Data-624 Homework 8
Mohammed Rahman
2024-04-03
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:
\(y = 10 sin(\pi x_1x_2) + 20(x_3 - 0.5)^2 + 10x_4 + 5x_5 + N(0, \sigma^2)\)
where the x values are random variables uniformly distributed between [0, 1] (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)
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)
## 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:
KNN Model
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 2.5683461NN Model
nnetGrid <- expand.grid(.decay = c(0,0.01,.1),
.size = c(1:5),
.bag = FALSE)
nnetFit <- train(trainingData$x, trainingData$y,
method = 'avNNet',
tuneGrid = nnetGrid,
preProc = c('center','scale'),
linout = TRUE,
trace = FALSE,
MaxNWts = 5 * (ncol(trainingData$x) + 1 + 5 + 1),
maxit = 100
)
nnetFit## Model Averaged Neural Network
##
## 200 samples
## 10 predictor
##
## Pre-processing: centered (10), scaled (10)
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 200, 200, 200, 200, 200, 200, ...
## Resampling results across tuning parameters:
##
## decay size RMSE Rsquared MAE
## 0.00 1 2.565214 0.7424510 2.011320
## 0.00 2 2.577406 0.7382329 2.028408
## 0.00 3 2.337417 0.7825332 1.839583
## 0.00 4 2.729590 0.7185699 2.068292
## 0.00 5 2.629962 0.7367168 2.040611
## 0.01 1 2.556163 0.7421467 1.992682
## 0.01 2 2.562614 0.7432748 1.996182
## 0.01 3 2.351816 0.7804277 1.860291
## 0.01 4 2.439330 0.7691751 1.927696
## 0.01 5 2.572200 0.7424606 2.028893
## 0.10 1 2.518290 0.7488257 1.952082
## 0.10 2 2.543715 0.7440260 2.007897
## 0.10 3 2.283904 0.7929747 1.807032
## 0.10 4 2.371849 0.7798611 1.883289
## 0.10 5 2.474275 0.7627753 1.959351
##
## Tuning parameter 'bag' was held constant at a value of FALSE
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were size = 3, decay = 0.1 and bag = FALSE.nnetPred <- predict(nnetFit, newdata = testData$x)
postResample(pred = nnetPred, obs = testData$y)## RMSE Rsquared MAE
## 2.2087518 0.8066003 1.6628115MARS Model
# create a tuning grid
marsGrid <- expand.grid(.degree = 1:2, .nprune = 2:38)
set.seed(100)
# tune
marsTune <- train(trainingData$x, trainingData$y,
method = "earth",
tuneGrid = marsGrid,
trControl = trainControl(method = "cv"))
marsTune## Multivariate Adaptive Regression Spline
##
## 200 samples
## 10 predictor
##
## No pre-processing
## 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 3.600474
## 1 3 3.572450 0.4912720 2.895811
## 1 4 2.596841 0.7183600 2.106341
## 1 5 2.370161 0.7659777 1.918669
## 1 6 2.276141 0.7881481 1.810001
## 1 7 1.766728 0.8751831 1.390215
## 1 8 1.780946 0.8723243 1.401345
## 1 9 1.665091 0.8819775 1.325515
## 1 10 1.663804 0.8821283 1.327657
## 1 11 1.657738 0.8822967 1.331730
## 1 12 1.653784 0.8827903 1.331504
## 1 13 1.648496 0.8823663 1.316407
## 1 14 1.639073 0.8841742 1.312833
## 1 15 1.639073 0.8841742 1.312833
## 1 16 1.639073 0.8841742 1.312833
## 1 17 1.639073 0.8841742 1.312833
## 1 18 1.639073 0.8841742 1.312833
## 1 19 1.639073 0.8841742 1.312833
## 1 20 1.639073 0.8841742 1.312833
## 1 21 1.639073 0.8841742 1.312833
## 1 22 1.639073 0.8841742 1.312833
## 1 23 1.639073 0.8841742 1.312833
## 1 24 1.639073 0.8841742 1.312833
## 1 25 1.639073 0.8841742 1.312833
## 1 26 1.639073 0.8841742 1.312833
## 1 27 1.639073 0.8841742 1.312833
## 1 28 1.639073 0.8841742 1.312833
## 1 29 1.639073 0.8841742 1.312833
## 1 30 1.639073 0.8841742 1.312833
## 1 31 1.639073 0.8841742 1.312833
## 1 32 1.639073 0.8841742 1.312833
## 1 33 1.639073 0.8841742 1.312833
## 1 34 1.639073 0.8841742 1.312833
## 1 35 1.639073 0.8841742 1.312833
## 1 36 1.639073 0.8841742 1.312833
## 1 37 1.639073 0.8841742 1.312833
## 1 38 1.639073 0.8841742 1.312833
## 2 2 4.327937 0.2544880 3.600474
## 2 3 3.572450 0.4912720 2.895811
## 2 4 2.661826 0.7070510 2.173471
## 2 5 2.404015 0.7578971 1.975387
## 2 6 2.243927 0.7914805 1.783072
## 2 7 1.856336 0.8605482 1.435682
## 2 8 1.754607 0.8763186 1.396841
## 2 9 1.603578 0.8938666 1.261361
## 2 10 1.492421 0.9084998 1.168700
## 2 11 1.317350 0.9292504 1.033926
## 2 12 1.304327 0.9320133 1.019108
## 2 13 1.277510 0.9323681 1.002927
## 2 14 1.269626 0.9350024 1.003346
## 2 15 1.266217 0.9359400 1.013893
## 2 16 1.268470 0.9354868 1.011414
## 2 17 1.268470 0.9354868 1.011414
## 2 18 1.268470 0.9354868 1.011414
## 2 19 1.268470 0.9354868 1.011414
## 2 20 1.268470 0.9354868 1.011414
## 2 21 1.268470 0.9354868 1.011414
## 2 22 1.268470 0.9354868 1.011414
## 2 23 1.268470 0.9354868 1.011414
## 2 24 1.268470 0.9354868 1.011414
## 2 25 1.268470 0.9354868 1.011414
## 2 26 1.268470 0.9354868 1.011414
## 2 27 1.268470 0.9354868 1.011414
## 2 28 1.268470 0.9354868 1.011414
## 2 29 1.268470 0.9354868 1.011414
## 2 30 1.268470 0.9354868 1.011414
## 2 31 1.268470 0.9354868 1.011414
## 2 32 1.268470 0.9354868 1.011414
## 2 33 1.268470 0.9354868 1.011414
## 2 34 1.268470 0.9354868 1.011414
## 2 35 1.268470 0.9354868 1.011414
## 2 36 1.268470 0.9354868 1.011414
## 2 37 1.268470 0.9354868 1.011414
## 2 38 1.268470 0.9354868 1.011414
##
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were nprune = 15 and degree = 2.marsPred <- predict(marsTune, testData$x)
postResample(marsPred, testData$y)## RMSE Rsquared MAE
## 1.1589948 0.9460418 0.9250230varImp(marsTune)## earth variable importance
##
## Overall
## X1 100.00
## X4 75.24
## X2 48.73
## X5 15.52
## X3 0.00SVM Model
set.seed(100)
# tune
svmRTune <- train(trainingData$x, trainingData$y,
method = "svmRadial",
preProc = c("center", "scale"),
tuneLength = 14,
trControl = trainControl(method = "cv"))
svmRTune## Support Vector Machines with Radial Basis Function Kernel
##
## 200 samples
## 10 predictor
##
## Pre-processing: centered (10), scaled (10)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 180, 180, 180, 180, 180, 180, ...
## Resampling results across tuning parameters:
##
## C RMSE Rsquared MAE
## 0.25 2.530787 0.7922715 2.013175
## 0.50 2.259539 0.8064569 1.789962
## 1.00 2.099789 0.8274242 1.656154
## 2.00 2.002943 0.8412934 1.583791
## 4.00 1.943618 0.8504425 1.546586
## 8.00 1.918711 0.8547582 1.532981
## 16.00 1.920651 0.8536189 1.536116
## 32.00 1.920651 0.8536189 1.536116
## 64.00 1.920651 0.8536189 1.536116
## 128.00 1.920651 0.8536189 1.536116
## 256.00 1.920651 0.8536189 1.536116
## 512.00 1.920651 0.8536189 1.536116
## 1024.00 1.920651 0.8536189 1.536116
## 2048.00 1.920651 0.8536189 1.536116
##
## Tuning parameter 'sigma' was held constant at a value of 0.06509124
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were sigma = 0.06509124 and C = 8.svmRPred <- predict(svmRTune, testData$x)
postResample(svmRPred, testData$y)## RMSE Rsquared MAE
## 2.0631908 0.8275736 1.5662213Which models appear to give the best performance? Does MARS select the informative predictors (those named X1–X5)?
The MARS model produces the best results with a Rsquared of 0.9460418 on the test set. The Mars model only uses the informative predictors, X1-X5.
Question 7.5:
Exercise 6.3 describes data for a chemical manufacturing process. Use the same data imputation, data splitting, and pre-processing steps as before and train several nonlinear regression models.
data(ChemicalManufacturingProcess)
# imputation
miss <- preProcess(ChemicalManufacturingProcess, method = "bagImpute")
Chemical <- predict(miss, ChemicalManufacturingProcess)
# filtering low frequencies
Chemical <- Chemical[, -nearZeroVar(Chemical)]
set.seed(624)
# index for training
index <- createDataPartition(Chemical$Yield, p = .8, list = FALSE)
# train
train_x <- Chemical[index, -1]
train_y <- Chemical[index, 1]
# test
test_x <- Chemical[-index, -1]
test_y <- Chemical[-index, 1]- Which nonlinear regression model gives the optimal resampling and test set performance?
KNN Model
knnModel <- train(train_x, train_y,
method = "knn",
preProc = c("center", "scale"),
tuneLength = 10)
knnModel## 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 1.471125 0.3330992 1.161484
## 7 1.447346 0.3519621 1.150975
## 9 1.439505 0.3614781 1.153856
## 11 1.440067 0.3597565 1.157491
## 13 1.446347 0.3556436 1.165135
## 15 1.437409 0.3693582 1.165991
## 17 1.448196 0.3618152 1.176400
## 19 1.452990 0.3601724 1.182114
## 21 1.456702 0.3606783 1.183356
## 23 1.457503 0.3658775 1.185981
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was k = 15.knnPred <- predict(knnModel, test_x)
## The function 'postResample' can be used to get the test set
## perforamnce values
postResample(pred = knnPred, test_y)## RMSE Rsquared MAE
## 1.5262067 0.6187302 1.1800625NN Model
# remove predictors to ensure maximum abs pairwise corr between predictors < 0.75
tooHigh <- findCorrelation(cor(train_x), cutoff = .75)
# removing 21 variables
train_x_nnet <- train_x[, -tooHigh]
test_x_nnet <- test_x[, -tooHigh]
# create a tuning grid
nnetGrid <- expand.grid(.decay = c(0, 0.01, .1),
.size = c(1:10))
# 10-fold cross-validation to make reasonable estimates
ctrl <- trainControl(method = "cv", number = 10)
set.seed(100)
# tune
nnetTune <- train(train_x_nnet, train_y,
method = "nnet",
tuneGrid = nnetGrid,
trControl = ctrl,
preProc = c("center", "scale"),
linout = TRUE,
trace = FALSE,
MaxNWts = 10 * (ncol(train_x_nnet) + 1) + 10 + 1,
maxit = 500)
nnetTune## Neural Network
##
## 144 samples
## 35 predictor
##
## Pre-processing: centered (35), scaled (35)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 129, 130, 130, 130, 130, 130, ...
## Resampling results across tuning parameters:
##
## decay size RMSE Rsquared MAE
## 0.00 1 1.653183 0.2181442 1.345706
## 0.00 2 2.534424 0.2369899 1.836159
## 0.00 3 3.171155 0.2926531 2.287708
## 0.00 4 3.711481 0.1209223 2.917563
## 0.00 5 3.431171 0.1500184 2.741639
## 0.00 6 4.519146 0.1324394 3.247006
## 0.00 7 4.572852 0.1511347 3.586819
## 0.00 8 4.897815 0.1777553 3.195740
## 0.00 9 6.323278 0.1664817 4.360992
## 0.00 10 8.667370 0.1152399 5.988899
## 0.01 1 1.667606 0.3154025 1.388167
## 0.01 2 2.265838 0.1993149 1.714076
## 0.01 3 2.332248 0.2440199 1.842895
## 0.01 4 3.002585 0.1568784 2.241891
## 0.01 5 2.559003 0.2072487 1.958315
## 0.01 6 2.615888 0.2014615 2.003966
## 0.01 7 2.704167 0.1873030 2.115345
## 0.01 8 2.884852 0.1905781 2.225486
## 0.01 9 2.664823 0.2242711 2.139448
## 0.01 10 3.327161 0.2317687 2.496622
## 0.10 1 1.618516 0.3543468 1.325739
## 0.10 2 1.852789 0.3901490 1.390430
## 0.10 3 2.907373 0.1839412 2.024455
## 0.10 4 2.664748 0.1941929 1.965063
## 0.10 5 2.946770 0.2249056 2.098324
## 0.10 6 2.533430 0.2964670 1.884063
## 0.10 7 2.175251 0.3069320 1.702581
## 0.10 8 2.696990 0.1964820 1.966580
## 0.10 9 2.282723 0.2395294 1.862798
## 0.10 10 2.780285 0.1640235 2.034794
##
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were size = 1 and decay = 0.1.nnPred <- predict(nnetTune, test_x_nnet)
postResample(nnPred, test_y)## RMSE Rsquared MAE
## 1.5064579 0.5140357 1.1159762Mars Model
# create a tuning grid
marsGrid <- expand.grid(.degree = 1:2, .nprune = 2:38)
set.seed(100)
# tune
marsTune <- train(train_x, train_y,
method = "earth",
tuneGrid = marsGrid,
trControl = trainControl(method = "cv"))
marsTune## Multivariate Adaptive Regression Spline
##
## 144 samples
## 56 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 129, 130, 130, 130, 130, 130, ...
## Resampling results across tuning parameters:
##
## degree nprune RMSE Rsquared MAE
## 1 2 1.382295 0.4386629 1.1032611
## 1 3 1.240867 0.5448952 0.9985512
## 1 4 1.259935 0.5341424 1.0107010
## 1 5 1.245790 0.5272274 1.0113559
## 1 6 1.269935 0.5136793 1.0204522
## 1 7 1.310209 0.5055710 1.0295204
## 1 8 1.288293 0.5221112 1.0036609
## 1 9 1.293021 0.5193283 1.0156268
## 1 10 1.286486 0.5258144 1.0107051
## 1 11 1.350612 0.5108572 1.0494019
## 1 12 1.354690 0.5164837 1.0502417
## 1 13 1.371710 0.5124198 1.0535178
## 1 14 1.386234 0.5064731 1.0729218
## 1 15 1.377159 0.5169364 1.0708723
## 1 16 1.377159 0.5169364 1.0708723
## 1 17 1.377159 0.5169364 1.0708723
## 1 18 1.377159 0.5169364 1.0708723
## 1 19 1.377159 0.5169364 1.0708723
## 1 20 1.377159 0.5169364 1.0708723
## 1 21 1.377159 0.5169364 1.0708723
## 1 22 1.377159 0.5169364 1.0708723
## 1 23 1.377159 0.5169364 1.0708723
## 1 24 1.377159 0.5169364 1.0708723
## 1 25 1.377159 0.5169364 1.0708723
## 1 26 1.377159 0.5169364 1.0708723
## 1 27 1.377159 0.5169364 1.0708723
## 1 28 1.377159 0.5169364 1.0708723
## 1 29 1.377159 0.5169364 1.0708723
## 1 30 1.377159 0.5169364 1.0708723
## 1 31 1.377159 0.5169364 1.0708723
## 1 32 1.377159 0.5169364 1.0708723
## 1 33 1.377159 0.5169364 1.0708723
## 1 34 1.377159 0.5169364 1.0708723
## 1 35 1.377159 0.5169364 1.0708723
## 1 36 1.377159 0.5169364 1.0708723
## 1 37 1.377159 0.5169364 1.0708723
## 1 38 1.377159 0.5169364 1.0708723
## 2 2 1.382295 0.4386629 1.1032611
## 2 3 1.237952 0.5375297 1.0083290
## 2 4 1.253568 0.5221886 1.0335088
## 2 5 1.204199 0.5507043 0.9713244
## 2 6 1.241877 0.5180123 1.0022903
## 2 7 1.228535 0.5360710 0.9772064
## 2 8 1.236188 0.5297973 0.9891217
## 2 9 1.224202 0.5377333 0.9943605
## 2 10 1.196350 0.5532418 0.9855648
## 2 11 1.217007 0.5502910 1.0105749
## 2 12 1.236600 0.5473328 1.0021900
## 2 13 1.227170 0.5587354 0.9909744
## 2 14 1.263470 0.5599646 1.0158323
## 2 15 1.230580 0.5620079 1.0103784
## 2 16 1.241609 0.5506318 0.9964320
## 2 17 1.233933 0.5689345 0.9858733
## 2 18 1.241566 0.5806316 1.0029570
## 2 19 1.236775 0.5859195 0.9987440
## 2 20 1.317821 0.5266260 1.0648319
## 2 21 1.388138 0.5126592 1.1035179
## 2 22 1.402762 0.5068048 1.1134955
## 2 23 1.396884 0.5054997 1.1196368
## 2 24 1.380184 0.5113281 1.1059875
## 2 25 1.380184 0.5113281 1.1059875
## 2 26 1.386388 0.5070473 1.1174699
## 2 27 1.380683 0.5101973 1.1123044
## 2 28 1.361918 0.5211907 1.0932094
## 2 29 1.366147 0.5191619 1.0957169
## 2 30 1.366147 0.5191619 1.0957169
## 2 31 1.366147 0.5191619 1.0957169
## 2 32 1.360840 0.5200205 1.0921339
## 2 33 1.360840 0.5200205 1.0921339
## 2 34 1.360840 0.5200205 1.0921339
## 2 35 1.360840 0.5200205 1.0921339
## 2 36 1.360840 0.5200205 1.0921339
## 2 37 1.360840 0.5200205 1.0921339
## 2 38 1.360840 0.5200205 1.0921339
##
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were nprune = 10 and degree = 2.marsPred <- predict(marsTune, test_x)
postResample(marsPred, test_y)## RMSE Rsquared MAE
## 1.3464789 0.6138875 0.9826902SVM Model
set.seed(100)
# tune
svmRTune <- train(train_x, train_y,
method = "svmRadial",
preProc = c("center", "scale"),
tuneLength = 14,
trControl = trainControl(method = "cv"))
svmRTune## 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 1.413177 0.4630126 1.1760898
## 0.50 1.314625 0.5018046 1.0947625
## 1.00 1.217731 0.5647210 1.0095889
## 2.00 1.164634 0.5994161 0.9630243
## 4.00 1.124391 0.6199423 0.9192936
## 8.00 1.119796 0.6170091 0.9287431
## 16.00 1.118734 0.6174115 0.9308110
## 32.00 1.118734 0.6174115 0.9308110
## 64.00 1.118734 0.6174115 0.9308110
## 128.00 1.118734 0.6174115 0.9308110
## 256.00 1.118734 0.6174115 0.9308110
## 512.00 1.118734 0.6174115 0.9308110
## 1024.00 1.118734 0.6174115 0.9308110
## 2048.00 1.118734 0.6174115 0.9308110
##
## Tuning parameter 'sigma' was held constant at a value of 0.0139359
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were sigma = 0.0139359 and C = 16.svmRPred <- predict(svmRTune, test_x)
postResample(svmRPred, test_y)## RMSE Rsquared MAE
## 1.1412463 0.7513994 0.8006586rbind(knn = postResample(knnPred, test_y),
nn = postResample(nnPred, test_y),
mars = postResample(marsPred, test_y),
svmR = postResample(svmRPred, test_y))## RMSE Rsquared MAE
## knn 1.526207 0.6187302 1.1800625
## nn 1.506458 0.5140357 1.1159762
## mars 1.346479 0.6138875 0.9826902
## svmR 1.141246 0.7513994 0.8006586SVM gives the best performance with the radial method as it has the lowest RMSE and MAE and the highest RSquared = 0.7513994.
- 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(svmRTune)## loess r-squared variable importance
##
## only 20 most important variables shown (out of 56)
##
## Overall
## ManufacturingProcess32 100.00
## BiologicalMaterial06 89.32
## BiologicalMaterial03 77.48
## ManufacturingProcess36 76.64
## ManufacturingProcess09 73.90
## ManufacturingProcess13 73.24
## ManufacturingProcess31 67.06
## BiologicalMaterial02 66.92
## BiologicalMaterial12 64.94
## ManufacturingProcess06 59.23
## ManufacturingProcess17 53.07
## BiologicalMaterial11 49.11
## BiologicalMaterial04 48.27
## ManufacturingProcess11 45.42
## ManufacturingProcess29 45.31
## ManufacturingProcess33 44.62
## BiologicalMaterial01 40.70
## BiologicalMaterial08 38.19
## ManufacturingProcess30 35.52
## BiologicalMaterial09 29.60plot(varImp(svmRTune), top = 20) 
set.seed(100)
larsTune <- train(train_x, train_y,
method = "lars",
metric = "Rsquared",
tuneLength = 20,
trControl = ctrl,
preProc = c("center", "scale"))
lars_predict <- predict(larsTune, test_x)The top ten important predictors are the same as the top ten predictors from the optimal linear model, which was the LARS model.
plot(varImp(svmRTune), top = 10,
main = "Nonlinear: Top 10 Important Predictors")
plot(varImp(larsTune), top = 10,
main = "Linear: Top 10 Important Predictors")
- 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?
top10 <- varImp(svmRTune)$importance %>%
arrange(-Overall) %>%
head(10)
Chemical %>%
select(c("Yield", row.names(top10))) %>%
cor() %>%
corrplot()
train_x %>%
select(row.names(top10)) %>%
featurePlot(., train_y)
ManufacturingProcess32 has the most robust relationship
with Yield, as seen by the correlation plot.
Yield and two of the top 10 factors have a negative
correlation.
While the relationship between the manufacturing methods and yield
varies, it appears that the biological predictors have a favorable
relationship with the yield. For example,
ManufacturingProcess36 has levels, and
ManufacturingProcess31 is primarily focused on a value.