HW_8
Joyce Aldrich
2025-11-15
HW_8 Instructions : Do problems 7.2 and 7.5 in Kuhn and Johnson. There are only two but they have many parts. Please submit both a link to your Rpubs and the .rmd file.
7.2
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 = 10 sin(πx1x2) + 20(x3 − 0.5)2 + 10x4 + 5x5 + N(0, σ2) where the x values are random variables uniformly distributed between [0, 1] (there are also 5 other non-informative variables also created in the simulation). The package mlbench contains a function called mlbench.friedman1 that simulates these data:
library(mlbench)
#install.packages("caret")
library(caret)## Loading required package: ggplot2## Loading required package: latticeset.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:
Model_1 : K-Nearest Neighbors (KNN)
library(caret)
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$x)
## The function 'postResample' can be used to get the test set
## perforamnce values
postResample(pred = knnPred, obs = testData$y)## RMSE Rsquared MAE
## 3.2040595 0.6819919 2.5683461Model_2:Multivariate Adaptive Regression Splines (MARS)
# Define the candidate models to test
marsGrid <- expand.grid(.degree = 1:2, .nprune = 2:38)
# Fix the seed so that the results can be reproduced
set.seed(100)
marsTuned <- train(
x=trainingData$x,
y=trainingData$y,
method = "earth",
# Explicitly declare the candidate models to test
preProcess = c("center","scale"),
tuneGrid = marsGrid,
trControl = trainControl(method = "cv")
)## Loading required package: earth## Loading required package: Formula## Loading required package: plotmo## Loading required package: plotrixmarsTuned## Multivariate Adaptive Regression Spline
##
## 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:
##
## degree nprune RMSE Rsquared MAE
## 1 2 4.327937 0.2544880 3.6004742
## 1 3 3.572450 0.4912720 2.8958113
## 1 4 2.596841 0.7183600 2.1063410
## 1 5 2.370161 0.7659777 1.9186686
## 1 6 2.276141 0.7881481 1.8100006
## 1 7 1.766728 0.8751831 1.3902146
## 1 8 1.780946 0.8723243 1.4013449
## 1 9 1.665091 0.8819775 1.3255147
## 1 10 1.663804 0.8821283 1.3276573
## 1 11 1.657738 0.8822967 1.3317299
## 1 12 1.653784 0.8827903 1.3315041
## 1 13 1.648496 0.8823663 1.3164065
## 1 14 1.639073 0.8841742 1.3128329
## 1 15 1.639073 0.8841742 1.3128329
## 1 16 1.639073 0.8841742 1.3128329
## 1 17 1.639073 0.8841742 1.3128329
## 1 18 1.639073 0.8841742 1.3128329
## 1 19 1.639073 0.8841742 1.3128329
## 1 20 1.639073 0.8841742 1.3128329
## 1 21 1.639073 0.8841742 1.3128329
## 1 22 1.639073 0.8841742 1.3128329
## 1 23 1.639073 0.8841742 1.3128329
## 1 24 1.639073 0.8841742 1.3128329
## 1 25 1.639073 0.8841742 1.3128329
## 1 26 1.639073 0.8841742 1.3128329
## 1 27 1.639073 0.8841742 1.3128329
## 1 28 1.639073 0.8841742 1.3128329
## 1 29 1.639073 0.8841742 1.3128329
## 1 30 1.639073 0.8841742 1.3128329
## 1 31 1.639073 0.8841742 1.3128329
## 1 32 1.639073 0.8841742 1.3128329
## 1 33 1.639073 0.8841742 1.3128329
## 1 34 1.639073 0.8841742 1.3128329
## 1 35 1.639073 0.8841742 1.3128329
## 1 36 1.639073 0.8841742 1.3128329
## 1 37 1.639073 0.8841742 1.3128329
## 1 38 1.639073 0.8841742 1.3128329
## 2 2 4.327937 0.2544880 3.6004742
## 2 3 3.572450 0.4912720 2.8958113
## 2 4 2.661826 0.7070510 2.1734709
## 2 5 2.404015 0.7578971 1.9753867
## 2 6 2.243927 0.7914805 1.7830717
## 2 7 1.856336 0.8605482 1.4356822
## 2 8 1.754607 0.8763186 1.3968406
## 2 9 1.653859 0.8870129 1.2813884
## 2 10 1.434159 0.9166537 1.1339203
## 2 11 1.320482 0.9289120 1.0347278
## 2 12 1.317547 0.9306879 1.0359899
## 2 13 1.296910 0.9306902 1.0146112
## 2 14 1.221407 0.9395223 0.9631486
## 2 15 1.230516 0.9390469 0.9761484
## 2 16 1.236911 0.9387407 0.9745362
## 2 17 1.236911 0.9387407 0.9745362
## 2 18 1.236911 0.9387407 0.9745362
## 2 19 1.236911 0.9387407 0.9745362
## 2 20 1.236911 0.9387407 0.9745362
## 2 21 1.236911 0.9387407 0.9745362
## 2 22 1.236911 0.9387407 0.9745362
## 2 23 1.236911 0.9387407 0.9745362
## 2 24 1.236911 0.9387407 0.9745362
## 2 25 1.236911 0.9387407 0.9745362
## 2 26 1.236911 0.9387407 0.9745362
## 2 27 1.236911 0.9387407 0.9745362
## 2 28 1.236911 0.9387407 0.9745362
## 2 29 1.236911 0.9387407 0.9745362
## 2 30 1.236911 0.9387407 0.9745362
## 2 31 1.236911 0.9387407 0.9745362
## 2 32 1.236911 0.9387407 0.9745362
## 2 33 1.236911 0.9387407 0.9745362
## 2 34 1.236911 0.9387407 0.9745362
## 2 35 1.236911 0.9387407 0.9745362
## 2 36 1.236911 0.9387407 0.9745362
## 2 37 1.236911 0.9387407 0.9745362
## 2 38 1.236911 0.9387407 0.9745362
##
## 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.mars_Pred <- predict(marsTuned, newdata = testData$x)
## The function 'postResample' can be used to get the test set
## perforamnce values
postResample(pred = mars_Pred, obs = testData$y)## RMSE Rsquared MAE
## 1.2779993 0.9338365 1.0147070Model_3: Support Vector Machines (SVMs)
svm_Tuned <- train(
x=trainingData$x,
y=trainingData$y,
method = "svmRadial",
preProc = c("center", "scale"),
tuneLength = 14,
trControl = trainControl(method = "cv"))
svm_Tuned## 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 2.490737 0.8009120 1.982118
## 0.50 2.246868 0.8153042 1.774454
## 1.00 2.051872 0.8400992 1.614368
## 2.00 1.949707 0.8534618 1.524201
## 4.00 1.886125 0.8610205 1.465373
## 8.00 1.849220 0.8654721 1.436630
## 16.00 1.834598 0.8673606 1.429762
## 32.00 1.833194 0.8675744 1.428634
## 64.00 1.833194 0.8675744 1.428634
## 128.00 1.833194 0.8675744 1.428634
## 256.00 1.833194 0.8675744 1.428634
## 512.00 1.833194 0.8675744 1.428634
## 1024.00 1.833194 0.8675744 1.428634
## 2048.00 1.833194 0.8675744 1.428634
##
## Tuning parameter 'sigma' was held constant at a value of 0.06315483
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were sigma = 0.06315483 and C = 32.svm_Pred <- predict(svm_Tuned, newdata = testData$x)
## The function 'postResample' can be used to get the test set
## perforamnce values
postResample(pred = svm_Pred, obs = testData$y)## RMSE Rsquared MAE
## 2.0742046 0.8255756 1.5755441Model_4:Neural Networks
nnetGrid <- expand.grid(
.decay = c(0, 0.01, .1),
.size = c(1:5),
.bag = FALSE)
set.seed(100)
nnetTune <- train(
x=trainingData$x,
y=trainingData$y,
method = "avNNet",
tuneGrid = nnetGrid,
trControl = trainControl(method = "cv"),
## Automatically standardize data prior to modeling
## and prediction
preProc = c("center", "scale"),
linout = TRUE,
trace = FALSE,
MaxNWts = 10 * (ncol(trainingData$x) + 1) + 5 + 1,
maxit = 500)## Warning: executing %dopar% sequentially: no parallel backend registerednnetTune## Model Averaged Neural Network
##
## 200 samples
## 10 predictor
##
## Pre-processing: centered (10), scaled (10)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 180, 180, 180, 180, 180, 180, ...
## Resampling results across tuning parameters:
##
## decay size RMSE Rsquared MAE
## 0.00 1 2.435518 0.7513899 1.911881
## 0.00 2 2.433752 0.7550000 1.948642
## 0.00 3 1.996019 0.8333893 1.573741
## 0.00 4 1.988455 0.8360927 1.578655
## 0.00 5 2.132599 0.8114048 1.596225
## 0.01 1 2.385476 0.7602930 1.887838
## 0.01 2 2.438328 0.7544889 1.958866
## 0.01 3 2.048732 0.8232175 1.609293
## 0.01 4 2.051816 0.8227737 1.621138
## 0.01 5 2.098039 0.8261950 1.657384
## 0.10 1 2.393935 0.7596458 1.894179
## 0.10 2 2.493789 0.7401308 1.997616
## 0.10 3 2.173754 0.7968266 1.737418
## 0.10 4 2.034070 0.8227987 1.590931
## 0.10 5 2.060132 0.8240785 1.625409
##
## Tuning parameter 'bag' was held constant at a value of FALSE
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were size = 4, decay = 0 and bag = FALSE.nnet_Pred <- predict(nnetTune, newdata = testData$x)
## The function 'postResample' can be used to get the test set
## perforamnce values
postResample(pred = nnet_Pred, obs = testData$y)## RMSE Rsquared MAE
## 2.3462095 0.7880683 1.7537538Question: Which models appear to give the best performance? Does MARS select the informative predictors (those named X1–X5)?
- Performance Comparison of Models:
postResample(pred = knnPred, obs = testData$y)## RMSE Rsquared MAE
## 3.2040595 0.6819919 2.5683461postResample(pred = mars_Pred, obs = testData$y)## RMSE Rsquared MAE
## 1.2779993 0.9338365 1.0147070postResample(pred = svm_Pred, obs = testData$y)## RMSE Rsquared MAE
## 2.0742046 0.8255756 1.5755441postResample(pred = nnet_Pred, obs = testData$y)## RMSE Rsquared MAE
## 2.3462095 0.7880683 1.7537538Per the output above, noted that the MARS model had the best performance.
mars_vi <- varImp(marsTuned)
mars_vi## earth variable importance
##
## Overall
## X1 100.00
## X4 75.40
## X2 49.00
## X5 15.72
## X3 0.00Indeed, the MARS model identified the informative predictors (X1–X5), consistent with the structure of the simulated data. Among these, X1 had the greatest influence, followed by X4 and X2. Although X3 and X5 were included, their contributions were comparatively minor.
7.5
7.5. Exercise 6.3 describes data for a chemical manufacturing process. Use the same data imputation, data splitting, and pre-processing steps as before and train several nonlinear regression models.
library(AppliedPredictiveModeling)
data("ChemicalManufacturingProcess")
# Preprocessing
prep_obj <- preProcess(ChemicalManufacturingProcess,
method = c("BoxCox", "knnImpute", "center", "scale"))
processed_data <- predict(prep_obj, ChemicalManufacturingProcess)
processed_data$Yield <- ChemicalManufacturingProcess$Yield
set.seed(1234)
ind <- sample(seq_len(nrow(processed_data)), size = floor(0.7 * nrow(processed_data)))
train <- processed_data[ind, ]
test <- processed_data[-ind, ]#KNN
knn_Model_2 <- train(Yield~., data = train,
method = "knn",
preProc = c("center", "scale"),
tuneLength = 10)## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07
## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07knn_Pred_2 <- predict(knn_Model_2, newdata = test)
# MARS
mars_Tuned_2 <- train(Yield~., data = train,
method = "earth",
preProcess = c("center","scale"),
tuneGrid = marsGrid,
trControl = trainControl(method = "cv")
)
mars_Pred_2 <-predict(mars_Tuned_2, newdata = test)
# SVM
svm_Tuned_2 <- train(Yield~., data = train,
method = "svmRadial",
preProc = c("center", "scale"),
tuneLength = 14,
trControl = trainControl(method = "cv"))## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07## Warning in .local(x, ...): Variable(s) `' constant. Cannot scale data.## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07## Warning in .local(x, ...): Variable(s) `' constant. Cannot scale data.## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07## Warning in .local(x, ...): Variable(s) `' constant. Cannot scale data.## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07## Warning in .local(x, ...): Variable(s) `' constant. Cannot scale data.## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07## Warning in .local(x, ...): Variable(s) `' constant. Cannot scale data.## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07## Warning in .local(x, ...): Variable(s) `' constant. Cannot scale data.## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07## Warning in .local(x, ...): Variable(s) `' constant. Cannot scale data.## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07## Warning in .local(x, ...): Variable(s) `' constant. Cannot scale data.## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07## Warning in .local(x, ...): Variable(s) `' constant. Cannot scale data.## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07## Warning in .local(x, ...): Variable(s) `' constant. Cannot scale data.## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07## Warning in .local(x, ...): Variable(s) `' constant. Cannot scale data.## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07## Warning in .local(x, ...): Variable(s) `' constant. Cannot scale data.## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07## Warning in .local(x, ...): Variable(s) `' constant. Cannot scale data.## Warning in preProcess.default(thresh = 0.95, k = 5, freqCut = 19, uniqueCut =
## 10, : These variables have zero variances: BiologicalMaterial07## Warning in .local(x, ...): Variable(s) `' constant. Cannot scale data.svm_Pred_2 <- predict(svm_Tuned_2, newdata = test)
# Neural Networks Model
nnet_Tune_2 <- train(Yield~., data = train,
method = "avNNet",
tuneGrid = nnetGrid,
trControl = trainControl(method = "cv"),
preProc = c("center", "scale"),
linout = TRUE,
trace = FALSE,
MaxNWts = 10 * (ncol(train) + 1) + 5 + 1,
maxit = 500)
nnet_Pred_2 <- predict(nnet_Tune_2 , newdata = test)(a) Which nonlinear regression model gives the optimal resampling and test set performance?
as.data.frame(rbind(
"mars" = postResample(pred = mars_Pred_2, obs = test$Yield),
"svm" = postResample(pred = svm_Pred_2, obs = test$Yield),
"net" = postResample(pred = nnet_Pred_2, obs = test$Yield),
"knn" = postResample(pred = knn_Pred_2, obs = test$Yield)
))## RMSE Rsquared MAE
## mars 1.143137 0.6080421 0.9365946
## svm 1.119109 0.6242347 0.9259233
## net 1.300152 0.5708694 1.0844035
## knn 1.281322 0.5464574 1.0755629Based on the outputs, the SVM model gives the optimal test performance.
(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(svm_Tuned_2, 10)## loess r-squared variable importance
##
## only 20 most important variables shown (out of 57)
##
## Overall
## ManufacturingProcess32 100.00
## ManufacturingProcess13 75.95
## ManufacturingProcess36 64.61
## BiologicalMaterial12 64.56
## BiologicalMaterial06 64.51
## ManufacturingProcess17 64.04
## BiologicalMaterial03 59.78
## ManufacturingProcess09 59.66
## BiologicalMaterial11 50.12
## ManufacturingProcess06 49.66
## BiologicalMaterial02 49.41
## ManufacturingProcess31 47.63
## ManufacturingProcess33 46.45
## ManufacturingProcess11 40.78
## BiologicalMaterial04 35.76
## BiologicalMaterial08 34.42
## ManufacturingProcess18 32.34
## BiologicalMaterial09 32.01
## ManufacturingProcess29 30.00
## ManufacturingProcess02 28.79Per the question, the top 10 predictors identified by the SVM (non-linear) model represent the most important features.
When comparing these to the top 10 predictors from the PLS model (Homework 7), the PLS top features were:
ManufacturingProcess32
ManufacturingProcess09
ManufacturingProcess17
ManufacturingProcess13
ManufacturingProcess36
ManufacturingProcess06
BiologicalMaterial02
ManufacturingProcess33
ManufacturingProcess11
BiologicalMaterial06
In the PLS model, 8 of the top 10 predictors were related to ManufacturingProcess, while *2 were BiologicalMaterial.
In contrast, the SVM model shows a more balanced distribution, with 6 ManufacturingProcess features and 4 BiologicalMaterial features.
(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?
svm_importance <- varImp(svm_Tuned_2)$importance
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, uniontop_vars <- svm_importance %>%
tibble::rownames_to_column(var = "Predictor") %>%
arrange(desc(Overall)) %>%
slice(1:10) %>%
pull(Predictor)
featurePlot(x = train[, top_vars],
y = train$Yield,
plot = "scatter",
layout = c(5, 2))
The plots show the relationship between the top 10 predictors and the
response variable. For the SVM model (identified as the optimal choice),
these predictors exhibit a largely linear association with the response.
In addition, this suggests that strategically adjusting biological or
process variables either increasing or decreasing them in line with the
observed slope can meaningfully optimize yield outcomes.