id,])
truth <- triceps[-x$in_id,]$triceps
rmse <- mlr3measures::rmse(truth = truth,response = pred)
mae <- mlr3measures::mae(truth = truth,response = pred)
metric <- c(rmse,mae)
names(metric) <- c("rmse","mae")
return(metric)
}
)
metric_linear## # A tibble: 10 x 2
## rmse mae
## <dbl> <dbl>
## 1 3.65 2.82
## 2 4.62 3.22
## 3 4.38 3.00
## 4 3.85 2.80
## 5 3.08 2.36
## 6 3.83 2.81
## 7 3.59 2.78
## 8 4.66 3.06
## 9 3.50 2.56
## 10 4.59 2.93# menghitung rata-rata untuk 10 folds
mean_metric_linear <- colMeans(metric_linear)
mean_metric_linear## rmse mae
## 3.973249 2.833886#Polynomial Derajat 2 (ordo 2)
set.seed(123)
cross_val <- vfold_cv(triceps,v=10,strata = "triceps") #V(lipatan) biasa dipakai 10 dan 5
metric_poly2 <- map_dfr(cross_val$splits,
function(x){
mod <- lm(triceps ~ poly(age,2,raw = T),data=triceps[x$in_id,])
pred <- predict(mod,newdata=triceps[-x$in_id,])
truth <- triceps[-x$in_id,]$triceps
rmse <- mlr3measures::rmse(truth = truth,response = pred)
mae <- mlr3measures::mae(truth = truth,response = pred)
metric <- c(rmse,mae)
names(metric) <- c("rmse","mae") #mae absolut
return(metric)
}
)
metric_poly2## # A tibble: 10 x 2
## rmse mae
## <dbl> <dbl>
## 1 3.64 2.82
## 2 4.62 3.26
## 3 4.39 3.02
## 4 3.85 2.81
## 5 3.10 2.38
## 6 3.82 2.81
## 7 3.62 2.83
## 8 4.65 3.07
## 9 3.50 2.57
## 10 4.59 2.94# menghitung rata-rata untuk 10 folds
mean_metric_poly2 <- colMeans(metric_poly2)
mean_metric_poly2## rmse mae
## 3.977777 2.851787#Polynomial Derajat 3 (ordo 3)
set.seed(123)
cross_val <- vfold_cv(triceps,v=10,strata = "triceps")
metric_poly3 <- map_dfr(cross_val$splits,
function(x){
mod <- lm(triceps ~ poly(age,3,raw = T),data=triceps[x$in_id,])
pred <- predict(mod,newdata=triceps[-x$in_id,])
truth <- triceps[-x$in_id,]$triceps
rmse <- mlr3measures::rmse(truth = truth,response = pred)
mae <- mlr3measures::mae(truth = truth,response = pred)
metric <- c(rmse,mae)
names(metric) <- c("rmse","mae")
return(metric)
}
)
metric_poly3## # A tibble: 10 x 2
## rmse mae
## <dbl> <dbl>
## 1 3.49 2.60
## 2 4.48 2.99
## 3 4.21 2.85
## 4 4.02 2.75
## 5 3.03 2.09
## 6 3.63 2.59
## 7 3.53 2.52
## 8 4.54 2.91
## 9 3.27 2.33
## 10 4.27 2.68# menghitung rata-rata untuk 10 folds
mean_metric_poly3 <- colMeans(metric_poly3)
mean_metric_poly3## rmse mae
## 3.845976 2.632125#Fungsi Tangga
set.seed(123)
cross_val <- vfold_cv(triceps,v=10,strata = "triceps")
breaks <- 3:10 #titik cut nya
best_tangga <- map_dfr(breaks, function(i){
metric_tangga <- map_dfr(cross_val$splits,
function(x){
training <- triceps[x$in_id,]
training$age <- cut(training$age,i)
mod <- lm(triceps ~ age,data=training)
labs_x <- levels(mod$model[,2])
labs_x_breaks <- cbind(lower = as.numeric( sub("\\((.+),.*", "\\1", labs_x) ),
upper = as.numeric( sub("[^,]*,([^]]*)\\]", "\\1", labs_x) ))
testing <- triceps[-x$in_id,]
age_new <- cut(testing$age,c(labs_x_breaks[1,1],labs_x_breaks[,2]))
pred <- predict(mod,newdata=list(age=age_new))
truth <- testing$triceps
data_eval <- na.omit(data.frame(truth,pred))
rmse <- mlr3measures::rmse(truth = data_eval$truth,response = data_eval$pred)
mae <- mlr3measures::mae(truth = data_eval$truth,response = data_eval$pred)
metric <- c(rmse,mae)
names(metric) <- c("rmse","mae")
return(metric)
}
)
metric_tangga
# menghitung rata-rata untuk 10 folds
mean_metric_tangga <- colMeans(metric_tangga)
mean_metric_tangga
}
)
best_tangga <- cbind(breaks=breaks,best_tangga)
# menampilkan hasil all breaks
best_tangga## breaks rmse mae
## 1 3 3.835357 2.618775
## 2 4 3.882932 2.651911
## 3 5 3.917840 2.724368
## 4 6 3.836068 2.622939
## 5 7 3.789715 2.555062
## 6 8 3.812789 2.555563
## 7 9 3.781720 2.518706
## 8 10 3.795877 2.529479#berdasarkan rmse terkecil
best_tangga %>% slice_min(rmse)## breaks rmse mae
## 1 9 3.78172 2.518706#berdasarkan mae terkecil
best_tangga %>% slice_min(mae)## breaks rmse mae
## 1 9 3.78172 2.518706#Perbandingan Model
nilai_metric <- rbind(mean_metric_linear,
mean_metric_poly2,
mean_metric_poly3,
best_tangga %>% select(-1) %>% slice_min(mae))
nama_model <- c("Linear","Poly2","Poly3","Tangga (breaks=9)")
data.frame(nama_model,nilai_metric)## nama_model rmse mae
## 1 Linear 3.973249 2.833886
## 2 Poly2 3.977777 2.851787
## 3 Poly3 3.845976 2.632125
## 4 Tangga (breaks=9) 3.781720 2.518706