Data624_HW8
Mengqin Cai
4/23/2021
Question 7.2
Friedman (1991) introduced several benchmark data sets create by simulation.One of these simulations used the following nonlinear equation to create data: \(y=10sin(\pi x_1 x_2)+20(x_3-0.5)^2+10x_4+5X_5+N(0,\sigma ^2)\)
where the x values are random variables uniformly distributed between 0, 1.The package mlbench contains a function called mlbench.friedman1 thatsimulates these data:
set.seed(200)
trainingData <- mlbench.friedman1(200, sd = 1)
## We convert the 'x' data from a matrix to a data frame
## One reason is that this will give the columns names.
trainingData$x <- data.frame(trainingData$x)
## Look at the data using
featurePlot(trainingData$x, trainingData$y)
## or other methods.
## This creates a list with a vector 'y' and a matrix
## of predictors 'x'. Also simulate a large test set to
## estimate the true error rate with good precision:
testData <- mlbench.friedman1(5000, sd = 1)
testData$x <- data.frame(testData$x)Tune several models on these data. For example:
knnModel <- train(x = trainingData$x,
y = trainingData$y,
method = "knn",
preProc = c("center", "scale"),
tuneLength = 10)
knnModel## k-Nearest Neighbors
##
## 200 samples
## 10 predictor
##
## Pre-processing: centered (10), scaled (10)
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 200, 200, 200, 200, 200, 200, ...
## Resampling results across tuning parameters:
##
## k RMSE Rsquared MAE
## 5 3.466085 0.5121775 2.816838
## 7 3.349428 0.5452823 2.727410
## 9 3.264276 0.5785990 2.660026
## 11 3.214216 0.6024244 2.603767
## 13 3.196510 0.6176570 2.591935
## 15 3.184173 0.6305506 2.577482
## 17 3.183130 0.6425367 2.567787
## 19 3.198752 0.6483184 2.592683
## 21 3.188993 0.6611428 2.588787
## 23 3.200458 0.6638353 2.604529
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was k = 17.knnPred <- predict(knnModel, newdata = testData$x)
## The function 'postResample' can be used to get the test set
## perforamnce values
knnEval=postResample(pred = knnPred, obs = testData$y)
knnEval## RMSE Rsquared MAE
## 3.2040595 0.6819919 2.5683461Which models appear to give the best performance? Does MARS select the informative predictors (those named X1–X5)?
MARS Model:
#MARS
marsGrid <- expand.grid(.degree = 1:2, .nprune = 2:20)
MarsModel <- train(x = trainingData$x,
y = trainingData$y,
method = "earth",
preProc = c("center", "scale"),
tuneGrid = marsGrid)## Loading required package: earth## Warning: package 'earth' was built under R version 3.6.3## Loading required package: Formula## Loading required package: plotmo## Warning: package 'plotmo' was built under R version 3.6.3## Loading required package: plotrix## Warning: package 'plotrix' was built under R version 3.6.3## Loading required package: TeachingDemos## Warning: package 'TeachingDemos' was built under R version 3.6.3MarsModel## Multivariate Adaptive Regression Spline
##
## 200 samples
## 10 predictor
##
## Pre-processing: centered (10), scaled (10)
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 200, 200, 200, 200, 200, 200, ...
## Resampling results across tuning parameters:
##
## degree nprune RMSE Rsquared MAE
## 1 2 4.383438 0.2405683 3.597961
## 1 3 3.645469 0.4745962 2.930453
## 1 4 2.727602 0.7035031 2.184240
## 1 5 2.449243 0.7611230 1.939231
## 1 6 2.331605 0.7835496 1.833420
## 1 7 1.976830 0.8421599 1.562591
## 1 8 1.870959 0.8585503 1.464551
## 1 9 1.804342 0.8683110 1.410395
## 1 10 1.787676 0.8711960 1.386944
## 1 11 1.790700 0.8707740 1.393076
## 1 12 1.821005 0.8670619 1.419893
## 1 13 1.858688 0.8617344 1.445459
## 1 14 1.862343 0.8623072 1.446050
## 1 15 1.871033 0.8607099 1.457618
## 1 16 1.875619 0.8597499 1.460975
## 1 17 1.879956 0.8591348 1.464279
## 1 18 1.879956 0.8591348 1.464279
## 1 19 1.879956 0.8591348 1.464279
## 1 20 1.879956 0.8591348 1.464279
## 2 2 4.383438 0.2405683 3.597961
## 2 3 3.644919 0.4742570 2.929647
## 2 4 2.730222 0.7028372 2.183075
## 2 5 2.481291 0.7545789 1.965749
## 2 6 2.338369 0.7827873 1.825542
## 2 7 2.030065 0.8328250 1.602024
## 2 8 1.890997 0.8551326 1.477422
## 2 9 1.742626 0.8757904 1.371910
## 2 10 1.608221 0.8943432 1.255416
## 2 11 1.474325 0.9111463 1.157848
## 2 12 1.437483 0.9157967 1.120977
## 2 13 1.439395 0.9164721 1.128309
## 2 14 1.428565 0.9184503 1.118634
## 2 15 1.434093 0.9182413 1.121622
## 2 16 1.471527 0.9145952 1.148351
## 2 17 1.473439 0.9145110 1.147595
## 2 18 1.464591 0.9158838 1.141467
## 2 19 1.461660 0.9161917 1.138989
## 2 20 1.464129 0.9159565 1.140982
##
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were nprune = 14 and degree = 2.Marspred <- predict(MarsModel, newdata = testData$x)
MarsEval<-postResample(Marspred,testData$y)
MarsEval## RMSE Rsquared MAE
## 1.2779993 0.9338365 1.0147070SVM Model:
svmModel <- train(x = trainingData$x,
y = trainingData$y,
method = "svmRadial",
preProc = c("center", "scale"),
tuneLength = 14,
trControl = trainControl(method = "cv"))
svmModel## Support Vector Machines with Radial Basis Function Kernel
##
## 200 samples
## 10 predictor
##
## Pre-processing: centered (10), scaled (10)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 180, 180, 180, 180, 180, 180, ...
## Resampling results across tuning parameters:
##
## C RMSE Rsquared MAE
## 0.25 2.548095 0.7967225 2.001583
## 0.50 2.290826 0.8118225 1.779407
## 1.00 2.095918 0.8337552 1.634192
## 2.00 1.989469 0.8462100 1.539721
## 4.00 1.901332 0.8565135 1.510431
## 8.00 1.879815 0.8588126 1.514502
## 16.00 1.878866 0.8591568 1.518094
## 32.00 1.878866 0.8591568 1.518094
## 64.00 1.878866 0.8591568 1.518094
## 128.00 1.878866 0.8591568 1.518094
## 256.00 1.878866 0.8591568 1.518094
## 512.00 1.878866 0.8591568 1.518094
## 1024.00 1.878866 0.8591568 1.518094
## 2048.00 1.878866 0.8591568 1.518094
##
## Tuning parameter 'sigma' was held constant at a value of 0.06670077
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were sigma = 0.06670077 and C = 16.svmpred <- predict(svmModel, newdata = testData$x)
svmEval<-postResample(svmpred,testData$y)
svmEval## RMSE Rsquared MAE
## 2.0829707 0.8242096 1.5826017Neural Networks
nnetGrid <- expand.grid(.decay = c(0, 0.01, .1),
.size = c(1:10),
.bag = FALSE)
ctrl = trainControl(method='cv', number = 10)
set.seed(200)
nnetModel <- train(trainingData$x, trainingData$y,
method = "avNNet",
tuneGrid = nnetGrid,
trControl = ctrl,
preProc = c("center", "scale"),
linout = TRUE,
trace = FALSE,
MaxNWts = 10 * (ncol(trainingData$x) + 1) + 10 + 1,
maxit = 500)## Warning: executing %dopar% sequentially: no parallel backend registerednnetModel## Model Averaged Neural Network
##
## 200 samples
## 10 predictor
##
## Pre-processing: centered (10), scaled (10)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 180, 180, 180, 180, 180, 180, ...
## Resampling results across tuning parameters:
##
## decay size RMSE Rsquared MAE
## 0.00 1 2.409283 0.7621183 1.899438
## 0.00 2 2.422970 0.7596059 1.940174
## 0.00 3 2.050680 0.8164736 1.639116
## 0.00 4 1.945570 0.8359932 1.553962
## 0.00 5 2.459608 0.7843926 1.852817
## 0.00 6 3.619609 0.6518455 2.367746
## 0.00 7 3.732346 0.5465485 2.505487
## 0.00 8 5.341921 0.4925666 3.027228
## 0.00 9 4.448181 0.5628776 2.637284
## 0.00 10 3.736545 0.6189292 2.529286
## 0.01 1 2.380838 0.7641924 1.871203
## 0.01 2 2.456920 0.7487966 1.925584
## 0.01 3 2.152614 0.8037282 1.690702
## 0.01 4 1.926277 0.8453345 1.547266
## 0.01 5 2.129094 0.8103702 1.698914
## 0.01 6 2.140650 0.8117168 1.698805
## 0.01 7 2.414589 0.7646608 1.911319
## 0.01 8 2.366556 0.7741779 1.873354
## 0.01 9 2.368192 0.7641654 1.781225
## 0.01 10 2.336267 0.7855705 1.857180
## 0.10 1 2.392300 0.7614548 1.873846
## 0.10 2 2.437038 0.7557138 1.918843
## 0.10 3 2.136582 0.8043180 1.702665
## 0.10 4 2.009698 0.8245209 1.574401
## 0.10 5 2.015296 0.8345946 1.586740
## 0.10 6 2.038841 0.8283220 1.586032
## 0.10 7 2.129954 0.8133844 1.707177
## 0.10 8 2.148353 0.8099883 1.690601
## 0.10 9 2.254190 0.7942883 1.759231
## 0.10 10 2.359693 0.7719593 1.873586
##
## Tuning parameter 'bag' was held constant at a value of FALSE
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were size = 4, decay = 0.01 and bag
## = FALSE.nnetpred <- predict(nnetModel, newdata = testData$x)
nnetEval<-postResample(nnetpred,testData$y)
nnetEval## RMSE Rsquared MAE
## 2.0603901 0.8320669 1.5289876Compare the Model
eval<-cbind(nnetEval,MarsEval,knnEval,svmEval)
eval<-data.frame(eval)
colnames(eval)<-c('Neural Network','MARS','KNN','SVM')
evalvaluePre<-varImp(MarsModel)
valuePre## earth variable importance
##
## Overall
## X1 100.00
## X4 75.40
## X2 49.00
## X5 15.72
## X3 0.00plot(valuePre)
MARS model has the lowest RMSE, 1.277993 and highest R squared, 0.9338365, so it is the best performance model. For Mars Model, the most important variable is X1, and only X1, X4, X2 and X5 were selected to the model.
Question 7.5
Exercise 6.3 describes data for a chemical manufacturing process. Use the same data imputation, data splitting, and pre-processing steps as before and train several nonlinear regression models.
data(ChemicalManufacturingProcess)
# imputation
chemical<-kNN(ChemicalManufacturingProcess,imp_var = FALSE)
chemical_remove <- nearZeroVar(chemical) # remove predictors
chemical <- chemical[,-chemical_remove]
#data splitting,
indx<-createDataPartition(chemical$Yield,p=0.8,list=FALSE)
chemical_train<-chemical[indx,]
chemical_test<-chemical[-indx,]
X_train <- chemical_train[,-1]
Y_train <- chemical_train[,1]
X_test <- chemical_train[,-1]
Y_test <- chemical_train[,1]a.
Which nonlinear regression model gives the optimal resampling and test set performance?
Neural Networks
set.seed(200)
nnetGrid <- expand.grid(.decay = c(0, 0.01, 0.1),
.size = c(1:8),
.bag = FALSE)
nnetModel_chemical <- train(X_train,
Y_train,
method = "avNNet",
tuneGrid = nnetGrid,
trControl = ctrl,
preProc = c("center", "scale"),
linout = TRUE,
trace = FALSE,
maxit = 500)
nnetModel_chemical## Model Averaged Neural Network
##
## 144 samples
## 56 predictor
##
## Pre-processing: centered (56), scaled (56)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 130, 129, 129, 130, 131, 131, ...
## Resampling results across tuning parameters:
##
## decay size RMSE Rsquared MAE
## 0.00 1 1.551732 0.3524223 1.280294
## 0.00 2 1.488753 0.3639473 1.183896
## 0.00 3 1.546534 0.3902995 1.175509
## 0.00 4 1.859141 0.3684386 1.498639
## 0.00 5 2.069060 0.3168275 1.629967
## 0.00 6 2.204153 0.3695348 1.751427
## 0.00 7 2.570028 0.3319244 2.037320
## 0.00 8 3.820263 0.1579420 2.811813
## 0.01 1 1.481336 0.4439399 1.173887
## 0.01 2 1.430823 0.5597962 1.120769
## 0.01 3 1.462122 0.5185533 1.193115
## 0.01 4 1.703229 0.4294136 1.294110
## 0.01 5 1.860628 0.3793874 1.328236
## 0.01 6 1.608408 0.4514521 1.222713
## 0.01 7 1.580330 0.4276253 1.257689
## 0.01 8 1.378950 0.5321537 1.134111
## 0.10 1 1.657510 0.4473551 1.220769
## 0.10 2 1.481176 0.5434424 1.068092
## 0.10 3 1.607767 0.4559312 1.311747
## 0.10 4 1.788061 0.4134498 1.277393
## 0.10 5 1.954365 0.3922934 1.407200
## 0.10 6 1.863297 0.4070747 1.304668
## 0.10 7 1.975611 0.3909674 1.397907
## 0.10 8 1.937982 0.3722276 1.408850
##
## Tuning parameter 'bag' was held constant at a value of FALSE
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were size = 8, decay = 0.01 and bag
## = FALSE.nnetpred_chemical <- predict(nnetModel_chemical, newdata = X_test)
nnetEval_chemical<-postResample(nnetpred_chemical,Y_test)
nnetEval_chemical## RMSE Rsquared MAE
## 0.007721307 0.999981598 0.006089000MARS Model:
ctrl = trainControl(method='cv', number = 10)
marsGrid <- expand.grid(.degree = 1:2, .nprune = 2:38)
set.seed(200)
marsModel_chemical <- train(X_train,
Y_train,
method="earth",
tuneGrid = marsGrid,
trControl = ctrl)
marsModel_chemical## Multivariate Adaptive Regression Spline
##
## 144 samples
## 56 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 130, 129, 129, 130, 131, 131, ...
## Resampling results across tuning parameters:
##
## degree nprune RMSE Rsquared MAE
## 1 2 1.369833 0.4467048 1.0860424
## 1 3 1.211507 0.5686188 0.9589247
## 1 4 1.249621 0.5425630 0.9791137
## 1 5 1.274046 0.5475672 0.9918768
## 1 6 1.257202 0.5483783 0.9713915
## 1 7 1.286116 0.5268436 0.9977956
## 1 8 1.248025 0.5461736 0.9528328
## 1 9 1.219865 0.5599196 0.9497539
## 1 10 1.284223 0.5315448 0.9901312
## 1 11 1.304482 0.5262653 1.0010708
## 1 12 1.328601 0.5164286 1.0405815
## 1 13 1.431916 0.4656114 1.0807038
## 1 14 1.415393 0.4798418 1.0558050
## 1 15 1.405107 0.4831515 1.0462950
## 1 16 1.405107 0.4831515 1.0462950
## 1 17 1.405107 0.4831515 1.0462950
## 1 18 1.405107 0.4831515 1.0462950
## 1 19 1.405107 0.4831515 1.0462950
## 1 20 1.405107 0.4831515 1.0462950
## 1 21 1.405107 0.4831515 1.0462950
## 1 22 1.405107 0.4831515 1.0462950
## 1 23 1.405107 0.4831515 1.0462950
## 1 24 1.405107 0.4831515 1.0462950
## 1 25 1.405107 0.4831515 1.0462950
## 1 26 1.405107 0.4831515 1.0462950
## 1 27 1.405107 0.4831515 1.0462950
## 1 28 1.405107 0.4831515 1.0462950
## 1 29 1.405107 0.4831515 1.0462950
## 1 30 1.405107 0.4831515 1.0462950
## 1 31 1.405107 0.4831515 1.0462950
## 1 32 1.405107 0.4831515 1.0462950
## 1 33 1.405107 0.4831515 1.0462950
## 1 34 1.405107 0.4831515 1.0462950
## 1 35 1.405107 0.4831515 1.0462950
## 1 36 1.405107 0.4831515 1.0462950
## 1 37 1.405107 0.4831515 1.0462950
## 1 38 1.405107 0.4831515 1.0462950
## 2 2 1.369833 0.4467048 1.0860424
## 2 3 1.151354 0.6017934 0.9490535
## 2 4 1.195602 0.5683107 0.9789112
## 2 5 1.212729 0.5544613 0.9811140
## 2 6 1.259476 0.5233797 1.0149549
## 2 7 1.276080 0.5169745 0.9971014
## 2 8 1.254041 0.5358384 0.9816998
## 2 9 1.204493 0.5503540 0.9412522
## 2 10 1.217828 0.5565367 0.9512749
## 2 11 1.254498 0.5505529 0.9560064
## 2 12 1.255923 0.5703603 0.9365228
## 2 13 1.237292 0.5773041 0.9362430
## 2 14 1.220458 0.5997714 0.9346536
## 2 15 1.232675 0.5927902 0.9434397
## 2 16 1.210087 0.6020661 0.9195078
## 2 17 1.209727 0.6033106 0.9211479
## 2 18 1.290372 0.5759040 0.9509552
## 2 19 1.311399 0.5664008 0.9395244
## 2 20 1.306793 0.5680164 0.9390429
## 2 21 1.309745 0.5706859 0.9513013
## 2 22 1.309097 0.5702884 0.9501327
## 2 23 1.302850 0.5742954 0.9445891
## 2 24 1.315983 0.5697364 0.9521754
## 2 25 1.311220 0.5713247 0.9514975
## 2 26 1.302313 0.5724254 0.9544148
## 2 27 1.299771 0.5737160 0.9509811
## 2 28 1.299771 0.5737160 0.9509811
## 2 29 1.299771 0.5737160 0.9509811
## 2 30 1.299771 0.5737160 0.9509811
## 2 31 1.299771 0.5737160 0.9509811
## 2 32 1.299771 0.5737160 0.9509811
## 2 33 1.299771 0.5737160 0.9509811
## 2 34 1.299771 0.5737160 0.9509811
## 2 35 1.299771 0.5737160 0.9509811
## 2 36 1.299771 0.5737160 0.9509811
## 2 37 1.299771 0.5737160 0.9509811
## 2 38 1.299771 0.5737160 0.9509811
##
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were nprune = 3 and degree = 2.marspred_chemical <- predict(marsModel_chemical,
newdata = X_test)
marsEval_chemical<-postResample(marspred_chemical,Y_test)
marsEval_chemical## RMSE Rsquared MAE
## 1.1721267 0.5730574 0.9321591SVM Model:
set.seed(100)
svmModel_chemical <- train(X_train,
Y_train,
method = "svmRadial",
preProc = c("center", "scale"),
tuneLength = 14,
trControl = ctrl)
svmModel_chemical## Support Vector Machines with Radial Basis Function Kernel
##
## 144 samples
## 56 predictor
##
## Pre-processing: centered (56), scaled (56)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 129, 130, 130, 130, 130, 130, ...
## Resampling results across tuning parameters:
##
## C RMSE Rsquared MAE
## 0.25 1.379436 0.4678935 1.1305379
## 0.50 1.275603 0.5142810 1.0315086
## 1.00 1.206832 0.5595208 0.9637462
## 2.00 1.126680 0.6117098 0.8992539
## 4.00 1.111241 0.6093522 0.8970187
## 8.00 1.097502 0.6125754 0.8950234
## 16.00 1.095846 0.6132911 0.8938544
## 32.00 1.095846 0.6132911 0.8938544
## 64.00 1.095846 0.6132911 0.8938544
## 128.00 1.095846 0.6132911 0.8938544
## 256.00 1.095846 0.6132911 0.8938544
## 512.00 1.095846 0.6132911 0.8938544
## 1024.00 1.095846 0.6132911 0.8938544
## 2048.00 1.095846 0.6132911 0.8938544
##
## Tuning parameter 'sigma' was held constant at a value of 0.01466014
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were sigma = 0.01466014 and C = 16.svmpred_chemical <- predict(svmModel_chemical, newdata = X_test)
svmEval_chemical<-postResample(svmpred_chemical,Y_test)
svmEval_chemical## RMSE Rsquared MAE
## 0.1705339 0.9932473 0.1663201KNN Model:
knnModel_chemical <- train(X_train,
Y_train,
method = "knn",
preProc = c("center", "scale"),
tuneLength = 10)
knnModel_chemical## k-Nearest Neighbors
##
## 144 samples
## 56 predictor
##
## Pre-processing: centered (56), scaled (56)
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 144, 144, 144, 144, 144, 144, ...
## Resampling results across tuning parameters:
##
## k RMSE Rsquared MAE
## 5 1.399081 0.4141256 1.114851
## 7 1.402945 0.4173434 1.113450
## 9 1.406982 0.4159282 1.115845
## 11 1.403096 0.4199128 1.115177
## 13 1.404135 0.4241972 1.120698
## 15 1.411768 0.4221908 1.129910
## 17 1.415262 0.4238179 1.129149
## 19 1.423660 0.4210621 1.138323
## 21 1.428925 0.4233843 1.145877
## 23 1.445039 0.4141874 1.156086
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was k = 5.knnPred_chemical <- predict(knnModel_chemical, newdata = X_test)
knnEval_chemical<-postResample(knnPred_chemical, Y_test)
knnEval_chemical## RMSE Rsquared MAE
## 0.9699690 0.7395897 0.7470694eval2<-cbind(nnetEval_chemical,marsEval_chemical,knnEval_chemical,svmEval_chemical)
eval2<-data.frame(eval2)
colnames(eval2)<-c('Neural Network','MARS','KNN','SVM')
eval2SVM Model give out the best performance with 0.007721307 of RMSE and 0.999981598 of Rsquared .
b.
Which predictors are most important in the optimal nonlinear regression model? Do either the biological or process variables dominate the list? How do the top ten important predictors compare to the top ten predictors from the optimal linear model?
varImp(svmModel_chemical)## loess r-squared variable importance
##
## only 20 most important variables shown (out of 56)
##
## Overall
## ManufacturingProcess32 100.00
## BiologicalMaterial06 89.04
## ManufacturingProcess13 85.75
## BiologicalMaterial03 73.17
## BiologicalMaterial12 66.20
## ManufacturingProcess36 65.62
## ManufacturingProcess09 63.19
## ManufacturingProcess17 60.35
## ManufacturingProcess31 57.55
## BiologicalMaterial02 56.91
## ManufacturingProcess06 51.64
## ManufacturingProcess29 49.75
## ManufacturingProcess11 49.48
## ManufacturingProcess33 47.11
## BiologicalMaterial04 44.69
## ManufacturingProcess30 41.94
## BiologicalMaterial11 41.68
## BiologicalMaterial09 41.07
## BiologicalMaterial01 39.32
## BiologicalMaterial08 37.21The most important predictor is ManufacturingProcess32. For the top ten most important variables, process variables account for seven, so we can say process variables dominate the list. Comparing to the top 10 predictors from the PLS model (we showed the list in question 6.3 before. https://rpubs.com/DaisyCai/Data624_HW7), the name of the predictor variables are similar except some minor changes of the order. For example, BiologicalMaterial06 is the 7th most important variable on the list of pls model, but it become the second most important variable when we use SVM model.
c.
Explore the relationships between the top predictors and the response for the predictors that are unique to the optimal nonlinear regression model.Do these plots reveal intuition about the biological or process predictors and their relationship with yield?
I choose the top 5 most important variables to explore the relationship between predictors and response.
chemical%>%
select(c('Yield','ManufacturingProcess32','BiologicalMaterial06','ManufacturingProcess09',
'ManufacturingProcess13','ManufacturingProcess36'))%>%
cor()## Yield ManufacturingProcess32
## Yield 1.0000000 0.60833215
## ManufacturingProcess32 0.6083321 1.00000000
## BiologicalMaterial06 0.4781634 0.60059580
## ManufacturingProcess09 0.5034705 0.04100301
## ManufacturingProcess13 -0.5036797 -0.10120679
## ManufacturingProcess36 -0.5257340 -0.78800943
## BiologicalMaterial06 ManufacturingProcess09
## Yield 0.4781634 0.50347051
## ManufacturingProcess32 0.6005958 0.04100301
## BiologicalMaterial06 1.0000000 0.23005968
## ManufacturingProcess09 0.2300597 1.00000000
## ManufacturingProcess13 -0.1218676 -0.79135366
## ManufacturingProcess36 -0.5304800 -0.05005281
## ManufacturingProcess13 ManufacturingProcess36
## Yield -0.5036797 -0.52573401
## ManufacturingProcess32 -0.1012068 -0.78800943
## BiologicalMaterial06 -0.1218676 -0.53048003
## ManufacturingProcess09 -0.7913537 -0.05005281
## ManufacturingProcess13 1.0000000 0.09558950
## ManufacturingProcess36 0.0955895 1.00000000value <- c('ManufacturingProcess32','BiologicalMaterial06',
'ManufacturingProcess09','ManufacturingProcess13',
'ManufacturingProcess36')
featurePlot(X_train[,value], Y_train)
We can see from the table, as well as the plot, ManufacturingProcess13 and ManufacturingProcess36 have negative correlation with the response. ManufacturingProcess32 has the highest positive correlation with the response yield. In addition, we detect that ManufacturingProcess32 and ManufacturingProcess36 has a very high negative correlation, -0.78800943.