Libraries

library(kableExtra)
library(tidyverse)
library(ggplot2)
library(dplyr)
library(TSstudio)
library(RColorBrewer)
library(GGally)
library(grid)
library(gridExtra)
library(mlbench)
library(psych)
library(cowplot)
library(corrplot)
library(caret)
library(geoR)
library(reshape)
library(naniar)
library(mice)
library(DMwR)
library(AppliedPredictiveModeling)
library(pls)
library(glmnet)
library(elasticnet)

Applied Predictive Modeling

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:

  1. Start R and use these commands to load the data: > library(AppliedPredictiveModeling) > data(permeability)

The matrix fingerprints contains the 1,107 binary molecular predictors for the 165 compounds, while permeability contains permeability response.

data(permeability)

permeability %>% kable() %>% kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive")) %>% 
  scroll_box(width="100%",height="300px")
## Warning: namespace 'highr' is not available and has been replaced
## by .GlobalEnv when processing object '<unknown>'
permeability
12.5200
1.1200
19.4050
1.7300
1.6800
0.5100
25.3650
0.5500
39.4550
4.9100
0.5500
1.5700
0.0600
5.5600
3.8500
2.4300
0.7250
1.6800
5.2750
5.5100
3.8000
47.6650
32.3750
6.1200
0.8050
14.1500
20.6050
4.1950
0.6400
2.7100
13.6750
8.2700
3.9200
24.0150
13.5325
3.6100
40.8550
19.3600
2.3700
5.5650
8.1800
45.6800
2.4600
4.0700
1.2250
14.9850
13.7650
1.2100
1.5500
7.2200
1.7650
5.9850
8.9800
20.7400
3.9300
3.9300
1.8000
2.4900
8.3850
1.7100
45.7650
4.1900
12.9050
20.3400
2.7400
9.1200
45.0650
28.1000
6.9350
1.6950
6.4275
1.9150
47.0050
5.3550
8.3100
1.6950
1.1250
13.2950
1.8350
2.5900
40.8550
8.8300
9.5100
18.5550
18.9150
5.7650
0.1050
13.7650
2.0200
1.1900
2.5500
49.7650
8.9000
5.7500
12.4900
43.7500
11.3125
1.0800
2.5250
8.6200
0.4800
17.6100
4.3800
1.7750
1.1950
1.7050
0.9775
2.7300
4.0450
4.4950
42.0600
5.5800
42.0600
35.4300
31.6700
48.7050
51.4150
50.2100
31.7075
15.4700
30.5700
48.5100
47.1050
48.5100
47.1050
5.7650
0.8650
0.3750
8.5850
19.9400
5.5250
12.4900
1.7400
0.5400
0.7750
0.2350
0.8200
1.6850
0.5650
0.7550
50.5100
55.6000
26.3000
37.8450
0.5600
0.5600
0.4550
7.4100
1.7000
12.0150
1.0900
0.5300
0.5200
0.3200
0.7500
4.1350
1.1950
1.0850
1.1550
0.7450
0.7050
0.5250
1.5450
39.5550
0.7950
  1. 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?

Fingerprints Data Set

fingerprints %>% kable() %>% kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive")) %>% 
  scroll_box(width="100%",height="300px")
X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12 X13 X14 X15 X16 X17 X18 X19 X20 X21 X22 X23 X24 X25 X26 X27 X28 X29 X30 X31 X32 X33 X34 X35 X36 X37 X38 X39 X40 X41 X42 X43 X44 X45 X46 X47 X48 X49 X50 X51 X52 X53 X54 X55 X56 X57 X58 X59 X60 X61 X62 X63 X64 X65 X66 X67 X68 X69 X70 X71 X72 X73 X74 X75 X76 X77 X78 X79 X80 X81 X82 X83 X84 X85 X86 X87 X88 X89 X90 X91 X92 X93 X94 X95 X96 X97 X98 X99 X100 X101 X102 X103 X104 X105 X106 X107 X108 X109 X110 X111 X112 X113 X114 X115 X116 X117 X118 X119 X120 X121 X122 X123 X124 X125 X126 X127 X128 X129 X130 X131 X132 X133 X134 X135 X136 X137 X138 X139 X140 X141 X142 X143 X144 X145 X146 X147 X148 X149 X150 X151 X152 X153 X154 X155 X156 X157 X158 X159 X160 X161 X162 X163 X164 X165 X166 X167 X168 X169 X170 X171 X172 X173 X174 X175 X176 X177 X178 X179 X180 X181 X182 X183 X184 X185 X186 X187 X188 X189 X190 X191 X192 X193 X194 X195 X196 X197 X198 X199 X200 X201 X202 X203 X204 X205 X206 X207 X208 X209 X210 X211 X212 X213 X214 X215 X216 X217 X218 X219 X220 X221 X222 X223 X224 X225 X226 X227 X228 X229 X230 X231 X232 X233 X234 X235 X236 X237 X238 X239 X240 X241 X242 X243 X244 X245 X246 X247 X248 X249 X250 X251 X252 X253 X254 X255 X256 X257 X258 X259 X260 X261 X262 X263 X264 X265 X266 X267 X268 X269 X270 X271 X272 X273 X274 X275 X276 X277 X278 X279 X280 X281 X282 X283 X284 X285 X286 X287 X288 X289 X290 X291 X292 X293 X294 X295 X296 X297 X298 X299 X300 X301 X302 X303 X304 X305 X306 X307 X308 X309 X310 X311 X312 X313 X314 X315 X316 X317 X318 X319 X320 X321 X322 X323 X324 X325 X326 X327 X328 X329 X330 X331 X332 X333 X334 X335 X336 X337 X338 X339 X340 X341 X342 X343 X344 X345 X346 X347 X348 X349 X350 X351 X352 X353 X354 X355 X356 X357 X358 X359 X360 X361 X362 X363 X364 X365 X366 X367 X368 X369 X370 X371 X372 X373 X374 X375 X376 X377 X378 X379 X380 X381 X382 X383 X384 X385 X386 X387 X388 X389 X390 X391 X392 X393 X394 X395 X396 X397 X398 X399 X400 X401 X402 X403 X404 X405 X406 X407 X408 X409 X410 X411 X412 X413 X414 X415 X416 X417 X418 X419 X420 X421 X422 X423 X424 X425 X426 X427 X428 X429 X430 X431 X432 X433 X434 X435 X436 X437 X438 X439 X440 X441 X442 X443 X444 X445 X446 X447 X448 X449 X450 X451 X452 X453 X454 X455 X456 X457 X458 X459 X460 X461 X462 X463 X464 X465 X466 X467 X468 X469 X470 X471 X472 X473 X474 X475 X476 X477 X478 X479 X480 X481 X482 X483 X484 X485 X486 X487 X488 X489 X490 X491 X492 X493 X494 X495 X496 X497 X498 X499 X500 X501 X502 X503 X504 X505 X506 X507 X508 X509 X510 X511 X512 X513 X514 X515 X516 X517 X518 X519 X520 X521 X522 X523 X524 X525 X526 X527 X528 X529 X530 X531 X532 X533 X534 X535 X536 X537 X538 X539 X540 X541 X542 X543 X544 X545 X546 X547 X548 X549 X550 X551 X552 X553 X554 X555 X556 X557 X558 X559 X560 X561 X562 X563 X564 X565 X566 X567 X568 X569 X570 X571 X572 X573 X574 X575 X576 X577 X578 X579 X580 X581 X582 X583 X584 X585 X586 X587 X588 X589 X590 X591 X592 X593 X594 X595 X596 X597 X598 X599 X600 X601 X602 X603 X604 X605 X606 X607 X608 X609 X610 X611 X612 X613 X614 X615 X616 X617 X618 X619 X620 X621 X622 X623 X624 X625 X626 X627 X628 X629 X630 X631 X632 X633 X634 X635 X636 X637 X638 X639 X640 X641 X642 X643 X644 X645 X646 X647 X648 X649 X650 X651 X652 X653 X654 X655 X656 X657 X658 X659 X660 X661 X662 X663 X664 X665 X666 X667 X668 X669 X670 X671 X672 X673 X674 X675 X676 X677 X678 X679 X680 X681 X682 X683 X684 X685 X686 X687 X688 X689 X690 X691 X692 X693 X694 X695 X696 X697 X698 X699 X700 X701 X702 X703 X704 X705 X706 X707 X708 X709 X710 X711 X712 X713 X714 X715 X716 X717 X718 X719 X720 X721 X722 X723 X724 X725 X726 X727 X728 X729 X730 X731 X732 X733 X734 X735 X736 X737 X738 X739 X740 X741 X742 X743 X744 X745 X746 X747 X748 X749 X750 X751 X752 X753 X754 X755 X756 X757 X758 X759 X760 X761 X762 X763 X764 X765 X766 X767 X768 X769 X770 X771 X772 X773 X774 X775 X776 X777 X778 X779 X780 X781 X782 X783 X784 X785 X786 X787 X788 X789 X790 X791 X792 X793 X794 X795 X796 X797 X798 X799 X800 X801 X802 X803 X804 X805 X806 X807 X808 X809 X810 X811 X812 X813 X814 X815 X816 X817 X818 X819 X820 X821 X822 X823 X824 X825 X826 X827 X828 X829 X830 X831 X832 X833 X834 X835 X836 X837 X838 X839 X840 X841 X842 X843 X844 X845 X846 X847 X848 X849 X850 X851 X852 X853 X854 X855 X856 X857 X858 X859 X860 X861 X862 X863 X864 X865 X866 X867 X868 X869 X870 X871 X872 X873 X874 X875 X876 X877 X878 X879 X880 X881 X882 X883 X884 X885 X886 X887 X888 X889 X890 X891 X892 X893 X894 X895 X896 X897 X898 X899 X900 X901 X902 X903 X904 X905 X906 X907 X908 X909 X910 X911 X912 X913 X914 X915 X916 X917 X918 X919 X920 X921 X922 X923 X924 X925 X926 X927 X928 X929 X930 X931 X932 X933 X934 X935 X936 X937 X938 X939 X940 X941 X942 X943 X944 X945 X946 X947 X948 X949 X950 X951 X952 X953 X954 X955 X956 X957 X958 X959 X960 X961 X962 X963 X964 X965 X966 X967 X968 X969 X970 X971 X972 X973 X974 X975 X976 X977 X978 X979 X980 X981 X982 X983 X984 X985 X986 X987 X988 X989 X990 X991 X992 X993 X994 X995 X996 X997 X998 X999 X1000 X1001 X1002 X1003 X1004 X1005 X1006 X1007 X1008 X1009 X1010 X1011 X1012 X1013 X1014 X1015 X1016 X1017 X1018 X1019 X1020 X1021 X1022 X1023 X1024 X1025 X1026 X1027 X1028 X1029 X1030 X1031 X1032 X1033 X1034 X1035 X1036 X1037 X1038 X1039 X1040 X1041 X1042 X1043 X1044 X1045 X1046 X1047 X1048 X1049 X1050 X1051 X1052 X1053 X1054 X1055 X1056 X1057 X1058 X1059 X1060 X1061 X1062 X1063 X1064 X1065 X1066 X1067 X1068 X1069 X1070 X1071 X1072 X1073 X1074 X1075 X1076 X1077 X1078 X1079 X1080 X1081 X1082 X1083 X1084 X1085 X1086 X1087 X1088 X1089 X1090 X1091 X1092 X1093 X1094 X1095 X1096 X1097 X1098 X1099 X1100 X1101 X1102 X1103 X1104 X1105 X1106 X1107
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Near Zero Variance Predictors for Fingerprints

nZVIndices <- nearZeroVar(fingerprints)

cat("No. of Columns with near zero variance:",length(nZVIndices))
## No. of Columns with near zero variance: 719
### Removing the near zero variance predictors from the dataset

fingerprintsTrans <- as.data.frame(fingerprints[,-nZVIndices])
#fingerprintsTrans <- fingerprints[,-nZVIndices]
cat("No. of predictors left in the data set:", ncol(fingerprintsTrans))
## No. of predictors left in the data set: 388
  1. 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 \({ R }^{ 2 }\)?

Reduce predictors with high correlation

corThresh <- 0.9
tooHigh <- findCorrelation(cor(fingerprintsTrans), corThresh)
corrPred <- names(fingerprintsTrans)[tooHigh]
fingerprintsTrans <- fingerprintsTrans[,-tooHigh]

Train/Test strategy

Considering the fact that no. of predictors (388) is actually much higher than the data sample size (165), I am going to use a 80-20 split for train/test, and then I am planning to use a k fold cross validation (CV) as a viable resampling strategy for model fitting.

## Merging the permeability dataset with fingerprints
fingerprintsTrans$permeability <- permeability

trainingrows <- createDataPartition(fingerprintsTrans$permeability, times = 1, p = 0.8, list = FALSE)

trainData <- fingerprintsTrans[trainingrows,]
testData <- fingerprintsTrans[-trainingrows,]

Pre-Processing

Since in this case, all the finegrprint predictors are binary in nature, pre-processing will have very little accomplishment with pre-processing steps like Box Cox, Center, Scale etc.

PLS Model Training

I have used train() function to fit a Partial Least Square (PLS) model with k-fold cross validation estimate, and 10 components as below -

ctrl <- trainControl("cv", number = 10)

pls_model_fit <- train(permeability ~ ., data = trainData,
                   method = "pls",
                   tuneLength = 25,
                   trControl = ctrl,
                   preProc = c("center", "scale"))

summary(pls_model_fit)
## Data:    X dimension: 133 110 
##  Y dimension: 133 1
## Fit method: oscorespls
## Number of components considered: 5
## TRAINING: % variance explained
##           1 comps  2 comps  3 comps  4 comps  5 comps
## X           12.82    20.68    25.25    32.92    39.07
## .outcome    47.65    58.74    67.51    71.08    73.55
# Plot model RMSE vs different values of components
title <- paste("Training Set RMSE Minimized at",
               pls_model_fit$bestTune$ncomp,
               "Components")

plot(pls_model_fit, main = title)

Estimated No. of latent variables (components)

nComp <- pls_model_fit$bestTune$ncomp
  
cat("Optimal no. of latent variables:", nComp)
## Optimal no. of latent variables: 5

Estimate of \({ R }^{ 2 }\)

pls_model_fit$results %>%
  filter(ncomp == pls_model_fit$bestTune$ncomp) %>%
  select(ncomp, RMSE, Rsquared) %>% kable() %>% kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive")) %>% 
  scroll_box(width="100%",height="150px")
ncomp RMSE Rsquared
5 10.87842 0.5255775

Based on above, the optimal no. of latent variables are 6 and they explain 54% of the variance.

  1. Predict the response for the test set. What is the test set estimate of \({ R }^{ 2 }\)?

Prediction on Test Data

plsPredict <- predict(pls_model_fit, newdata = testData)

plsPredict
##  [1] -1.9267982  7.3446338  8.7456010  1.0396690 18.3345446  7.1084301
##  [7] -0.8999869 17.0157827 -6.5943957 10.8528926  3.7166889 17.0157827
## [13] 14.3214338 35.0972369 18.7377264 22.4157545  9.4191152  7.6288780
## [19]  9.3758167 20.7800960 -3.1424171 -1.8051811  6.3094212 32.1277481
## [25] 40.2810068 42.0118153 -2.3268382 28.3545620  8.4545866  0.2037227
## [31] 13.5634125  9.7652590

Plot for PLS Rediction

plot(testData$permeability, plsPredict, ylim=c(-20,80), xlim=c(-20,80),main="Test Dataset", xlab="observed", ylab="PLS Predicted")
abline(0, 1, col="red")

Estimate of \({ R }^{ 2 }\)

results <- data.frame(Model = "PLS",
                      RMSE = caret::RMSE(plsPredict, testData$permeability),
                      Rsquared = caret::R2(plsPredict, testData$permeability))

results %>% kable() %>% kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive")) %>% 
  scroll_box(width="100%",height="150px")
Model RMSE Rsquared
permeability PLS 11.13834 0.5255599

Test set estimate of \({ R }^{ 2 }\) is 75%.

  1. Try building other models discussed in this chapter. Do any have better predictive performance?

Model2: Principal Component Regression (PCR) Model

pcr_model_fit <- train(
  permeability ~ ., data = trainData, method = "pcr",
  center = TRUE,
  trControl = ctrl,
  tuneLength = 25
)

summary(pcr_model_fit)
## Data:    X dimension: 133 110 
##  Y dimension: 133 1
## Fit method: svdpc
## Number of components considered: 25
## TRAINING: % variance explained
##           1 comps  2 comps  3 comps  4 comps  5 comps  6 comps  7 comps
## X           19.15    31.40    39.58    46.85    53.31    58.52    63.04
## .outcome    19.59    24.07    42.87    44.74    45.36    46.33    46.68
##           8 comps  9 comps  10 comps  11 comps  12 comps  13 comps  14 comps
## X           67.24    70.63     73.34     75.78     77.88     79.73     81.45
## .outcome    46.88    47.61     48.79     52.46     52.52     52.56     53.11
##           15 comps  16 comps  17 comps  18 comps  19 comps  20 comps  21 comps
## X            82.93     84.31     85.48     86.59     87.62     88.55     89.44
## .outcome     57.41     59.33     59.91     60.51     61.16     61.19     63.64
##           22 comps  23 comps  24 comps  25 comps
## X            90.26     91.02     91.67     92.27
## .outcome     63.65     65.14     65.23     65.24
# Plot model RMSE vs different values of components
title <- paste("Training Set RMSE Minimized at",
               pcr_model_fit$bestTune$ncomp,
               "Components")

plot(pcr_model_fit, main = title)

PCR Model Predition and Metrics

pcr_predictions <- predict(pcr_model_fit, testData)

pcr_results <- data.frame(Model = "PCR",
                          RMSE = caret::RMSE(pcr_predictions, testData$permeability),
                          Rsquared = caret::R2(pcr_predictions, testData$permeability))

pcr_results %>% kable() %>% kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive")) %>% 
  scroll_box(width="100%",height="150px")
Model RMSE Rsquared
permeability PCR 12.36182 0.4208261

Model3: Ridge Regression

I have used enet() function of elasticnet package with lambda argument specifying the ridge-regression penalty -

ridgeModel <- enet(x = as.matrix(trainData[,-ncol(trainData)]), y = trainData$permeability, lambda = 0.001)

summary(ridgeModel)
##           Length Class  Mode     
## call          4  -none- call     
## actions     185  -none- list     
## allset      110  -none- numeric  
## beta.pure 20350  -none- numeric  
## vn          110  -none- character
## mu            1  -none- numeric  
## normx       110  -none- numeric  
## meanx       110  -none- numeric  
## lambda        1  -none- numeric  
## L1norm      185  -none- numeric  
## penalty     185  -none- numeric  
## df          185  -none- numeric  
## Cp          185  -none- numeric  
## sigma2        1  -none- numeric
plot(ridgeModel)

Ridge Regression Model Predition and Metrics

ridgePred <- predict(ridgeModel, newx = as.matrix(testData), s = 1, mode = "fraction", type = "fit")



df <- as.data.frame(ridgePred$fit, row.names = NULL, col.names=c("Index","Pred"))

ridge_results <- data.frame(Model = "Ridge Regression",
                          RMSE = caret::RMSE(df$`ridgePred$fit`, testData$permeability),
                          Rsquared = caret::R2(df$`ridgePred$fit`, testData$permeability))

ridge_results %>% kable() %>% kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive")) %>% 
  scroll_box(width="100%",height="150px")
Model RMSE Rsquared
permeability Ridge Regression 14.40168 0.30547

Further to tune over the penalty term lambda, train() can be used with a different method -

ridgeGrid <- data.frame(.lambda = seq(0, .1, length = 15))

ctrl <- trainControl(method = "cv", number = 10)

ridgeRegFit <- train(permeability~.,data = trainData, method = "ridge", tuneGrid = ridgeGrid, trControl = ctrl, preProc = c("center", "scale"))

ridgeRegFit
## Ridge Regression 
## 
## 133 samples
## 110 predictors
## 
## Pre-processing: centered (110), scaled (110) 
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 119, 120, 121, 119, 120, 118, ... 
## Resampling results across tuning parameters:
## 
##   lambda       RMSE          Rsquared   MAE         
##   0.000000000  6.884794e+06  0.1347097  1.910905e+06
##   0.007142857  1.480276e+01  0.3621217  1.076722e+01
##   0.014285714  1.406054e+01  0.3800321  1.024993e+01
##   0.021428571  1.364187e+01  0.3919257  9.924294e+00
##   0.028571429  1.335330e+01  0.4014247  9.733680e+00
##   0.035714286  1.313593e+01  0.4094403  9.583856e+00
##   0.042857143  1.296378e+01  0.4163896  9.473928e+00
##   0.050000000  1.282301e+01  0.4225196  9.391291e+00
##   0.057142857  1.270534e+01  0.4279947  9.318818e+00
##   0.064285714  1.260537e+01  0.4329319  9.262764e+00
##   0.071428571  1.251943e+01  0.4374179  9.212622e+00
##   0.078571429  1.244485e+01  0.4415196  9.166393e+00
##   0.085714286  1.237967e+01  0.4452893  9.124926e+00
##   0.092857143  1.232240e+01  0.4487692  9.090496e+00
##   0.100000000  1.227185e+01  0.4519937  9.060533e+00
## 
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was lambda = 0.1.

Model4: Lasso Regression Model

lr_cv <- cv.glmnet(as.matrix(trainData[,-ncol(trainData)]), trainData$permeability, alpha = 1)
lr_model <- glmnet(as.matrix(trainData[,-ncol(trainData)]), trainData$permeability, alpha = 1, lambda = lr_cv$lambda.min)

summary(lr_model)
##           Length Class     Mode   
## a0          1    -none-    numeric
## beta      110    dgCMatrix S4     
## df          1    -none-    numeric
## dim         2    -none-    numeric
## lambda      1    -none-    numeric
## dev.ratio   1    -none-    numeric
## nulldev     1    -none-    numeric
## npasses     1    -none-    numeric
## jerr        1    -none-    numeric
## offset      1    -none-    logical
## call        5    -none-    call   
## nobs        1    -none-    numeric

Lasso Regression Model Prediction and Results

lr_predictions <- as.vector(predict(lr_model, as.matrix(testData[,-ncol(testData)])))
lr_results <- data.frame(Model = "Lasso Regression",
                         RMSE = caret::RMSE(lr_predictions, testData$permeability),
                         Rsquared = caret::R2(lr_predictions, testData$permeability))

lr_results %>% kable() %>% kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive")) %>% 
  scroll_box(width="100%",height="150px")
Model RMSE Rsquared
permeability Lasso Regression 12.34414 0.4171132

Model5: Elastic Net Regression

en_model_fit <- train(
  permeability ~ ., data = trainData, method = "glmnet",
  trControl = ctrl,
  tuneLength = 10
)
## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo, :
## There were missing values in resampled performance measures.
summary(en_model_fit)
##             Length Class      Mode     
## a0            100  -none-     numeric  
## beta        11000  dgCMatrix  S4       
## df            100  -none-     numeric  
## dim             2  -none-     numeric  
## lambda        100  -none-     numeric  
## dev.ratio     100  -none-     numeric  
## nulldev         1  -none-     numeric  
## npasses         1  -none-     numeric  
## jerr            1  -none-     numeric  
## offset          1  -none-     logical  
## call            5  -none-     call     
## nobs            1  -none-     numeric  
## lambdaOpt       1  -none-     numeric  
## xNames        110  -none-     character
## problemType     1  -none-     character
## tuneValue       2  data.frame list     
## obsLevels       1  -none-     logical  
## param           0  -none-     list
plot(en_model_fit)

Model Prediction and Results

en_predictions <- en_model_fit %>% predict(testData[,-ncol(testData)])
# Model performance metrics
en_results <- data.frame(Model = "Elastic Net Regression",
                         RMSE = caret::RMSE(en_predictions, testData$permeability),
                         Rsquared = caret::R2(en_predictions, testData$permeability))

en_results %>% kable() %>% kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive")) %>% 
  scroll_box(width="100%",height="150px")
Model RMSE Rsquared
permeability Elastic Net Regression 12.1962 0.4324368
  1. Would you recommend any of your models to replace the permeability laboratory experiment?
model_results <- rbind(results, pcr_results, ridge_results, lr_results, en_results)

rownames(model_results) <- NULL

model_results %>% kable() %>% kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive")) %>% 
  scroll_box(width="100%",height="300px")
Model RMSE Rsquared
PLS 11.13834 0.5255599
PCR 12.36182 0.4208261
Ridge Regression 14.40168 0.3054700
Lasso Regression 12.34414 0.4171132
Elastic Net Regression 12.19620 0.4324368

Out of all the models, the one that produce the best \({ R }^{ 2 }\) is Elastic Net. Hence I propose using that model for predicting permeability and this model can replace the lab expreiment after further tuning.

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:

  1. Start R and use these commands to load the data:

> library(AppliedPredictiveModeling) > data(chemicalManufacturing)

The matrix processPredictors contains the 57 predictors (12 describing the input biological material and 45 describing the process predictors) for the 176 manufacturing runs. yield contains the percent yield for each run.

Data set Preview

data(ChemicalManufacturingProcess)

ChemicalManufacturingProcess %>% kable() %>% kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive")) %>% 
  scroll_box(width="100%",height="300px")
Yield BiologicalMaterial01 BiologicalMaterial02 BiologicalMaterial03 BiologicalMaterial04 BiologicalMaterial05 BiologicalMaterial06 BiologicalMaterial07 BiologicalMaterial08 BiologicalMaterial09 BiologicalMaterial10 BiologicalMaterial11 BiologicalMaterial12 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess09 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess13 ManufacturingProcess14 ManufacturingProcess15 ManufacturingProcess16 ManufacturingProcess17 ManufacturingProcess18 ManufacturingProcess19 ManufacturingProcess20 ManufacturingProcess21 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess32 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess37 ManufacturingProcess38 ManufacturingProcess39 ManufacturingProcess40 ManufacturingProcess41 ManufacturingProcess42 ManufacturingProcess43 ManufacturingProcess44 ManufacturingProcess45
38.00 6.25 49.58 56.97 12.74 19.51 43.73 100.00 16.66 11.44 3.46 138.09 18.83 NA NA NA NA NA NA NA NA 43.00 NA NA NA 35.5 4898 6108 4682 35.5 4865 6049 4665 0.0 NA NA NA 4873 6074 4685 10.7 21.0 9.9 69.1 156 66 2.4 486 0.019 0.5 3 7.2 NA NA 11.6 3.0 1.8 2.4
42.44 8.01 60.97 67.48 14.65 19.36 53.14 100.00 19.04 12.55 3.46 153.67 21.05 0.0 0.0 NA 917 1032.2 210.0 177 178 46.57 NA NA 0 34.0 4869 6095 4617 34.0 4867 6097 4621 0.0 3 0 3 4869 6107 4630 11.2 21.4 9.9 68.7 169 66 2.6 508 0.019 2.0 2 7.2 0.1 0.15 11.1 0.9 1.9 2.2
42.03 8.01 60.97 67.48 14.65 19.36 53.14 100.00 19.04 12.55 3.46 153.67 21.05 0.0 0.0 NA 912 1003.6 207.1 178 178 45.07 NA NA 0 34.8 4878 6087 4617 34.8 4877 6078 4621 0.0 4 1 4 4897 6116 4637 11.1 21.3 9.4 69.3 173 66 2.6 509 0.018 0.7 2 7.2 0.0 0.00 12.0 1.0 1.8 2.3
41.42 8.01 60.97 67.48 14.65 19.36 53.14 100.00 19.04 12.55 3.46 153.67 21.05 0.0 0.0 NA 911 1014.6 213.3 177 177 44.92 NA NA 0 34.8 4897 6102 4635 34.8 4872 6073 4611 0.0 5 2 5 4892 6111 4630 11.1 21.3 9.4 69.3 171 68 2.5 496 0.018 1.2 2 7.2 0.0 0.00 10.6 1.1 1.8 2.1
42.49 7.47 63.33 72.25 14.02 17.91 54.66 100.00 18.22 12.80 3.05 147.61 21.05 10.7 0.0 NA 918 1027.5 205.7 178 178 44.96 NA NA 0 34.6 4992 6233 4733 33.9 4886 6102 4659 -0.7 8 4 18 4930 6151 4684 11.3 21.6 9.0 69.4 171 70 2.5 468 0.017 0.2 2 7.3 0.0 0.00 11.0 1.1 1.7 2.1
43.57 6.12 58.36 65.31 15.17 21.79 51.23 100.00 18.30 12.13 3.78 151.88 20.76 12.0 0.0 NA 924 1016.8 208.9 178 178 45.32 NA NA 0 34.0 4985 6222 4786 33.4 4862 6115 4696 -0.6 9 1 1 4871 6128 4687 11.4 21.7 10.1 68.2 173 70 2.5 490 0.018 0.4 2 7.2 0.0 0.00 11.5 2.2 1.8 2.0
43.12 7.48 64.47 72.41 13.82 17.71 54.45 100.00 18.72 12.95 3.04 147.11 20.75 11.5 0.0 1.56 933 988.9 210.0 177 178 49.36 11.6 11.5 0 32.4 4745 5999 4486 33.8 4758 6013 4522 1.4 1 1 1 4795 6057 4572 11.2 21.2 11.2 67.6 159 65 2.5 475 0.019 0.8 2 7.3 0.0 0.00 11.7 0.7 2.0 2.2
43.06 6.94 63.60 72.06 15.70 19.42 54.72 100.00 18.85 13.13 3.85 154.20 21.45 12.0 0.0 1.55 929 1010.9 211.7 178 178 48.68 10.2 11.3 0 33.6 4854 6105 4626 33.6 4766 6022 4552 0.0 2 2 2 4806 6059 4586 11.1 21.2 10.9 67.9 161 65 2.5 478 0.019 1.0 2 7.3 0.0 0.00 11.4 0.8 2.0 2.2
41.49 6.94 63.60 72.06 15.70 19.42 54.72 100.00 18.85 13.13 3.85 154.20 21.45 12.0 0.0 1.56 928 1003.5 208.7 177 177 47.20 9.7 11.1 0 33.9 4893 6144 4658 33.9 4769 6033 4556 0.0 3 3 3 4842 6103 4609 11.3 21.5 10.5 68.0 160 65 2.5 491 0.019 1.2 3 7.4 0.0 0.00 11.4 0.9 1.9 2.1
42.45 6.94 63.60 72.06 15.70 19.42 54.72 100.00 18.85 13.13 3.85 154.20 21.45 12.0 0.0 1.55 938 1003.8 209.8 177 177 47.11 10.1 10.2 0 34.3 4846 6077 4614 35.3 4840 6091 4614 1.0 4 1 4 4893 6135 4650 11.4 21.7 9.8 68.5 164 66 2.5 488 0.019 1.8 3 7.1 0.0 0.00 11.3 0.8 1.9 2.4
42.04 7.17 61.23 70.01 13.36 18.67 52.83 100.00 17.88 12.62 2.90 143.28 20.21 10.3 0.0 1.55 932 983.1 209.4 177 177 46.24 9.0 9.5 0 35.8 4944 6156 4690 35.8 4900 6126 4665 0.0 6 3 6 4925 6161 4687 11.5 21.9 9.4 68.7 166 67 2.5 493 0.019 1.5 2 7.0 0.0 0.00 11.0 1.0 1.9 1.8
42.68 7.17 61.23 70.01 13.36 18.67 52.83 100.00 17.88 12.62 2.90 143.28 20.21 10.3 0.0 1.55 930 992.0 209.4 178 178 46.10 8.8 9.7 0 35.6 4959 6178 4708 35.2 4878 6134 4673 -0.4 7 4 7 4924 6161 4692 11.5 22.0 9.4 68.6 169 67 2.5 498 0.018 0.3 3 7.0 0.0 0.00 11.2 0.8 2.0 1.8
43.44 7.17 61.23 70.01 13.36 18.67 52.83 100.00 17.88 12.62 2.90 143.28 20.21 10.3 0.0 1.55 934 1004.1 207.8 177 177 47.53 9.3 10.4 0 35.1 4917 6158 4704 35.1 4835 6090 4651 0.0 8 1 8 4888 6129 4653 11.4 21.7 9.9 68.4 166 68 2.4 490 0.018 1.1 3 7.1 0.0 0.00 11.1 0.8 1.9 2.4
40.28 7.63 60.51 69.24 17.59 20.67 52.83 100.00 18.74 13.21 4.94 158.42 21.77 11.1 0.0 1.59 934 1036.8 209.1 178 178 45.28 9.6 9.8 0 34.9 4882 6108 4655 35.8 4858 6070 4628 0.9 10 2 2 4911 6124 4684 11.1 21.5 9.4 69.1 161 66 2.4 490 0.019 0.6 3 7.4 0.0 0.00 11.7 0.6 1.7 1.9
41.50 6.23 62.93 69.74 11.80 20.54 54.57 100.00 18.89 12.82 2.30 152.83 22.18 11.3 0.0 NA 930 1120.7 207.8 177 177 46.44 9.4 10.2 0 35.3 4918 6156 4690 35.3 4849 6093 4646 0.0 11 3 15 4874 6125 4659 11.3 21.6 9.9 68.5 160 64 2.5 490 0.019 1.6 3 7.2 0.0 0.00 11.6 0.8 1.9 2.0
41.21 7.13 60.30 68.18 13.80 20.72 52.49 100.00 18.68 12.75 3.25 152.82 21.35 11.1 0.0 NA 928 1073.6 207.1 177 177 45.40 9.6 10.2 0 35.4 4805 6124 4666 35.5 4842 6091 4641 0.1 12 4 16 4848 6095 4630 11.1 21.2 10.3 68.5 166 66 2.5 493 0.019 1.2 3 7.3 0.1 0.20 11.6 1.0 1.9 2.5
40.89 7.85 58.22 66.95 15.38 20.86 50.84 100.00 18.51 12.70 4.01 152.82 20.70 11.1 0.0 NA 928 1027.5 205.9 177 177 45.54 9.0 10.0 0 35.8 4942 6177 4725 35.8 4858 6100 4656 0.0 1 1 1 4860 6100 4659 11.1 21.3 10.0 68.7 167 68 2.5 495 0.019 1.3 3 7.4 0.0 0.00 11.5 1.1 1.9 2.3
40.14 7.64 59.44 67.22 15.67 21.50 52.02 100.00 18.72 12.86 4.16 156.51 21.47 12.4 0.0 NA 930 1021.4 208.4 177 177 45.73 9.5 10.6 0 35.5 4899 6123 4692 35.5 4811 6041 4636 0.0 2 1 2 4815 6055 4631 10.8 20.9 10.6 69.0 157 64 2.5 497 0.020 1.1 3 7.4 0.0 0.00 11.7 1.7 1.8 2.2
39.30 7.51 59.74 67.28 15.72 21.80 52.30 100.00 18.81 12.98 4.24 158.36 21.82 12.7 0.0 NA 929 1092.2 207.5 178 178 44.46 8.9 9.8 0 35.5 4957 6181 4751 35.5 4887 6124 4710 0.0 3 2 3 4876 6109 4696 11.1 21.4 9.8 68.8 156 64 2.4 514 0.021 0.7 3 7.3 0.0 0.00 11.6 1.8 1.7 2.3
39.53 7.51 59.74 67.28 15.72 21.80 52.30 100.00 18.81 12.98 4.24 158.36 21.82 12.7 0.0 NA 929 1175.3 204.1 177 177 45.02 8.9 9.9 0 35.6 4961 6180 4775 35.6 4869 6094 4690 0.0 4 3 4 4850 6094 4665 11.0 21.2 10.1 68.7 155 62 2.5 490 0.020 1.2 2 7.3 0.0 0.00 11.4 1.5 1.5 2.0
40.22 7.51 59.74 67.28 15.72 21.80 52.30 100.00 18.81 12.98 4.24 158.36 21.82 12.7 0.0 1.56 925 1102.8 206.6 178 178 45.22 9.0 10.0 0 35.2 4949 6161 4766 35.2 4871 6108 4705 0.0 5 4 5 4879 6117 4696 11.1 21.5 9.9 68.7 157 63 2.5 495 0.020 0.9 3 7.3 0.1 0.20 11.4 2.0 1.6 2.0
41.18 7.08 61.83 70.69 13.43 17.72 53.27 100.00 19.14 13.38 3.02 153.10 21.90 10.9 0.0 NA 936 1024.4 218.7 178 178 47.04 NA NA 0 33.2 4791 6026 4482 35.7 0 6111 0 2.5 6 2 16 4918 6152 4618 11.4 21.1 8.8 70.1 162 68 2.4 479 0.018 0.9 2 7.4 0.0 0.00 11.9 0.8 1.9 2.1
40.70 6.58 58.38 67.17 12.22 18.46 51.45 100.00 18.22 12.83 2.69 148.49 21.23 11.1 0.0 NA 937 997.7 209.6 177 177 46.43 NA NA 0 32.9 NA 6002 0 36.5 4902 6120 4621 3.6 7 3 17 4906 6134 4626 11.2 21.0 8.9 70.1 160 66 2.4 492 0.019 1.5 3 7.4 0.0 0.00 11.6 0.8 1.9 2.4
41.89 6.27 56.23 64.98 11.47 18.93 50.31 100.00 17.64 12.48 2.49 145.61 20.81 11.3 0.0 NA 940 1031.3 215.1 177 177 47.09 NA NA 0 33.6 4864 6085 4615 35.1 4847 6072 4607 1.5 1 1 1 4875 6095 4606 11.2 20.9 9.5 69.7 161 65 2.5 468 0.018 1.3 2 7.2 0.0 0.00 11.4 1.1 2.0 1.8
43.38 8.17 63.66 73.44 18.37 23.76 56.64 100.00 17.94 12.18 4.15 151.54 20.27 9.0 0.0 1.54 934 1007.3 209.4 178 178 47.28 11.1 9.0 0 33.3 4750 5994 4517 36.3 4887 6146 4653 3.0 5 5 12 4907 6150 4631 11.5 21.3 9.2 69.5 167 66 2.5 505 0.019 1.0 2 7.2 0.0 0.00 11.5 0.7 1.7 2.4
36.83 6.60 55.74 66.25 11.83 22.52 48.95 100.00 16.67 12.11 2.75 140.84 19.07 11.6 0.0 1.52 930 950.7 203.6 178 178 38.89 9.2 7.6 0 37.3 4840 5988 4577 40.0 4971 6114 4657 2.7 1 1 6 4990 6160 4693 11.0 21.0 7.5 71.5 161 65 2.5 500 0.019 0.9 3 6.9 0.0 0.00 11.8 0.8 1.7 2.2
35.25 6.90 54.26 60.99 12.22 20.16 47.23 100.00 16.57 11.73 3.06 139.52 18.62 9.2 0.0 1.53 926 955.8 203.0 177 178 39.02 8.4 7.5 0 38.0 4894 6022 4590 40.0 4971 6107 4675 2.0 2 2 7 4966 6112 4660 10.7 20.6 7.6 71.9 159 65 2.4 492 0.019 0.9 3 7.1 0.0 0.00 11.7 0.7 1.7 2.0
36.12 6.86 55.66 63.43 12.53 20.39 48.94 100.00 16.71 11.94 3.07 142.45 19.12 9.2 0.0 1.54 922 975.8 203.6 178 178 40.46 7.8 7.5 0 38.1 4942 6081 4645 39.3 4967 6117 4664 1.2 3 3 8 4961 6112 4649 10.7 20.5 7.6 71.8 157 64 2.5 522 0.021 0.9 3 7.4 0.0 0.00 11.6 1.3 1.7 2.2
38.52 6.67 63.44 76.94 14.28 21.67 58.42 100.00 17.47 13.12 3.10 158.66 21.88 9.2 0.0 1.52 924 986.9 206.4 177 177 42.67 7.5 7.7 0 38.6 5055 6213 4714 37.7 4960 6123 4639 -0.9 4 4 9 4966 6137 4641 10.8 20.7 7.6 71.7 158 63 2.5 499 0.020 1.9 3 7.3 0.1 0.20 11.7 0.8 1.7 2.2
38.35 6.53 61.68 77.15 11.81 21.12 59.38 100.00 17.31 12.83 2.14 154.56 22.18 10.4 0.0 1.52 921 1001.1 205.5 178 178 44.95 9.4 9.0 0 35.3 4831 6017 4556 35.3 4866 6028 4573 0.0 6 4 4 4863 6039 4564 10.6 20.1 9.0 70.9 157 64 2.5 504 0.020 0.7 3 6.8 0.0 0.00 11.6 0.5 1.9 2.2
39.98 6.89 61.54 76.07 12.41 21.14 57.89 100.00 17.42 12.79 2.35 153.00 21.58 10.3 0.0 1.54 928 1006.7 206.2 177 177 46.27 9.0 9.1 0 35.4 4872 6050 4585 35.0 4857 6036 4579 -0.4 7 1 5 4872 6060 4583 10.7 20.4 9.1 70.6 160 63 2.5 486 0.019 1.6 2 7.1 0.0 0.00 11.7 0.6 2.0 2.4
41.87 7.13 61.39 74.10 13.27 20.96 55.95 100.00 17.58 12.63 2.61 151.00 20.80 11.2 0.0 1.53 926 1024.0 208.2 178 178 47.08 10.7 9.5 0 33.5 4756 5972 4515 34.0 4854 6069 4600 0.5 8 2 6 4842 6057 4574 10.9 20.4 9.7 69.9 163 66 2.5 486 0.019 0.7 2 7.1 0.0 0.00 11.6 0.6 2.0 2.1
43.62 6.84 61.46 73.91 13.18 20.77 56.39 100.00 17.56 12.55 2.53 151.48 20.99 11.6 0.0 1.52 923 1041.2 207.3 177 177 48.77 10.1 10.5 0 33.4 4815 6033 4569 33.4 4773 5991 4521 0.0 9 3 7 4820 6042 4563 10.9 20.4 10.0 69.6 161 64 2.5 476 0.018 1.6 2 7.2 0.1 0.10 11.6 0.7 1.9 2.4
38.60 5.17 61.17 76.39 12.51 20.32 58.17 100.00 17.79 13.05 2.50 157.45 22.21 10.6 0.0 1.52 928 999.5 209.4 178 178 45.78 9.8 9.7 0 34.5 4811 5992 4578 34.5 4823 6010 4579 0.0 5 5 12 4829 6020 4590 10.6 20.1 9.7 70.3 156 61 2.5 496 0.020 1.1 2 7.5 0.1 0.10 11.6 0.5 1.8 2.3
39.65 7.01 61.30 72.71 13.23 24.85 54.89 100.00 17.38 12.47 2.76 149.46 20.42 11.6 0.0 1.53 925 1010.3 209.1 177 177 44.77 9.4 9.3 0 34.6 4852 6047 4852 34.4 4861 6073 4759 -0.2 3 3 16 4854 6061 4654 10.7 20.4 9.5 70.1 155 61 2.5 507 0.020 1.7 3 7.3 0.0 0.00 11.7 0.6 1.9 2.6
40.87 6.30 57.04 70.03 11.70 18.04 50.50 100.00 17.27 12.79 2.41 145.62 20.18 12.5 0.0 1.53 930 1002.4 207.5 177 177 46.65 9.7 10.0 4549 33.9 4844 6057 4562 33.1 4821 6033 4547 -0.8 1 1 13 4818 6041 4537 10.9 20.4 10.1 69.5 153 63 2.4 481 0.020 1.0 2 7.4 0.1 0.20 11.0 0.9 2.0 2.1
42.46 5.32 59.14 71.05 13.02 21.17 52.58 100.00 16.94 12.32 2.46 144.80 20.03 11.9 19.7 1.53 926 1019.6 206.4 178 178 46.17 9.4 10.2 4549 33.4 4854 6051 4595 32.2 4794 5992 4552 -1.2 3 2 2 4798 5982 4534 10.4 19.8 10.1 70.1 166 65 2.6 495 0.019 0.9 3 7.1 0.0 0.00 11.2 1.1 1.9 2.4
42.66 5.32 59.14 71.05 13.02 21.17 52.58 100.00 16.94 12.32 2.46 144.80 20.03 11.9 19.9 1.52 924 1008.6 208.7 177 177 46.38 9.7 10.0 4549 33.1 4825 6028 4571 32.6 4798 5986 4552 -0.5 4 3 3 4820 6006 4552 10.5 20.0 9.8 70.2 166 65 2.5 484 0.018 1.7 2 7.1 0.0 0.00 11.1 1.2 1.8 2.4
42.23 5.32 59.14 71.05 13.02 21.17 52.58 100.00 16.94 12.32 2.46 144.80 20.03 11.9 19.3 1.54 926 1014.3 208.7 178 178 45.92 9.5 10.0 4549 33.0 4838 6029 4593 32.6 4800 5991 4562 -0.4 5 4 4 4820 6013 4554 10.6 20.1 9.8 70.1 166 68 2.4 506 0.019 0.0 2 7.1 0.1 0.20 11.0 1.5 1.8 2.4
41.43 5.71 57.68 69.37 12.26 21.32 50.79 100.00 17.01 12.44 2.46 143.94 19.78 11.0 19.5 1.52 924 1027.0 206.6 177 177 46.77 10.2 9.8 4549 32.8 4806 6002 4591 32.8 4831 6027 4603 0.0 7 2 6 4847 6053 4607 10.9 20.5 9.7 69.9 160 65 2.5 488 0.019 0.0 2 7.2 0.0 0.00 11.4 1.0 1.9 2.3
41.47 6.60 58.80 71.17 12.40 22.14 52.24 100.00 17.21 12.77 2.58 148.28 20.33 11.3 19.3 1.52 925 1015.0 205.9 178 178 46.69 9.8 10.0 4549 33.0 4828 6020 4587 32.6 4815 6005 4582 -0.4 8 3 7 4837 6050 4598 10.9 20.4 9.8 59.8 159 64 2.5 493 0.019 0.0 2 7.2 0.0 0.00 10.9 1.0 1.9 2.2
42.07 6.76 55.42 69.80 11.25 18.15 49.89 100.00 17.61 13.40 2.57 151.50 20.88 10.8 22.5 1.48 936 954.7 211.2 177 177 45.95 11.1 10.5 4549 32.8 4713 5904 4467 32.8 4750 5927 4497 0.0 1 1 1 4784 5974 4543 10.3 19.6 10.1 70.3 157 61 2.6 509 0.020 1.1 3 7.4 0.0 0.00 11.4 0.7 1.8 2.4
44.35 6.76 55.42 69.80 11.25 18.15 49.89 100.00 17.61 13.40 2.57 151.50 20.88 10.8 20.5 1.53 923 954.0 210.0 178 177 46.66 8.1 8.9 4549 33.3 4934 6110 4635 32.5 4873 6058 4598 -0.8 2 2 2 4900 6089 4617 10.8 20.5 8.6 70.8 163 64 2.5 498 0.019 0.9 3 7.3 0.1 0.10 11.4 0.7 2.0 2.4
44.16 6.76 55.42 69.80 11.25 18.15 49.89 100.00 17.61 13.40 2.57 151.50 20.88 10.8 21.5 1.55 930 969.3 208.7 177 178 47.33 9.3 9.3 4549 32.5 4836 6014 4564 32.3 4844 6032 4577 -0.2 3 3 3 4869 6061 4603 10.7 20.3 9.0 70.7 160 63 2.5 501 0.020 1.0 3 7.1 0.0 0.00 11.0 0.7 1.8 2.4
43.33 6.77 58.76 72.74 12.12 20.65 53.17 100.00 17.59 13.31 2.61 154.06 21.31 11.4 20.5 1.56 928 980.3 208.2 178 178 46.78 9.0 8.8 4549 32.8 4869 6061 4583 32.3 4905 6117 4635 -0.5 4 4 4 4885 6098 4611 11.0 20.6 8.9 70.4 162 64 2.5 490 0.019 0.3 2 7.1 0.0 0.00 10.5 0.9 1.8 2.1
42.61 6.95 60.31 73.97 12.42 19.05 52.31 100.00 17.64 13.28 2.75 151.21 20.75 12.2 20.5 1.50 926 986.4 208.7 177 177 46.48 8.5 9.2 4549 33.2 4914 6108 4594 32.4 4850 6025 4535 -0.8 5 5 5 4854 6034 4547 10.6 20.0 9.1 70.9 165 65 2.5 490 0.019 1.2 3 7.0 0.0 0.00 10.7 0.7 1.8 2.3
42.96 6.95 60.31 73.97 12.42 19.05 52.31 100.00 17.64 13.28 2.75 151.21 20.75 12.2 20.5 1.50 925 977.8 227.4 178 178 46.03 9.4 9.1 4549 32.6 4833 6009 4521 32.6 4853 6027 4538 0.0 6 6 6 4864 6056 4556 10.7 20.2 9.0 70.7 168 65 2.6 492 0.018 0.7 3 7.4 0.0 0.00 11.1 1.1 1.8 2.1
43.84 6.95 60.31 73.97 12.42 19.05 52.31 100.00 17.64 13.28 2.75 151.21 20.75 12.2 20.0 1.56 927 1006.4 210.7 177 177 48.11 8.9 9.9 4549 32.6 4883 6146 4533 31.3 4812 6082 4484 -1.3 7 1 7 4816 6086 4481 11.0 20.2 9.9 69.9 164 69 2.4 493 0.019 1.8 3 6.7 0.1 0.10 11.6 1.4 1.8 2.4
46.34 7.97 64.75 74.10 15.11 22.66 56.22 100.00 18.82 12.76 3.18 157.34 21.33 11.7 18.0 1.52 921 1002.4 209.8 177 178 47.45 9.5 9.6 4549 32.1 4855 6077 4563 31.5 4836 6055 4551 -0.6 9 3 9 4850 6099 4548 11.2 20.7 9.6 69.7 167 68 2.4 490 0.018 0.6 3 7.3 0.0 0.00 11.6 1.3 1.8 2.1
39.74 6.94 57.02 69.51 13.45 18.44 50.16 100.00 17.55 12.83 3.09 149.60 20.25 10.4 19.0 1.52 923 971.2 207.8 178 178 44.65 8.9 9.1 4549 33.9 4852 6013 4518 33.6 4849 6015 4525 -0.3 10 4 10 4866 6045 4531 10.6 20.0 8.8 71.2 170 68 2.5 490 0.018 0.8 3 7.3 0.0 0.00 11.6 0.9 1.8 2.0
41.12 6.94 57.02 69.51 13.45 18.44 50.16 100.00 17.55 12.83 3.09 149.60 20.25 10.4 18.0 1.53 918 977.6 204.8 177 177 46.47 8.9 9.4 4549 33.4 4869 6043 4547 32.8 4827 6014 4526 -0.6 11 5 11 4846 6032 4521 10.6 20.0 9.2 70.8 169 67 2.5 504 0.019 1.3 3 7.1 0.0 0.00 11.4 2.5 1.8 2.1
40.14 6.94 57.02 69.51 13.45 18.44 50.16 100.00 17.55 12.83 3.09 149.60 20.25 10.4 19.5 1.54 926 989.2 206.4 178 178 47.33 8.7 11.0 4549 33.8 4874 6049 4551 33.1 4701 5890 4392 -0.7 12 6 12 4721 5901 4416 10.0 18.9 10.8 70.2 162 65 2.5 496 0.019 0.4 3 7.1 0.1 0.20 11.4 1.0 1.8 2.2
42.69 7.56 61.62 72.17 14.46 21.02 53.78 100.00 18.33 12.82 3.18 154.71 20.95 11.1 19.5 1.54 929 989.6 205.5 177 177 46.34 9.0 9.5 4549 33.1 4867 6061 4567 32.5 4836 6033 4541 -0.6 1 1 13 4861 6071 4550 10.9 20.5 9.3 70.3 165 66 2.5 495 0.019 1.9 3 7.4 0.0 0.00 11.4 1.1 2.0 2.3
40.15 6.87 57.33 71.52 13.22 15.62 50.85 100.00 17.74 13.16 2.91 148.45 20.44 9.7 19.5 1.54 923 1003.8 206.8 178 177 48.84 8.7 10.8 4549 33.6 4867 6039 4539 33.1 4718 5898 4404 -0.5 2 2 14 4747 5929 4423 10.1 19.2 10.5 70.3 157 63 2.5 501 0.020 1.4 3 7.3 0.0 0.00 11.6 1.2 1.9 2.2
39.77 6.87 57.33 71.52 13.22 15.62 50.85 100.00 17.74 13.16 2.91 148.45 20.44 9.7 19.5 1.54 925 984.2 205.2 177 178 46.32 8.4 8.6 4549 33.7 4891 6059 4563 33.1 4880 6048 4555 -0.6 3 3 15 4890 6069 4552 10.7 20.3 8.6 71.2 164 67 2.5 483 0.018 0.9 3 7.2 0.0 0.00 11.2 0.9 1.9 2.1
39.40 6.87 57.33 71.52 13.22 15.62 50.85 100.00 17.74 13.16 2.91 148.45 20.44 9.7 19.5 1.52 924 992.5 207.3 178 178 47.03 8.2 9.4 4549 33.9 4901 6055 4571 34.8 4816 5992 4493 0.9 4 4 16 4847 6021 4518 10.5 19.9 9.1 71.0 160 66 2.4 509 0.020 0.6 3 7.3 0.0 0.00 11.0 0.9 2.1 2.2
39.14 6.65 55.61 68.93 12.72 15.91 48.64 100.00 17.87 13.31 2.98 146.08 20.33 10.7 19.5 1.50 924 987.0 206.2 177 177 45.66 10.3 9.4 4549 33.8 4747 5918 4447 34.5 4829 6006 4531 0.7 5 5 17 4853 6033 4545 10.6 20.1 9.2 70.7 156 63 2.5 463 0.019 1.1 2 7.3 0.1 0.20 11.0 1.0 1.9 2.2
40.36 6.65 55.61 68.93 12.72 15.91 48.64 100.00 17.87 13.31 2.98 146.08 20.33 10.7 19.5 1.52 926 991.5 211.4 178 178 47.09 10.3 9.8 4549 33.5 4765 5946 4471 33.9 4808 5991 4509 0.4 6 6 18 4820 6016 4524 10.6 20.0 9.7 70.3 156 64 2.4 488 0.020 0.5 3 7.3 0.0 0.00 11.3 0.0 2.0 2.2
42.31 6.65 55.61 68.93 12.72 15.91 48.64 100.00 17.87 13.31 2.98 146.08 20.33 10.7 18.0 1.58 920 1003.2 207.8 177 177 49.04 11.1 10.2 4549 32.5 4724 5926 4441 33.5 4792 6002 4506 1.0 7 1 1 4811 6016 4519 10.7 20.1 10.0 69.9 157 63 2.5 512 0.020 1.4 3 7.1 0.0 0.00 11.8 11.0 1.9 2.3
40.49 6.72 57.24 71.27 12.25 16.58 50.88 100.00 18.18 13.60 2.75 151.23 21.30 9.3 20.0 1.57 928 983.2 208.0 177 178 46.30 9.4 9.1 4549 34.6 4813 5957 4491 35.2 4834 5983 4514 0.6 9 3 3 4863 6019 4541 10.4 19.9 8.8 71.3 160 63 2.5 499 0.019 0.8 3 7.0 0.0 0.00 11.5 0.7 1.8 2.3
40.57 6.57 55.93 69.48 11.95 18.00 50.50 100.00 17.92 13.23 2.63 151.67 21.29 8.7 19.0 1.60 921 980.8 206.2 178 178 46.37 9.6 9.1 4549 34.6 4803 5958 4506 35.0 4846 6009 4535 0.4 10 4 4 4867 6041 4554 10.6 20.1 8.9 71.0 161 64 2.5 513 0.020 0.7 3 7.1 0.1 0.10 11.6 0.9 1.8 2.2
38.20 6.16 54.67 66.95 11.15 17.25 48.12 100.83 17.97 13.12 2.48 149.03 20.88 9.1 20.0 1.51 925 982.3 205.9 177 177 46.32 10.4 9.0 4549 34.0 4756 5917 4484 35.3 4858 6039 4557 1.3 11 5 5 4877 6051 4587 10.7 20.3 8.9 70.8 153 61 2.5 484 0.020 1.3 2 7.1 0.0 0.00 11.7 0.8 1.8 2.1
38.70 6.16 54.67 66.95 11.15 17.25 48.12 100.83 17.97 13.12 2.48 149.03 20.88 9.1 19.5 1.51 923 983.4 206.2 178 178 46.02 10.2 8.7 4549 34.1 4772 5957 4494 35.4 4885 6065 4571 1.3 12 6 6 4889 6069 4590 10.8 20.4 8.8 70.8 156 62 2.5 502 0.020 0.5 3 7.1 0.0 0.00 11.6 0.8 1.8 2.0
38.94 6.16 54.67 66.95 11.15 17.25 48.12 100.83 17.97 13.12 2.48 149.03 20.88 9.1 19.5 1.49 928 1004.5 206.8 177 177 48.17 9.6 10.2 4549 33.9 4828 6010 4550 33.9 4763 5949 4510 0.0 1 1 7 4814 6010 4545 10.4 19.8 9.7 70.5 150 60 2.5 492 0.021 1.1 2 7.1 0.0 0.00 11.5 0.7 1.9 2.3
41.90 6.37 52.67 64.34 12.02 17.40 46.52 100.00 17.38 12.48 2.75 144.50 19.82 11.0 20.0 1.50 927 1016.1 210.3 178 177 47.44 11.2 9.9 4549 32.7 4716 5937 4476 34.1 4818 6043 4586 1.4 2 2 8 4835 6074 4592 10.9 20.4 9.7 69.8 162 63 2.6 492 0.019 1.0 2 7.0 0.0 0.00 11.6 0.9 2.0 2.3
42.03 6.37 52.67 64.34 12.02 17.40 46.52 100.00 17.38 12.48 2.75 144.50 19.82 11.0 19.5 1.51 922 999.7 213.3 177 178 47.30 10.9 10.1 4549 33.3 4742 5963 4505 33.9 4800 6038 4578 0.6 3 3 9 4841 6084 4593 11.0 20.5 9.7 69.8 163 63 2.6 498 0.019 1.0 3 6.9 0.0 0.00 11.7 1.4 1.9 1.8
41.96 6.37 52.67 64.34 12.02 17.40 46.52 100.00 17.38 12.48 2.75 144.50 19.82 11.0 19.5 1.50 923 1013.9 209.6 178 178 48.11 11.0 10.4 4549 32.9 4737 5967 4499 33.5 4785 6025 4558 0.6 4 4 10 4819 6065 4575 10.9 20.4 10.0 69.6 160 62 2.6 504 0.020 0.5 3 6.8 0.0 0.00 11.7 1.4 1.9 1.8
41.85 6.31 54.42 66.13 11.97 18.40 48.01 100.00 17.81 12.75 2.76 147.17 20.41 12.0 19.5 1.48 923 994.0 206.8 178 178 46.00 9.7 9.6 4549 34.2 4818 6019 4583 34.2 4830 6031 4603 0.0 6 6 12 4857 6065 4613 10.7 20.3 9.3 70.4 162 64 2.5 494 0.019 0.4 3 7.0 0.0 0.00 11.2 1.2 1.9 1.8
39.71 6.27 53.51 66.52 11.83 16.95 46.62 100.00 17.76 13.31 2.87 143.65 20.35 10.0 20.0 1.49 929 960.0 210.7 177 177 45.05 9.4 9.0 0 34.8 4824 5974 4534 35.4 4862 6021 4567 0.6 1 1 13 4877 6036 4569 10.4 20.0 8.7 71.3 156 62 2.5 500 0.020 1.1 3 7.3 0.0 0.00 11.9 1.2 1.8 2.5
39.38 6.27 53.51 66.52 11.83 16.95 46.62 100.00 17.76 13.31 2.87 143.65 20.35 10.2 19.0 1.48 921 961.3 205.0 178 177 43.83 8.9 8.4 0 35.5 4862 6023 4568 35.5 4905 6066 4597 0.0 2 2 14 4901 6063 4588 10.6 20.2 8.4 71.4 159 63 2.5 487 0.019 0.9 3 7.1 0.1 0.10 11.9 1.7 1.8 2.3
39.16 6.27 53.51 66.52 11.83 16.95 46.62 100.00 17.76 13.31 2.87 143.65 20.35 10.2 19.0 1.48 921 969.7 207.8 177 178 43.86 8.4 8.3 0 35.5 4897 6043 4584 35.5 4907 6064 4596 0.0 3 3 15 4916 6075 4595 10.6 20.3 8.2 70.5 158 62 2.6 484 0.019 0.7 3 7.0 0.0 0.00 11.5 1.7 1.9 2.2
39.38 6.58 52.50 63.29 12.24 18.28 46.04 100.00 17.67 12.47 2.85 144.40 19.85 9.5 19.0 1.47 923 989.7 205.7 177 177 47.40 9.7 9.5 0 34.2 4836 6047 4588 33.9 4854 6072 4603 -0.3 5 5 17 4876 6106 4609 11.1 20.8 9.3 69.9 162 65 2.5 494 0.019 1.3 3 7.1 0.0 0.00 11.7 1.2 1.8 1.9
40.08 6.45 53.18 64.98 12.11 18.77 46.80 100.00 17.58 12.69 2.79 145.90 19.96 10.9 19.5 1.51 923 996.4 206.2 178 178 47.52 10.2 9.9 0 33.5 4810 6039 4568 33.5 4827 6057 4580 0.0 6 6 18 4825 6063 4582 11.0 20.5 9.9 69.6 160 63 2.6 500 0.020 0.6 2 7.0 0.0 0.00 11.5 1.2 1.8 1.8
39.17 6.39 58.85 73.45 12.69 16.92 51.25 100.00 17.92 13.50 2.62 151.25 20.89 11.3 21.5 1.55 935 976.4 204.8 177 177 45.88 8.5 9.1 0 34.8 4879 6044 4574 34.4 4841 6018 4565 -0.4 7 1 1 4849 6041 4557 10.3 19.6 8.9 71.6 158 64 2.5 495 0.020 1.1 3 7.4 0.1 0.10 11.7 0.8 2.0 2.3
38.37 6.39 58.85 73.45 12.69 16.92 51.25 100.00 17.92 13.50 2.62 151.25 20.89 11.3 22.2 1.54 933 971.6 208.0 178 177 45.52 8.2 8.7 0 35.2 4899 6059 4609 34.5 4867 6037 4583 -0.7 8 2 2 4883 6045 4583 10.2 19.6 8.3 72.1 156 62 2.5 497 0.020 1.9 2 7.1 0.0 0.00 11.8 0.8 2.0 2.1
38.76 6.39 58.85 73.45 12.69 16.92 51.25 100.00 17.92 13.50 2.62 151.25 20.89 11.3 22.0 1.54 933 974.0 205.9 177 178 45.11 8.7 8.6 0 35.0 4857 6028 4569 34.6 4870 6051 4582 -0.4 9 3 3 4890 6058 4587 10.3 19.7 8.3 72.0 159 64 2.5 497 0.020 0.7 2 7.0 0.0 0.00 11.6 1.3 1.9 2.4
38.73 6.35 56.93 70.87 12.27 18.06 49.92 100.00 17.76 13.29 2.61 150.06 20.65 11.5 22.5 1.55 932 978.0 209.4 178 178 45.57 9.8 9.3 0 34.2 4795 5991 4520 34.2 4844 6031 4579 0.0 10 4 4 4859 6058 4581 10.5 19.8 8.9 71.2 157 61 2.6 507 0.020 0.8 3 7.1 0.0 0.00 11.6 0.6 2.0 2.3
38.95 6.17 53.80 65.53 12.70 18.65 47.67 100.00 16.82 12.11 2.58 142.66 19.64 11.4 21.5 1.55 932 980.2 205.7 177 177 44.92 8.7 9.1 0 35.1 4889 6089 4619 34.5 4857 6063 4594 -0.6 11 5 5 4876 6087 4601 10.6 20.0 8.8 71.2 163 65 2.5 498 0.019 1.7 3 7.0 0.0 0.00 11.4 1.3 1.9 2.2
40.41 6.97 58.18 71.85 14.25 17.08 50.06 100.00 18.02 13.51 3.37 148.92 20.33 11.0 21.5 1.55 937 993.4 205.5 177 177 46.11 9.3 9.4 0 34.5 4835 6014 4527 34.5 4827 5994 4525 0.0 1 1 7 4835 6015 4537 10.3 19.5 9.1 71.3 156 63 2.5 494 0.020 1.0 3 7.1 0.0 0.00 11.4 0.8 2.0 2.5
39.90 6.97 58.18 71.85 14.25 17.08 50.06 100.00 18.02 13.51 3.37 148.92 20.33 11.0 22.0 1.52 931 990.5 207.1 178 177 46.12 8.4 9.3 0 35.2 4899 6061 4572 33.8 4813 5977 4515 -1.4 2 2 8 4834 6015 4526 10.3 19.5 9.1 71.4 154 61 2.5 517 0.021 1.2 3 7.1 0.0 0.00 11.3 0.9 2.1 2.2
39.79 6.97 58.18 71.85 14.25 17.08 50.06 100.00 18.02 13.51 3.37 148.92 20.33 11.0 22.0 1.53 935 982.9 206.6 177 178 44.55 8.2 8.4 0 35.2 4897 6048 4572 34.8 4881 6059 4584 -0.4 3 3 9 4898 6073 4573 10.5 19.9 8.3 71.8 159 65 2.4 495 0.019 0.3 2 7.1 0.0 0.00 11.3 1.0 1.9 2.1
41.25 8.81 63.99 78.25 23.09 19.96 53.87 100.00 18.84 14.08 6.87 158.73 20.57 12.7 22.0 1.55 934 1000.7 205.5 178 178 45.10 8.6 8.8 0 34.9 4844 5990 4524 34.9 4825 5981 4517 0.0 4 4 10 4878 6049 4546 10.3 19.6 8.4 72.1 167 65 2.6 507 0.019 0.2 3 7.1 0.0 0.00 11.6 1.2 1.9 2.2
41.00 6.80 57.21 70.34 13.98 16.81 48.46 100.00 17.91 13.34 3.37 146.67 19.95 11.2 20.5 1.55 934 1000.8 205.2 178 178 44.99 9.1 8.5 0 34.7 4829 5998 4550 34.7 4879 6040 4573 0.0 6 6 12 4881 6060 4576 10.5 19.9 8.6 71.5 164 65 2.5 492 0.019 0.3 3 7.1 0.0 0.00 11.5 1.6 1.9 2.4
41.59 6.80 57.21 70.34 13.98 16.81 48.46 100.00 17.91 13.34 3.37 146.67 19.95 11.2 21.0 1.55 939 1171.2 206.4 177 178 45.64 8.9 9.1 0 35.1 4853 6022 4582 34.8 4826 5996 4564 -0.3 1 1 13 4866 6051 4567 10.4 19.7 8.7 71.6 164 66 2.5 506 0.019 0.9 2 7.2 0.0 0.00 11.5 1.5 1.9 2.4
40.91 6.80 57.21 70.34 13.98 16.81 48.46 100.00 17.91 13.34 3.37 146.67 19.95 11.2 22.0 1.54 936 979.2 208.7 178 178 44.62 8.6 8.4 0 35.0 4864 6030 4577 34.8 4887 6068 4599 -0.2 2 2 14 4907 6087 4602 10.5 20.0 8.2 71.8 165 68 2.4 493 0.019 0.9 2 7.1 0.0 0.00 11.6 1.6 2.0 2.4
38.99 6.30 51.96 64.07 12.65 19.23 44.66 100.00 17.16 12.71 3.15 142.11 19.13 11.6 21.0 1.55 932 994.5 207.8 177 177 45.45 9.4 9.4 0 34.8 4841 6048 4631 34.1 4839 6062 4631 -0.7 3 3 15 4867 6082 4642 10.7 20.2 9.1 70.7 160 64 2.5 499 0.019 1.4 3 7.2 0.0 0.00 11.5 1.0 1.9 2.4
38.81 6.30 51.96 64.07 12.65 19.23 44.66 100.00 17.16 12.71 3.15 142.11 19.13 11.6 21.5 1.55 937 989.2 205.2 178 178 45.52 9.3 9.5 0 34.5 4841 6052 4635 33.9 4830 6038 4618 -0.6 4 4 16 4844 6067 4632 10.7 20.1 9.4 70.5 159 64 2.5 513 0.020 0.9 2 7.1 0.1 0.10 11.7 1.1 1.8 2.1
39.30 6.30 51.96 64.07 12.65 19.23 44.66 100.00 17.16 12.71 3.15 142.11 19.13 11.6 21.5 1.55 939 983.7 206.4 177 177 46.10 9.4 9.6 0 34.6 4832 6035 4624 34.3 4822 6039 4617 -0.3 5 5 17 4838 6053 4622 10.6 20.0 9.4 70.6 159 62 2.5 498 0.020 1.2 2 7.2 0.0 0.00 11.7 1.1 1.9 2.3
40.77 6.45 55.09 69.18 11.98 17.22 47.12 100.00 17.74 13.47 2.86 148.00 20.04 10.8 21.5 1.54 937 960.4 204.8 177 178 43.52 8.1 8.3 0 35.8 4893 6028 4564 35.5 4879 6026 4556 -0.3 7 2 2 4873 6023 4546 10.2 19.5 8.4 72.1 163 65 2.5 486 0.019 0.8 2 7.2 0.0 0.00 11.5 1.1 1.9 2.3
39.27 6.45 55.09 69.18 11.98 17.22 47.12 100.00 17.74 13.47 2.86 148.00 20.04 10.8 21.5 1.55 935 954.8 NA 178 178 43.52 8.4 8.3 0 35.6 4866 6005 4550 35.6 4893 6046 4569 0.0 8 3 3 4897 6047 4572 10.3 19.7 8.1 72.2 157 64 2.5 493 0.020 1.2 2 7.2 0.0 0.00 11.3 0.8 1.9 2.1
40.06 6.45 55.09 69.18 11.98 17.22 47.12 100.00 17.74 13.47 2.86 148.00 20.04 10.8 21.7 1.55 938 975.8 205.2 177 177 44.11 8.4 8.3 0 35.4 4874 6012 4561 35.3 4885 6046 4571 -0.1 9 4 4 4885 6042 4546 10.3 19.7 8.3 72.0 158 63 2.5 478 0.019 1.0 2 7.2 0.1 0.10 11.6 0.9 1.9 2.5
39.17 6.28 54.33 68.30 12.37 15.46 46.72 100.00 17.41 13.28 2.96 143.47 19.85 12.4 22.0 1.54 941 1009.1 206.4 178 178 46.33 8.7 9.2 0 34.2 4867 6034 4588 33.8 4835 6015 4569 -0.4 10 5 5 4846 6019 4572 10.3 19.6 9.1 71.3 156 62 2.5 522 0.021 0.8 3 7.2 0.0 0.00 11.6 1.1 1.8 2.2
39.98 7.33 56.87 70.17 14.20 20.16 49.06 100.00 18.01 13.34 3.62 147.63 19.77 9.9 21.5 1.54 933 992.6 205.9 177 177 45.69 8.4 9.1 0 35.3 4896 6062 4614 34.5 4844 6021 4583 -0.8 11 6 6 4870 6054 4595 10.5 19.9 8.8 71.3 154 60 2.5 492 0.020 1.1 2 7.2 0.0 0.00 11.5 0.9 1.8 2.0
39.91 7.22 57.32 71.02 14.05 19.16 49.21 100.00 18.02 13.43 3.52 148.07 19.87 10.0 21.5 1.55 937 1003.7 205.0 178 178 44.22 8.6 8.9 0 35.6 4848 6005 4559 35.6 4866 6028 4579 0.0 1 1 7 4887 6056 4575 10.4 19.8 8.4 71.8 158 63 2.5 491 0.019 0.9 2 7.2 0.0 0.00 11.9 0.9 1.9 2.5
40.77 6.19 53.59 66.40 11.99 18.73 47.41 100.00 17.04 12.58 2.45 146.20 19.83 9.1 21.5 1.53 931 1006.1 206.8 178 177 45.49 9.1 8.9 0 35.2 4839 6020 4559 35.2 4849 6024 4576 0.0 3 3 9 4872 6054 4566 10.5 19.9 8.8 71.4 164 66 2.5 490 0.019 1.0 2 7.2 0.1 0.10 11.8 0.8 1.9 2.3
39.86 5.98 54.10 66.50 11.73 18.80 47.98 100.00 17.35 12.75 2.51 147.95 20.25 10.6 22.0 1.53 934 1001.0 204.8 177 177 44.09 8.8 8.7 0 35.3 4853 6021 4566 35.3 4864 6043 4582 0.0 4 4 10 4889 6070 4590 10.5 20.0 8.5 71.6 160 64 2.5 482 0.019 1.0 2 7.2 0.0 0.00 11.6 0.8 1.9 2.2
40.03 5.98 54.10 66.50 11.73 18.80 47.98 100.00 17.35 12.75 2.51 147.95 20.25 10.6 22.0 1.54 937 994.9 205.0 178 178 44.56 9.3 9.0 0 35.2 4815 5991 4541 35.2 4834 6008 4555 0.0 5 5 11 4862 6040 4562 10.4 19.7 8.8 71.5 159 64 2.5 499 0.020 0.7 2 7.2 0.0 0.00 11.6 0.9 2.0 2.1
40.81 5.98 54.10 66.50 11.73 18.80 47.98 100.00 17.35 12.75 2.51 147.95 20.25 10.6 20.9 1.55 933 1001.3 205.2 177 177 45.14 9.1 NA 0 35.1 4834 6022 4560 34.8 4859 6030 4568 -0.3 6 6 12 4869 6050 4574 10.5 19.9 8.8 71.3 160 64 2.5 493 0.019 0.9 2 7.3 0.0 0.00 11.5 0.9 1.9 2.1
37.94 5.85 51.75 64.02 10.41 20.40 44.30 100.00 16.96 12.68 2.34 143.33 19.63 11.5 22.0 1.54 934 1004.3 205.0 177 178 43.73 11.4 8.7 0 34.3 4701 5914 4579 35.7 4911 6124 4705 1.4 2 2 14 4923 6137 4710 11.0 20.7 8.6 70.7 154 63 2.4 490 0.020 0.8 3 7.2 0.1 0.10 11.7 1.1 1.9 2.2
37.73 5.85 51.75 64.02 10.41 20.40 44.30 100.00 16.96 12.68 2.34 143.33 19.63 11.5 21.0 1.55 934 1008.1 204.6 178 177 44.35 8.7 9.2 0 35.3 4895 6079 4670 34.3 4850 6022 4634 -1.0 3 3 15 4855 6046 4644 10.5 19.9 9.2 70.9 151 60 2.5 491 0.020 1.3 2 7.2 0.0 0.00 11.5 0.9 1.9 2.3
37.30 5.85 51.75 64.02 10.41 20.40 44.30 100.00 16.96 12.68 2.34 143.33 19.63 11.5 21.5 1.53 937 1004.8 206.6 177 177 44.13 8.9 9.3 0 35.3 4865 6037 4651 34.8 4839 6003 4619 -0.5 4 4 16 4856 6041 4634 10.4 19.9 9.1 71.1 150 60 2.5 486 0.020 1.6 2 7.2 0.0 0.00 11.5 0.8 1.9 2.3
37.86 6.01 51.83 63.80 11.22 19.69 44.57 100.00 17.09 12.57 2.55 143.07 19.47 11.8 21.9 1.54 937 992.8 204.6 178 178 43.49 8.8 9.0 0 35.4 4864 6025 4607 35.0 4847 6024 4614 -0.4 5 5 17 4865 6041 4606 10.4 19.7 8.8 71.4 154 62 2.5 507 0.021 0.8 3 7.2 0.0 0.00 11.6 1.1 1.8 2.3
38.05 5.89 51.28 64.04 9.99 16.90 44.74 100.00 16.79 13.04 2.33 142.66 19.67 12.3 21.7 1.55 936 974.0 206.4 177 177 42.66 8.9 8.7 0 35.5 4838 5997 4571 35.5 4855 6021 4584 0.0 6 6 18 4886 6051 4594 10.3 19.7 8.3 72.0 157 63 2.5 498 0.020 1.3 3 7.2 0.0 0.00 11.4 1.0 1.8 2.4
37.87 5.90 51.44 63.61 10.49 18.04 44.73 100.00 17.18 12.95 2.46 143.84 19.85 11.8 21.6 1.55 937 987.7 206.6 178 178 43.58 8.7 9.1 0 35.3 4861 6020 4611 34.9 4837 6007 4593 -0.4 7 1 1 4845 6019 4590 10.2 19.6 9.0 71.4 156 62 2.5 496 0.020 0.7 3 7.3 0.1 0.10 11.8 0.6 1.9 2.1
38.60 5.90 51.44 63.61 10.49 18.04 44.73 100.00 17.18 12.95 2.46 143.84 19.85 11.8 21.8 1.55 936 987.9 205.5 177 177 44.70 9.3 9.1 0 35.2 4816 5983 4579 35.2 4834 5997 4583 0.0 8 2 2 4841 6010 4583 10.2 19.5 9.1 71.4 155 62 2.5 481 0.019 1.0 2 6.9 0.0 0.00 11.7 0.8 1.9 2.0
38.44 5.90 51.44 63.61 10.49 18.04 44.73 100.00 17.18 12.95 2.46 143.84 19.85 11.8 20.8 1.55 933 986.6 205.5 178 178 44.23 8.7 9.0 0 35.2 4873 6031 4606 34.8 4846 6014 4595 -0.4 9 3 3 4853 6027 4605 0.0 19.7 9.0 71.4 156 62 2.5 493 0.020 0.5 3 7.1 0.0 0.00 11.9 0.8 1.9 2.3
39.42 5.79 53.96 66.53 10.40 18.26 47.57 100.00 17.24 12.99 2.16 146.64 20.57 9.8 22.0 1.54 932 992.3 208.4 177 177 45.61 9.0 8.9 0 35.1 4843 6016 4564 35.1 4850 6016 4569 0.0 10 4 4 4857 6036 4577 0.0 19.7 8.9 71.5 156 63 2.5 495 0.020 1.4 3 7.0 0.0 0.00 11.7 0.8 1.9 1.9
39.75 5.79 53.96 66.53 10.40 18.26 47.57 100.00 17.24 12.99 2.16 146.64 20.57 9.8 21.9 1.50 934 987.9 208.9 178 178 45.99 9.4 9.3 0 34.7 4807 5967 4536 34.7 4819 5997 4544 0.0 11 5 5 0 0 0 0.0 0.0 0.0 0.0 156 62 2.5 485 0.019 0.7 3 7.0 0.0 0.00 11.6 0.8 1.9 2.4
39.51 5.79 53.96 66.53 10.40 18.26 47.57 100.00 17.24 12.99 2.16 146.64 20.57 9.8 22.4 1.48 937 994.3 211.4 177 177 46.01 9.0 8.9 0 35.0 4839 6013 4561 35.0 4856 6032 4571 0.0 12 6 6 4859 6037 4590 0.0 19.7 8.8 71.5 155 62 2.5 491 0.020 1.5 2 7.1 0.0 0.10 11.7 0.8 1.9 1.9
38.35 5.94 51.27 63.54 10.48 17.72 44.43 100.00 17.13 13.00 2.52 143.19 19.69 11.7 22.0 1.52 940 980.3 205.2 178 178 43.75 9.6 9.4 0 35.1 4793 5953 4550 35.4 4808 5972 4551 0.3 1 1 7 4854 6013 4594 0.0 19.5 8.9 71.6 155 63 2.5 510 0.021 0.6 3 7.3 0.0 0.00 11.5 0.9 1.8 2.4
40.38 6.40 58.73 71.51 12.29 17.09 50.62 100.00 17.44 13.10 2.58 147.66 20.25 11.4 20.5 1.57 929 976.0 204.8 178 177 43.75 9.5 7.9 0 35.2 4783 5932 4485 35.7 4935 6105 4602 0.5 3 3 9 4912 6080 4572 0.0 19.9 8.0 72.1 162 65 2.5 494 0.019 0.7 2 7.0 0.0 0.00 11.6 1.7 1.8 2.2
40.19 6.40 58.73 71.51 12.29 17.09 50.62 100.00 17.44 13.10 2.58 147.66 20.25 11.4 22.2 1.54 937 994.1 208.9 177 177 44.64 7.8 8.7 0 35.9 4937 6098 4602 34.7 4845 6014 4533 -1.2 4 4 10 4859 6011 4535 0.0 19.3 8.6 72.1 158 63 2.5 488 0.019 0.7 3 7.0 0.0 0.00 11.3 1.2 1.9 2.3
39.96 6.40 58.73 71.51 12.29 17.09 50.62 100.00 17.44 13.10 2.58 147.66 20.25 11.4 22.3 1.53 936 983.2 213.7 178 178 43.84 8.1 8.7 0 35.7 4896 6050 4559 35.0 4849 6010 4536 -0.7 5 5 11 4871 6027 4544 0.0 19.5 8.4 72.1 160 64 2.5 497 0.019 0.9 2 7.0 0.1 0.10 11.3 0.9 1.8 2.3
39.79 6.10 56.36 69.52 11.71 16.35 49.10 100.00 17.15 12.99 2.44 146.29 20.16 11.7 22.0 1.51 935 981.6 204.3 177 177 43.37 7.8 8.1 0 36.2 4936 6076 4602 35.3 4887 6033 4567 -0.9 6 6 12 4884 6037 4563 0.0 19.5 8.2 72.3 161 65 2.5 500 0.019 0.7 3 7.1 0.0 0.00 11.4 1.1 1.8 2.3
41.86 5.78 53.70 67.22 11.17 15.44 47.33 100.00 16.76 12.81 2.30 144.34 19.95 12.0 21.2 1.55 942 992.0 204.1 177 177 44.94 9.1 9.0 0 34.7 4808 5941 4504 35.1 4822 5959 4526 0.4 7 1 13 4848 5976 4524 0.0 19.2 8.7 72.1 163 65 2.5 492 0.019 1.3 3 7.1 0.0 0.00 11.8 0.5 1.9 2.3
42.15 6.15 53.06 70.29 11.87 16.59 49.97 100.00 16.78 12.63 2.31 144.75 19.94 12.3 21.1 1.54 934 980.0 206.4 178 178 43.12 8.3 8.3 0 35.2 4880 6031 4567 35.2 4877 6035 4570 0.0 8 2 14 4902 6060 4566 0.0 19.9 8.1 72.0 167 68 2.5 501 0.019 0.4 3 7.2 0.0 0.00 11.8 0.6 1.9 2.2
43.88 6.40 52.62 72.39 12.34 17.38 51.77 100.00 16.80 12.51 2.32 145.03 19.93 12.5 21.0 1.55 938 997.8 205.7 177 177 45.23 8.5 9.1 0 34.9 4879 6047 4564 34.4 4827 6000 4535 -0.5 1 1 15 4858 6029 4546 0.0 19.6 8.8 71.6 163 65 2.5 495 0.019 1.0 3 6.9 0.0 0.00 11.8 0.7 1.9 2.2
39.58 5.60 51.45 63.44 10.50 19.17 45.06 100.00 16.83 12.53 2.27 142.90 19.64 11.4 21.0 1.55 934 991.9 205.0 178 177 44.10 8.8 9.2 0 35.1 4869 6037 4622 34.7 4835 5999 4585 -0.4 2 2 16 4857 6032 4598 0.0 19.7 9.0 71.3 153 61 2.5 500 0.020 0.9 3 7.0 0.1 0.10 11.7 0.8 1.9 2.0
40.19 5.60 51.45 63.44 10.50 19.17 45.06 100.00 16.83 12.53 2.27 142.90 19.64 11.4 20.9 1.54 934 986.1 204.1 177 178 43.92 9.0 9.1 0 35.1 4849 6011 4584 35.0 4844 6013 4589 -0.1 3 3 17 4863 6036 4608 0.0 19.7 8.9 71.4 156 61 2.6 501 0.020 0.7 2 7.1 0.0 0.00 11.6 0.8 1.7 2.4
39.84 5.60 51.45 63.44 10.50 19.17 45.06 100.00 16.83 12.53 2.27 142.90 19.64 11.4 21.1 1.55 935 923.0 204.8 178 178 43.26 8.7 8.6 0 35.6 4876 6040 4598 35.2 4880 6037 4611 -0.4 4 4 18 4873 6043 4601 0.0 19.8 8.7 71.5 157 61 2.6 497 0.020 0.5 3 6.9 0.0 0.00 11.9 0.5 1.9 2.2
40.59 5.43 49.10 62.08 10.11 19.09 44.45 100.00 16.54 12.21 2.11 141.49 19.46 12.0 21.2 1.55 935 1003.2 206.8 177 177 45.63 9.0 9.6 0 34.7 4872 6060 4633 34.1 4828 6015 4592 -0.6 5 5 19 4844 6055 4617 0.0 20.0 9.4 70.6 149 59 2.6 486 0.020 1.1 3 6.9 0.0 0.00 11.6 0.5 1.7 1.9
40.66 6.02 50.01 60.82 11.79 19.43 43.24 100.00 17.54 12.61 3.08 142.33 19.17 12.3 21.5 1.55 939 995.2 205.7 178 178 46.51 9.8 10.1 0 33.9 4839 6053 4654 33.1 4806 6022 4623 -0.8 6 6 20 4825 6053 4657 0.0 20.2 10.0 69.9 146 56 2.6 499 0.021 0.5 2 7.0 0.0 0.00 11.8 0.5 1.8 2.1
42.58 6.03 52.58 65.05 11.45 19.11 46.06 100.00 17.23 12.84 2.67 145.08 19.74 11.3 21.2 1.55 936 991.8 208.2 177 178 45.85 8.8 9.7 0 34.9 4882 6056 4600 33.9 4814 6004 4580 -1.0 7 1 1 4820 6022 4585 0.0 19.8 9.6 70.6 159 64 2.5 489 0.019 0.9 2 7.1 0.1 0.20 11.5 0.5 1.9 2.2
43.42 6.08 52.89 66.72 11.23 19.06 47.29 100.00 17.03 12.96 2.49 147.33 20.04 11.2 20.8 1.55 935 994.7 207.3 178 178 46.95 8.9 9.8 0 34.3 4878 6072 4614 33.2 4811 6018 4567 -1.1 8 2 2 4824 6045 4578 0.0 20.0 9.7 70.3 160 64 2.6 481 0.019 0.7 2 7.1 0.0 0.00 11.6 0.7 1.8 2.2
41.45 5.76 52.73 63.88 10.59 20.49 47.29 100.00 17.70 12.48 2.23 150.39 20.62 12.1 20.9 1.54 934 996.9 207.3 177 178 47.21 10.0 10.2 0 33.7 4812 6032 4626 33.2 4797 6019 4611 -0.5 9 3 3 4809 6057 4623 0.0 20.2 10.1 69.7 151 58 2.5 498 0.021 1.1 3 7.1 0.0 0.00 11.5 0.6 1.9 2.2
41.31 5.79 52.70 64.33 10.70 20.09 47.21 100.00 17.54 12.55 2.27 149.52 20.48 11.9 21.2 1.55 935 996.5 209.1 178 178 46.23 9.3 10.0 0 34.4 4859 6063 4635 33.3 4804 6024 4601 -1.1 10 4 4 4820 6050 4606 0.0 20.1 9.9 70.1 154 60 2.5 505 0.020 0.7 3 7.0 0.0 0.00 11.5 0.7 1.9 2.1
42.28 6.23 52.95 66.71 12.75 16.31 45.84 100.00 16.70 12.75 2.98 140.93 19.10 11.4 21.3 1.54 939 987.3 211.4 177 178 45.71 8.1 9.1 0 35.0 4905 6061 4595 33.8 4820 5982 4529 -1.2 11 5 5 4829 6009 4534 0.0 19.5 9.1 71.4 160 63 2.5 507 0.020 1.0 3 7.2 0.0 0.00 11.4 0.6 1.9 2.2
41.62 6.23 52.95 66.71 12.75 16.31 45.84 100.00 16.70 12.75 2.98 140.93 19.10 11.4 21.3 1.55 939 981.9 205.7 178 178 44.99 8.3 8.8 0 34.8 4883 6030 4577 34.2 4855 6024 4558 -0.6 12 6 6 4862 6035 4564 0.0 19.7 8.8 71.6 160 66 2.4 502 0.020 0.7 2 7.2 0.1 0.10 11.4 0.7 1.9 2.0
42.73 6.23 52.95 66.71 12.75 16.31 45.84 100.00 16.70 12.75 2.98 140.93 19.10 11.4 21.4 1.54 941 990.0 207.1 177 178 45.62 8.2 9.4 0 35.2 4903 6056 4550 34.1 4805 5955 4496 -1.1 1 1 7 4832 5990 4533 0.0 19.3 9.1 71.6 162 65 2.5 500 0.019 0.4 2 7.0 0.0 0.00 11.7 0.5 2.0 2.2
41.66 6.26 55.94 69.22 12.07 18.08 48.92 100.00 17.56 13.14 2.60 148.53 20.45 12.2 21.5 1.55 939 1004.4 206.4 178 178 46.67 9.1 10.1 0 33.8 4853 6027 4544 33.4 4777 5962 4509 -0.4 2 2 8 4856 6058 4580 0.0 20.0 9.1 70.9 158 64 2.5 516 0.020 0.8 3 7.0 0.0 0.00 11.4 0.5 1.9 2.3
40.89 6.26 55.94 69.22 12.07 18.08 48.92 100.00 17.56 13.14 2.60 148.53 20.45 12.2 21.4 1.55 936 990.8 208.2 177 177 45.23 8.9 8.2 0 34.4 4865 6034 4562 34.4 4926 6122 4643 0.0 3 3 9 4935 6145 4651 0.0 20.7 8.1 71.2 160 65 2.5 490 0.019 1.0 2 7.2 0.0 0.00 11.4 0.4 1.9 2.2
40.82 6.26 55.94 69.22 12.07 18.08 48.92 100.00 17.56 13.14 2.60 148.53 20.45 12.2 21.5 1.54 939 999.2 206.4 178 178 45.73 7.9 8.8 0 34.6 4950 6143 4665 33.6 4884 6084 4615 -1.0 4 4 10 4895 6120 4632 0.0 20.5 8.6 70.9 158 65 2.4 501 0.020 0.4 3 7.2 0.0 0.00 11.6 0.6 1.8 2.1
39.77 6.36 53.18 66.57 12.07 16.22 46.51 100.00 17.19 12.97 2.80 144.38 19.51 10.8 21.2 1.55 940 998.9 208.9 178 178 46.36 8.2 9.2 0 34.9 4912 6091 4625 33.5 4842 6027 4575 -1.4 1 1 12 4846 6040 4574 0.0 19.8 9.1 71.1 158 65 2.5 499 0.020 0.6 2 7.2 0.0 0.00 11.9 0.4 2.0 2.3
38.05 6.72 53.85 67.10 12.50 16.15 46.87 100.00 17.61 13.15 3.02 145.80 19.56 10.9 NA 1.55 934 1000.1 208.7 177 178 47.06 8.7 9.4 0 34.5 4875 6056 4596 33.4 4821 6003 4550 -1.1 2 2 13 4816 6037 4568 0.0 19.8 9.6 70.6 152 62 2.5 495 0.020 1.3 2 7.3 0.0 0.00 11.8 0.4 1.9 2.2
37.86 5.18 48.60 61.04 9.38 16.30 43.78 100.00 15.88 12.16 1.87 138.14 19.20 11.3 21.4 1.54 936 1001.2 206.2 178 177 46.95 9.3 9.6 0 34.3 4830 6001 4581 33.6 4809 5977 4569 -0.7 3 3 14 4817 6012 4584 0.0 19.6 9.6 70.8 150 62 2.4 502 0.021 1.1 3 7.2 0.0 0.00 11.8 0.4 1.9 2.4
38.03 5.18 48.60 61.04 9.38 16.30 43.78 100.00 15.88 12.16 1.87 138.14 19.20 11.3 21.3 1.55 936 1011.9 207.5 177 177 47.47 8.5 10.0 0 34.4 4893 6061 4635 32.6 4780 5952 4559 -1.8 4 4 15 4785 5973 4557 0.0 19.3 10.0 70.6 149 60 2.5 500 0.021 1.1 2 7.2 0.0 0.00 11.7 0.5 1.8 2.4
37.39 5.18 48.60 61.04 9.38 16.30 43.78 100.00 15.88 12.16 1.87 138.14 19.20 11.3 21.3 1.55 936 998.6 206.2 178 178 46.06 9.3 9.3 0 34.4 4833 6004 4589 34.0 4831 6005 4601 -0.4 5 5 16 4843 6014 4599 0.0 19.6 9.2 71.2 151 61 2.5 495 0.020 1.1 3 7.3 0.1 0.10 11.7 0.5 1.9 2.4
39.16 6.29 50.64 63.92 11.46 13.24 43.50 100.00 16.58 12.88 2.90 136.35 18.35 12.2 21.6 1.55 940 1002.1 207.5 178 178 46.58 9.7 9.3 0 33.4 4792 5964 4540 33.8 4822 5985 4562 0.4 7 1 1 4841 5996 4569 0.0 19.4 9.1 71.5 153 64 2.4 502 0.021 1.1 3 7.3 0.0 0.00 11.8 0.5 1.8 2.1
37.64 6.10 50.60 63.37 10.90 19.05 44.18 100.00 17.37 13.10 2.67 146.66 19.73 10.0 NA 1.55 935 986.1 205.2 177 178 46.06 9.5 9.5 0 34.7 4823 6003 4617 34.4 4831 6015 4609 -0.3 8 2 2 4822 6018 4606 0.0 19.8 9.6 70.6 152 60 2.6 497 0.020 1.1 3 7.2 0.0 0.00 11.7 0.7 1.9 2.3
39.77 5.30 46.87 57.56 9.93 18.07 40.60 100.00 16.34 12.12 2.43 135.81 18.57 13.1 21.3 1.55 936 983.6 207.5 178 178 45.30 10.4 9.8 0 33.7 4772 5962 4606 34.4 4812 5995 4621 0.7 9 3 3 4806 6000 4612 0.0 19.7 9.9 70.4 151 59 2.6 509 0.021 1.3 3 7.3 0.0 0.00 11.8 0.4 1.8 2.4
38.66 5.83 50.17 63.11 10.32 17.24 44.31 100.00 16.86 12.88 2.38 143.75 19.59 10.2 21.2 1.54 934 989.8 206.8 177 178 46.53 8.6 9.3 0 34.9 4883 6042 4623 33.9 4826 5997 4590 -1.0 10 4 4 4840 6001 4588 0.0 19.6 9.2 71.3 152 60 2.5 494 0.020 1.0 3 7.2 0.1 0.10 11.7 0.5 1.8 2.3
40.31 6.25 54.57 67.56 12.10 17.66 47.80 100.00 17.32 12.89 2.73 145.57 19.76 12.4 21.2 1.55 935 1008.1 206.6 178 178 46.12 8.7 9.5 0 34.4 4877 6059 4604 33.4 4821 6008 4568 -1.0 11 5 5 4829 6026 4572 0.0 19.8 9.4 70.7 156 61 2.5 497 0.020 1.0 3 7.2 0.0 0.00 11.7 0.6 1.8 2.3
40.54 6.25 54.57 67.56 12.10 17.66 47.80 100.00 17.32 12.89 2.73 145.57 19.76 12.4 21.4 1.54 934 1000.6 207.3 177 178 46.39 8.9 9.6 0 34.3 4864 6044 4589 33.4 4820 6008 4550 -0.9 12 6 6 4823 6022 4558 0.0 19.7 9.5 70.8 156 61 2.5 509 0.020 1.0 3 7.2 0.0 0.00 11.7 0.5 1.8 2.3
40.64 6.25 54.57 67.56 12.10 17.66 47.80 100.00 17.32 12.89 2.73 145.57 19.76 12.4 21.4 1.55 939 1011.6 206.8 178 178 46.50 9.0 10.0 0 33.9 4858 6035 4577 33.1 4790 5980 4531 -0.8 1 1 7 4802 5993 4533 0.0 19.5 9.8 70.7 156 64 2.4 493 0.020 1.1 2 7.3 0.0 0.00 11.8 0.5 1.9 2.3
38.60 6.00 53.29 65.50 11.71 18.80 46.34 100.00 17.32 12.75 2.63 145.37 19.75 12.7 21.4 1.55 937 1005.1 208.9 177 178 44.78 9.3 9.7 0 34.2 4846 6027 4608 33.7 4612 5999 4581 -0.5 2 2 8 4851 6049 4596 0.0 20.0 9.3 70.7 153 62 2.5 485 0.020 1.8 2 7.3 0.1 0.10 11.5 0.5 1.9 2.2
38.13 6.00 53.29 65.50 11.71 18.80 46.34 100.00 17.32 12.75 2.63 145.37 19.75 12.7 21.6 1.54 938 1014.4 206.4 178 178 44.52 9.3 9.4 0 34.2 4847 6029 4610 33.7 4831 6012 4605 -0.5 3 3 9 4844 6035 4588 0.0 19.9 9.4 70.7 152 63 2.4 517 0.021 1.0 3 7.3 0.0 0.00 11.8 0.5 1.9 1.8
40.10 6.00 53.29 65.50 11.71 18.80 46.34 100.00 17.32 12.75 2.63 145.37 19.75 12.7 21.6 1.55 941 1012.5 206.6 177 177 46.46 9.1 9.6 0 34.4 4858 6046 4619 33.5 4813 6004 4590 -0.9 4 1 10 4827 6011 4581 0.0 19.7 9.6 70.7 153 61 2.5 472 0.019 2.0 2 7.1 0.0 0.00 11.7 0.5 1.8 1.9
39.14 5.49 48.03 58.99 10.24 18.30 41.50 100.00 16.61 12.34 2.55 137.49 18.77 13.0 21.4 1.54 939 998.5 209.8 177 178 45.23 9.9 10.1 0 34.2 4802 5990 4620 34.0 4786 5983 4614 -0.2 6 3 12 4783 5983 4597 0.0 19.5 10.2 70.3 149 59 2.5 490 0.021 0.7 2 7.2 0.0 0.00 11.9 0.6 1.8 2.1
38.63 5.30 46.87 57.56 9.93 18.07 40.60 100.00 16.34 12.12 2.43 135.81 18.57 13.3 21.4 1.54 940 1012.2 209.4 178 178 46.74 9.4 10.6 0 34.0 4858 6067 4677 32.8 4768 5964 4596 -1.2 7 4 13 4776 5995 4607 0.0 19.7 10.5 69.8 143 56 2.5 496 0.022 1.0 3 7.1 0.1 0.10 11.9 0.4 1.7 1.8
41.43 5.54 52.48 64.98 10.30 18.24 45.86 100.00 17.07 12.90 2.18 145.88 20.08 13.4 21.4 1.54 939 1007.6 208.9 177 177 45.54 9.0 9.4 0 34.4 4862 6036 4601 33.5 4832 6003 4578 -0.9 8 5 14 4841 6023 4581 0.0 19.8 9.3 70.9 151 60 2.5 470 0.019 1.3 2 7.2 0.0 0.00 12.0 0.5 1.8 1.9
40.96 5.54 52.29 64.61 10.32 18.52 45.76 100.00 17.05 12.82 2.19 145.59 20.02 13.3 21.1 1.54 936 1022.3 206.4 178 178 46.26 9.3 10.1 0 34.2 4843 6021 4597 33.2 4780 5971 4553 -1.0 9 6 15 4781 5983 4551 0.0 19.5 10.1 70.4 148 59 2.5 507 0.021 0.6 3 7.2 0.0 0.00 11.7 0.6 1.7 2.3
37.89 6.25 52.68 65.12 11.64 18.11 45.42 100.00 17.51 13.01 2.88 145.07 19.56 12.7 21.5 1.60 946 1005.0 210.5 178 178 45.76 8.3 9.8 0 34.6 4920 6093 4648 33.3 4797 5977 4570 -1.3 1 1 16 4812 6008 4567 0.0 19.7 9.7 70.6 154 63 2.5 500 0.020 0.8 3 7.4 0.0 0.00 11.6 0.7 1.9 1.9
37.42 6.25 52.68 65.12 11.64 18.11 45.42 100.00 17.51 13.01 2.88 145.07 19.56 12.7 21.7 1.59 939 998.0 205.5 177 177 44.90 9.5 9.5 0 34.3 4831 6017 4591 34.2 4821 6009 4586 -0.1 2 2 17 4864 6056 4600 0.0 20.0 9.0 71.0 155 63 2.4 493 0.020 1.8 2 7.3 0.0 0.00 11.3 0.5 1.9 2.1
37.51 6.25 52.68 65.12 11.64 18.11 45.42 100.00 17.51 13.01 2.88 145.07 19.56 12.7 21.3 1.60 934 997.1 206.2 178 178 45.30 9.5 9.4 0 34.4 4824 6003 4586 34.3 4832 6012 4589 -0.1 3 3 18 4839 6019 4585 0.0 19.7 9.3 70.9 154 61 2.5 501 0.020 0.7 3 7.3 0.1 0.10 10.7 0.7 1.8 2.1
37.92 6.22 52.76 65.13 11.50 18.55 45.48 100.00 17.57 13.08 2.88 145.10 19.64 12.7 21.2 1.60 936 1006.1 207.3 177 177 45.28 8.7 9.5 0 34.7 4887 6076 4637 33.9 4829 6012 4599 -0.8 4 4 19 4844 6025 4594 0.0 19.8 9.3 70.9 152 61 2.5 470 0.019 1.7 2 7.3 0.0 0.00 11.3 0.5 1.8 1.8
36.77 5.90 51.37 63.65 10.76 19.90 45.07 100.00 17.06 12.78 2.46 144.98 19.73 12.4 21.3 1.54 935 990.5 205.7 177 177 44.38 9.1 9.1 0 35.0 4850 6015 4611 34.9 4856 6027 4618 -0.1 7 3 3 4852 6031 4606 0.0 19.8 9.1 71.0 152 65 2.3 505 0.021 1.5 3 7.3 0.0 0.00 11.0 0.4 1.9 2.3
37.14 5.90 51.37 63.65 10.76 19.90 45.07 100.00 17.06 12.78 2.46 144.98 19.73 12.4 21.0 1.55 934 1002.4 206.2 178 178 44.25 9.1 9.3 0 34.9 4854 6014 4617 34.6 4834 6009 4601 -0.3 8 4 4 4839 6015 4594 0.0 19.7 9.3 71.0 154 64 2.4 517 0.021 0.4 3 7.3 0.1 0.20 10.9 0.5 1.9 2.3
37.73 5.90 51.37 63.65 10.76 19.90 45.07 100.00 17.06 12.78 2.46 144.98 19.73 12.4 21.2 1.55 940 984.3 204.3 177 177 44.38 9.0 9.7 0 35.3 4861 6025 4611 34.8 4805 5975 4570 -0.5 9 5 5 4862 6060 4609 0.0 20.1 9.1 70.8 156 63 2.5 502 0.020 1.7 3 7.3 0.0 0.00 12.0 0.5 1.8 2.3
38.03 5.70 52.77 66.25 10.50 15.18 47.07 100.00 16.67 12.84 2.17 144.39 19.93 12.1 21.4 1.55 938 1005.3 207.1 178 178 44.86 8.5 8.8 0 34.8 4868 6012 4561 34.5 4844 5982 4542 -0.3 10 1 6 4852 6009 4556 0.0 19.4 8.8 71.8 156 64 2.5 502 0.020 0.9 3 7.3 0.0 0.00 12.1 0.3 1.8 2.3
37.86 5.70 52.77 66.25 10.50 15.18 47.07 100.00 16.67 12.84 2.17 144.39 19.93 12.1 21.3 1.55 936 1003.8 206.2 177 177 44.09 7.7 8.1 0 35.3 4924 6050 4597 34.8 4897 6022 4586 -0.5 11 2 7 4906 6040 4586 0.0 19.7 8.0 72.3 158 65 2.4 481 0.019 1.3 2 7.2 0.0 0.00 12.1 0.7 1.8 2.1
38.31 5.70 52.77 66.25 10.50 15.18 47.07 100.00 16.67 12.84 2.17 144.39 19.93 12.1 21.5 1.54 934 1009.5 205.7 178 178 44.62 7.8 8.6 0 35.2 4925 6058 4601 34.6 4863 6016 4594 -0.6 12 3 8 4906 6047 4585 0.0 19.7 8.1 72.2 158 63 2.5 506 0.020 0.9 3 7.3 0.0 0.00 12.0 0.3 1.8 2.3
38.66 5.97 53.13 66.58 11.00 16.55 46.77 100.00 16.97 13.00 2.40 145.03 19.88 12.1 21.1 1.54 938 1015.1 207.5 178 178 45.51 8.8 9.2 0 34.5 4856 6022 4579 34.1 4820 5989 4544 -0.4 2 1 10 4846 6015 4541 0.0 19.6 9.0 71.4 158 64 2.5 520 0.021 0.5 3 7.4 0.0 0.00 11.7 0.3 1.9 1.8
38.65 6.39 53.72 67.13 11.75 18.61 46.32 100.00 17.44 13.25 2.75 145.96 19.80 12.4 21.0 1.55 936 1020.8 206.6 177 177 46.22 8.8 9.2 0 34.7 4866 6040 4571 34.0 4844 6028 4553 -0.7 9 5 17 4855 6055 4581 0.0 19.9 9.1 71.0 158 65 2.4 482 0.019 1.6 3 7.3 0.0 0.00 11.5 0.6 1.8 2.2
38.67 5.36 53.39 65.30 12.05 18.57 46.91 100.00 16.42 12.32 2.31 144.29 19.71 11.5 21.2 1.55 939 1014.5 206.6 177 177 45.87 9.3 9.9 0 34.4 4833 6020 4569 34.1 4789 5973 4532 -0.3 1 1 19 4809 5990 4536 0.0 19.5 9.6 70.9 155 61 2.5 488 0.020 1.0 3 7.3 0.1 0.10 11.8 0.4 1.8 2.4
38.42 5.27 52.45 64.09 10.84 18.10 46.02 100.00 16.35 12.22 1.77 143.59 19.66 11.4 21.2 1.55 933 1029.0 205.9 178 177 47.70 10.5 10.3 0 33.5 4750 5952 4516 33.5 4765 5956 4520 0.0 2 2 20 4790 5993 4541 0.0 19.5 10.1 70.4 149 59 2.5 512 0.021 1.8 3 7.3 0.0 0.00 11.6 0.4 1.8 2.3
39.15 4.58 49.56 61.08 9.84 18.68 43.53 100.00 16.16 12.14 1.99 139.64 18.80 11.6 21.2 1.55 933 1008.0 205.5 177 178 45.51 9.3 10.1 0 34.4 4795 5982 4600 34.4 4785 5984 4587 0.0 3 3 21 4815 5991 4597 0.0 19.6 9.7 70.7 151 61 2.5 511 0.021 1.1 3 7.2 0.0 0.00 11.4 0.8 1.7 2.2
38.82 4.58 49.56 61.08 9.84 18.68 43.53 100.00 16.16 12.14 1.99 139.64 18.80 11.6 21.2 1.55 934 999.9 208.2 178 178 45.13 9.4 9.6 0 34.8 4832 6024 4625 34.7 4816 6001 4601 -0.1 4 4 22 4837 6024 4608 0.0 19.8 9.4 70.8 151 60 2.5 507 0.021 1.9 3 7.3 0.0 0.00 11.4 0.7 1.8 2.4
39.08 4.58 49.56 61.08 9.84 18.68 43.53 100.00 16.16 12.14 1.99 139.64 18.80 11.6 20.0 1.55 928 1003.2 206.6 177 177 45.73 9.7 10.0 0 34.4 4815 6010 4618 34.4 4786 5986 4590 0.0 5 5 23 4815 6011 4594 0.0 19.7 9.7 70.5 150 60 2.5 518 0.022 1.6 3 7.3 0.0 0.00 11.3 0.5 1.7 2.1
38.90 7.70 62.92 75.91 13.49 16.10 55.29 100.00 18.28 13.83 3.20 149.91 21.23 11.3 20.8 1.55 934 1014.6 208.7 177 177 46.04 8.2 8.2 0 34.8 4882 6022 4606 34.8 4884 6026 4613 0.0 7 1 1 4903 6034 4606 0.0 19.5 8.0 72.5 158 66 2.4 475 0.019 1.6 3 0.0 0.0 0.00 11.8 0.2 1.8 2.2
39.62 6.39 59.10 71.04 11.52 21.82 53.53 100.00 17.93 12.92 2.38 155.77 20.76 12.5 19.9 1.55 933 1005.1 205.2 178 177 45.31 8.8 9.1 0 34.9 4878 6058 4641 34.6 4853 6047 4630 -0.3 8 2 2 4872 6058 4629 0.0 20.1 8.9 71.0 160 66 2.4 496 0.019 1.4 3 0.0 0.0 0.00 11.6 0.3 1.8 2.5
39.77 6.63 59.81 71.94 11.89 20.76 53.86 100.00 17.99 13.09 2.53 154.68 20.85 14.1 20.0 1.54 936 1029.7 206.8 177 178 44.77 9.0 9.4 0 34.7 4860 6041 4617 34.0 4822 6000 4588 -0.7 9 3 3 4832 6013 4585 0.0 19.7 9.4 71.0 160 63 2.5 496 0.019 0.6 3 0.0 0.0 0.00 11.7 0.5 1.8 2.2
39.66 6.71 56.32 66.19 12.35 20.02 50.26 100.00 17.54 12.50 2.82 143.45 20.32 12.8 21.5 1.54 935 1027.0 206.2 178 177 46.78 9.6 9.6 0 33.9 4829 6026 4621 33.5 4815 6011 4612 -0.4 2 2 8 NA NA NA NA NA NA NA 156 NA NA NA NA 2.3 0 0.0 0.0 0.00 0.0 0.6 0.0 0.0
39.68 6.87 56.74 66.61 12.55 20.18 50.80 100.00 17.48 12.41 2.82 143.10 20.24 12.8 21.5 1.56 933 1032.0 206.6 177 178 46.51 9.5 9.9 0 34.0 4833 6029 4608 33.5 4807 6001 4584 -0.5 0 0 0 NA NA NA NA NA NA NA 158 NA NA NA NA 1.0 0 0.0 0.0 0.00 0.0 0.6 0.0 0.0
42.23 7.50 58.41 68.30 13.33 20.81 52.96 100.00 17.23 12.04 2.83 141.72 19.92 13.0 20.4 1.55 930 1040.0 208.7 178 177 48.05 10.1 10.4 0 33.1 4795 6000 4557 32.8 4764 5977 4538 -0.3 0 0 0 NA NA NA NA NA NA NA 167 NA NA NA NA 1.3 0 0.0 0.0 0.00 0.0 0.6 0.0 0.0
38.48 7.53 58.36 69.25 14.35 20.57 51.31 100.00 17.87 12.77 3.55 145.56 20.04 14.1 21.6 1.55 935 1044.8 208.0 177 177 48.11 10.2 10.3 0 32.9 4793 6029 4600 32.4 4787 6030 4592 -0.5 0 0 0 NA NA NA NA NA NA NA 156 NA NA NA NA 2.3 0 0.0 0.0 0.00 0.0 0.5 0.0 0.0
39.49 7.53 58.36 69.25 14.35 20.57 51.31 100.00 17.87 12.77 3.55 145.56 20.04 14.1 20.8 1.55 932 1053.8 207.5 178 178 48.13 9.9 10.3 0 32.9 4824 6068 4630 32.0 4795 6050 4607 -0.9 0 0 0 NA NA NA NA NA NA NA 160 NA NA NA NA 0.9 0 0.0 0.0 0.00 0.0 0.6 0.0 0.0

Statistical Summary of the data set

stat_desc <- function(df){
df %>% 
    describe() %>%
    kbl() %>%
    kable_styling(bootstrap_options = c("striped", "hover", "condensed")) %>%
    scroll_box(width="100%",height="350px")
}

stat_desc(ChemicalManufacturingProcess)
vars n mean sd median trimmed mad min max range skew kurtosis se
Yield 1 176 40.1765341 1.8456664 39.970 40.1150000 1.9718580 35.250 46.340 11.090 0.3109596 -0.1132944 0.1391223
BiologicalMaterial01 2 176 6.4114205 0.7139225 6.305 6.3933803 0.6745830 4.580 8.810 4.230 0.2733165 0.4567758 0.0538139
BiologicalMaterial02 3 176 55.6887500 4.0345806 55.090 55.5810563 4.5812340 46.870 64.750 17.880 0.2441269 -0.7050911 0.3041180
BiologicalMaterial03 4 176 67.7050000 4.0010641 67.220 67.6780986 4.2773010 56.970 78.250 21.280 0.0285108 -0.1235203 0.3015916
BiologicalMaterial04 5 176 12.3492614 1.7746607 12.100 12.1860563 1.3714050 9.380 23.090 13.710 1.7323153 7.0564614 0.1337701
BiologicalMaterial05 6 176 18.5986364 1.8441408 18.490 18.5488732 1.8829020 13.240 24.850 11.610 0.3040053 0.2198005 0.1390073
BiologicalMaterial06 7 176 48.9103977 3.7460718 48.460 48.7379577 3.9437160 40.600 59.380 18.780 0.3685344 -0.3654933 0.2823708
BiologicalMaterial07 8 176 100.0141477 0.1077423 100.000 100.0000000 0.0000000 100.000 100.830 0.830 7.3986642 53.0417012 0.0081214
BiologicalMaterial08 9 176 17.4947727 0.6769536 17.510 17.4687324 0.5930400 15.880 19.140 3.260 0.2200539 0.0627721 0.0510273
BiologicalMaterial09 10 176 12.8500568 0.4151757 12.835 12.8635211 0.4225410 11.440 14.080 2.640 -0.2684177 0.2927765 0.0312950
BiologicalMaterial10 11 176 2.8006250 0.5991433 2.710 2.7328873 0.4003020 1.770 6.870 5.100 2.4023783 11.6471845 0.0451621
BiologicalMaterial11 12 176 146.9531818 4.8204704 146.080 146.7863380 4.1142150 135.810 158.730 22.920 0.3588211 0.0162456 0.3633566
BiologicalMaterial12 13 176 20.1998864 0.7735440 20.120 20.1776056 0.6671700 18.350 22.210 3.860 0.3038443 0.0146595 0.0583081
ManufacturingProcess01 14 175 11.2074286 1.8224342 11.400 11.4078014 1.0378200 0.000 14.100 14.100 -3.9201855 21.8688069 0.1377631
ManufacturingProcess02 15 173 16.6826590 8.4715694 21.000 18.0575540 1.4826000 0.000 22.500 22.500 -1.4307675 0.1062466 0.6440815
ManufacturingProcess03 16 161 1.5395652 0.0223983 1.540 1.5410078 0.0148260 1.470 1.600 0.130 -0.4799447 1.7280557 0.0017652
ManufacturingProcess04 17 175 931.8514286 6.2744406 934.000 932.2836879 5.9304000 911.000 946.000 35.000 -0.6979357 0.0631282 0.4743031
ManufacturingProcess05 18 175 1001.6931429 30.5272134 999.200 998.6248227 17.3464200 923.000 1175.300 252.300 2.5872769 11.7446904 2.3076404
ManufacturingProcess06 19 174 207.4017241 2.6993999 206.800 207.0928571 1.9273800 203.000 227.400 24.400 3.0419007 17.3764864 0.2046410
ManufacturingProcess07 20 175 177.4800000 0.5010334 177.000 177.4751773 0.0000000 177.000 178.000 1.000 0.0793788 -2.0050587 0.0378746
ManufacturingProcess08 21 175 177.5542857 0.4984706 178.000 177.5673759 0.0000000 177.000 178.000 1.000 -0.2165645 -1.9642262 0.0376808
ManufacturingProcess09 22 176 45.6601136 1.5464407 45.730 45.7188732 1.2157320 38.890 49.360 10.470 -0.9406685 3.2701986 0.1165674
ManufacturingProcess10 23 167 9.1790419 0.7666884 9.100 9.1318519 0.5930400 7.500 11.600 4.100 0.6492504 0.6317264 0.0593281
ManufacturingProcess11 24 166 9.3855422 0.7157336 9.400 9.3932836 0.6671700 7.500 11.500 4.000 -0.0193109 0.3227966 0.0555517
ManufacturingProcess12 25 175 857.8114286 1784.5282624 0.000 516.1985816 0.0000000 0.000 4549.000 4549.000 1.5786729 0.4951353 134.8976569
ManufacturingProcess13 26 176 34.5079545 1.0152800 34.600 34.5119718 0.8895600 32.100 38.600 6.500 0.4802776 1.9593883 0.0765296
ManufacturingProcess14 27 175 4853.8685714 54.5236412 4856.000 4854.5744681 40.0302000 4701.000 5055.000 354.000 -0.0109687 1.0781378 4.1215999
ManufacturingProcess15 28 176 6038.9204545 58.3125023 6031.500 6035.5211268 40.7715000 5904.000 6233.000 329.000 0.6743478 1.2162163 4.3954702
ManufacturingProcess16 29 176 4565.8011364 351.6973215 4588.000 4588.3591549 42.9954000 0.000 4852.000 4852.000 -12.4202248 158.3981993 26.5101831
ManufacturingProcess17 30 176 34.3437500 1.2482059 34.400 34.3126761 1.1860800 31.300 40.000 8.700 1.1629715 4.6626982 0.0940871
ManufacturingProcess18 31 176 4809.6818182 367.4777364 4835.000 4837.0704225 34.8411000 0.000 4971.000 4971.000 -12.7361378 163.7375845 27.6996766
ManufacturingProcess19 32 176 6028.1988636 45.5785689 6022.000 6026.1549296 36.3237000 5890.000 6146.000 256.000 0.2973414 0.2962151 3.4356139
ManufacturingProcess20 33 176 4556.4602273 349.0089784 4582.000 4580.9788732 42.9954000 0.000 4759.000 4759.000 -12.6383268 162.0663905 26.3075416
ManufacturingProcess21 34 176 -0.1642045 0.7782930 -0.300 -0.2556338 0.4447800 -1.800 3.600 5.400 1.7291140 5.0274763 0.0586660
ManufacturingProcess22 35 175 5.4057143 3.3306262 5.000 5.2482270 4.4478000 0.000 12.000 12.000 0.3148909 -1.0175458 0.2517717
ManufacturingProcess23 36 175 3.0171429 1.6625499 3.000 2.9432624 1.4826000 0.000 6.000 6.000 0.1967985 -0.9975572 0.1256770
ManufacturingProcess24 37 175 8.8342857 5.7994224 8.000 8.5744681 7.4130000 0.000 23.000 23.000 0.3593200 -1.0207362 0.4383951
ManufacturingProcess25 38 171 4828.1754386 373.4810865 4855.000 4855.5620438 34.0998000 0.000 4990.000 4990.000 -12.6310220 160.3293620 28.5608125
ManufacturingProcess26 39 171 6015.5964912 464.8674900 6047.000 6048.5547445 38.5476000 0.000 6161.000 6161.000 -12.6694398 160.9849144 35.5493055
ManufacturingProcess27 40 171 4562.5087719 353.9848679 4587.000 4587.4452555 35.5824000 0.000 4710.000 4710.000 -12.5174778 158.3931091 27.0698994
ManufacturingProcess28 41 171 6.5918129 5.2489823 10.400 6.8248175 1.0378200 0.000 11.500 11.500 -0.4556335 -1.7907822 0.4013997
ManufacturingProcess29 42 171 20.0111111 1.6638879 19.900 20.0437956 0.4447800 0.000 22.000 22.000 -10.0848133 119.4378857 0.1272407
ManufacturingProcess30 43 171 9.1614035 0.9760824 9.100 9.2145985 0.7413000 0.000 11.200 11.200 -4.7557268 43.0848842 0.0746429
ManufacturingProcess31 44 171 70.1847953 5.5557816 70.800 70.7240876 0.8895600 0.000 72.500 72.500 -11.8231008 146.0094297 0.4248612
ManufacturingProcess32 45 176 158.4659091 5.3972456 158.000 158.3380282 4.4478000 143.000 173.000 30.000 0.2112252 0.0602714 0.4068327
ManufacturingProcess33 46 171 63.5438596 2.4833813 64.000 63.5474453 1.4826000 56.000 70.000 14.000 -0.1310030 0.2740324 0.1899089
ManufacturingProcess34 47 171 2.4935673 0.0543910 2.500 2.4927007 0.0000000 2.300 2.600 0.300 -0.2634497 1.0013075 0.0041594
ManufacturingProcess35 48 171 495.5964912 10.8196874 495.000 495.7445255 8.8956000 463.000 522.000 59.000 -0.1556154 0.4130958 0.8274022
ManufacturingProcess36 49 171 0.0195731 0.0008739 0.020 0.0195620 0.0014826 0.017 0.022 0.005 0.1453141 -0.0557822 0.0000668
ManufacturingProcess37 50 176 1.0136364 0.4450828 1.000 0.9964789 0.4447800 0.000 2.300 2.300 0.3783578 0.0698597 0.0335494
ManufacturingProcess38 51 176 2.5340909 0.6493753 3.000 2.6126761 0.0000000 0.000 3.000 3.000 -1.6818052 3.9189211 0.0489485
ManufacturingProcess39 52 176 6.8511364 1.5054943 7.200 7.1718310 0.1482600 0.000 7.500 7.500 -4.2691214 16.4987895 0.1134809
ManufacturingProcess40 53 175 0.0177143 0.0382885 0.000 0.0099291 0.0000000 0.000 0.100 0.100 1.6768073 0.8164458 0.0028943
ManufacturingProcess41 54 175 0.0237143 0.0538242 0.000 0.0106383 0.0000000 0.000 0.200 0.200 2.1686898 3.6290714 0.0040687
ManufacturingProcess42 55 176 11.2062500 1.9416092 11.600 11.5429577 0.2965200 0.000 12.100 12.100 -5.4500082 28.5288867 0.1463543
ManufacturingProcess43 56 176 0.9119318 0.8679860 0.800 0.8077465 0.2965200 0.000 11.000 11.000 9.0548747 101.0332345 0.0654269
ManufacturingProcess44 57 176 1.8051136 0.3220062 1.900 1.8549296 0.1482600 0.000 2.100 2.100 -4.9703552 25.0876065 0.0242721
ManufacturingProcess45 58 176 2.1380682 0.4069043 2.200 2.2042254 0.1482600 0.000 2.600 2.600 -4.0779411 18.7565001 0.0306716
  1. 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 Sect. 3.8).

Missing Value Analysis

## Counts of missing data per feature
train_na_df <- data.frame(apply(ChemicalManufacturingProcess, 2, function(x) length(which(is.na(x)))))
train_na_df1 <- data.frame(apply(ChemicalManufacturingProcess, 2,function(x) {sum(is.na(x)) / length(x) * 100}))

train_na_df <- cbind(Feature = rownames(train_na_df), train_na_df, train_na_df1)
colnames(train_na_df) <- c('Feature Name','No. of NA Recocrds','Percentage of NA Records')
rownames(train_na_df) <- NULL


train_na_df%>% filter(`No. of NA Recocrds` != 0) %>% arrange(desc(`No. of NA Recocrds`)) %>% kable() %>% kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive")) %>% scroll_box(width="100%",height="300px")
Feature Name No. of NA Recocrds Percentage of NA Records
ManufacturingProcess03 15 8.5227273
ManufacturingProcess11 10 5.6818182
ManufacturingProcess10 9 5.1136364
ManufacturingProcess25 5 2.8409091
ManufacturingProcess26 5 2.8409091
ManufacturingProcess27 5 2.8409091
ManufacturingProcess28 5 2.8409091
ManufacturingProcess29 5 2.8409091
ManufacturingProcess30 5 2.8409091
ManufacturingProcess31 5 2.8409091
ManufacturingProcess33 5 2.8409091
ManufacturingProcess34 5 2.8409091
ManufacturingProcess35 5 2.8409091
ManufacturingProcess36 5 2.8409091
ManufacturingProcess02 3 1.7045455
ManufacturingProcess06 2 1.1363636
ManufacturingProcess01 1 0.5681818
ManufacturingProcess04 1 0.5681818
ManufacturingProcess05 1 0.5681818
ManufacturingProcess07 1 0.5681818
ManufacturingProcess08 1 0.5681818
ManufacturingProcess12 1 0.5681818
ManufacturingProcess14 1 0.5681818
ManufacturingProcess22 1 0.5681818
ManufacturingProcess23 1 0.5681818
ManufacturingProcess24 1 0.5681818
ManufacturingProcess40 1 0.5681818
ManufacturingProcess41 1 0.5681818

Imputation Process

K Nearest Neighbor Technique

I have adopted the KNN approach for imputation for the current data set using the knnImputation() fruntion from DMwR package. I am using k=10 as a tuning parameter.

ChemicalManProcessImputed <- knnImputation(ChemicalManufacturingProcess, k = 10)
  1. 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?

Pre-Processing

Excluding Near Zero Variance Predictors

nZVIndices <- nearZeroVar(ChemicalManProcessImputed)

ChemicalManProcessTransformed <- ChemicalManProcessImputed[,-nZVIndices]

Excluding highly Correlated Predictors

corThresh <- 0.9
tooHigh <- findCorrelation(cor(ChemicalManProcessTransformed), corThresh)
corrPred <- names(ChemicalManProcessTransformed)[tooHigh]
ChemicalManProcessTransformed <- ChemicalManProcessTransformed[,-tooHigh]

Test/Train Split

trainingRows <- createDataPartition(ChemicalManProcessTransformed$Yield, times = 1, p = 0.8, list = FALSE)

train_df <- ChemicalManProcessTransformed[trainingRows,]
test_df <- ChemicalManProcessTransformed[-trainingRows,]

PLS Model Training

## Using k fold cross validation with parameter 10
ctrl <- trainControl("cv", number = 10)

model_fit <- train(Yield ~ ., data = train_df, 
                   method = "pls",
                   tuneLength = 25,
                   trControl = ctrl,
                   preProc = c("center", "scale"))

summary(model_fit)
## Data:    X dimension: 144 46 
##  Y dimension: 144 1
## Fit method: oscorespls
## Number of components considered: 3
## TRAINING: % variance explained
##           1 comps  2 comps  3 comps
## X           16.14    28.13    34.60
## .outcome    48.09    58.10    65.72
# Plot model RMSE vs different values of components
title <- paste("Training Set RMSE Minimized at",
               model_fit$bestTune$ncomp,
               "Components")

plot(model_fit, main = title)

Model Performance Metrics

model_fit$results %>%
  filter(ncomp == model_fit$bestTune$ncomp) %>%
  select(ncomp, RMSE, Rsquared)
ncomp RMSE Rsquared
3 1.246705 0.5684517
  1. Predict the response for the test set.What is the value of the performance metric and how does this compare with the resampled performance metric on the training set?

Model Predictions

# Make predictions
pls_predictions <- predict(model_fit, test_df)
# Model performance metrics
results <- data.frame(RMSE = caret::RMSE(pls_predictions, test_df$Yield),
           Rsquared = caret::R2(pls_predictions, test_df$Yield))
results
RMSE Rsquared
3.614925 0.200272

The RMSE of the predictions is 0.665027 which is better than the RMSE of the trainng set 0.625914. Normally test set RMSE is expected to be lower than the training set.

  1. Which predictors are most important in the model you have trained? Do either the biological or process predictors dominate the list?

Important Predictors

pls_importance <- varImp(model_fit)$importance %>% 
  as.data.frame() %>%
  rownames_to_column("Variable") %>%
  filter(Overall >= 50) %>%
  arrange(desc(Overall)) %>%
  mutate(importance = row_number())

varImp(model_fit) %>%
  plot(, top = max(pls_importance$importance), main = "Important Variables")

From the chart above, it looks like Manufacturing Process related predictors dominate the list of most important predictors.

  1. 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?

Correlation Plot of Most Important Predictors

corrdf <- ChemicalManProcessTransformed[,pls_importance$Variable]

corrdf$Yield <- ChemicalManProcessTransformed["Yield"]

corrMatrix <- round(cor(corrdf),4)

corrMatrix %>% corrplot::corrplot(., method = "color", outline = T, addgrid.col = "darkgray", order="hclust", addrect = 4, rect.col = "black", rect.lwd = 5,cl.pos = "b", tl.col = "indianred4", tl.cex = 1.0, cl.cex = 1.0, addCoef.col = "white", number.digits = 2, number.cex = 0.8, col = colorRampPalette(c("darkred","white","dodgerblue4"))(100))

From the above Correlation plot, it can be observed that -

  • Manufacturing Processes 32, 09, 33 etc. and Biological materials 06 and 03 have strong positive correlations with Yield.
  • Whereas Manufacturing Processes 36, 13 and 17 have strong negative correlations with Yield.