Developing a model to predict permeability 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)
data(permeability)The matrix fingerprints contains the 1,107 binary molecular predictors for the 165 compounds, while permeability contains permeability response.
(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?
# See how many predictors are present before filtering.
paste(dim(fingerprints)[2], ' predictors exist before filtering.' , sep = '') %>% print()## [1] "1107 predictors exist before filtering."# Filter out predictors wirth low frequencies using the nearZeroVar() function.
filteredData <- nearZeroVar(fingerprints)
# Filtered results.
filteredResults <- fingerprints[, - filteredData]
# See how many predictors are present after filtering.
paste(dim(filteredResults)[2], ' predictors remain for modeling after filtering.' , sep = '') %>% print()## [1] "388 predictors remain for modeling after filtering."Answer:
388 predictors are left for modeling after filtering out predictors with low frequencies.
(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?
set.seed(5)
# Split the training data using an 80% training data split.
trainingData <- createDataPartition(permeability, p = 0.8, list = FALSE)
xTrainData <- filteredResults[trainingData, ]
yTrainData <- permeability[trainingData, ]
# Split the test data.
xTestData <- filteredResults[-trainingData, ]
yTestData <- permeability[-trainingData, ]
# Pre-process the data and tune a PLS model.
plsModel <- train(x = xTrainData, y = yTrainData, method = 'pls', metric = 'Rsquared',
tuneLength = 20, trControl = trainControl(method = 'cv'), preProcess = c('center', 'scale'))
# Print out the results.
plsModel## Partial Least Squares
##
## 133 samples
## 388 predictors
##
## Pre-processing: centered (388), scaled (388)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 120, 119, 118, 120, 121, 119, ...
## Resampling results across tuning parameters:
##
## ncomp RMSE Rsquared MAE
## 1 12.76281 0.3174163 9.801324
## 2 11.70129 0.4751294 8.071228
## 3 11.47024 0.4599176 8.604095
## 4 11.54034 0.4515853 8.726725
## 5 11.22248 0.4617327 8.418250
## 6 11.22014 0.4589468 8.556390
## 7 11.02084 0.4799481 8.311601
## 8 10.96545 0.4838870 8.568745
## 9 11.08967 0.4853797 8.357197
## 10 11.19828 0.4885690 8.378020
## 11 11.43588 0.4713522 8.474291
## 12 11.30182 0.4731638 8.592116
## 13 11.22463 0.4804070 8.487040
## 14 11.27657 0.4826057 8.606557
## 15 11.37346 0.4781552 8.824008
## 16 11.51128 0.4729540 8.970150
## 17 11.79375 0.4598752 9.196114
## 18 11.85114 0.4533310 9.198911
## 19 12.11646 0.4400425 9.382643
## 20 12.31271 0.4301286 9.538435
##
## Rsquared was used to select the optimal model using the largest value.
## The final value used for the model was ncomp = 10.Answer:
Using R2 to select the optimal model, 10 latent variables are optimal (ncomp = 10), and the corresponding resampled estimate of R2 is 0.4885690.
(d) Predict the response for the test set. What is the test set estimate of R2?
# Predict the response for the test set.
testSetResponsePrediction <- predict(plsModel, xTestData) %>% postResample(obs = yTestData)
testSetResponsePrediction## RMSE Rsquared MAE
## 12.523716 0.457552 8.794433Answer:
The test set estimate of R2 is 0.457552.
(e) Try building other models discussed in this chapter. Do any have better predictive performance?
set.seed(5)
# Build a PCR model for performance comparision.
pcrModel <- train(x = xTrainData, y = yTrainData, method = 'pcr', metric = 'Rsquared',
tuneLength = 20, trControl = trainControl(method = 'cv'), preProcess = c('center', 'scale'))
# Print out the results.
pcrModel## Principal Component Analysis
##
## 133 samples
## 388 predictors
##
## Pre-processing: centered (388), scaled (388)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 120, 119, 121, 119, 119, 120, ...
## Resampling results across tuning parameters:
##
## ncomp RMSE Rsquared MAE
## 1 14.42118 0.1324585 11.122153
## 2 14.43670 0.1309422 11.135403
## 3 13.61295 0.2867805 10.377237
## 4 12.87381 0.3474533 9.748440
## 5 12.31801 0.3844983 8.967160
## 6 12.21920 0.3878923 8.812631
## 7 12.27294 0.3869846 8.809974
## 8 11.84946 0.4293802 8.465001
## 9 11.99299 0.4287386 8.803507
## 10 11.63500 0.4545615 8.504614
## 11 11.72869 0.4464945 8.599709
## 12 11.60268 0.4500838 8.520559
## 13 11.68449 0.4421662 8.576183
## 14 11.69077 0.4427715 8.631258
## 15 11.65695 0.4453246 8.659155
## 16 11.69982 0.4418126 8.680035
## 17 11.69822 0.4411631 8.642403
## 18 11.53751 0.4807247 8.655468
## 19 11.26883 0.5046219 8.468657
## 20 11.16160 0.5184676 8.411848
##
## Rsquared was used to select the optimal model using the largest value.
## The final value used for the model was ncomp = 20.# Predict the response for the test set.
pcrPredictionResults <- predict(pcrModel, xTestData) %>% postResample(obs = yTestData)
pcrPredictionResults## RMSE Rsquared MAE
## 13.9603138 0.3241302 9.5628119
set.seed(5)
# Build a Ridge model for performance comparision.
ridgeGrid <- data.frame(.lambda = seq(0, 1, by = 0.1))
ridgeModel <- train(x = xTrainData, y = yTrainData, method = 'ridge', metric = 'Rsquared',
tuneGrid = ridgeGrid, trControl = trainControl(method = 'cv'), preProcess = c('center', 'scale'))
# Print out the results.
ridgeModel## Ridge Regression
##
## 133 samples
## 388 predictors
##
## Pre-processing: centered (388), scaled (388)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 120, 119, 121, 119, 119, 120, ...
## Resampling results across tuning parameters:
##
## lambda RMSE Rsquared MAE
## 0.0 12.52803 0.4848279 9.370395
## 0.1 10.74949 0.5706409 8.236826
## 0.2 10.80990 0.5894287 8.237838
## 0.3 11.10459 0.5912255 8.586023
## 0.4 11.51123 0.5895893 8.973789
## 0.5 12.00376 0.5871437 9.383268
## 0.6 12.55219 0.5841590 9.813966
## 0.7 13.15572 0.5813421 10.262435
## 0.8 13.80079 0.5786183 10.760244
## 0.9 14.47974 0.5760086 11.274210
## 1.0 15.18635 0.5735331 11.793268
##
## Rsquared was used to select the optimal model using the largest value.
## The final value used for the model was lambda = 0.3.# Predict the response for the test set.
ridgePredictionResults <- predict(ridgeModel, xTestData) %>% postResample(obs = yTestData)
ridgePredictionResults## RMSE Rsquared MAE
## 13.1562787 0.4519973 9.7999235Answer:
R2 values for each model:
PLS Model: 0.457552
PCR Model: 0.3241302
Ridge Model: 0.4519973
The model with the best R2 value is the original PLS Model.
(f) Would you recommend any of your models to replace the permeability laboratory experiment?
I would not recommend replacing the permeability laboratory experiment with one of my models. The original PLS model has the highest R2 value and is therefore the most accurate model. The Ridge model is close to the PLS model in terms of accuracy (R2 value is 0.4519973), where as the PCR model is the least accurate with an R2 value of 0.3241302.
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)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.
(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 Sect. 3.8).
# Take a look at which predictors have missing values.
summary(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
## # Impute the missing values using KNN.
cmpImputed <- preProcess(ChemicalManufacturingProcess, 'knnImpute')# Predict after imputation.
chemicalMPData <- predict(cmpImputed, ChemicalManufacturingProcess)
(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(5)
# Split the training data using an 80% training data split.
trainingData <- createDataPartition(ChemicalManufacturingProcess$Yield, p = 0.8, list = FALSE)
xTrainData <- chemicalMPData[trainingData, ]
yTrainData <- ChemicalManufacturingProcess$Yield[trainingData]
# Split the test data.
xTestData <- chemicalMPData[-trainingData, ]
yTestData <- ChemicalManufacturingProcess$Yield[-trainingData]
# Pre-process the data and tune a PLS model.
plsModel <- train(x = xTrainData, y = yTrainData, method = 'pls', metric = 'Rsquared',
tuneLength = 20, trControl = trainControl(method = 'cv'), preProcess = c('center', 'scale'))
# Print out the results.
plsModel## Partial Least Squares
##
## 144 samples
## 58 predictor
##
## Pre-processing: centered (58), scaled (58)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 129, 128, 131, 130, 129, 130, ...
## Resampling results across tuning parameters:
##
## ncomp RMSE Rsquared MAE
## 1 1.31187408 0.5757936 0.98205137
## 2 1.63909325 0.6463069 0.97220369
## 3 0.74577523 0.8340859 0.61819233
## 4 1.28254537 0.7507618 0.68430186
## 5 1.40032766 0.7759725 0.63711229
## 6 1.09264563 0.8015110 0.51450403
## 7 0.86777065 0.8294942 0.41581460
## 8 0.62366470 0.8720275 0.31439302
## 9 0.47280576 0.9177633 0.24528345
## 10 0.36241024 0.9409604 0.18255241
## 11 0.28599361 0.9571149 0.14752052
## 12 0.19529391 0.9806123 0.11395188
## 13 0.11537802 0.9946256 0.07874321
## 14 0.10078295 0.9955548 0.06438427
## 15 0.09158776 0.9953864 0.05475921
## 16 0.06902192 0.9977279 0.04422640
## 17 0.06828083 0.9974566 0.03985153
## 18 0.07726584 0.9959235 0.04075533
## 19 0.07056089 0.9962683 0.03488554
## 20 0.06717188 0.9956081 0.03210811
##
## Rsquared was used to select the optimal model using the largest value.
## The final value used for the model was ncomp = 16.Answer:
For this question, I tuned a PLS model. Using Rsquared as the performance metric, the optimal value is ncomp = 16, with an R2 of 0.9977279.
(d) 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?
# Predict the response for the test set.
testSetResponsePrediction <- predict(plsModel, xTestData) %>% postResample(obs = yTestData)
testSetResponsePrediction## RMSE Rsquared MAE
## 0.04431181 0.99938957 0.03318241Answer:
The test set R2 is 0.99938957 which is higher than that of the training set.
(e) Which predictors are most important in the model you have trained? Do either the biological or process predictors dominate the list?
plsModel$finalModel$coefficients## , , 1 comps
##
## .outcome
## Yield 0.2230087478
## BiologicalMaterial01 0.0795932024
## BiologicalMaterial02 0.1064811572
## BiologicalMaterial03 0.1052266611
## BiologicalMaterial04 0.0786508138
## BiologicalMaterial05 0.0277203722
## BiologicalMaterial06 0.1099507260
## BiologicalMaterial07 -0.0276548821
## BiologicalMaterial08 0.0877427943
## BiologicalMaterial09 0.0291738316
## BiologicalMaterial10 0.0401087581
## BiologicalMaterial11 0.0839400203
## BiologicalMaterial12 0.0912345592
## ManufacturingProcess01 -0.0015157766
## ManufacturingProcess02 -0.0374969959
## ManufacturingProcess03 -0.0188330869
## ManufacturingProcess04 -0.0651952469
## ManufacturingProcess05 0.0135095780
## ManufacturingProcess06 0.0815440230
## ManufacturingProcess07 -0.0193489458
## ManufacturingProcess08 -0.0075696275
## ManufacturingProcess09 0.1134406599
## ManufacturingProcess10 0.0562619501
## ManufacturingProcess11 0.0852541595
## ManufacturingProcess12 0.0882027968
## ManufacturingProcess13 -0.1223772949
## ManufacturingProcess14 -0.0109946524
## ManufacturingProcess15 0.0413461776
## ManufacturingProcess16 -0.0280764951
## ManufacturingProcess17 -0.1068986199
## ManufacturingProcess18 -0.0146285091
## ManufacturingProcess19 0.0164093898
## ManufacturingProcess20 -0.0163047016
## ManufacturingProcess21 -0.0122348444
## ManufacturingProcess22 0.0025584719
## ManufacturingProcess23 -0.0281233010
## ManufacturingProcess24 -0.0528471490
## ManufacturingProcess25 0.0014636234
## ManufacturingProcess26 0.0078292330
## ManufacturingProcess27 0.0001712513
## ManufacturingProcess28 0.0557585277
## ManufacturingProcess29 0.0303882061
## ManufacturingProcess30 0.0526068566
## ManufacturingProcess31 -0.0137774479
## ManufacturingProcess32 0.1312048261
## ManufacturingProcess33 0.0932121949
## ManufacturingProcess34 0.0355304336
## ManufacturingProcess35 -0.0495388115
## ManufacturingProcess36 -0.1218109332
## ManufacturingProcess37 -0.0363875644
## ManufacturingProcess38 -0.0196247116
## ManufacturingProcess39 0.0040873717
## ManufacturingProcess40 -0.0067193136
## ManufacturingProcess41 -0.0037281177
## ManufacturingProcess42 -0.0099422604
## ManufacturingProcess43 0.0413854819
## ManufacturingProcess44 0.0099192935
## ManufacturingProcess45 0.0030533598
##
## , , 2 comps
##
## .outcome
## Yield 0.471735828
## BiologicalMaterial01 0.018748653
## BiologicalMaterial02 0.056551401
## BiologicalMaterial03 0.090347085
## BiologicalMaterial04 0.020523676
## BiologicalMaterial05 -0.009726324
## BiologicalMaterial06 0.076883803
## BiologicalMaterial07 -0.085233438
## BiologicalMaterial08 0.024102088
## BiologicalMaterial09 -0.018120583
## BiologicalMaterial10 -0.040700545
## BiologicalMaterial11 0.029519000
## BiologicalMaterial12 0.043530729
## ManufacturingProcess01 0.037629705
## ManufacturingProcess02 0.033141752
## ManufacturingProcess03 -0.037746942
## ManufacturingProcess04 -0.024400792
## ManufacturingProcess05 -0.045650661
## ManufacturingProcess06 0.114569416
## ManufacturingProcess07 -0.052035921
## ManufacturingProcess08 -0.006811906
## ManufacturingProcess09 0.191198053
## ManufacturingProcess10 0.071259313
## ManufacturingProcess11 0.131121341
## ManufacturingProcess12 0.131325287
## ManufacturingProcess13 -0.221919672
## ManufacturingProcess14 -0.030736539
## ManufacturingProcess15 0.037798970
## ManufacturingProcess16 -0.070765067
## ManufacturingProcess17 -0.231329008
## ManufacturingProcess18 0.014860180
## ManufacturingProcess19 -0.026828944
## ManufacturingProcess20 0.010992023
## ManufacturingProcess21 -0.089696995
## ManufacturingProcess22 0.008644570
## ManufacturingProcess23 -0.024852632
## ManufacturingProcess24 -0.043537329
## ManufacturingProcess25 -0.019915878
## ManufacturingProcess26 -0.009833555
## ManufacturingProcess27 -0.021439371
## ManufacturingProcess28 -0.008987614
## ManufacturingProcess29 0.010169004
## ManufacturingProcess30 0.072371116
## ManufacturingProcess31 -0.031537583
## ManufacturingProcess32 0.190499436
## ManufacturingProcess33 0.106353580
## ManufacturingProcess34 0.105368173
## ManufacturingProcess35 -0.064751492
## ManufacturingProcess36 -0.176093971
## ManufacturingProcess37 -0.100540744
## ManufacturingProcess38 -0.016972193
## ManufacturingProcess39 0.049937874
## ManufacturingProcess40 0.001589947
## ManufacturingProcess41 -0.005704726
## ManufacturingProcess42 0.016112563
## ManufacturingProcess43 0.052156330
## ManufacturingProcess44 0.050045900
## ManufacturingProcess45 0.033725670
##
## , , 3 comps
##
## .outcome
## Yield 0.7141318113
## BiologicalMaterial01 0.0108311800
## BiologicalMaterial02 0.0367668590
## BiologicalMaterial03 0.0793160450
## BiologicalMaterial04 0.0144178592
## BiologicalMaterial05 0.0068067840
## BiologicalMaterial06 0.0715089524
## BiologicalMaterial07 -0.1455256378
## BiologicalMaterial08 -0.0029108953
## BiologicalMaterial09 -0.0689039329
## BiologicalMaterial10 -0.0582307678
## BiologicalMaterial11 0.0097542289
## BiologicalMaterial12 0.0197815275
## ManufacturingProcess01 0.0583853137
## ManufacturingProcess02 0.0247028683
## ManufacturingProcess03 -0.0188615386
## ManufacturingProcess04 0.0351181460
## ManufacturingProcess05 -0.0908984023
## ManufacturingProcess06 0.0724628480
## ManufacturingProcess07 -0.0903733285
## ManufacturingProcess08 -0.0091700342
## ManufacturingProcess09 0.1501157358
## ManufacturingProcess10 0.0113679267
## ManufacturingProcess11 0.0837563598
## ManufacturingProcess12 0.0777825403
## ManufacturingProcess13 -0.1790369597
## ManufacturingProcess14 0.0412608579
## ManufacturingProcess15 0.1058364744
## ManufacturingProcess16 -0.0291058716
## ManufacturingProcess17 -0.2136059686
## ManufacturingProcess18 0.0523242180
## ManufacturingProcess19 0.0435428818
## ManufacturingProcess20 0.0465274815
## ManufacturingProcess21 -0.1209598732
## ManufacturingProcess22 -0.0020014158
## ManufacturingProcess23 -0.0387873700
## ManufacturingProcess24 -0.0507876832
## ManufacturingProcess25 -0.0007535192
## ManufacturingProcess26 0.0089929915
## ManufacturingProcess27 -0.0024616241
## ManufacturingProcess28 -0.0594929230
## ManufacturingProcess29 0.0386267663
## ManufacturingProcess30 0.0500832039
## ManufacturingProcess31 -0.0138545919
## ManufacturingProcess32 0.2629996272
## ManufacturingProcess33 0.1400367957
## ManufacturingProcess34 0.1524568028
## ManufacturingProcess35 -0.0649136233
## ManufacturingProcess36 -0.2250422761
## ManufacturingProcess37 -0.1567781961
## ManufacturingProcess38 -0.0156283749
## ManufacturingProcess39 0.0919357019
## ManufacturingProcess40 0.0077817200
## ManufacturingProcess41 -0.0048711226
## ManufacturingProcess42 0.0432836060
## ManufacturingProcess43 0.0538165268
## ManufacturingProcess44 0.0732341382
## ManufacturingProcess45 0.0612538433
##
## , , 4 comps
##
## .outcome
## Yield 1.0771426927
## BiologicalMaterial01 0.0235360770
## BiologicalMaterial02 -0.0016302878
## BiologicalMaterial03 0.0403695899
## BiologicalMaterial04 0.0033865227
## BiologicalMaterial05 0.0295361607
## BiologicalMaterial06 0.0598437080
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## ManufacturingProcess01 0.0711387887
## ManufacturingProcess02 0.0023445809
## ManufacturingProcess03 -0.0275220894
## ManufacturingProcess04 0.1368063883
## ManufacturingProcess05 -0.1056314972
## ManufacturingProcess06 -0.0016953876
## ManufacturingProcess07 -0.1140601804
## ManufacturingProcess08 -0.0111194569
## ManufacturingProcess09 0.1339796038
## ManufacturingProcess10 0.0528446964
## ManufacturingProcess11 0.0504085681
## ManufacturingProcess12 0.0056181063
## ManufacturingProcess13 -0.1394229040
## ManufacturingProcess14 -0.0002529728
## ManufacturingProcess15 0.0728263071
## ManufacturingProcess16 -0.0527991821
## ManufacturingProcess17 -0.1234042830
## ManufacturingProcess18 0.0168398210
## ManufacturingProcess19 0.1330141071
## ManufacturingProcess20 0.0099077816
## ManufacturingProcess21 -0.0168499861
## ManufacturingProcess22 -0.0383176631
## ManufacturingProcess23 -0.0687766522
## ManufacturingProcess24 -0.0942335145
## ManufacturingProcess25 -0.0230453250
## ManufacturingProcess26 -0.0134702595
## ManufacturingProcess27 -0.0223904164
## ManufacturingProcess28 -0.1248089823
## ManufacturingProcess29 0.0353520960
## ManufacturingProcess30 -0.0104895509
## ManufacturingProcess31 -0.0358215056
## ManufacturingProcess32 0.2507246247
## ManufacturingProcess33 0.0701952747
## ManufacturingProcess34 0.1915868192
## ManufacturingProcess35 -0.0314996061
## ManufacturingProcess36 -0.1722480089
## ManufacturingProcess37 -0.1982781469
## ManufacturingProcess38 -0.0566228348
## ManufacturingProcess39 0.0891315637
## ManufacturingProcess40 -0.0132566646
## ManufacturingProcess41 -0.0314969087
## ManufacturingProcess42 0.0018503097
## ManufacturingProcess43 0.0716673670
## ManufacturingProcess44 0.0140400485
## ManufacturingProcess45 0.0171759686
##
## , , 5 comps
##
## .outcome
## Yield 1.335181e+00
## BiologicalMaterial01 3.487662e-02
## BiologicalMaterial02 -2.750899e-02
## BiologicalMaterial03 3.236428e-02
## BiologicalMaterial04 1.386994e-03
## BiologicalMaterial05 2.639571e-02
## BiologicalMaterial06 5.329128e-02
## BiologicalMaterial07 -2.952928e-02
## BiologicalMaterial08 4.817090e-02
## BiologicalMaterial09 -8.397355e-02
## BiologicalMaterial10 -6.106703e-02
## BiologicalMaterial11 3.715850e-02
## BiologicalMaterial12 8.226965e-02
## ManufacturingProcess01 6.737211e-02
## ManufacturingProcess02 -2.150750e-03
## ManufacturingProcess03 -4.742119e-02
## ManufacturingProcess04 1.857298e-01
## ManufacturingProcess05 -1.022033e-01
## ManufacturingProcess06 -6.210120e-02
## ManufacturingProcess07 -1.167661e-01
## ManufacturingProcess08 -3.437335e-02
## ManufacturingProcess09 1.494633e-01
## ManufacturingProcess10 5.004265e-02
## ManufacturingProcess11 4.085372e-02
## ManufacturingProcess12 4.753169e-04
## ManufacturingProcess13 -1.140991e-01
## ManufacturingProcess14 -6.162316e-03
## ManufacturingProcess15 6.438391e-02
## ManufacturingProcess16 -5.933918e-02
## ManufacturingProcess17 -8.262249e-02
## ManufacturingProcess18 -5.835025e-04
## ManufacturingProcess19 1.530590e-01
## ManufacturingProcess20 -1.042232e-02
## ManufacturingProcess21 1.929605e-02
## ManufacturingProcess22 -3.444237e-02
## ManufacturingProcess23 -3.696840e-02
## ManufacturingProcess24 -9.030733e-02
## ManufacturingProcess25 5.746658e-03
## ManufacturingProcess26 1.537308e-02
## ManufacturingProcess27 6.665453e-03
## ManufacturingProcess28 -1.484697e-01
## ManufacturingProcess29 6.867123e-02
## ManufacturingProcess30 -2.699838e-03
## ManufacturingProcess31 5.957617e-05
## ManufacturingProcess32 1.902620e-01
## ManufacturingProcess33 -1.498849e-02
## ManufacturingProcess34 1.732369e-01
## ManufacturingProcess35 3.399793e-02
## ManufacturingProcess36 -6.716699e-02
## ManufacturingProcess37 -1.954759e-01
## ManufacturingProcess38 -3.041325e-02
## ManufacturingProcess39 1.231936e-01
## ManufacturingProcess40 1.973955e-02
## ManufacturingProcess41 5.461690e-04
## ManufacturingProcess42 1.768242e-02
## ManufacturingProcess43 8.138114e-02
## ManufacturingProcess44 1.312379e-02
## ManufacturingProcess45 3.371311e-02
##
## , , 6 comps
##
## .outcome
## Yield 1.459293499
## BiologicalMaterial01 0.053717388
## BiologicalMaterial02 -0.031289327
## BiologicalMaterial03 0.041818322
## BiologicalMaterial04 0.005218815
## BiologicalMaterial05 0.022410489
## BiologicalMaterial06 0.059310270
## BiologicalMaterial07 -0.008418522
## BiologicalMaterial08 0.055845005
## BiologicalMaterial09 -0.070715951
## BiologicalMaterial10 -0.056978946
## BiologicalMaterial11 0.046690936
## BiologicalMaterial12 0.096473197
## ManufacturingProcess01 0.058916277
## ManufacturingProcess02 0.004614015
## ManufacturingProcess03 -0.066003783
## ManufacturingProcess04 0.191116856
## ManufacturingProcess05 -0.094017390
## ManufacturingProcess06 -0.090961954
## ManufacturingProcess07 -0.096331915
## ManufacturingProcess08 -0.054687719
## ManufacturingProcess09 0.157661528
## ManufacturingProcess10 0.012493002
## ManufacturingProcess11 0.029094768
## ManufacturingProcess12 0.010832610
## ManufacturingProcess13 -0.093748328
## ManufacturingProcess14 0.017491545
## ManufacturingProcess15 0.075141848
## ManufacturingProcess16 -0.049553670
## ManufacturingProcess17 -0.071478098
## ManufacturingProcess18 0.004295553
## ManufacturingProcess19 0.139926266
## ManufacturingProcess20 -0.008716326
## ManufacturingProcess21 0.009383753
## ManufacturingProcess22 -0.022800618
## ManufacturingProcess23 -0.005885021
## ManufacturingProcess24 -0.074386255
## ManufacturingProcess25 -0.016045688
## ManufacturingProcess26 -0.007686530
## ManufacturingProcess27 -0.017162180
## ManufacturingProcess28 -0.156846103
## ManufacturingProcess29 0.044796963
## ManufacturingProcess30 -0.029082585
## ManufacturingProcess31 -0.013974195
## ManufacturingProcess32 0.162983504
## ManufacturingProcess33 -0.043671608
## ManufacturingProcess34 0.122347489
## ManufacturingProcess35 0.051215790
## ManufacturingProcess36 -0.024139303
## ManufacturingProcess37 -0.167881797
## ManufacturingProcess38 -0.023741882
## ManufacturingProcess39 0.113873822
## ManufacturingProcess40 0.043385936
## ManufacturingProcess41 0.023633384
## ManufacturingProcess42 0.002595191
## ManufacturingProcess43 0.069696392
## ManufacturingProcess44 -0.009934311
## ManufacturingProcess45 0.025865518
##
## , , 7 comps
##
## .outcome
## Yield 1.563020469
## BiologicalMaterial01 0.075840082
## BiologicalMaterial02 -0.040555690
## BiologicalMaterial03 0.036679279
## BiologicalMaterial04 0.005663225
## BiologicalMaterial05 0.012755184
## BiologicalMaterial06 0.055115350
## BiologicalMaterial07 -0.008954414
## BiologicalMaterial08 0.045971525
## BiologicalMaterial09 -0.085486677
## BiologicalMaterial10 -0.055344789
## BiologicalMaterial11 0.018925709
## BiologicalMaterial12 0.075224773
## ManufacturingProcess01 0.042108287
## ManufacturingProcess02 0.005328189
## ManufacturingProcess03 -0.080316435
## ManufacturingProcess04 0.172144039
## ManufacturingProcess05 -0.089480876
## ManufacturingProcess06 -0.099328896
## ManufacturingProcess07 -0.062288779
## ManufacturingProcess08 -0.071407790
## ManufacturingProcess09 0.156442078
## ManufacturingProcess10 -0.012163366
## ManufacturingProcess11 0.022048266
## ManufacturingProcess12 0.035153769
## ManufacturingProcess13 -0.080930261
## ManufacturingProcess14 0.024185645
## ManufacturingProcess15 0.069702285
## ManufacturingProcess16 -0.047836031
## ManufacturingProcess17 -0.053849001
## ManufacturingProcess18 0.003774477
## ManufacturingProcess19 0.116470872
## ManufacturingProcess20 -0.011944203
## ManufacturingProcess21 0.022251818
## ManufacturingProcess22 -0.029856801
## ManufacturingProcess23 0.009264319
## ManufacturingProcess24 -0.035288307
## ManufacturingProcess25 -0.002799609
## ManufacturingProcess26 0.003721116
## ManufacturingProcess27 -0.006679803
## ManufacturingProcess28 -0.139683640
## ManufacturingProcess29 0.052644652
## ManufacturingProcess30 -0.029010078
## ManufacturingProcess31 0.006201196
## ManufacturingProcess32 0.150304825
## ManufacturingProcess33 -0.047998988
## ManufacturingProcess34 0.051829810
## ManufacturingProcess35 0.042540053
## ManufacturingProcess36 -0.007076030
## ManufacturingProcess37 -0.122958864
## ManufacturingProcess38 -0.030691531
## ManufacturingProcess39 0.091556381
## ManufacturingProcess40 0.045615445
## ManufacturingProcess41 0.020694863
## ManufacturingProcess42 -0.022659751
## ManufacturingProcess43 0.053683891
## ManufacturingProcess44 -0.042897356
## ManufacturingProcess45 0.002910505
##
## , , 8 comps
##
## .outcome
## Yield 1.631452029
## BiologicalMaterial01 0.089238811
## BiologicalMaterial02 -0.046673281
## BiologicalMaterial03 0.031472775
## BiologicalMaterial04 0.007326098
## BiologicalMaterial05 0.003415200
## BiologicalMaterial06 0.048521288
## BiologicalMaterial07 -0.017906474
## BiologicalMaterial08 0.043828797
## BiologicalMaterial09 -0.088681726
## BiologicalMaterial10 -0.048979583
## BiologicalMaterial11 0.001680336
## BiologicalMaterial12 0.059600191
## ManufacturingProcess01 0.019684220
## ManufacturingProcess02 -0.002984544
## ManufacturingProcess03 -0.087690936
## ManufacturingProcess04 0.151701632
## ManufacturingProcess05 -0.090688944
## ManufacturingProcess06 -0.089089419
## ManufacturingProcess07 -0.030635251
## ManufacturingProcess08 -0.066994188
## ManufacturingProcess09 0.143399041
## ManufacturingProcess10 -0.023331596
## ManufacturingProcess11 0.016283658
## ManufacturingProcess12 0.051632822
## ManufacturingProcess13 -0.066599373
## ManufacturingProcess14 0.020832500
## ManufacturingProcess15 0.055818819
## ManufacturingProcess16 -0.050390643
## ManufacturingProcess17 -0.028061174
## ManufacturingProcess18 0.001724367
## ManufacturingProcess19 0.097766822
## ManufacturingProcess20 -0.015749730
## ManufacturingProcess21 0.047587134
## ManufacturingProcess22 -0.025936859
## ManufacturingProcess23 0.021184894
## ManufacturingProcess24 -0.006143600
## ManufacturingProcess25 -0.006226420
## ManufacturingProcess26 -0.001236202
## ManufacturingProcess27 -0.011741254
## ManufacturingProcess28 -0.112210777
## ManufacturingProcess29 0.047174658
## ManufacturingProcess30 -0.039096020
## ManufacturingProcess31 0.007927786
## ManufacturingProcess32 0.141843404
## ManufacturingProcess33 -0.049948571
## ManufacturingProcess34 0.009126640
## ManufacturingProcess35 0.029729597
## ManufacturingProcess36 -0.003511351
## ManufacturingProcess37 -0.097401441
## ManufacturingProcess38 -0.016268384
## ManufacturingProcess39 0.094859682
## ManufacturingProcess40 0.037258877
## ManufacturingProcess41 0.007065496
## ManufacturingProcess42 -0.008926206
## ManufacturingProcess43 0.045530372
## ManufacturingProcess44 -0.037261294
## ManufacturingProcess45 0.014005259
##
## , , 9 comps
##
## .outcome
## Yield 1.705880092
## BiologicalMaterial01 0.097350664
## BiologicalMaterial02 -0.054042479
## BiologicalMaterial03 0.018507061
## BiologicalMaterial04 0.012301059
## BiologicalMaterial05 0.011231265
## BiologicalMaterial06 0.037661691
## BiologicalMaterial07 -0.045145010
## BiologicalMaterial08 0.050379317
## BiologicalMaterial09 -0.086329401
## BiologicalMaterial10 -0.030437448
## BiologicalMaterial11 -0.009716355
## BiologicalMaterial12 0.045112979
## ManufacturingProcess01 0.019896703
## ManufacturingProcess02 -0.016460492
## ManufacturingProcess03 -0.060306948
## ManufacturingProcess04 0.141305937
## ManufacturingProcess05 -0.060206361
## ManufacturingProcess06 -0.058621050
## ManufacturingProcess07 0.008536599
## ManufacturingProcess08 -0.042149548
## ManufacturingProcess09 0.128197899
## ManufacturingProcess10 -0.029362114
## ManufacturingProcess11 0.032701827
## ManufacturingProcess12 0.046302239
## ManufacturingProcess13 -0.051697723
## ManufacturingProcess14 0.017532029
## ManufacturingProcess15 0.046402780
## ManufacturingProcess16 -0.025720179
## ManufacturingProcess17 -0.010216423
## ManufacturingProcess18 0.012038276
## ManufacturingProcess19 0.058832531
## ManufacturingProcess20 -0.002709116
## ManufacturingProcess21 0.057773503
## ManufacturingProcess22 -0.017617005
## ManufacturingProcess23 0.018220522
## ManufacturingProcess24 0.008462316
## ManufacturingProcess25 -0.009774932
## ManufacturingProcess26 -0.005630772
## ManufacturingProcess27 -0.013164124
## ManufacturingProcess28 -0.088987256
## ManufacturingProcess29 0.041849791
## ManufacturingProcess30 -0.030509614
## ManufacturingProcess31 0.010263567
## ManufacturingProcess32 0.111147964
## ManufacturingProcess33 -0.076998902
## ManufacturingProcess34 -0.022969067
## ManufacturingProcess35 -0.001303592
## ManufacturingProcess36 0.004876027
## ManufacturingProcess37 -0.061916851
## ManufacturingProcess38 -0.008922824
## ManufacturingProcess39 0.082361656
## ManufacturingProcess40 0.024497121
## ManufacturingProcess41 -0.013315418
## ManufacturingProcess42 0.008419222
## ManufacturingProcess43 0.031859405
## ManufacturingProcess44 -0.035822946
## ManufacturingProcess45 0.024677182
##
## , , 10 comps
##
## .outcome
## Yield 1.7573951717
## BiologicalMaterial01 0.0915226481
## BiologicalMaterial02 -0.0573545307
## BiologicalMaterial03 0.0218374558
## BiologicalMaterial04 0.0040554124
## BiologicalMaterial05 0.0172902375
## BiologicalMaterial06 0.0336880423
## BiologicalMaterial07 -0.0460103048
## BiologicalMaterial08 0.0532213455
## BiologicalMaterial09 -0.0659209903
## BiologicalMaterial10 -0.0295710108
## BiologicalMaterial11 -0.0101117849
## BiologicalMaterial12 0.0423762218
## ManufacturingProcess01 0.0113259364
## ManufacturingProcess02 -0.0067148182
## ManufacturingProcess03 -0.0474393412
## ManufacturingProcess04 0.1174870588
## ManufacturingProcess05 -0.0508954356
## ManufacturingProcess06 -0.0314334648
## ManufacturingProcess07 0.0253450984
## ManufacturingProcess08 -0.0196970547
## ManufacturingProcess09 0.0980023187
## ManufacturingProcess10 -0.0408242565
## ManufacturingProcess11 0.0203520954
## ManufacturingProcess12 0.0501410175
## ManufacturingProcess13 -0.0329153325
## ManufacturingProcess14 0.0091641313
## ManufacturingProcess15 0.0219474405
## ManufacturingProcess16 -0.0198823984
## ManufacturingProcess17 0.0049792675
## ManufacturingProcess18 0.0320432055
## ManufacturingProcess19 0.0246172088
## ManufacturingProcess20 0.0177356156
## ManufacturingProcess21 0.0574698372
## ManufacturingProcess22 0.0018492738
## ManufacturingProcess23 0.0138236790
## ManufacturingProcess24 -0.0050244048
## ManufacturingProcess25 -0.0038295295
## ManufacturingProcess26 -0.0021168743
## ManufacturingProcess27 -0.0076065581
## ManufacturingProcess28 -0.0666680316
## ManufacturingProcess29 0.0382250725
## ManufacturingProcess30 -0.0337239093
## ManufacturingProcess31 0.0241009467
## ManufacturingProcess32 0.0956815841
## ManufacturingProcess33 -0.0998404240
## ManufacturingProcess34 -0.0230901635
## ManufacturingProcess35 -0.0282696097
## ManufacturingProcess36 -0.0005795083
## ManufacturingProcess37 -0.0371307479
## ManufacturingProcess38 -0.0130612170
## ManufacturingProcess39 0.0533551976
## ManufacturingProcess40 0.0214757377
## ManufacturingProcess41 -0.0214838596
## ManufacturingProcess42 0.0167872577
## ManufacturingProcess43 0.0283754204
## ManufacturingProcess44 -0.0415655650
## ManufacturingProcess45 0.0322430717
##
## , , 11 comps
##
## .outcome
## Yield 1.782643407
## BiologicalMaterial01 0.072635702
## BiologicalMaterial02 -0.060937110
## BiologicalMaterial03 0.018258275
## BiologicalMaterial04 -0.004729540
## BiologicalMaterial05 0.025471743
## BiologicalMaterial06 0.028812042
## BiologicalMaterial07 -0.036252454
## BiologicalMaterial08 0.050700049
## BiologicalMaterial09 -0.062280601
## BiologicalMaterial10 -0.035686569
## BiologicalMaterial11 -0.012912804
## BiologicalMaterial12 0.040719688
## ManufacturingProcess01 0.005508308
## ManufacturingProcess02 -0.004804960
## ManufacturingProcess03 -0.035969147
## ManufacturingProcess04 0.092807418
## ManufacturingProcess05 -0.033543367
## ManufacturingProcess06 -0.014030415
## ManufacturingProcess07 0.024427216
## ManufacturingProcess08 -0.008077062
## ManufacturingProcess09 0.076972108
## ManufacturingProcess10 -0.043708912
## ManufacturingProcess11 0.020883389
## ManufacturingProcess12 0.048588898
## ManufacturingProcess13 -0.021604218
## ManufacturingProcess14 0.006770813
## ManufacturingProcess15 0.017133327
## ManufacturingProcess16 -0.008141278
## ManufacturingProcess17 0.009751923
## ManufacturingProcess18 0.017087909
## ManufacturingProcess19 0.012551786
## ManufacturingProcess20 0.004482082
## ManufacturingProcess21 0.049399972
## ManufacturingProcess22 0.008976794
## ManufacturingProcess23 0.003990441
## ManufacturingProcess24 -0.005417368
## ManufacturingProcess25 -0.003945094
## ManufacturingProcess26 -0.003102213
## ManufacturingProcess27 -0.007313051
## ManufacturingProcess28 -0.051926275
## ManufacturingProcess29 0.034461236
## ManufacturingProcess30 -0.035686067
## ManufacturingProcess31 0.027695578
## ManufacturingProcess32 0.092459231
## ManufacturingProcess33 -0.100097105
## ManufacturingProcess34 -0.023993165
## ManufacturingProcess35 -0.033464439
## ManufacturingProcess36 -0.004780266
## ManufacturingProcess37 -0.025502902
## ManufacturingProcess38 -0.016740988
## ManufacturingProcess39 0.038090573
## ManufacturingProcess40 0.031997464
## ManufacturingProcess41 -0.011241127
## ManufacturingProcess42 0.022415711
## ManufacturingProcess43 0.034354794
## ManufacturingProcess44 -0.045764235
## ManufacturingProcess45 0.039997864
##
## , , 12 comps
##
## .outcome
## Yield 1.806393e+00
## BiologicalMaterial01 5.587982e-02
## BiologicalMaterial02 -6.267144e-02
## BiologicalMaterial03 1.922191e-02
## BiologicalMaterial04 -1.350034e-04
## BiologicalMaterial05 2.318266e-02
## BiologicalMaterial06 2.041549e-02
## BiologicalMaterial07 -1.924623e-02
## BiologicalMaterial08 5.120080e-02
## BiologicalMaterial09 -4.765669e-02
## BiologicalMaterial10 -2.762722e-02
## BiologicalMaterial11 -1.785965e-02
## BiologicalMaterial12 3.206317e-02
## ManufacturingProcess01 4.331125e-03
## ManufacturingProcess02 6.996855e-03
## ManufacturingProcess03 -2.089822e-02
## ManufacturingProcess04 6.596278e-02
## ManufacturingProcess05 -1.610039e-02
## ManufacturingProcess06 -7.262284e-03
## ManufacturingProcess07 1.611134e-02
## ManufacturingProcess08 1.106887e-03
## ManufacturingProcess09 5.609330e-02
## ManufacturingProcess10 -4.620164e-02
## ManufacturingProcess11 2.069470e-02
## ManufacturingProcess12 4.275714e-02
## ManufacturingProcess13 -1.125658e-02
## ManufacturingProcess14 2.742612e-03
## ManufacturingProcess15 1.153726e-02
## ManufacturingProcess16 8.564202e-04
## ManufacturingProcess17 7.794724e-03
## ManufacturingProcess18 7.994966e-03
## ManufacturingProcess19 -1.857516e-03
## ManufacturingProcess20 -3.299769e-03
## ManufacturingProcess21 3.062725e-02
## ManufacturingProcess22 2.748054e-03
## ManufacturingProcess23 -1.153564e-02
## ManufacturingProcess24 6.474715e-04
## ManufacturingProcess25 -4.731592e-03
## ManufacturingProcess26 -4.674593e-03
## ManufacturingProcess27 -8.176868e-03
## ManufacturingProcess28 -3.624047e-02
## ManufacturingProcess29 2.883057e-02
## ManufacturingProcess30 -3.886633e-02
## ManufacturingProcess31 3.132757e-02
## ManufacturingProcess32 9.358843e-02
## ManufacturingProcess33 -8.980702e-02
## ManufacturingProcess34 -2.279323e-02
## ManufacturingProcess35 -1.732325e-02
## ManufacturingProcess36 -5.175226e-05
## ManufacturingProcess37 -1.802730e-02
## ManufacturingProcess38 -1.513608e-02
## ManufacturingProcess39 2.278514e-02
## ManufacturingProcess40 2.079937e-02
## ManufacturingProcess41 -2.034144e-02
## ManufacturingProcess42 2.645905e-02
## ManufacturingProcess43 4.052741e-02
## ManufacturingProcess44 -4.900922e-02
## ManufacturingProcess45 4.725320e-02
##
## , , 13 comps
##
## .outcome
## Yield 1.8225966347
## BiologicalMaterial01 0.0366611015
## BiologicalMaterial02 -0.0589687927
## BiologicalMaterial03 0.0220552939
## BiologicalMaterial04 0.0046018616
## BiologicalMaterial05 0.0241241625
## BiologicalMaterial06 0.0171582515
## BiologicalMaterial07 -0.0043737113
## BiologicalMaterial08 0.0485910043
## BiologicalMaterial09 -0.0405397599
## BiologicalMaterial10 -0.0225500951
## BiologicalMaterial11 -0.0243504149
## BiologicalMaterial12 0.0254885691
## ManufacturingProcess01 0.0092111430
## ManufacturingProcess02 0.0061951957
## ManufacturingProcess03 -0.0177197378
## ManufacturingProcess04 0.0430515184
## ManufacturingProcess05 -0.0045838503
## ManufacturingProcess06 -0.0035466905
## ManufacturingProcess07 0.0018500086
## ManufacturingProcess08 0.0017181374
## ManufacturingProcess09 0.0417898609
## ManufacturingProcess10 -0.0327512330
## ManufacturingProcess11 0.0222081606
## ManufacturingProcess12 0.0308353121
## ManufacturingProcess13 -0.0037277771
## ManufacturingProcess14 -0.0094143720
## ManufacturingProcess15 0.0061558991
## ManufacturingProcess16 0.0076601577
## ManufacturingProcess17 0.0071858859
## ManufacturingProcess18 0.0135317347
## ManufacturingProcess19 -0.0019976836
## ManufacturingProcess20 0.0036921877
## ManufacturingProcess21 0.0184368662
## ManufacturingProcess22 0.0004223328
## ManufacturingProcess23 -0.0105029591
## ManufacturingProcess24 0.0074993774
## ManufacturingProcess25 -0.0068904573
## ManufacturingProcess26 -0.0067337302
## ManufacturingProcess27 -0.0096190078
## ManufacturingProcess28 -0.0210349996
## ManufacturingProcess29 0.0268226737
## ManufacturingProcess30 -0.0387362637
## ManufacturingProcess31 0.0302727899
## ManufacturingProcess32 0.0924675046
## ManufacturingProcess33 -0.0772453071
## ManufacturingProcess34 -0.0237542829
## ManufacturingProcess35 -0.0110858147
## ManufacturingProcess36 0.0050863819
## ManufacturingProcess37 -0.0112224786
## ManufacturingProcess38 -0.0142136148
## ManufacturingProcess39 0.0166396361
## ManufacturingProcess40 0.0178141261
## ManufacturingProcess41 -0.0185722318
## ManufacturingProcess42 0.0289023239
## ManufacturingProcess43 0.0248955467
## ManufacturingProcess44 -0.0483748803
## ManufacturingProcess45 0.0481641292
##
## , , 14 comps
##
## .outcome
## Yield 1.833872e+00
## BiologicalMaterial01 2.248075e-02
## BiologicalMaterial02 -5.418434e-02
## BiologicalMaterial03 2.737517e-02
## BiologicalMaterial04 8.326831e-03
## BiologicalMaterial05 1.509847e-02
## BiologicalMaterial06 1.488645e-02
## BiologicalMaterial07 7.807956e-05
## BiologicalMaterial08 4.743898e-02
## BiologicalMaterial09 -2.727509e-02
## BiologicalMaterial10 -1.810432e-02
## BiologicalMaterial11 -2.957128e-02
## BiologicalMaterial12 2.145679e-02
## ManufacturingProcess01 1.567233e-02
## ManufacturingProcess02 5.986595e-03
## ManufacturingProcess03 -1.143540e-02
## ManufacturingProcess04 3.166964e-02
## ManufacturingProcess05 -1.823566e-03
## ManufacturingProcess06 4.521815e-03
## ManufacturingProcess07 -1.598621e-03
## ManufacturingProcess08 6.778216e-03
## ManufacturingProcess09 3.207842e-02
## ManufacturingProcess10 -2.470554e-02
## ManufacturingProcess11 2.134995e-02
## ManufacturingProcess12 1.698516e-02
## ManufacturingProcess13 1.928183e-03
## ManufacturingProcess14 -1.684326e-02
## ManufacturingProcess15 2.538160e-03
## ManufacturingProcess16 6.966233e-03
## ManufacturingProcess17 6.481230e-03
## ManufacturingProcess18 1.042673e-02
## ManufacturingProcess19 -1.033791e-03
## ManufacturingProcess20 8.322129e-04
## ManufacturingProcess21 8.833523e-03
## ManufacturingProcess22 1.763324e-03
## ManufacturingProcess23 -6.501093e-03
## ManufacturingProcess24 9.010134e-03
## ManufacturingProcess25 -6.614555e-03
## ManufacturingProcess26 -6.527646e-03
## ManufacturingProcess27 -9.455287e-03
## ManufacturingProcess28 -1.463077e-02
## ManufacturingProcess29 2.629323e-02
## ManufacturingProcess30 -3.958404e-02
## ManufacturingProcess31 3.145313e-02
## ManufacturingProcess32 8.993551e-02
## ManufacturingProcess33 -6.406937e-02
## ManufacturingProcess34 -2.692433e-02
## ManufacturingProcess35 -7.644215e-03
## ManufacturingProcess36 9.589518e-03
## ManufacturingProcess37 -1.005650e-02
## ManufacturingProcess38 -1.430304e-02
## ManufacturingProcess39 1.264748e-02
## ManufacturingProcess40 1.709748e-02
## ManufacturingProcess41 -1.461458e-02
## ManufacturingProcess42 2.937654e-02
## ManufacturingProcess43 7.314294e-03
## ManufacturingProcess44 -4.689582e-02
## ManufacturingProcess45 4.332599e-02
##
## , , 15 comps
##
## .outcome
## Yield 1.843203e+00
## BiologicalMaterial01 9.843033e-03
## BiologicalMaterial02 -4.988842e-02
## BiologicalMaterial03 2.743352e-02
## BiologicalMaterial04 8.419748e-03
## BiologicalMaterial05 3.578734e-03
## BiologicalMaterial06 1.154720e-02
## BiologicalMaterial07 -4.227468e-03
## BiologicalMaterial08 4.451614e-02
## BiologicalMaterial09 -1.771489e-02
## BiologicalMaterial10 -1.604032e-02
## BiologicalMaterial11 -3.555490e-02
## BiologicalMaterial12 1.857182e-02
## ManufacturingProcess01 1.217496e-02
## ManufacturingProcess02 -1.074804e-03
## ManufacturingProcess03 -3.442368e-03
## ManufacturingProcess04 1.009155e-02
## ManufacturingProcess05 -5.057128e-03
## ManufacturingProcess06 8.393467e-03
## ManufacturingProcess07 -6.861061e-05
## ManufacturingProcess08 4.334813e-03
## ManufacturingProcess09 2.707802e-02
## ManufacturingProcess10 -1.617178e-02
## ManufacturingProcess11 2.281755e-02
## ManufacturingProcess12 8.444068e-03
## ManufacturingProcess13 7.690229e-03
## ManufacturingProcess14 -1.759912e-02
## ManufacturingProcess15 5.786948e-03
## ManufacturingProcess16 5.718369e-03
## ManufacturingProcess17 6.106505e-03
## ManufacturingProcess18 1.034000e-02
## ManufacturingProcess19 2.790811e-03
## ManufacturingProcess20 2.409012e-04
## ManufacturingProcess21 -3.318273e-04
## ManufacturingProcess22 1.892400e-03
## ManufacturingProcess23 -2.122283e-03
## ManufacturingProcess24 9.863577e-04
## ManufacturingProcess25 -7.359240e-03
## ManufacturingProcess26 -7.044747e-03
## ManufacturingProcess27 -1.034840e-02
## ManufacturingProcess28 -7.849322e-03
## ManufacturingProcess29 2.670715e-02
## ManufacturingProcess30 -3.800994e-02
## ManufacturingProcess31 2.933801e-02
## ManufacturingProcess32 8.029094e-02
## ManufacturingProcess33 -5.563486e-02
## ManufacturingProcess34 -2.047807e-02
## ManufacturingProcess35 -3.426016e-03
## ManufacturingProcess36 1.813656e-02
## ManufacturingProcess37 -6.517072e-03
## ManufacturingProcess38 -1.189510e-02
## ManufacturingProcess39 1.287481e-02
## ManufacturingProcess40 1.257082e-02
## ManufacturingProcess41 -1.134649e-02
## ManufacturingProcess42 2.830292e-02
## ManufacturingProcess43 3.809129e-03
## ManufacturingProcess44 -4.498462e-02
## ManufacturingProcess45 2.920015e-02
##
## , , 16 comps
##
## .outcome
## Yield 1.847117143
## BiologicalMaterial01 0.004387738
## BiologicalMaterial02 -0.046428585
## BiologicalMaterial03 0.028625649
## BiologicalMaterial04 0.007784843
## BiologicalMaterial05 0.002700292
## BiologicalMaterial06 0.010871170
## BiologicalMaterial07 -0.006723763
## BiologicalMaterial08 0.041911393
## BiologicalMaterial09 -0.012638280
## BiologicalMaterial10 -0.016072135
## BiologicalMaterial11 -0.035165328
## BiologicalMaterial12 0.017665844
## ManufacturingProcess01 0.013575767
## ManufacturingProcess02 -0.002891557
## ManufacturingProcess03 0.001797602
## ManufacturingProcess04 0.002613222
## ManufacturingProcess05 -0.006175172
## ManufacturingProcess06 0.004870618
## ManufacturingProcess07 -0.001877019
## ManufacturingProcess08 -0.002209169
## ManufacturingProcess09 0.023130921
## ManufacturingProcess10 -0.012933000
## ManufacturingProcess11 0.022009590
## ManufacturingProcess12 0.007801960
## ManufacturingProcess13 0.009395445
## ManufacturingProcess14 -0.017674095
## ManufacturingProcess15 0.006016079
## ManufacturingProcess16 0.002585072
## ManufacturingProcess17 0.005743767
## ManufacturingProcess18 0.008511425
## ManufacturingProcess19 0.002376059
## ManufacturingProcess20 -0.002233343
## ManufacturingProcess21 -0.003497861
## ManufacturingProcess22 -0.001212689
## ManufacturingProcess23 -0.002932385
## ManufacturingProcess24 -0.002306453
## ManufacturingProcess25 -0.007397091
## ManufacturingProcess26 -0.007059687
## ManufacturingProcess27 -0.010738352
## ManufacturingProcess28 -0.007964952
## ManufacturingProcess29 0.026443359
## ManufacturingProcess30 -0.037387557
## ManufacturingProcess31 0.028080162
## ManufacturingProcess32 0.071759717
## ManufacturingProcess33 -0.050656775
## ManufacturingProcess34 -0.019993254
## ManufacturingProcess35 -0.007634367
## ManufacturingProcess36 0.019469284
## ManufacturingProcess37 -0.004386731
## ManufacturingProcess38 -0.009147765
## ManufacturingProcess39 0.011758448
## ManufacturingProcess40 0.008899787
## ManufacturingProcess41 -0.010075252
## ManufacturingProcess42 0.030448115
## ManufacturingProcess43 0.001629217
## ManufacturingProcess44 -0.040515550
## ManufacturingProcess45 0.023261400Answer:
Looking at the above comps, the ManufacturingProcess predictors appear to be most important.
(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?
The highest scoring BiologicalMaterial predictor is BiologicalMaterial08, which has an outcome score of 9.064827e-03. Being able to identify which materials are more important will improve yield in future runs as more emphasis can be placed on these materials. Additionally, being able to indentify the most important ManufacturingProcesses allows for further refinement of the process.