hw7
2025-03-31
Developing a model to predict permeability (see Sect. 1.4) could save significant resources for a pharmaceutical company, while at the same time more rapidly identifying molecules that have a sufficient permeability to become a drug:
- Start R and use these commands to load the data:
library(AppliedPredictiveModeling)## Warning: package 'AppliedPredictiveModeling' was built under R version 4.4.3data(permeability)The matrix fingerprints contains the 1,107 binary molecular predictors for the 165 compounds, while permeability contains permeability response.
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 near ZeroVar function from the caret package. How many predictors are left for modeling?
Went from 1107 to just 388 predictors.
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?
9 components were considered optimal, with R2 of 0.5195.
Predict the response for the test set. What is the test set estimate of R2?
R2 is 0.3673.
Try building other models discussed in this chapter. Do any have better predictive performance?
The first model has performed better compared to the other model.
Would you recommend any of your models to replace the permeability laboratory experiment?
I recommend Partial Least Squares model because it had higher R2.
library(caret)## Warning: package 'caret' was built under R version 4.4.3## Loading required package: ggplot2## Loading required package: latticelibrary(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, uniondim(fingerprints)## [1] 165 1107fingerprints <- fingerprints[, -nearZeroVar(fingerprints)] dim(fingerprints)## [1] 165 388
set.seed(111)
index <- createDataPartition(permeability, p = .75, list = FALSE)
# train
train1 <- permeability[index, ]
train2 <- fingerprints[index, ]
# test
test1 <- permeability[-index, ]
test2 <- fingerprints [-index, ]
ctrl <- trainControl(method = "cv", number = 8)
plotting <- train(train2, train1, method = "pls", metric = "Rsquared",
tuneLength = 15, trControl = ctrl, preProc = c("center", "scale"))
plotting## Partial Least Squares
##
## 125 samples
## 388 predictors
##
## Pre-processing: centered (388), scaled (388)
## Resampling: Cross-Validated (8 fold)
## Summary of sample sizes: 109, 109, 110, 109, 110, 109, ...
## Resampling results across tuning parameters:
##
## ncomp RMSE Rsquared MAE
## 1 12.76592 0.3776333 9.815992
## 2 11.40519 0.5078635 8.253262
## 3 11.53084 0.4868592 8.778235
## 4 11.97248 0.4611414 9.434752
## 5 11.96809 0.4664318 8.991471
## 6 11.92453 0.4785022 8.744012
## 7 11.94447 0.4810436 8.791578
## 8 11.81916 0.4983004 8.715324
## 9 11.79335 0.5195373 8.414370
## 10 12.22976 0.4992911 8.837210
## 11 12.57865 0.4857728 9.112221
## 12 12.71654 0.4872855 9.106980
## 13 13.02366 0.4777870 9.403427
## 14 13.63921 0.4575121 9.920551
## 15 14.11936 0.4341340 10.318592
##
## Rsquared was used to select the optimal model using the largest value.
## The final value used for the model was ncomp = 9.plot(plotting) 
predict2 <- predict(plotting, test2)
postResample(predict2, train1)## Warning in pred - obs: longer object length is not a multiple of shorter object
## length
## Warning in pred - obs: longer object length is not a multiple of shorter object
## length## RMSE Rsquared MAE
## 19.28790 NA 14.85754plotting$results |> inner_join(plotting$bestTune)## Joining with `by = join_by(ncomp)`plotp <- predict(plotting, test2)
postResample(plotp, test1)## RMSE Rsquared MAE
## 12.5931592 0.3673063 9.2945799# grid of penalties
enetg <- expand.grid(.lambda = c(0, 0.01, .1), .fraction = seq(.05, 1, length = 20))
# tuning penalized regression model
enetT <- train(train2, train1, method = "enet",
tuneGrid = enetg, trControl = ctrl, preProc = c("center", "scale"))## Warning: model fit failed for Fold4: lambda=0.00, fraction=1 Error in if (zmin < gamhat) { : missing value where TRUE/FALSE needed## Warning in nominalTrainWorkflow(x = x, y = y, wts = weights, info = trainInfo,
## : There were missing values in resampled performance measures.enetT## Elasticnet
##
## 125 samples
## 388 predictors
##
## Pre-processing: centered (388), scaled (388)
## Resampling: Cross-Validated (8 fold)
## Summary of sample sizes: 109, 110, 110, 109, 109, 110, ...
## Resampling results across tuning parameters:
##
## lambda fraction RMSE Rsquared MAE
## 0.00 0.05 30481.27963 0.4292787 8.153720e+03
## 0.00 0.10 59520.83323 0.4418802 1.703814e+04
## 0.00 0.15 88661.49911 0.4240393 2.588565e+04
## 0.00 0.20 117803.06516 0.3970320 3.470807e+04
## 0.00 0.25 146957.62969 0.3838957 4.353028e+04
## 0.00 0.30 176118.67526 0.3813290 5.235238e+04
## 0.00 0.35 205283.57554 0.3696072 6.117459e+04
## 0.00 0.40 234450.88510 0.3512829 6.999693e+04
## 0.00 0.45 263619.84565 0.3330654 7.881933e+04
## 0.00 0.50 292789.83988 0.3247918 8.764165e+04
## 0.00 0.55 321960.52673 0.3253290 9.646387e+04
## 0.00 0.60 351131.86379 0.3243580 1.052861e+05
## 0.00 0.65 380303.72506 0.3213973 1.141084e+05
## 0.00 0.70 409476.11739 0.3086267 1.229307e+05
## 0.00 0.75 438648.80642 0.2969719 1.317530e+05
## 0.00 0.80 467821.70505 0.2876825 1.405754e+05
## 0.00 0.85 496994.77190 0.2803339 1.493977e+05
## 0.00 0.90 526167.96034 0.2758102 1.582199e+05
## 0.00 0.95 555341.39003 0.2666238 1.670423e+05
## 0.00 1.00 584514.94958 0.2593920 1.758647e+05
## 0.01 0.05 11.97090 0.4993364 8.503784e+00
## 0.01 0.10 11.35435 0.5257815 8.244001e+00
## 0.01 0.15 11.10789 0.5324969 8.242124e+00
## 0.01 0.20 11.45246 0.5063530 8.587873e+00
## 0.01 0.25 11.87519 0.4837519 8.866184e+00
## 0.01 0.30 12.33365 0.4583002 9.245963e+00
## 0.01 0.35 12.58593 0.4499965 9.450912e+00
## 0.01 0.40 12.85662 0.4387065 9.643957e+00
## 0.01 0.45 13.06077 0.4296960 9.767804e+00
## 0.01 0.50 13.23662 0.4235138 9.884790e+00
## 0.01 0.55 13.44376 0.4169569 1.004188e+01
## 0.01 0.60 13.64430 0.4103143 1.016496e+01
## 0.01 0.65 13.84249 0.4038919 1.027265e+01
## 0.01 0.70 14.07515 0.3941451 1.037727e+01
## 0.01 0.75 14.26050 0.3874334 1.045456e+01
## 0.01 0.80 14.42779 0.3830204 1.052523e+01
## 0.01 0.85 14.61389 0.3774797 1.063585e+01
## 0.01 0.90 14.85299 0.3701958 1.078713e+01
## 0.01 0.95 15.11980 0.3636500 1.098777e+01
## 0.01 1.00 15.34354 0.3585219 1.117518e+01
## 0.10 0.05 11.94762 0.5253833 9.111061e+00
## 0.10 0.10 11.87160 0.5079963 8.356451e+00
## 0.10 0.15 11.83472 0.5044326 8.323712e+00
## 0.10 0.20 11.55149 0.5216011 8.305906e+00
## 0.10 0.25 11.38479 0.5314412 8.341782e+00
## 0.10 0.30 11.34914 0.5352393 8.391422e+00
## 0.10 0.35 11.43840 0.5297517 8.509078e+00
## 0.10 0.40 11.63593 0.5185904 8.655131e+00
## 0.10 0.45 11.84261 0.5072624 8.782906e+00
## 0.10 0.50 12.00880 0.4981932 8.876809e+00
## 0.10 0.55 12.15593 0.4915649 8.977954e+00
## 0.10 0.60 12.29890 0.4861654 9.079283e+00
## 0.10 0.65 12.43018 0.4813938 9.190681e+00
## 0.10 0.70 12.55208 0.4770321 9.283027e+00
## 0.10 0.75 12.66045 0.4723571 9.338851e+00
## 0.10 0.80 12.76165 0.4680022 9.386194e+00
## 0.10 0.85 12.85474 0.4640445 9.426468e+00
## 0.10 0.90 12.94552 0.4598024 9.473281e+00
## 0.10 0.95 13.05098 0.4556771 9.534642e+00
## 0.10 1.00 13.14528 0.4521864 9.580251e+00
##
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were fraction = 0.15 and lambda = 0.01.plot(enetT)
enetp <- predict(enetT, test2)
postResample(enetp, test1)## RMSE Rsquared MAE
## 12.2403848 0.3517408 8.12021416.3. A chemical manufacturing process for a pharmaceutical product was discussed in Sect. 1.4. In this problem, the objective is to understand the re- lationship 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 pro- cess. Improving product yield by 1 % will boost revenue by approximately one hundred thousand dollars per batch:
- 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.
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).
160 missing values
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?
RMSE is 7961275
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?
R2 of 0.8031260 using pls method, higher than train set
Which predictors are most important in the model you have trained? Do either the biological or process predictors dominate the list?
ManufacturingProcess32, ManufacturingProcess13, ManufacturingProcess36, ManufacturingProcess09, ManufacturingProcess17 are the most important predictors used for modeling, and dominates the list.
Explore the relationships between each of the top predictors and the re- sponse. How could this information be helpful in improving yield in future runs of the manufacturing process?
The plot tell us that many correlation would lead to less yield, only a few combination would improve the yield like biologicalmaterial9 and manufactoringprocess09
ChemicalManufacturingProcesssum(is.na(ChemicalManufacturingProcess))## [1] 106missing <- preProcess(ChemicalManufacturingProcess, method = "bagImpute")
chemical <- predict(missing, ChemicalManufacturingProcess)
sum(is.na(chemical))## [1] 0# filtering low frequencies
chemical <- chemical[, -nearZeroVar(chemical)]
# index for training
index <- createDataPartition(chemical$Yield, p = .9, list = FALSE)
# train
train_chem <- chemical[index, ]
# test
test_chem <- chemical[-index, ]
plsT <- train(Yield ~ ., chemical , method = "pls",
tuneLength = 15, trControl = ctrl, preProc = c("center", "scale"))
plsT ## Partial Least Squares
##
## 176 samples
## 56 predictor
##
## Pre-processing: centered (56), scaled (56)
## Resampling: Cross-Validated (8 fold)
## Summary of sample sizes: 155, 155, 153, 155, 154, 153, ...
## Resampling results across tuning parameters:
##
## ncomp RMSE Rsquared MAE
## 1 1.490913 0.4234020 1.177767
## 2 1.854481 0.5037120 1.242113
## 3 1.520139 0.5710656 1.075256
## 4 1.624426 0.5474911 1.154110
## 5 1.825080 0.5353433 1.219167
## 6 1.874234 0.5227565 1.230690
## 7 1.930315 0.5155914 1.232501
## 8 2.020598 0.5036775 1.258564
## 9 2.041942 0.4935666 1.269258
## 10 2.065987 0.4921261 1.265742
## 11 1.997603 0.5002811 1.245103
## 12 1.972232 0.5025815 1.245685
## 13 1.880550 0.5247905 1.206295
## 14 1.824223 0.5388444 1.172811
## 15 1.802969 0.5422419 1.152112
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was ncomp = 1.plot(plsT) 
enetGrid <- expand.grid(.lambda = c(0, 0.01, .1), .fraction = seq(.1, 1, length = 25))
enetT <- train(Yield ~ ., chemical , method = "enet",
tuneGrid = enetGrid, trControl = ctrl, preProc = c("center", "scale"))
enetT## Elasticnet
##
## 176 samples
## 56 predictor
##
## Pre-processing: centered (56), scaled (56)
## Resampling: Cross-Validated (8 fold)
## Summary of sample sizes: 153, 156, 155, 153, 153, 155, ...
## Resampling results across tuning parameters:
##
## lambda fraction RMSE Rsquared MAE
## 0.00 0.1000 1.207331 0.5978623 0.9569458
## 0.00 0.1375 1.324607 0.5621426 0.9895011
## 0.00 0.1750 1.538919 0.5355144 1.0310770
## 0.00 0.2125 1.589234 0.5344367 1.0520268
## 0.00 0.2500 1.730925 0.4954886 1.1134145
## 0.00 0.2875 1.707424 0.4915925 1.1207487
## 0.00 0.3250 1.703017 0.4859474 1.1293331
## 0.00 0.3625 1.642489 0.4928759 1.1234124
## 0.00 0.4000 1.577436 0.5068484 1.1115689
## 0.00 0.4375 1.476431 0.5370977 1.0876597
## 0.00 0.4750 1.430996 0.5531546 1.0701728
## 0.00 0.5125 1.780415 0.4982220 1.1585399
## 0.00 0.5500 2.251001 0.4803639 1.2662560
## 0.00 0.5875 2.616397 0.4725896 1.3441325
## 0.00 0.6250 3.004431 0.4630931 1.4256121
## 0.00 0.6625 3.437026 0.4373990 1.5299531
## 0.00 0.7000 3.891834 0.4121174 1.6343379
## 0.00 0.7375 4.354967 0.3916589 1.7394552
## 0.00 0.7750 4.822157 0.3764792 1.8462864
## 0.00 0.8125 5.290092 0.3656410 1.9532045
## 0.00 0.8500 5.774969 0.3585026 2.0632708
## 0.00 0.8875 6.224207 0.3530210 2.1654957
## 0.00 0.9250 6.661895 0.3486991 2.2633130
## 0.00 0.9625 7.160535 0.3449146 2.3731546
## 0.00 1.0000 7.627006 0.3416514 2.4757928
## 0.01 0.1000 1.303930 0.6132325 1.0605619
## 0.01 0.1375 1.222196 0.6034488 0.9950007
## 0.01 0.1750 1.227819 0.5830197 0.9771749
## 0.01 0.2125 1.218043 0.5907455 0.9633317
## 0.01 0.2500 1.205897 0.6002927 0.9515431
## 0.01 0.2875 1.214403 0.6009651 0.9480287
## 0.01 0.3250 1.235343 0.5981000 0.9528313
## 0.01 0.3625 1.254530 0.5977652 0.9555235
## 0.01 0.4000 1.299327 0.5924323 0.9632277
## 0.01 0.4375 1.326394 0.5859124 0.9820789
## 0.01 0.4750 1.400062 0.5633033 1.0112497
## 0.01 0.5125 1.531019 0.5291596 1.0605355
## 0.01 0.5500 1.687262 0.4919515 1.1090516
## 0.01 0.5875 1.792510 0.4759005 1.1388082
## 0.01 0.6250 1.844829 0.4692182 1.1547790
## 0.01 0.6625 1.879985 0.4640821 1.1672257
## 0.01 0.7000 1.920132 0.4591206 1.1804327
## 0.01 0.7375 1.970980 0.4542185 1.1952388
## 0.01 0.7750 2.033463 0.4488508 1.2127914
## 0.01 0.8125 2.002314 0.4494825 1.2089180
## 0.01 0.8500 1.917560 0.4571726 1.1928867
## 0.01 0.8875 1.847321 0.4688804 1.1792176
## 0.01 0.9250 1.782173 0.4858622 1.1645221
## 0.01 0.9625 1.728535 0.5024984 1.1472102
## 0.01 1.0000 1.715237 0.5018991 1.1427518
## 0.10 0.1000 1.494869 0.5972803 1.2124796
## 0.10 0.1375 1.392957 0.6095156 1.1321717
## 0.10 0.1750 1.309280 0.6107641 1.0653720
## 0.10 0.2125 1.247076 0.6127554 1.0157471
## 0.10 0.2500 1.214549 0.6047069 0.9887146
## 0.10 0.2875 1.208770 0.5958584 0.9743990
## 0.10 0.3250 1.203215 0.5966161 0.9645080
## 0.10 0.3625 1.193808 0.6027521 0.9556947
## 0.10 0.4000 1.192736 0.6054448 0.9504059
## 0.10 0.4375 1.193442 0.6073676 0.9473647
## 0.10 0.4750 1.230561 0.5975903 0.9552203
## 0.10 0.5125 1.300753 0.5857970 0.9709291
## 0.10 0.5500 1.368343 0.5789347 0.9875984
## 0.10 0.5875 1.435716 0.5762059 1.0018755
## 0.10 0.6250 1.476726 0.5745453 1.0155836
## 0.10 0.6625 1.535181 0.5643222 1.0323130
## 0.10 0.7000 1.612147 0.5464156 1.0585143
## 0.10 0.7375 1.696472 0.5259372 1.0878757
## 0.10 0.7750 1.780811 0.5078655 1.1153995
## 0.10 0.8125 1.808678 0.5020110 1.1260408
## 0.10 0.8500 1.830015 0.4976426 1.1351344
## 0.10 0.8875 1.862698 0.4938794 1.1460052
## 0.10 0.9250 1.893092 0.4909857 1.1561965
## 0.10 0.9625 1.919196 0.4886921 1.1648443
## 0.10 1.0000 1.935204 0.4868378 1.1707266
##
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were fraction = 0.4 and lambda = 0.1.plot(enetT)
lm_model <- lm(Yield ~ ., chemical)
summary(lm_model)##
## Call:
## lm(formula = Yield ~ ., data = chemical)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.16927 -0.54577 -0.03172 0.50904 2.00004
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.960e+00 8.736e+01 0.057 0.95481
## BiologicalMaterial01 2.529e-01 3.346e-01 0.756 0.45131
## BiologicalMaterial02 -1.130e-01 1.280e-01 -0.883 0.37913
## BiologicalMaterial03 1.541e-01 2.363e-01 0.652 0.51537
## BiologicalMaterial04 -1.013e-01 5.288e-01 -0.191 0.84847
## BiologicalMaterial05 1.512e-01 1.067e-01 1.417 0.15920
## BiologicalMaterial06 1.578e-02 3.021e-01 0.052 0.95844
## BiologicalMaterial08 3.848e-01 6.381e-01 0.603 0.54756
## BiologicalMaterial09 -7.929e-01 1.372e+00 -0.578 0.56434
## BiologicalMaterial10 5.728e-02 1.380e+00 0.042 0.96696
## BiologicalMaterial11 -8.874e-02 8.291e-02 -1.070 0.28663
## BiologicalMaterial12 3.298e-01 6.346e-01 0.520 0.60426
## ManufacturingProcess01 6.666e-02 9.485e-02 0.703 0.48355
## ManufacturingProcess02 1.404e-02 4.459e-02 0.315 0.75338
## ManufacturingProcess03 -3.335e+00 5.121e+00 -0.651 0.51618
## ManufacturingProcess04 6.350e-02 2.943e-02 2.158 0.03292 *
## ManufacturingProcess05 7.740e-04 3.862e-03 0.200 0.84149
## ManufacturingProcess06 3.297e-02 4.326e-02 0.762 0.44750
## ManufacturingProcess07 -1.725e-01 2.134e-01 -0.808 0.42066
## ManufacturingProcess08 -7.092e-02 2.521e-01 -0.281 0.77892
## ManufacturingProcess09 2.638e-01 1.796e-01 1.469 0.14445
## ManufacturingProcess10 -1.017e-01 5.728e-01 -0.177 0.85942
## ManufacturingProcess11 1.899e-01 7.123e-01 0.267 0.79019
## ManufacturingProcess12 3.486e-05 1.027e-04 0.340 0.73474
## ManufacturingProcess13 -2.556e-01 3.826e-01 -0.668 0.50539
## ManufacturingProcess14 8.961e-04 1.114e-02 0.080 0.93605
## ManufacturingProcess15 1.426e-03 8.929e-03 0.160 0.87335
## ManufacturingProcess16 -4.999e-05 3.193e-04 -0.157 0.87587
## ManufacturingProcess17 -1.469e-01 3.012e-01 -0.488 0.62672
## ManufacturingProcess18 4.254e-03 4.454e-03 0.955 0.34144
## ManufacturingProcess19 -2.604e-03 7.305e-03 -0.356 0.72214
## ManufacturingProcess20 -4.506e-03 4.713e-03 -0.956 0.34097
## ManufacturingProcess21 NA NA NA NA
## ManufacturingProcess22 -1.571e-02 4.197e-02 -0.374 0.70884
## ManufacturingProcess23 -4.324e-02 8.345e-02 -0.518 0.60526
## ManufacturingProcess24 -1.906e-02 2.337e-02 -0.816 0.41633
## ManufacturingProcess25 -7.629e-03 1.395e-02 -0.547 0.58556
## ManufacturingProcess26 6.883e-03 1.058e-02 0.651 0.51638
## ManufacturingProcess27 -6.951e-03 7.822e-03 -0.889 0.37595
## ManufacturingProcess28 -7.652e-02 3.111e-02 -2.460 0.01534 *
## ManufacturingProcess29 1.406e+00 9.034e-01 1.556 0.12233
## ManufacturingProcess30 -4.007e-01 6.269e-01 -0.639 0.52388
## ManufacturingProcess31 5.243e-02 1.209e-01 0.434 0.66534
## ManufacturingProcess32 3.322e-01 6.928e-02 4.795 4.71e-06 ***
## ManufacturingProcess33 -3.975e-01 1.301e-01 -3.054 0.00278 **
## ManufacturingProcess34 -1.324e+00 2.802e+00 -0.473 0.63735
## ManufacturingProcess35 -1.955e-02 1.763e-02 -1.109 0.26959
## ManufacturingProcess36 2.977e+02 3.095e+02 0.962 0.33805
## ManufacturingProcess37 -6.997e-01 2.898e-01 -2.414 0.01729 *
## ManufacturingProcess38 -1.846e-01 2.419e-01 -0.763 0.44701
## ManufacturingProcess39 7.242e-02 1.311e-01 0.552 0.58165
## ManufacturingProcess40 4.544e-01 6.581e+00 0.069 0.94507
## ManufacturingProcess41 2.881e-01 4.761e+00 0.061 0.95184
## ManufacturingProcess42 2.910e-02 2.125e-01 0.137 0.89130
## ManufacturingProcess43 2.282e-01 1.187e-01 1.922 0.05702 .
## ManufacturingProcess44 -4.892e-01 1.181e+00 -0.414 0.67946
## ManufacturingProcess45 9.578e-01 5.422e-01 1.766 0.07989 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.041 on 120 degrees of freedom
## Multiple R-squared: 0.7818, Adjusted R-squared: 0.6818
## F-statistic: 7.816 on 55 and 120 DF, p-value: < 2.2e-16lm_model##
## Call:
## lm(formula = Yield ~ ., data = chemical)
##
## Coefficients:
## (Intercept) BiologicalMaterial01 BiologicalMaterial02
## 4.960e+00 2.529e-01 -1.130e-01
## BiologicalMaterial03 BiologicalMaterial04 BiologicalMaterial05
## 1.541e-01 -1.013e-01 1.512e-01
## BiologicalMaterial06 BiologicalMaterial08 BiologicalMaterial09
## 1.578e-02 3.848e-01 -7.929e-01
## BiologicalMaterial10 BiologicalMaterial11 BiologicalMaterial12
## 5.728e-02 -8.874e-02 3.298e-01
## ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03
## 6.666e-02 1.404e-02 -3.335e+00
## ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06
## 6.350e-02 7.740e-04 3.297e-02
## ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess09
## -1.725e-01 -7.092e-02 2.638e-01
## ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12
## -1.017e-01 1.899e-01 3.486e-05
## ManufacturingProcess13 ManufacturingProcess14 ManufacturingProcess15
## -2.556e-01 8.961e-04 1.426e-03
## ManufacturingProcess16 ManufacturingProcess17 ManufacturingProcess18
## -4.999e-05 -1.469e-01 4.254e-03
## ManufacturingProcess19 ManufacturingProcess20 ManufacturingProcess21
## -2.604e-03 -4.506e-03 NA
## ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24
## -1.571e-02 -4.324e-02 -1.906e-02
## ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27
## -7.629e-03 6.883e-03 -6.951e-03
## ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30
## -7.652e-02 1.406e+00 -4.007e-01
## ManufacturingProcess31 ManufacturingProcess32 ManufacturingProcess33
## 5.243e-02 3.322e-01 -3.975e-01
## ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36
## -1.324e+00 -1.955e-02 2.977e+02
## ManufacturingProcess37 ManufacturingProcess38 ManufacturingProcess39
## -6.997e-01 -1.846e-01 7.242e-02
## ManufacturingProcess40 ManufacturingProcess41 ManufacturingProcess42
## 4.544e-01 2.881e-01 2.910e-02
## ManufacturingProcess43 ManufacturingProcess44 ManufacturingProcess45
## 2.282e-01 -4.892e-01 9.578e-01lm_predict <- predict(lm_model, test_chem[ ,-1])
postResample(lm_predict, test_chem[ ,1])## RMSE Rsquared MAE
## 0.8719894 0.6547831 0.6328814pls_predict <- predict(plsT, test_chem[ ,-1])
postResample(pls_predict, test_chem[ ,1])## RMSE Rsquared MAE
## 1.2759739 0.2746225 1.0764468enet_predict <- predict(enetT, test_chem[ ,-1])
postResample(enet_predict, test_chem[ ,1])## RMSE Rsquared MAE
## 1.0480148 0.4872262 0.8797834varImp(plsT)## Warning: package 'pls' was built under R version 4.4.3##
## Attaching package: 'pls'## The following object is masked from 'package:caret':
##
## R2## The following object is masked from 'package:stats':
##
## loadings## pls variable importance
##
## only 20 most important variables shown (out of 56)
##
## Overall
## ManufacturingProcess32 100.00
## ManufacturingProcess36 86.88
## ManufacturingProcess13 82.77
## ManufacturingProcess09 82.73
## BiologicalMaterial02 79.12
## BiologicalMaterial06 78.57
## BiologicalMaterial03 73.12
## ManufacturingProcess33 70.72
## ManufacturingProcess17 69.95
## ManufacturingProcess06 64.34
## BiologicalMaterial08 62.56
## BiologicalMaterial04 62.38
## BiologicalMaterial12 60.35
## BiologicalMaterial01 58.94
## BiologicalMaterial11 58.27
## ManufacturingProcess12 57.05
## ManufacturingProcess11 53.14
## ManufacturingProcess28 43.30
## ManufacturingProcess04 41.85
## ManufacturingProcess30 37.22library(DataExplorer)## Warning: package 'DataExplorer' was built under R version 4.4.3chemical |> select(Yield , ends_with(c("32","13","36","09") )) |>
plot_correlation()