Homework 7
Abdelmalek Hajjam
4/18/2021
library(tidyverse)
library(dbplyr)
library(caret)
# library(grid)
# library(gridExtra)
library(DMwR)
library(pls)
library(elasticnet)Exercise 6.2
Developing a model to predict permeability (see Sect. 1.4) could save significant resources for a pharmaceutical company, while at the same time more rapidly identifying molecules that have a sufficient permeability to become a drug:
(a) Start R and use these commands to load the data:
library(AppliedPredictiveModeling)
library(knitr)
data(permeability)
summary(permeability)## permeability
## Min. : 0.06
## 1st Qu.: 1.55
## Median : 4.91
## Mean :12.24
## 3rd Qu.:15.47
## Max. :55.60(b) The fingerprint predictors indicate the presence or absence of substructures of a molecule and are often sparse meaning that relatively few of the molecules contain each substructure. Filter out the predictors that have low frequencies using the nearZeroVar function from the caret package. How many predictors are left for modeling?
#using library(caret)
near.zero.var <- nearZeroVar(fingerprints)
near.zero.var## [1] 7 8 9 10 13 14 17 18 19 22 23 24 30 31 32
## [16] 33 34 45 77 81 82 83 84 85 89 90 91 92 95 100
## [31] 104 105 106 107 109 110 112 113 114 115 116 117 119 120 122
## [46] 123 124 128 131 132 134 135 136 137 139 140 144 145 147 148
## [61] 149 151 155 160 161 164 165 166 216 217 218 219 220 222 243
## [76] 252 259 273 275 277 282 283 287 288 289 292 346 347 348 349
## [91] 350 351 352 353 354 363 364 365 369 375 379 384 391 393 397
## [106] 399 402 404 405 407 408 409 410 411 412 413 414 415 416 417
## [121] 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432
## [136] 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447
## [151] 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462
## [166] 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477
## [181] 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492
## [196] 493 494 495 498 500 501 502 513 523 525 526 527 528 530 531
## [211] 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546
## [226] 547 548 550 552 555 562 563 564 566 567 569 570 572 575 578
## [241] 579 580 581 582 583 584 585 586 587 588 589 596 605 606 607
## [256] 608 609 610 611 612 614 615 616 617 618 619 620 622 623 624
## [271] 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639
## [286] 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654
## [301] 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669
## [316] 670 671 672 673 674 675 676 677 678 680 681 682 683 684 685
## [331] 686 687 688 689 690 691 692 693 694 695 696 697 706 707 708
## [346] 709 710 711 712 713 714 715 716 717 718 720 721 722 723 724
## [361] 725 726 727 728 729 730 731 734 735 736 737 738 739 740 741
## [376] 742 743 744 745 746 747 748 749 756 757 758 759 760 761 762
## [391] 763 764 765 766 767 768 769 770 771 772 777 778 779 781 783
## [406] 784 785 786 787 788 789 790 791 794 796 797 799 802 803 804
## [421] 807 808 809 810 811 814 815 816 817 818 819 820 821 822 823
## [436] 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838
## [451] 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853
## [466] 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868
## [481] 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883
## [496] 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898
## [511] 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913
## [526] 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928
## [541] 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943
## [556] 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958
## [571] 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973
## [586] 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988
## [601] 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003
## [616] 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018
## [631] 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033
## [646] 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048
## [661] 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063
## [676] 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078
## [691] 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093
## [706] 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107length(near.zero.var)## [1] 719fingerprints.nz <- fingerprints[,-near.zero.var]
dim(fingerprints.nz)## [1] 165 388str(fingerprints.nz)## num [1:165, 1:388] 0 0 0 0 0 0 0 0 0 0 ...
## - attr(*, "dimnames")=List of 2
## ..$ : chr [1:165] "1" "2" "3" "4" ...
## ..$ : chr [1:388] "X1" "X2" "X3" "X4" ...There are 388 variables left out of 719 variables that have zero or near zero variance predictors.
So there are 388 predictors left for modeling. 719 columns were removed.
(c) Split the data into a training and a test set, pre-process the data, and tune a PLS model. How many latent variables are optimal and what is the corresponding resampled estimate of R2?
highCorr <- findCorrelation(cor(fingerprints.nz), 0.90)
fingerprints.nz.2 <- fingerprints.nz[, -highCorr]
dim(fingerprints.nz.2)## [1] 165 110set.seed(777)
split_index <- createDataPartition(permeability, p = 0.7, list = FALSE)
X_train <- fingerprints.nz.2[split_index, ]
y_train <- permeability[split_index, ]
X_test <- fingerprints.nz.2[-split_index, ]
y_test <- permeability[-split_index, ]Using PLS Model
#using library(pls)
plsFit <- train(x = X_train, y = y_train, method = "pls", preProc = c("center", "scale"), trControl = trainControl("cv", number = 10), tuneLength = 25)
plsFit$results %>% filter(ncomp == plsFit$bestTune$ncomp) %>% select(ncomp, RMSE, Rsquared)## ncomp RMSE Rsquared
## 1 5 12.18165 0.4601662plot(plsFit, main = "Training Set RMSE")
(d) Predict the response for the test set. What is the test set estimate of \(R^2\) ?
Using our testing data set. we split our test set into X predictors and Y response variable
pls.prediction <- predict(plsFit, newdata = X_test)
results <- data.frame(Model = "PLS", RMSE = caret::RMSE(pls.prediction, y_test), Rsquared = caret::R2(pls.prediction, y_test))
results ## Model RMSE Rsquared
## 1 PLS 10.4266 0.5764468(e) Try building other models discussed in this chapter. Do any have better predictive performance?
Consider the following Models:
Ridge regression
ridgeFit <- train(x = X_train, y = y_train, method = 'ridge', metric = 'Rsquared', tuneGrid = data.frame(.lambda = seq(0, 1, by = 0.1)), trControl = trainControl(method = 'cv'),
preProcess = c('center', 'scale'))
plot(ridgeFit)
ridge.predictions <- predict(ridgeFit, newdata = X_test)
ridge.results <- data.frame(Model = "Ridge Regression", RMSE = caret::RMSE(ridge.predictions, y_test), Rsquared = caret::R2(ridge.predictions, y_test))
ridge.results ## Model RMSE Rsquared
## 1 Ridge Regression 13.2473 0.6062653Lasso Regression
lassoFit <- train(x = X_train, y = y_train, method ='lasso', metric = 'Rsquared', tuneGrid = data.frame(.fraction = seq(0, 0.5, by = 0.05)), trControl=trainControl(method = 'cv'),
preProcess = c('center', 'scale'))
plot(lassoFit)
lasso.predictions <- predict(lassoFit, newdata = X_test)
lasso.results <- data.frame(Model = "Lasso Regression", RMSE = caret::RMSE(lasso.predictions, y_test), Rsquared = caret::R2(lasso.predictions, y_test))
lasso.results## Model RMSE Rsquared
## 1 Lasso Regression 194506524 0.01593297Elastic Net Regression
elasticFit <- train(x = X_train, y = y_train, method = 'enet', metric = 'Rsquared', tuneGrid = data.frame(.fraction = seq(0, 1, by = 0.1), .lambda = seq(0, 1, by = 0.1)),
trControl = trainControl(method = 'cv'), preProcess = c('center', 'scale'))
plot(elasticFit)
elastic.predictions <- predict(elasticFit, newdata = X_test)
elastic.results <- data.frame(Model = "Elastic Net Regression", RMSE = caret::RMSE(elastic.predictions, y_test), Rsquared = caret::R2(elastic.predictions, y_test))
elastic.results ## Model RMSE Rsquared
## 1 Elastic Net Regression 12.79535 0.6084177I see few improvements comparing to PLS.
Let’s summarize and organize:
plsFit$results %>%
filter(ncomp == plsFit$bestTune$ncomp) %>%
mutate("Model" = "PLS") %>%
select(Model, RMSE, Rsquared) %>%
as.data.frame() %>%
bind_rows(ridge.results) %>%
bind_rows(lasso.results) %>%
bind_rows(elastic.results) %>%
arrange(desc(Rsquared))## Model RMSE Rsquared
## 1 Elastic Net Regression 1.279535e+01 0.60841769
## 2 Ridge Regression 1.324730e+01 0.60626528
## 3 PLS 1.218165e+01 0.46016619
## 4 Lasso Regression 1.945065e+08 0.01593297Looks like Ridge and Elastic net models both have higher RMSE and Rsquared.Therefore have better performance.
(f) Would you recommend any of your models to replace the permeability laboratory experiment?
Because Ridge Regression and Elestic have higher Rsquared and RMSE, and they are close, so I will recommend those two to replace the permeability experiment.
Exercise 6.3
A chemical manufacturing process for a pharmaceutical product was discussed in Sect. 1.4. In this problem, the objective is to understand the relationship between biological measurements of the raw materials (predictors), measurements of the manufacturing process (predictors), and the response of product yield. Biological predictors cannot be changed but can be used to assess the quality of the raw material before processing. On the other hand, manufacturing process predictors can be changed in the manufacturing process. Improving product yield by 1% will boost revenue by approximately one hundred thousand dollars per batch:
A. Start R and use these commands to load the data:
#library(AppliedPredictiveModeling)
data("ChemicalManufacturingProcess")
dim(ChemicalManufacturingProcess)## [1] 176 58summary(ChemicalManufacturingProcess)## Yield BiologicalMaterial01 BiologicalMaterial02 BiologicalMaterial03
## Min. :35.25 Min. :4.580 Min. :46.87 Min. :56.97
## 1st Qu.:38.75 1st Qu.:5.978 1st Qu.:52.68 1st Qu.:64.98
## Median :39.97 Median :6.305 Median :55.09 Median :67.22
## Mean :40.18 Mean :6.411 Mean :55.69 Mean :67.70
## 3rd Qu.:41.48 3rd Qu.:6.870 3rd Qu.:58.74 3rd Qu.:70.43
## Max. :46.34 Max. :8.810 Max. :64.75 Max. :78.25
##
## BiologicalMaterial04 BiologicalMaterial05 BiologicalMaterial06
## Min. : 9.38 Min. :13.24 Min. :40.60
## 1st Qu.:11.24 1st Qu.:17.23 1st Qu.:46.05
## Median :12.10 Median :18.49 Median :48.46
## Mean :12.35 Mean :18.60 Mean :48.91
## 3rd Qu.:13.22 3rd Qu.:19.90 3rd Qu.:51.34
## Max. :23.09 Max. :24.85 Max. :59.38
##
## BiologicalMaterial07 BiologicalMaterial08 BiologicalMaterial09
## Min. :100.0 Min. :15.88 Min. :11.44
## 1st Qu.:100.0 1st Qu.:17.06 1st Qu.:12.60
## Median :100.0 Median :17.51 Median :12.84
## Mean :100.0 Mean :17.49 Mean :12.85
## 3rd Qu.:100.0 3rd Qu.:17.88 3rd Qu.:13.13
## Max. :100.8 Max. :19.14 Max. :14.08
##
## BiologicalMaterial10 BiologicalMaterial11 BiologicalMaterial12
## Min. :1.770 Min. :135.8 Min. :18.35
## 1st Qu.:2.460 1st Qu.:143.8 1st Qu.:19.73
## Median :2.710 Median :146.1 Median :20.12
## Mean :2.801 Mean :147.0 Mean :20.20
## 3rd Qu.:2.990 3rd Qu.:149.6 3rd Qu.:20.75
## Max. :6.870 Max. :158.7 Max. :22.21
##
## ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03
## Min. : 0.00 Min. : 0.00 Min. :1.47
## 1st Qu.:10.80 1st Qu.:19.30 1st Qu.:1.53
## Median :11.40 Median :21.00 Median :1.54
## Mean :11.21 Mean :16.68 Mean :1.54
## 3rd Qu.:12.15 3rd Qu.:21.50 3rd Qu.:1.55
## Max. :14.10 Max. :22.50 Max. :1.60
## NA's :1 NA's :3 NA's :15
## ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06
## Min. :911.0 Min. : 923.0 Min. :203.0
## 1st Qu.:928.0 1st Qu.: 986.8 1st Qu.:205.7
## Median :934.0 Median : 999.2 Median :206.8
## Mean :931.9 Mean :1001.7 Mean :207.4
## 3rd Qu.:936.0 3rd Qu.:1008.9 3rd Qu.:208.7
## Max. :946.0 Max. :1175.3 Max. :227.4
## NA's :1 NA's :1 NA's :2
## ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess09
## Min. :177.0 Min. :177.0 Min. :38.89
## 1st Qu.:177.0 1st Qu.:177.0 1st Qu.:44.89
## Median :177.0 Median :178.0 Median :45.73
## Mean :177.5 Mean :177.6 Mean :45.66
## 3rd Qu.:178.0 3rd Qu.:178.0 3rd Qu.:46.52
## Max. :178.0 Max. :178.0 Max. :49.36
## NA's :1 NA's :1
## ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12
## Min. : 7.500 Min. : 7.500 Min. : 0.0
## 1st Qu.: 8.700 1st Qu.: 9.000 1st Qu.: 0.0
## Median : 9.100 Median : 9.400 Median : 0.0
## Mean : 9.179 Mean : 9.386 Mean : 857.8
## 3rd Qu.: 9.550 3rd Qu.: 9.900 3rd Qu.: 0.0
## Max. :11.600 Max. :11.500 Max. :4549.0
## NA's :9 NA's :10 NA's :1
## ManufacturingProcess13 ManufacturingProcess14 ManufacturingProcess15
## Min. :32.10 Min. :4701 Min. :5904
## 1st Qu.:33.90 1st Qu.:4828 1st Qu.:6010
## Median :34.60 Median :4856 Median :6032
## Mean :34.51 Mean :4854 Mean :6039
## 3rd Qu.:35.20 3rd Qu.:4882 3rd Qu.:6061
## Max. :38.60 Max. :5055 Max. :6233
## NA's :1
## ManufacturingProcess16 ManufacturingProcess17 ManufacturingProcess18
## Min. : 0 Min. :31.30 Min. : 0
## 1st Qu.:4561 1st Qu.:33.50 1st Qu.:4813
## Median :4588 Median :34.40 Median :4835
## Mean :4566 Mean :34.34 Mean :4810
## 3rd Qu.:4619 3rd Qu.:35.10 3rd Qu.:4862
## Max. :4852 Max. :40.00 Max. :4971
##
## ManufacturingProcess19 ManufacturingProcess20 ManufacturingProcess21
## Min. :5890 Min. : 0 Min. :-1.8000
## 1st Qu.:6001 1st Qu.:4553 1st Qu.:-0.6000
## Median :6022 Median :4582 Median :-0.3000
## Mean :6028 Mean :4556 Mean :-0.1642
## 3rd Qu.:6050 3rd Qu.:4610 3rd Qu.: 0.0000
## Max. :6146 Max. :4759 Max. : 3.6000
##
## ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24
## Min. : 0.000 Min. :0.000 Min. : 0.000
## 1st Qu.: 3.000 1st Qu.:2.000 1st Qu.: 4.000
## Median : 5.000 Median :3.000 Median : 8.000
## Mean : 5.406 Mean :3.017 Mean : 8.834
## 3rd Qu.: 8.000 3rd Qu.:4.000 3rd Qu.:14.000
## Max. :12.000 Max. :6.000 Max. :23.000
## NA's :1 NA's :1 NA's :1
## ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27
## Min. : 0 Min. : 0 Min. : 0
## 1st Qu.:4832 1st Qu.:6020 1st Qu.:4560
## Median :4855 Median :6047 Median :4587
## Mean :4828 Mean :6016 Mean :4563
## 3rd Qu.:4877 3rd Qu.:6070 3rd Qu.:4609
## Max. :4990 Max. :6161 Max. :4710
## NA's :5 NA's :5 NA's :5
## ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30
## Min. : 0.000 Min. : 0.00 Min. : 0.000
## 1st Qu.: 0.000 1st Qu.:19.70 1st Qu.: 8.800
## Median :10.400 Median :19.90 Median : 9.100
## Mean : 6.592 Mean :20.01 Mean : 9.161
## 3rd Qu.:10.750 3rd Qu.:20.40 3rd Qu.: 9.700
## Max. :11.500 Max. :22.00 Max. :11.200
## NA's :5 NA's :5 NA's :5
## ManufacturingProcess31 ManufacturingProcess32 ManufacturingProcess33
## Min. : 0.00 Min. :143.0 Min. :56.00
## 1st Qu.:70.10 1st Qu.:155.0 1st Qu.:62.00
## Median :70.80 Median :158.0 Median :64.00
## Mean :70.18 Mean :158.5 Mean :63.54
## 3rd Qu.:71.40 3rd Qu.:162.0 3rd Qu.:65.00
## Max. :72.50 Max. :173.0 Max. :70.00
## NA's :5 NA's :5
## ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36
## Min. :2.300 Min. :463.0 Min. :0.01700
## 1st Qu.:2.500 1st Qu.:490.0 1st Qu.:0.01900
## Median :2.500 Median :495.0 Median :0.02000
## Mean :2.494 Mean :495.6 Mean :0.01957
## 3rd Qu.:2.500 3rd Qu.:501.5 3rd Qu.:0.02000
## Max. :2.600 Max. :522.0 Max. :0.02200
## NA's :5 NA's :5 NA's :5
## ManufacturingProcess37 ManufacturingProcess38 ManufacturingProcess39
## Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.700 1st Qu.:2.000 1st Qu.:7.100
## Median :1.000 Median :3.000 Median :7.200
## Mean :1.014 Mean :2.534 Mean :6.851
## 3rd Qu.:1.300 3rd Qu.:3.000 3rd Qu.:7.300
## Max. :2.300 Max. :3.000 Max. :7.500
##
## ManufacturingProcess40 ManufacturingProcess41 ManufacturingProcess42
## Min. :0.00000 Min. :0.00000 Min. : 0.00
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:11.40
## Median :0.00000 Median :0.00000 Median :11.60
## Mean :0.01771 Mean :0.02371 Mean :11.21
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:11.70
## Max. :0.10000 Max. :0.20000 Max. :12.10
## NA's :1 NA's :1
## ManufacturingProcess43 ManufacturingProcess44 ManufacturingProcess45
## Min. : 0.0000 Min. :0.000 Min. :0.000
## 1st Qu.: 0.6000 1st Qu.:1.800 1st Qu.:2.100
## Median : 0.8000 Median :1.900 Median :2.200
## Mean : 0.9119 Mean :1.805 Mean :2.138
## 3rd Qu.: 1.0250 3rd Qu.:1.900 3rd Qu.:2.300
## Max. :11.0000 Max. :2.100 Max. :2.600
## B. A small percentage of cells in the predictor set contain missing values. Use an imputation function to fill in these missing values (e.g., see Sec 3.8).
Finding the missing values:
is.na <- sort(colSums(is.na(ChemicalManufacturingProcess)))
is.na[is.na > 0]## ManufacturingProcess01 ManufacturingProcess04 ManufacturingProcess05
## 1 1 1
## ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess12
## 1 1 1
## ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23
## 1 1 1
## ManufacturingProcess24 ManufacturingProcess40 ManufacturingProcess41
## 1 1 1
## ManufacturingProcess06 ManufacturingProcess02 ManufacturingProcess25
## 2 3 5
## ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28
## 5 5 5
## ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31
## 5 5 5
## ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35
## 5 5 5
## ManufacturingProcess36 ManufacturingProcess10 ManufacturingProcess11
## 5 9 10
## ManufacturingProcess03
## 15Using KNN imputation function to fill the missing values
#using library(DMwR)
knn.df <- knnImputation(ChemicalManufacturingProcess[, 1:57], k = 3, meth = "weighAvg")
anyNA(knn.df)## [1] FALSEThe above KNN imputation shows that there are no more missing values present in the dataset.
C. Split the data into a training and a test set, pre-process the data, and tune a model of your choice from this chapter. What is the optimal value of the performance metric?
set.seed(777)
near_zero <- nearZeroVar(knn.df)
knn.df <- knn.df[,-near_zero]
library(caret)
inTraining <- createDataPartition(knn.df$Yield, p = 0.80, list=FALSE)
training <- knn.df[ inTraining,]
testing <- knn.df[-inTraining,]
X <- training[,2:(length(training))]
Y <- training$Yield
X_test <- testing[,2:(length(testing))]
Y_test <- testing$YieldUsing 10 fold cross validation method
fitControl <- trainControl(method = "repeatedcv",
number = 10,
repeats = 10)Choosing PLS as our model:
model.pls <- train(X, Y, method='pls', metric='RMSE',
tuneLength=20, trControl = fitControl,
preProcess= c('center','scale'))
model.pls## Partial Least Squares
##
## 144 samples
## 55 predictor
##
## Pre-processing: centered (55), scaled (55)
## Resampling: Cross-Validated (10 fold, repeated 10 times)
## Summary of sample sizes: 131, 131, 129, 129, 130, 130, ...
## Resampling results across tuning parameters:
##
## ncomp RMSE Rsquared MAE
## 1 1.454508 0.4230447 1.175809
## 2 1.702412 0.4816284 1.170186
## 3 1.416921 0.5408574 1.073509
## 4 1.698803 0.5284711 1.153657
## 5 2.004785 0.4983074 1.254895
## 6 2.072503 0.4920976 1.280428
## 7 2.172860 0.4936115 1.305929
## 8 2.192098 0.5020414 1.312443
## 9 2.123742 0.5183810 1.280424
## 10 2.125281 0.5145890 1.278942
## 11 2.091210 0.4995785 1.284465
## 12 2.107278 0.4940098 1.297461
## 13 2.124265 0.4912011 1.303125
## 14 2.126824 0.4892324 1.303143
## 15 2.129470 0.4935038 1.302971
## 16 2.176529 0.4937558 1.314730
## 17 2.263813 0.4875490 1.339907
## 18 2.278907 0.4818896 1.344732
## 19 2.332034 0.4750830 1.365788
## 20 2.424879 0.4699668 1.396539
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was ncomp = 3.#plot the model
plot(model.pls)
It looks like RMSE was used to select the optimal model using the smallest value. the final value for the model was ncomp = 3, yielding an RMSE of 1.414029 and an optimal Rsquared of 0.5367331.
D. Predict the response for the test set. What is the value of the performance metric and how does this compare with the resampled perfomance metric on the training set?
pls.pred <- predict(model.pls, X_test)
postResample(pls.pred, Y_test)## RMSE Rsquared MAE
## 1.2631505 0.6179720 0.9834409When evaluated against the test data, it looks like RMSE dropped to 1.263 from 1.414 in the PLS model where it was trained on. However the Rsquared has increased nicely. from 0.536 to 0.617.
E. Which predictors are most important in the model you have trained? Do either the biological or process predictors dominate the list?
model.pls$finalModel$coefficients## , , 1 comps
##
## .outcome
## BiologicalMaterial01 0.078530963
## BiologicalMaterial02 0.104634121
## BiologicalMaterial03 0.093245060
## BiologicalMaterial04 0.078967650
## BiologicalMaterial05 0.030481271
## BiologicalMaterial06 0.099600843
## BiologicalMaterial08 0.082325119
## BiologicalMaterial09 0.031353267
## BiologicalMaterial10 0.050221655
## BiologicalMaterial11 0.076941108
## BiologicalMaterial12 0.075616456
## ManufacturingProcess01 -0.029099303
## ManufacturingProcess02 -0.055710562
## ManufacturingProcess03 -0.011817223
## ManufacturingProcess04 -0.054566522
## ManufacturingProcess05 0.013594199
## ManufacturingProcess06 0.081175221
## ManufacturingProcess07 -0.011699158
## ManufacturingProcess08 0.003586114
## ManufacturingProcess09 0.099166693
## ManufacturingProcess10 0.038070848
## ManufacturingProcess11 0.065679799
## ManufacturingProcess12 0.070631571
## ManufacturingProcess13 -0.095961431
## ManufacturingProcess14 0.005942549
## ManufacturingProcess15 0.053627471
## ManufacturingProcess16 -0.015213406
## ManufacturingProcess17 -0.075380538
## ManufacturingProcess18 -0.011866856
## ManufacturingProcess19 0.038871157
## ManufacturingProcess20 -0.013308912
## ManufacturingProcess21 0.003018978
## ManufacturingProcess22 -0.001045175
## ManufacturingProcess23 -0.017620798
## ManufacturingProcess24 -0.052867152
## ManufacturingProcess25 0.003005819
## ManufacturingProcess26 0.008758739
## ManufacturingProcess27 0.002253490
## ManufacturingProcess28 0.065013133
## ManufacturingProcess29 0.032993017
## ManufacturingProcess30 0.042162167
## ManufacturingProcess31 -0.013131067
## ManufacturingProcess32 0.127059217
## ManufacturingProcess33 0.087046825
## ManufacturingProcess34 0.041990777
## ManufacturingProcess35 -0.034549158
## ManufacturingProcess36 -0.112875142
## ManufacturingProcess37 -0.028634487
## ManufacturingProcess38 -0.013227767
## ManufacturingProcess39 0.011605692
## ManufacturingProcess40 -0.002240412
## ManufacturingProcess41 0.002356966
## ManufacturingProcess42 0.006264572
## ManufacturingProcess43 0.034045175
## ManufacturingProcess44 0.024515530
##
## , , 2 comps
##
## .outcome
## BiologicalMaterial01 0.030688616
## BiologicalMaterial02 0.085145791
## BiologicalMaterial03 0.092815276
## BiologicalMaterial04 0.043547324
## BiologicalMaterial05 0.001395865
## BiologicalMaterial06 0.077704608
## BiologicalMaterial08 0.026762212
## BiologicalMaterial09 -0.005868124
## BiologicalMaterial10 -0.010402914
## BiologicalMaterial11 0.020981192
## BiologicalMaterial12 0.018578149
## ManufacturingProcess01 -0.015406532
## ManufacturingProcess02 -0.005185489
## ManufacturingProcess03 -0.040264483
## ManufacturingProcess04 -0.022738149
## ManufacturingProcess05 -0.037608382
## ManufacturingProcess06 0.183716444
## ManufacturingProcess07 -0.031163560
## ManufacturingProcess08 0.033537823
## ManufacturingProcess09 0.232184301
## ManufacturingProcess10 0.051625745
## ManufacturingProcess11 0.136528666
## ManufacturingProcess12 0.142999418
## ManufacturingProcess13 -0.238577370
## ManufacturingProcess14 0.009570907
## ManufacturingProcess15 0.090801378
## ManufacturingProcess16 -0.052376555
## ManufacturingProcess17 -0.246839174
## ManufacturingProcess18 0.019070708
## ManufacturingProcess19 0.012203917
## ManufacturingProcess20 0.015374911
## ManufacturingProcess21 -0.088680330
## ManufacturingProcess22 0.023095695
## ManufacturingProcess23 0.012559835
## ManufacturingProcess24 -0.062175258
## ManufacturingProcess25 -0.023212145
## ManufacturingProcess26 -0.010197069
## ManufacturingProcess27 -0.022719954
## ManufacturingProcess28 0.013768644
## ManufacturingProcess29 0.022047807
## ManufacturingProcess30 0.079501894
## ManufacturingProcess31 -0.044143951
## ManufacturingProcess32 0.239946586
## ManufacturingProcess33 0.122286314
## ManufacturingProcess34 0.145481540
## ManufacturingProcess35 -0.054925500
## ManufacturingProcess36 -0.208145089
## ManufacturingProcess37 -0.106952621
## ManufacturingProcess38 0.003352090
## ManufacturingProcess39 0.068447790
## ManufacturingProcess40 -0.008064720
## ManufacturingProcess41 -0.008512968
## ManufacturingProcess42 0.062499296
## ManufacturingProcess43 0.053040744
## ManufacturingProcess44 0.097587496
##
## , , 3 comps
##
## .outcome
## BiologicalMaterial01 0.023247662
## BiologicalMaterial02 0.082135176
## BiologicalMaterial03 0.080129675
## BiologicalMaterial04 0.049456439
## BiologicalMaterial05 0.031421636
## BiologicalMaterial06 0.065087490
## BiologicalMaterial08 0.003243837
## BiologicalMaterial09 -0.048286111
## BiologicalMaterial10 -0.015402768
## BiologicalMaterial11 -0.016718416
## BiologicalMaterial12 -0.026525383
## ManufacturingProcess01 0.001171243
## ManufacturingProcess02 -0.017067281
## ManufacturingProcess03 -0.022789238
## ManufacturingProcess04 0.046043122
## ManufacturingProcess05 -0.051037200
## ManufacturingProcess06 0.201923064
## ManufacturingProcess07 -0.046134058
## ManufacturingProcess08 0.057343264
## ManufacturingProcess09 0.240672868
## ManufacturingProcess10 0.024136039
## ManufacturingProcess11 0.122814370
## ManufacturingProcess12 0.100974552
## ManufacturingProcess13 -0.238496904
## ManufacturingProcess14 0.061852767
## ManufacturingProcess15 0.160962614
## ManufacturingProcess16 -0.020454811
## ManufacturingProcess17 -0.262948893
## ManufacturingProcess18 0.054710472
## ManufacturingProcess19 0.080875391
## ManufacturingProcess20 0.051238664
## ManufacturingProcess21 -0.114858537
## ManufacturingProcess22 0.026812178
## ManufacturingProcess23 0.020052349
## ManufacturingProcess24 -0.070976182
## ManufacturingProcess25 -0.006460317
## ManufacturingProcess26 0.009886727
## ManufacturingProcess27 -0.003634942
## ManufacturingProcess28 -0.028296286
## ManufacturingProcess29 0.056370890
## ManufacturingProcess30 0.083480715
## ManufacturingProcess31 -0.034691698
## ManufacturingProcess32 0.341128410
## ManufacturingProcess33 0.162000325
## ManufacturingProcess34 0.207640599
## ManufacturingProcess35 -0.051745169
## ManufacturingProcess36 -0.275998626
## ManufacturingProcess37 -0.162223255
## ManufacturingProcess38 0.001280808
## ManufacturingProcess39 0.099142288
## ManufacturingProcess40 -0.022535565
## ManufacturingProcess41 -0.031243256
## ManufacturingProcess42 0.093432000
## ManufacturingProcess43 0.059184631
## ManufacturingProcess44 0.128894622#important variables
varImp(model.pls)## pls variable importance
##
## only 20 most important variables shown (out of 55)
##
## Overall
## ManufacturingProcess32 100.00
## ManufacturingProcess36 86.15
## ManufacturingProcess09 82.59
## ManufacturingProcess13 82.24
## ManufacturingProcess17 77.17
## ManufacturingProcess06 66.33
## BiologicalMaterial02 61.84
## BiologicalMaterial06 59.97
## BiologicalMaterial08 57.53
## ManufacturingProcess33 56.99
## BiologicalMaterial11 55.29
## ManufacturingProcess12 55.28
## BiologicalMaterial12 55.17
## BiologicalMaterial01 52.79
## BiologicalMaterial03 51.80
## ManufacturingProcess11 50.45
## BiologicalMaterial04 50.37
## ManufacturingProcess28 47.62
## ManufacturingProcess34 46.23
## ManufacturingProcess02 40.31We can clearly see from the above output that ManufacturingProcess32 has the highter coefficient value = 0.341128410.
F. Explore the relationships between each of the top predictors and the response. How could this information be helpful in improving yield in future runs of the manufacturing process?
Using our PLS model, we can see that ManufacturingProcess32 has the highest positive impact (0.341128410), followed by ManufacturingProcess36 which has the second highest impact but negatively (-0.275998626). there are also some BiologicalMaterials that also impact positively and negatively. So there are some predictors that positively impact the manufacture and others that negatively impact the manufacture. Therefore, we need to increase those that have lower impact on the yield and decrease those that have negative impact on the yield.
In general, though the biological materials cannot be changed during the refinement process, identifying which ingredients/materials are more vital will help to ensure a higher yield as the company can focus on obtaining high quality ingredients of those materials. Likewise, knowing the most important manufacturing process steps allows the company to pinpoint where they can start fine tuning the procedure.