HW7
Diego Correa
11/7/2021
6.2
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)
data(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 nearZeroVar function from the caret package. How many predictors are left for modeling?
388
cols <- nearZeroVar(fingerprints)
df <- fingerprints[,-cols]
dim(df)## [1] 165 388- 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?
The \(R^2\) for the final pls model is 0.50305056.
set.seed(123)
trans_df <- preProcess(df,
method = c('center', 'scale'))
df <- predict(trans_df, df)
trans_y <- preProcess(permeability,
method = c('center', 'scale'))
y <- predict(trans_y, permeability)
sample <- sample.split(permeability, SplitRatio = 0.75)
X_train = subset(df, sample == TRUE)
X_test = subset(df, sample == FALSE)
X_train_index <- rownames(X_train)
X_test_index <- rownames(X_test)
y_train <- permeability[X_train_index,]
y_test <- permeability[X_test_index,]
plsFit <- train(X_train, y_train,
method = 'pls',
tuneLength = 100
)
plot(plsFit)
plsFit## Partial Least Squares
##
## 123 samples
## 388 predictors
##
## No pre-processing
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 123, 123, 123, 123, 123, 123, ...
## Resampling results across tuning parameters:
##
## ncomp RMSE Rsquared MAE
## 1 1.313590e+01 0.36409838 1.006912e+01
## 2 1.173318e+01 0.50305056 8.398168e+00
## 3 1.194183e+01 0.48457002 8.728066e+00
## 4 1.217053e+01 0.46531297 8.920300e+00
## 5 1.243519e+01 0.45182440 8.929871e+00
## 6 1.237136e+01 0.45594086 8.840693e+00
## 7 1.246311e+01 0.46024685 9.026476e+00
## 8 1.282372e+01 0.44526619 9.312521e+00
## 9 1.310751e+01 0.43120312 9.560647e+00
## 10 1.335129e+01 0.41995783 9.715772e+00
## 11 1.368865e+01 0.40562060 9.923026e+00
## 12 1.407642e+01 0.38586158 1.025378e+01
## 13 1.435950e+01 0.37261737 1.055176e+01
## 14 1.470524e+01 0.35418291 1.078616e+01
## 15 1.503831e+01 0.34154290 1.105538e+01
## 16 1.528744e+01 0.33179002 1.126493e+01
## 17 1.553257e+01 0.32445728 1.143651e+01
## 18 1.577033e+01 0.31601880 1.156091e+01
## 19 1.599650e+01 0.31005449 1.173316e+01
## 20 1.615790e+01 0.30707751 1.182389e+01
## 21 1.636741e+01 0.30053714 1.200249e+01
## 22 1.658494e+01 0.29453872 1.217463e+01
## 23 1.681194e+01 0.28916213 1.233477e+01
## 24 1.692943e+01 0.28652774 1.243593e+01
## 25 1.706439e+01 0.28281570 1.253751e+01
## 26 1.726310e+01 0.27678995 1.266198e+01
## 27 1.752742e+01 0.26802635 1.283991e+01
## 28 1.781676e+01 0.25992994 1.305552e+01
## 29 1.804387e+01 0.25407343 1.321147e+01
## 30 1.825607e+01 0.24821647 1.332373e+01
## 31 1.851019e+01 0.24249662 1.348190e+01
## 32 1.874355e+01 0.23802838 1.363168e+01
## 33 1.893384e+01 0.23459153 1.374585e+01
## 34 1.915217e+01 0.23029121 1.387028e+01
## 35 1.934845e+01 0.22587445 1.399724e+01
## 36 1.956014e+01 0.22186706 1.412503e+01
## 37 1.978251e+01 0.21730447 1.427350e+01
## 38 1.995825e+01 0.21325620 1.440217e+01
## 39 2.014389e+01 0.20940444 1.455477e+01
## 40 2.032538e+01 0.20612752 1.469726e+01
## 41 2.050260e+01 0.20329025 1.483522e+01
## 42 2.065974e+01 0.20115317 1.495327e+01
## 43 2.081970e+01 0.19860201 1.508617e+01
## 44 2.096592e+01 0.19613117 1.521269e+01
## 45 2.112725e+01 0.19382543 1.535017e+01
## 46 2.128709e+01 0.19169910 1.548573e+01
## 47 2.141461e+01 0.19019734 1.559209e+01
## 48 2.155552e+01 0.18857613 1.569913e+01
## 49 2.168345e+01 0.18779101 1.578440e+01
## 50 2.177523e+01 0.18712398 1.585672e+01
## 51 2.186003e+01 0.18624738 1.592510e+01
## 52 2.194594e+01 0.18556325 1.599479e+01
## 53 2.198671e+01 0.18520828 1.603381e+01
## 54 2.203954e+01 0.18436725 1.608941e+01
## 55 2.207053e+01 0.18387551 1.612456e+01
## 56 2.208968e+01 0.18369151 1.615423e+01
## 57 2.210630e+01 0.18338555 1.617514e+01
## 58 2.211886e+01 0.18304811 1.618968e+01
## 59 2.213350e+01 0.18255043 1.620946e+01
## 60 2.215297e+01 0.18197509 1.623079e+01
## 61 2.215828e+01 0.18179188 1.623516e+01
## 62 2.216464e+01 0.18159352 1.623797e+01
## 63 2.217464e+01 0.18126071 1.624647e+01
## 64 8.554129e+13 0.18262063 7.746166e+13
## 65 2.504005e+14 0.19424610 2.162647e+14
## 66 3.875450e+14 0.19823550 3.246961e+14
## 67 6.389449e+14 0.16577507 5.174777e+14
## 68 9.567928e+14 0.14623379 7.827708e+14
## 69 1.158929e+15 0.13666788 9.378908e+14
## 70 1.577296e+15 0.11921725 1.282490e+15
## 71 2.149375e+15 0.13782624 1.749616e+15
## 72 2.912614e+15 0.09959086 2.366944e+15
## 73 3.473111e+15 0.09585562 2.814467e+15
## 74 3.982906e+15 0.10803859 3.225095e+15
## 75 4.394517e+15 0.08503956 3.529501e+15
## 76 4.794231e+15 0.08055185 3.836159e+15
## 77 5.158014e+15 0.06588207 4.115213e+15
## 78 5.374079e+15 0.06844971 4.277338e+15
## 79 5.616175e+15 0.06253568 4.464704e+15
## 80 5.787938e+15 0.06342043 4.601607e+15
## 81 5.935658e+15 0.06546371 4.727325e+15
## 82 6.051815e+15 0.06578910 4.821721e+15
## 83 6.142418e+15 0.06783727 4.902926e+15
## 84 6.217174e+15 0.06768689 4.976541e+15
## 85 6.290093e+15 0.06845176 5.049149e+15
## 86 6.350006e+15 0.06850626 5.105401e+15
## 87 6.380118e+15 0.06929160 5.127040e+15
## 88 6.420616e+15 0.07043612 5.158596e+15
## 89 6.464087e+15 0.07060683 5.193817e+15
## 90 6.496616e+15 0.07049115 5.220262e+15
## 91 6.524400e+15 0.07051256 5.240007e+15
## 92 6.548530e+15 0.07099699 5.259174e+15
## 93 6.569980e+15 0.07097704 5.277930e+15
## 94 6.587641e+15 0.07138296 5.291235e+15
## 95 6.597902e+15 0.07168690 5.295818e+15
## 96 6.605882e+15 0.07191296 5.301831e+15
## 97 6.622695e+15 0.07206884 5.315484e+15
## 98 6.634395e+15 0.07191186 5.323387e+15
## 99 6.643287e+15 0.07196737 5.329066e+15
## 100 6.655584e+15 0.07182964 5.338716e+15
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was ncomp = 2.- Predict the response for the test set. What is the test set estimate of R2?
lmPred1 <- predict(plsFit, X_test)
lmValues1 <- data.frame(obs = y_test, pred = lmPred1)
defaultSummary(lmValues1)## RMSE Rsquared MAE
## 13.4624011 0.1352939 9.2452204- Try building other models discussed in this chapter. Do any have better predictive performance?
Yes, the Elastic Net model performed better in predicting the values of the test data set.
enetGrid <- expand.grid(.lambda = c(0,0.01,0.1),
.fraction = seq(0.05,1,length = 20))
set.seed(213)
enetTune <- train(X_train, y_train,
method = 'enet',
tuneGrid = enetGrid
)## Warning: model fit failed for Resample15: lambda=0.00, fraction=1 Error in if (zmin < gamhat) { : missing value where TRUE/FALSE needed## Warning: model fit failed for Resample17: 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.lmPred2 <- predict(enetTune, X_test)
lmValues2 <- data.frame(obs = y_test, pred = lmPred2)
defaultSummary(lmValues2)## RMSE Rsquared MAE
## 12.6824502 0.2074689 9.1989245- Would you recommend any of your models to replace the permeability laboratory experiment?
No, as the \(R^2\) values do not give me confidence in the models as they are relatively low.
6.3
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:
- Start R and use these commands to load the data:
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.
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).
df <- ChemicalManufacturingProcess
init <- mice(df, maxit = 0)
predM <- init$predictorMatrix
set.seed(123)
imputed <- mice(df, method = 'pmm', predictorMatrix = predM, m=5)##
## iter imp variable
## 1 1 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41
## 1 2 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41
## 1 3 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41
## 1 4 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41
## 1 5 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41
## 2 1 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41
## 2 2 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41
## 2 3 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41
## 2 4 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41
## 2 5 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41
## 3 1 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41
## 3 2 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41
## 3 3 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41
## 3 4 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41
## 3 5 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41
## 4 1 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41
## 4 2 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41
## 4 3 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41
## 4 4 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41
## 4 5 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41
## 5 1 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41
## 5 2 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41
## 5 3 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41
## 5 4 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41
## 5 5 ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03 ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06 ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12 ManufacturingProcess14 ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24 ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27 ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30 ManufacturingProcess31 ManufacturingProcess33 ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36 ManufacturingProcess40 ManufacturingProcess41## Warning: Number of logged events: 675df <- complete(imputed)- 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?
The best \(R^2\) is 0.58531241.
set.seed(123)
trans_df <- preProcess(df,
method = c('center', 'scale'))
df <- predict(trans_df, df)
sample <- sample.split(permeability, SplitRatio = 0.75)
X_train = subset(df[,-1], sample == TRUE)
X_test = subset(df[,-1], sample == FALSE)
y_train <- subset(df[,1], sample == TRUE)
y_test <- subset(df[,1], sample == FALSE)
enetGrid <- expand.grid(.lambda = c(0,0.01,0.1),
.fraction = seq(0.05,1,length = 20))
set.seed(213)
enetTune <- train(X_train, y_train,
method = 'enet',
tuneGrid = enetGrid
)
enetTune## Elasticnet
##
## 129 samples
## 57 predictor
##
## No pre-processing
## Resampling: Bootstrapped (25 reps)
## Summary of sample sizes: 129, 129, 129, 129, 129, 129, ...
## Resampling results across tuning parameters:
##
## lambda fraction RMSE Rsquared MAE
## 0.00 0.05 0.7810010 0.54710645 0.5752237
## 0.00 0.10 1.3578080 0.40427685 0.7327417
## 0.00 0.15 2.0694521 0.25093335 0.9056652
## 0.00 0.20 3.0579901 0.19694168 1.0956867
## 0.00 0.25 4.0809993 0.19555161 1.2683064
## 0.00 0.30 4.8927481 0.16779716 1.4207473
## 0.00 0.35 5.5310850 0.15066411 1.5453253
## 0.00 0.40 6.1364148 0.14042165 1.6634307
## 0.00 0.45 6.6544009 0.13099299 1.7660395
## 0.00 0.50 7.2317858 0.11978230 1.8767047
## 0.00 0.55 7.8510568 0.10959763 1.9977230
## 0.00 0.60 8.4611408 0.10240610 2.1128457
## 0.00 0.65 9.0579877 0.09722493 2.2236752
## 0.00 0.70 9.6143318 0.09304017 2.3254877
## 0.00 0.75 10.0745478 0.09073589 2.4034776
## 0.00 0.80 10.6036195 0.08534627 2.5024168
## 0.00 0.85 11.0566284 0.08221739 2.5838399
## 0.00 0.90 11.4339028 0.08211518 2.6506668
## 0.00 0.95 11.8057211 0.08187302 2.7040654
## 0.00 1.00 13.1002918 0.08082209 3.0670428
## 0.01 0.05 0.8325309 0.54972380 0.6732730
## 0.01 0.10 0.6959368 0.58878778 0.5661530
## 0.01 0.15 0.7389313 0.55264342 0.5593615
## 0.01 0.20 0.8487948 0.52459514 0.5846137
## 0.01 0.25 0.9927142 0.49952535 0.6187012
## 0.01 0.30 1.0701907 0.48304992 0.6438785
## 0.01 0.35 1.1121392 0.47503876 0.6651518
## 0.01 0.40 1.2487634 0.42903429 0.7084844
## 0.01 0.45 1.3943440 0.37725511 0.7474780
## 0.01 0.50 1.5775016 0.33769121 0.7888187
## 0.01 0.55 1.7638681 0.31046026 0.8297334
## 0.01 0.60 1.9187754 0.29625262 0.8653719
## 0.01 0.65 2.0834701 0.28096145 0.9030376
## 0.01 0.70 2.2750366 0.26451929 0.9438013
## 0.01 0.75 2.4723719 0.24909575 0.9855935
## 0.01 0.80 2.6657435 0.23606456 1.0260324
## 0.01 0.85 2.8491745 0.22589411 1.0638334
## 0.01 0.90 3.0201706 0.21555797 1.0999810
## 0.01 0.95 3.1953434 0.20703660 1.1348877
## 0.01 1.00 3.4924133 0.19888128 1.2273312
## 0.10 0.05 0.9394560 0.45794000 0.7563213
## 0.10 0.10 0.8312344 0.54631818 0.6718078
## 0.10 0.15 0.7454870 0.57698107 0.6061753
## 0.10 0.20 0.7007613 0.57913141 0.5667529
## 0.10 0.25 0.7217963 0.55639808 0.5592711
## 0.10 0.30 0.7727984 0.53675088 0.5689293
## 0.10 0.35 0.8210404 0.52413217 0.5815406
## 0.10 0.40 0.8684196 0.51147623 0.5949384
## 0.10 0.45 0.9167136 0.50047047 0.6059057
## 0.10 0.50 0.9799265 0.48885152 0.6229860
## 0.10 0.55 1.0432902 0.48134810 0.6413850
## 0.10 0.60 1.1140418 0.46899146 0.6636201
## 0.10 0.65 1.1848469 0.45391462 0.6875422
## 0.10 0.70 1.2699036 0.42948444 0.7144903
## 0.10 0.75 1.3590846 0.40300871 0.7397648
## 0.10 0.80 1.4455196 0.38153052 0.7628644
## 0.10 0.85 1.5300541 0.36403750 0.7864869
## 0.10 0.90 1.6192415 0.34641031 0.8092277
## 0.10 0.95 1.7021965 0.33049424 0.8296414
## 0.10 1.00 1.8118374 0.30719740 0.8655794
##
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were fraction = 0.1 and lambda = 0.01.- 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?
The performance metrics are slightly lower on the test set.
lmPred3 <- predict(enetTune, X_test)
lmValues3 <- data.frame(obs = y_test, pred = lmPred3)
defaultSummary(lmValues3)## RMSE Rsquared MAE
## 0.5726634 0.5154140 0.4802119- Which predictors are most important in the model you have trained? Do either the biological or process predictors dominate the list?
The process predictors dominate the list. The coefficients to the biological predictors are mostly set to 0. Based on the coefficients, ManufacturingProcess32 has the greatest impact on the target value.
predict(enetTune$finalModel, type = 'coefficients')## $s
## [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
## [26] 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
## [51] 51 52 53 54 55 56 57 58 59 60 61 62
##
## $fraction
## [1] 0.00000000 0.01639344 0.03278689 0.04918033 0.06557377 0.08196721
## [7] 0.09836066 0.11475410 0.13114754 0.14754098 0.16393443 0.18032787
## [13] 0.19672131 0.21311475 0.22950820 0.24590164 0.26229508 0.27868852
## [19] 0.29508197 0.31147541 0.32786885 0.34426230 0.36065574 0.37704918
## [25] 0.39344262 0.40983607 0.42622951 0.44262295 0.45901639 0.47540984
## [31] 0.49180328 0.50819672 0.52459016 0.54098361 0.55737705 0.57377049
## [37] 0.59016393 0.60655738 0.62295082 0.63934426 0.65573770 0.67213115
## [43] 0.68852459 0.70491803 0.72131148 0.73770492 0.75409836 0.77049180
## [49] 0.78688525 0.80327869 0.81967213 0.83606557 0.85245902 0.86885246
## [55] 0.88524590 0.90163934 0.91803279 0.93442623 0.95081967 0.96721311
## [61] 0.98360656 1.00000000
##
## $mode
## [1] "step"
##
## $coefficients
## BiologicalMaterial01 BiologicalMaterial02 BiologicalMaterial03
## 0 0.000000000 0.000000000 0.00000000
## 1 0.000000000 0.000000000 0.00000000
## 2 0.000000000 0.000000000 0.00000000
## 3 0.000000000 0.000000000 0.00000000
## 4 0.000000000 0.000000000 0.00000000
## 5 0.000000000 0.000000000 0.00000000
## 6 0.000000000 0.000000000 0.00000000
## 7 0.000000000 0.000000000 0.00000000
## 8 0.000000000 0.000000000 0.00000000
## 9 0.000000000 0.000000000 0.00000000
## 10 0.000000000 0.000000000 0.00000000
## 11 0.000000000 0.000000000 0.00000000
## 12 0.000000000 0.000000000 0.00000000
## 13 0.000000000 0.000000000 0.00000000
## 14 0.000000000 0.000000000 0.00000000
## 15 0.000000000 0.000000000 0.00000000
## 16 0.000000000 0.000000000 0.00000000
## 17 0.000000000 0.000000000 0.00000000
## 18 0.000000000 0.000000000 0.00000000
## 19 0.000000000 0.000000000 0.00000000
## 20 0.000000000 0.000000000 0.00000000
## 21 0.000000000 0.000000000 0.00000000
## 22 0.000000000 0.000000000 0.00000000
## 23 0.000000000 0.000000000 0.00000000
## 24 0.000000000 0.000000000 0.00000000
## 25 0.000000000 0.000000000 0.00000000
## 26 0.000000000 0.000000000 0.00000000
## 27 0.000000000 0.000000000 0.00000000
## 28 0.000000000 0.000000000 0.00000000
## 29 0.000000000 0.000000000 0.00000000
## 30 0.000000000 0.000000000 0.00000000
## 31 0.000000000 0.000000000 0.00000000
## 32 0.000000000 0.000000000 0.00000000
## 33 0.000000000 0.000000000 0.00000000
## 34 0.000000000 0.000000000 0.00000000
## 35 0.000000000 0.000000000 0.00000000
## 36 0.000000000 -0.002900933 0.00000000
## 37 0.004479708 -0.016783685 0.00000000
## 38 0.004647674 -0.017326847 0.00000000
## 39 0.006043473 -0.022726839 0.00221603
## 40 0.015508153 -0.045055493 0.01891123
## 41 0.025664340 -0.069238140 0.03665186
## 42 0.033100730 -0.091296149 0.05291373
## 43 0.036068956 -0.118380306 0.07230933
## 44 0.040038557 -0.141821016 0.09060182
## 45 0.042295714 -0.154649607 0.10031619
## 46 0.042947385 -0.160722611 0.10531771
## 47 0.043623270 -0.166866335 0.11025769
## 48 0.045069704 -0.178934658 0.11967684
## 49 0.046910569 -0.195044803 0.13396740
## 50 0.050030675 -0.224751437 0.15956349
## 51 0.053151642 -0.252805988 0.18343361
## 52 0.053710584 -0.257246414 0.18698478
## 53 0.055512987 -0.269623678 0.19679313
## 54 0.056453015 -0.276339982 0.20195954
## 55 0.058602294 -0.296590486 0.21538103
## 56 0.059589853 -0.304853597 0.22140183
## 57 0.062394394 -0.329230841 0.23660729
## 58 0.063426655 -0.337733208 0.24111455
## 59 0.063603609 -0.339288352 0.24192288
## 60 0.063010119 -0.344972005 0.24859984
## 61 0.062670410 -0.346997009 0.25080718
## BiologicalMaterial04 BiologicalMaterial05 BiologicalMaterial06
## 0 0.000000000 0.000000000 0.000000000
## 1 0.000000000 0.000000000 0.000000000
## 2 0.000000000 0.000000000 0.000000000
## 3 0.000000000 0.000000000 0.000000000
## 4 0.000000000 0.000000000 0.000000000
## 5 0.000000000 0.000000000 0.004945841
## 6 0.000000000 0.000000000 0.032096867
## 7 0.000000000 0.000000000 0.032352313
## 8 0.000000000 0.000000000 0.055388662
## 9 0.000000000 0.000000000 0.059056931
## 10 0.000000000 0.000000000 0.068171534
## 11 0.000000000 0.000894045 0.068078239
## 12 0.000000000 0.021890524 0.064605563
## 13 0.000000000 0.029498697 0.067143277
## 14 0.000000000 0.031607815 0.067518208
## 15 0.000000000 0.038916815 0.069558998
## 16 0.000000000 0.044130809 0.071293754
## 17 0.000000000 0.052461453 0.074181509
## 18 0.000000000 0.063019515 0.077092848
## 19 0.000000000 0.067099395 0.078322969
## 20 0.000000000 0.067959803 0.078602187
## 21 0.000000000 0.074123384 0.080318258
## 22 0.000000000 0.081061604 0.084007230
## 23 0.000000000 0.090082854 0.090056205
## 24 0.000000000 0.090760219 0.090623467
## 25 0.000000000 0.097615502 0.123347844
## 26 0.000000000 0.099096576 0.132375671
## 27 0.000000000 0.099141523 0.132556649
## 28 0.000000000 0.098306694 0.143686219
## 29 0.000000000 0.097813356 0.151603082
## 30 0.000000000 0.098178073 0.157487372
## 31 0.000000000 0.098600704 0.160536463
## 32 0.000000000 0.098453139 0.162266580
## 33 0.000000000 0.098827800 0.164918777
## 34 0.000000000 0.099075081 0.165535901
## 35 0.000000000 0.099346572 0.166157377
## 36 0.000000000 0.099685875 0.168829515
## 37 0.000000000 0.100852678 0.180606910
## 38 0.000000000 0.100855404 0.181125340
## 39 0.000000000 0.100861242 0.183811652
## 40 0.000000000 0.102506020 0.183355881
## 41 0.000000000 0.105185090 0.185024255
## 42 0.000000000 0.108121600 0.186787426
## 43 0.000000000 0.111343497 0.190616103
## 44 0.000000000 0.113284492 0.193664285
## 45 0.000000000 0.114587942 0.195165838
## 46 0.000000000 0.114980208 0.195487560
## 47 0.000000000 0.115445403 0.195921694
## 48 0.000000000 0.116557831 0.196539152
## 49 -0.004317062 0.117860962 0.197877084
## 50 -0.012395496 0.120511191 0.200765532
## 51 -0.018766266 0.124348001 0.204629061
## 52 -0.019190148 0.124978337 0.205149229
## 53 -0.020144597 0.126866143 0.206756846
## 54 -0.020493934 0.128461256 0.207576157
## 55 -0.021020148 0.134324111 0.210818074
## 56 -0.021305735 0.136836462 0.211725790
## 57 -0.022156359 0.144715953 0.215772003
## 58 -0.022381037 0.148318798 0.217636874
## 59 -0.022398981 0.148969482 0.217985081
## 60 -0.033232462 0.151340158 0.221196798
## 61 -0.036972943 0.152174270 0.222289986
## BiologicalMaterial07 BiologicalMaterial08 BiologicalMaterial09
## 0 0.000000000 0.00000000 0.00000000
## 1 0.000000000 0.00000000 0.00000000
## 2 0.000000000 0.00000000 0.00000000
## 3 0.000000000 0.00000000 0.00000000
## 4 0.000000000 0.00000000 0.00000000
## 5 0.000000000 0.00000000 0.00000000
## 6 0.000000000 0.00000000 0.00000000
## 7 0.000000000 0.00000000 0.00000000
## 8 0.000000000 0.00000000 0.00000000
## 9 0.000000000 0.00000000 0.00000000
## 10 0.000000000 0.00000000 0.00000000
## 11 0.000000000 0.00000000 0.00000000
## 12 0.000000000 0.00000000 0.00000000
## 13 0.000000000 0.00000000 0.00000000
## 14 0.000000000 0.00000000 0.00000000
## 15 0.000000000 0.00000000 0.00000000
## 16 0.000000000 0.00000000 0.00000000
## 17 -0.003432502 0.00000000 0.00000000
## 18 -0.007183852 0.00000000 0.00000000
## 19 -0.007989712 0.00000000 0.00000000
## 20 -0.008099896 0.00000000 0.00000000
## 21 -0.008732102 0.00000000 0.00000000
## 22 -0.009284148 0.00000000 0.00000000
## 23 -0.009840133 0.00000000 0.00000000
## 24 -0.009906049 0.00000000 0.00000000
## 25 -0.010218603 0.00000000 -0.02448490
## 26 -0.010616178 0.00000000 -0.03074417
## 27 -0.010680782 0.00000000 -0.03091184
## 28 -0.014917921 0.00000000 -0.04037388
## 29 -0.018057018 0.00000000 -0.04710142
## 30 -0.020602224 0.00000000 -0.05156790
## 31 -0.022805933 0.00000000 -0.05392110
## 32 -0.024414702 0.00000000 -0.05547780
## 33 -0.028779149 0.00000000 -0.05700902
## 34 -0.029018844 0.00000000 -0.05664289
## 35 -0.029299840 0.00000000 -0.05620064
## 36 -0.029398041 0.00000000 -0.05539828
## 37 -0.029591667 0.00000000 -0.05256946
## 38 -0.029600803 0.00000000 -0.05245105
## 39 -0.029707949 0.00000000 -0.05189609
## 40 -0.030575862 0.00000000 -0.05559695
## 41 -0.031346659 0.00000000 -0.05802258
## 42 -0.032836566 0.00000000 -0.05951633
## 43 -0.035170241 0.01510076 -0.06659620
## 44 -0.036955463 0.02636965 -0.07292741
## 45 -0.037900867 0.03212756 -0.07630455
## 46 -0.038370704 0.03549424 -0.07803490
## 47 -0.038817637 0.03874311 -0.07969340
## 48 -0.039777308 0.04572373 -0.08352170
## 49 -0.041133649 0.05569541 -0.09017458
## 50 -0.043741460 0.07455483 -0.10219528
## 51 -0.046567916 0.09356120 -0.11300221
## 52 -0.047001173 0.09650759 -0.11448982
## 53 -0.048338730 0.10454762 -0.11839282
## 54 -0.048929030 0.10900144 -0.12084842
## 55 -0.050625760 0.12244007 -0.12742664
## 56 -0.051396473 0.12835410 -0.13018997
## 57 -0.053988017 0.14744860 -0.13781966
## 58 -0.055140201 0.15391579 -0.13989662
## 59 -0.055353073 0.15517567 -0.14033540
## 60 -0.056454702 0.16109045 -0.14599191
## 61 -0.056848287 0.16326021 -0.14793453
## BiologicalMaterial10 BiologicalMaterial11 BiologicalMaterial12
## 0 0.000000000 0.0000000000 0.00000000
## 1 0.000000000 0.0000000000 0.00000000
## 2 0.000000000 0.0000000000 0.00000000
## 3 0.000000000 0.0000000000 0.00000000
## 4 0.000000000 0.0000000000 0.00000000
## 5 0.000000000 0.0000000000 0.00000000
## 6 0.000000000 0.0000000000 0.00000000
## 7 0.000000000 0.0000000000 0.00000000
## 8 0.000000000 0.0000000000 0.00000000
## 9 0.000000000 0.0000000000 0.00000000
## 10 0.000000000 0.0000000000 0.00000000
## 11 0.000000000 0.0000000000 0.00000000
## 12 0.000000000 0.0000000000 0.00000000
## 13 0.000000000 0.0000000000 0.00000000
## 14 0.000000000 0.0000000000 0.00000000
## 15 0.000000000 0.0000000000 0.00000000
## 16 0.000000000 0.0000000000 0.00000000
## 17 0.000000000 0.0000000000 0.00000000
## 18 0.000000000 0.0000000000 0.00000000
## 19 0.000000000 0.0000000000 0.00000000
## 20 0.000000000 0.0000000000 0.00000000
## 21 0.000000000 0.0000000000 0.00000000
## 22 0.000000000 0.0000000000 0.00000000
## 23 0.000000000 0.0000000000 0.00000000
## 24 0.000000000 0.0000000000 0.00000000
## 25 0.000000000 0.0000000000 0.00000000
## 26 0.000000000 0.0000000000 0.00000000
## 27 0.000000000 0.0000000000 0.00000000
## 28 0.000000000 0.0000000000 0.00000000
## 29 0.000000000 0.0000000000 0.00000000
## 30 -0.001730455 0.0000000000 0.00000000
## 31 -0.003945538 0.0000000000 0.00000000
## 32 -0.006475452 0.0000000000 0.00000000
## 33 -0.010802249 0.0000000000 0.00000000
## 34 -0.011000511 -0.0009496146 0.00000000
## 35 -0.011256023 -0.0019475112 0.00000000
## 36 -0.011079229 -0.0028537256 0.00000000
## 37 -0.012332101 -0.0069314415 0.00000000
## 38 -0.012380741 -0.0070803304 0.00000000
## 39 -0.012807988 -0.0080735433 0.00000000
## 40 -0.010748107 -0.0265777507 0.02089332
## 41 -0.010401712 -0.0457366502 0.04079590
## 42 -0.009439930 -0.0624918796 0.05892372
## 43 -0.009073476 -0.0796972926 0.07178085
## 44 -0.009332945 -0.0931695109 0.08152130
## 45 -0.009421998 -0.1004690260 0.08686289
## 46 -0.009776127 -0.1031410441 0.08850082
## 47 -0.010089520 -0.1059954194 0.09035894
## 48 -0.010786842 -0.1114690032 0.09373183
## 49 -0.008285541 -0.1186685259 0.09813725
## 50 -0.003627295 -0.1323914501 0.10659749
## 51 0.000000000 -0.1482742843 0.11484567
## 52 0.000000000 -0.1507213700 0.11606986
## 53 0.000000000 -0.1574030649 0.11924740
## 54 0.000000000 -0.1616199098 0.12184155
## 55 0.000000000 -0.1748163896 0.12916557
## 56 0.000000000 -0.1810736321 0.13263117
## 57 0.000000000 -0.2017099513 0.14460102
## 58 0.000000000 -0.2095578672 0.14910629
## 59 0.000000000 -0.2109959931 0.14992480
## 60 0.010725492 -0.2179429312 0.15472596
## 61 0.014482704 -0.2204185976 0.15645446
## ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03
## 0 0.00000000 0.000000000 0.00000000
## 1 0.00000000 0.000000000 0.00000000
## 2 0.00000000 0.000000000 0.00000000
## 3 0.00000000 0.000000000 0.00000000
## 4 0.00000000 0.000000000 0.00000000
## 5 0.00000000 0.000000000 0.00000000
## 6 0.00000000 0.000000000 0.00000000
## 7 0.00000000 0.000000000 0.00000000
## 8 0.00000000 0.000000000 0.00000000
## 9 0.00000000 0.000000000 0.00000000
## 10 0.00000000 0.000000000 0.00000000
## 11 0.00000000 0.000000000 0.00000000
## 12 0.00000000 0.000000000 0.00000000
## 13 0.00000000 0.000000000 0.00000000
## 14 0.00000000 0.000000000 0.00000000
## 15 0.00000000 0.000000000 0.00000000
## 16 0.00000000 0.000000000 0.00000000
## 17 0.00000000 0.000000000 0.00000000
## 18 0.00000000 0.000000000 0.00000000
## 19 0.00000000 0.000000000 0.00000000
## 20 0.00000000 0.000000000 0.00000000
## 21 0.00000000 0.000000000 0.00000000
## 22 0.00000000 0.000000000 0.00000000
## 23 0.00000000 0.000000000 0.00000000
## 24 0.00000000 0.000000000 0.00000000
## 25 0.00000000 0.000000000 0.00000000
## 26 0.00000000 0.000000000 0.00000000
## 27 0.00000000 0.000000000 0.00000000
## 28 0.00000000 0.000000000 0.00000000
## 29 0.00000000 0.000000000 0.00000000
## 30 0.00000000 0.000000000 0.00000000
## 31 0.00000000 -0.005648022 0.00000000
## 32 0.00764355 -0.011296853 0.00000000
## 33 0.02425450 -0.021939804 -0.01001938
## 34 0.02521116 -0.022566619 -0.01066673
## 35 0.02628024 -0.023305928 -0.01143533
## 36 0.02664416 -0.023785604 -0.01172910
## 37 0.02941264 -0.025477684 -0.01298956
## 38 0.02948638 -0.025465411 -0.01304788
## 39 0.02988122 -0.025785003 -0.01356326
## 40 0.03179722 -0.024843580 -0.01511022
## 41 0.03254101 -0.024809505 -0.01616611
## 42 0.03294348 -0.026194092 -0.01862711
## 43 0.03527189 -0.028719456 -0.02132084
## 44 0.03792608 -0.028198608 -0.02317986
## 45 0.03947154 -0.027600830 -0.02408025
## 46 0.04034501 -0.027457270 -0.02457554
## 47 0.04124772 -0.027223518 -0.02513871
## 48 0.04285619 -0.027640428 -0.02624434
## 49 0.04505994 -0.027603815 -0.02779420
## 50 0.04931569 -0.027975811 -0.03083593
## 51 0.05188965 -0.028434812 -0.03332838
## 52 0.05231463 -0.028607989 -0.03371225
## 53 0.05346949 -0.029000516 -0.03504201
## 54 0.05451346 -0.029339041 -0.03588150
## 55 0.05766447 -0.030915422 -0.03785850
## 56 0.05917485 -0.031623520 -0.03855418
## 57 0.06840104 -0.036886226 -0.04102202
## 58 0.07120359 -0.039416168 -0.04229450
## 59 0.07174704 -0.039941629 -0.04253114
## 60 0.07371879 -0.040434626 -0.04372333
## 61 0.07434774 -0.040857727 -0.04413038
## ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06
## 0 0.00000000 0.000000000 0.00000000
## 1 0.00000000 0.000000000 0.00000000
## 2 0.00000000 0.000000000 0.00000000
## 3 0.00000000 0.000000000 0.00000000
## 4 0.00000000 0.000000000 0.00000000
## 5 0.00000000 0.000000000 0.00000000
## 6 0.00000000 0.000000000 0.02450767
## 7 0.00000000 0.000000000 0.02473790
## 8 0.00000000 0.000000000 0.03635911
## 9 0.00000000 0.000000000 0.03841947
## 10 0.00000000 0.000000000 0.04334012
## 11 0.00000000 0.000000000 0.04363812
## 12 0.00000000 0.000000000 0.04968899
## 13 0.01385697 0.000000000 0.04909419
## 14 0.01774519 0.000000000 0.04885154
## 15 0.03231403 0.000000000 0.04887363
## 16 0.04198296 0.000000000 0.04904478
## 17 0.05732360 0.000000000 0.04921926
## 18 0.07474473 0.000000000 0.05035499
## 19 0.07964475 -0.006519114 0.05054922
## 20 0.08083693 -0.007870586 0.05056222
## 21 0.08958441 -0.017736291 0.05044107
## 22 0.09564876 -0.029465418 0.04996711
## 23 0.10337312 -0.043130827 0.04882253
## 24 0.10401364 -0.044260225 0.04870007
## 25 0.13271718 -0.076822882 0.04579118
## 26 0.13984498 -0.086138632 0.04521129
## 27 0.14013080 -0.086304951 0.04517819
## 28 0.15677861 -0.095677901 0.04265570
## 29 0.16855196 -0.102502777 0.04093084
## 30 0.17805585 -0.108028065 0.03945583
## 31 0.18756223 -0.113280183 0.03763197
## 32 0.19268221 -0.118783974 0.03588501
## 33 0.20580409 -0.125822298 0.02968314
## 34 0.20656814 -0.126121959 0.02926780
## 35 0.20743680 -0.126437173 0.02887067
## 36 0.20791014 -0.126466964 0.02884122
## 37 0.20990180 -0.125987168 0.02860956
## 38 0.20998312 -0.125981093 0.02859751
## 39 0.21062908 -0.125825913 0.02851016
## 40 0.21323042 -0.126325438 0.02799255
## 41 0.21764262 -0.126622097 0.02732772
## 42 0.22276643 -0.126959685 0.02665162
## 43 0.22766387 -0.127567469 0.02661303
## 44 0.23164677 -0.127997230 0.02655879
## 45 0.23377839 -0.128150193 0.02661437
## 46 0.23473619 -0.128286512 0.02670125
## 47 0.23569996 -0.128416751 0.02674814
## 48 0.23781357 -0.128454566 0.02688430
## 49 0.24093143 -0.128456462 0.02694985
## 50 0.24707232 -0.128583808 0.02710056
## 51 0.25269009 -0.128048124 0.02770381
## 52 0.25354686 -0.127963232 0.02781101
## 53 0.25599344 -0.128164724 0.02839089
## 54 0.25750786 -0.128259399 0.02878706
## 55 0.26182223 -0.128206911 0.03003954
## 56 0.26352761 -0.128412871 0.03054152
## 57 0.26858942 -0.130075125 0.03188074
## 58 0.27064586 -0.130365546 0.03212781
## 59 0.27103774 -0.130432029 0.03217839
## 60 0.27318033 -0.130743530 0.03216402
## 61 0.27393249 -0.130839617 0.03218050
## ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess09
## 0 0.000000000 0.0000000000 0.0000000
## 1 0.000000000 0.0000000000 0.0000000
## 2 0.000000000 0.0000000000 0.0000000
## 3 0.000000000 0.0000000000 0.1545126
## 4 0.000000000 0.0000000000 0.1893431
## 5 0.000000000 0.0000000000 0.1907043
## 6 0.000000000 0.0000000000 0.1984518
## 7 0.000000000 0.0000000000 0.1985287
## 8 0.000000000 0.0000000000 0.2015443
## 9 0.000000000 0.0000000000 0.2030729
## 10 0.000000000 0.0000000000 0.2096785
## 11 0.000000000 0.0000000000 0.2104339
## 12 0.000000000 0.0000000000 0.2254593
## 13 0.000000000 0.0000000000 0.2292666
## 14 0.000000000 0.0000000000 0.2303030
## 15 -0.008238076 0.0000000000 0.2334666
## 16 -0.012870757 0.0000000000 0.2351611
## 17 -0.020975609 0.0000000000 0.2390401
## 18 -0.030912968 0.0000000000 0.2442096
## 19 -0.033153017 0.0000000000 0.2480224
## 20 -0.033710907 0.0000000000 0.2487504
## 21 -0.037720787 0.0000000000 0.2542445
## 22 -0.041985620 0.0000000000 0.2605557
## 23 -0.047372895 0.0000000000 0.2675098
## 24 -0.047838562 0.0000000000 0.2682645
## 25 -0.058670807 0.0000000000 0.2867634
## 26 -0.062706921 0.0000000000 0.2914617
## 27 -0.062770329 0.0000000000 0.2916527
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## ManufacturingProcess16 ManufacturingProcess17 ManufacturingProcess18
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## ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24
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## 32 0.000000000 -0.055868351 -0.025248767
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## 34 0.000000000 -0.063463872 -0.025003436
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## 60 0.010164503 -0.075517949 -0.023529951
## 61 0.010548646 -0.075872464 -0.023371447
## ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27
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## ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30
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## 48 -0.139658545 0.079510277 -0.005439257
## 49 -0.142439498 0.102588724 -0.013008119
## 50 -0.147392904 0.144539653 -0.026329805
## 51 -0.152444548 0.185794638 -0.040299072
## 52 -0.153233909 0.192231266 -0.042482119
## 53 -0.155262396 0.210184426 -0.048704758
## 54 -0.156083274 0.220890231 -0.051510498
## 55 -0.158092579 0.251752499 -0.058993498
## 56 -0.158793166 0.264291276 -0.062665677
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## 58 -0.164311829 0.323504012 -0.085924990
## 59 -0.164618895 0.326380534 -0.087327910
## 60 -0.165971503 0.339199182 -0.093549723
## 61 -0.166460762 0.342350789 -0.096156222
## ManufacturingProcess31 ManufacturingProcess32 ManufacturingProcess33
## 0 0.000000000 0.0000000 0.00000000
## 1 0.000000000 0.1032762 0.00000000
## 2 0.000000000 0.1045459 0.00000000
## 3 0.000000000 0.3383201 0.00000000
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## 39 0.000000000 0.7355608 -0.25154911
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## 57 0.000000000 0.8285340 -0.36195770
## 58 0.009388104 0.8310798 -0.36501574
## 59 0.011130817 0.8315535 -0.36554898
## 60 0.019442165 0.8339954 -0.36813169
## 61 0.021650893 0.8348797 -0.36908954
## ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36
## 0 0.00000000 0.000000000 0.000000e+00
## 1 0.00000000 0.000000000 0.000000e+00
## 2 0.00000000 0.000000000 0.000000e+00
## 3 0.00000000 0.000000000 0.000000e+00
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## 7 0.00000000 0.000000000 -2.051102e-04
## 8 0.03620678 0.000000000 -1.395482e-02
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## 13 0.06928638 0.000000000 -3.834301e-02
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## 15 0.07756376 0.000000000 -3.846209e-02
## 16 0.08228665 -0.005624597 -3.163587e-02
## 17 0.09049207 -0.015962613 -1.910641e-02
## 18 0.10122011 -0.028138784 -3.850498e-03
## 19 0.10279974 -0.030534182 -5.944368e-04
## 20 0.10326406 -0.030883919 7.579861e-20
## 21 0.10649507 -0.031129658 0.000000e+00
## 22 0.10997483 -0.032525975 0.000000e+00
## 23 0.11400016 -0.034094519 0.000000e+00
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## 26 0.13069097 -0.036070942 0.000000e+00
## 27 0.13080378 -0.036034827 0.000000e+00
## 28 0.11703798 -0.035434494 0.000000e+00
## 29 0.10697760 -0.035371165 0.000000e+00
## 30 0.09871906 -0.035232291 0.000000e+00
## 31 0.09110641 -0.034709461 0.000000e+00
## 32 0.08388654 -0.033255867 0.000000e+00
## 33 0.07067252 -0.030222611 0.000000e+00
## 34 0.06988241 -0.030036207 0.000000e+00
## 35 0.06898895 -0.029840985 0.000000e+00
## 36 0.06846742 -0.029766526 0.000000e+00
## 37 0.06643755 -0.029259779 0.000000e+00
## 38 0.06634405 -0.029239027 0.000000e+00
## 39 0.06540310 -0.029104547 0.000000e+00
## 40 0.06173600 -0.027865198 0.000000e+00
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## 42 0.05474086 -0.025468053 0.000000e+00
## 43 0.05213162 -0.023484636 0.000000e+00
## 44 0.05008543 -0.021075668 0.000000e+00
## 45 0.04896585 -0.019617785 0.000000e+00
## 46 0.04844085 -0.019105096 0.000000e+00
## 47 0.04789682 -0.018640471 0.000000e+00
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## 49 0.04598803 -0.016622202 0.000000e+00
## 50 0.04390567 -0.014243392 0.000000e+00
## 51 0.04313577 -0.018015782 1.095808e-02
## 52 0.04302869 -0.018620281 1.267391e-02
## 53 0.04277246 -0.020087049 1.767806e-02
## 54 0.04280599 -0.020997224 2.050507e-02
## 55 0.04265740 -0.022997770 2.865341e-02
## 56 0.04237261 -0.023589795 3.199293e-02
## 57 0.04082192 -0.025061449 4.217345e-02
## 58 0.04033994 -0.025631487 4.539945e-02
## 59 0.04024978 -0.025748996 4.601642e-02
## 60 0.03962643 -0.025970197 4.863123e-02
## 61 0.03937040 -0.026065692 4.950671e-02
## ManufacturingProcess37 ManufacturingProcess38 ManufacturingProcess39
## 0 0.00000000 0.000000000 0.000000000
## 1 0.00000000 0.000000000 0.000000000
## 2 0.00000000 0.000000000 0.000000000
## 3 0.00000000 0.000000000 0.000000000
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## 9 0.00000000 0.000000000 0.000000000
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## 11 -0.01000123 0.000000000 0.000000000
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## 18 -0.06410804 0.000000000 0.000000000
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## 23 -0.08188844 0.000000000 0.008438320
## 24 -0.08236873 0.000000000 0.009146562
## 25 -0.09513992 0.000000000 0.030602450
## 26 -0.09882687 -0.005964857 0.037291899
## 27 -0.09889305 -0.006125272 0.037417732
## 28 -0.10519395 -0.015947285 0.049109902
## 29 -0.10972156 -0.022799473 0.057265960
## 30 -0.11369117 -0.028326411 0.064083800
## 31 -0.11715461 -0.033701770 0.069699514
## 32 -0.12060313 -0.040700297 0.076087283
## 33 -0.12667627 -0.053082713 0.089929489
## 34 -0.12704949 -0.053788404 0.090893253
## 35 -0.12747923 -0.054600204 0.091953502
## 36 -0.12766192 -0.055034891 0.092437827
## 37 -0.12850270 -0.057518308 0.095477923
## 38 -0.12852202 -0.057620891 0.095590796
## 39 -0.12874131 -0.058499391 0.096370730
## 40 -0.12957801 -0.063210760 0.099618486
## 41 -0.13022953 -0.067502206 0.103513828
## 42 -0.13103483 -0.072575425 0.107478536
## 43 -0.13143609 -0.077267649 0.111121131
## 44 -0.13130363 -0.082083513 0.113678985
## 45 -0.13122183 -0.084858263 0.114694850
## 46 -0.13149554 -0.085857476 0.115892928
## 47 -0.13154210 -0.086890138 0.117110284
## 48 -0.13161709 -0.088727501 0.119274889
## 49 -0.13174197 -0.091348675 0.122604283
## 50 -0.13195359 -0.096158209 0.128654678
## 51 -0.13173170 -0.099740949 0.133081380
## 52 -0.13170816 -0.100289287 0.133755782
## 53 -0.13188274 -0.102212242 0.135500510
## 54 -0.13195730 -0.102922634 0.136373767
## 55 -0.13224107 -0.105247760 0.138437276
## 56 -0.13245764 -0.106474282 0.138831058
## 57 -0.13498266 -0.110884630 0.142251431
## 58 -0.13628415 -0.112569944 0.143745935
## 59 -0.13652567 -0.112874124 0.144040084
## 60 -0.13743163 -0.114426153 0.145713092
## 61 -0.13777249 -0.114926713 0.146230156
## ManufacturingProcess40 ManufacturingProcess41 ManufacturingProcess42
## 0 0.0000000000 0.00000000 0.00000000
## 1 0.0000000000 0.00000000 0.00000000
## 2 0.0000000000 0.00000000 0.00000000
## 3 0.0000000000 0.00000000 0.00000000
## 4 0.0000000000 0.00000000 0.00000000
## 5 0.0000000000 0.00000000 0.00000000
## 6 0.0000000000 0.00000000 0.00000000
## 7 0.0000000000 0.00000000 0.00000000
## 8 0.0000000000 0.00000000 0.00000000
## 9 0.0000000000 0.00000000 0.00000000
## 10 0.0000000000 0.00000000 0.00000000
## 11 0.0000000000 0.00000000 0.00000000
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## 19 0.0000000000 0.00000000 0.00000000
## 20 0.0005046218 0.00000000 0.00000000
## 21 0.0043388466 0.00000000 0.00000000
## 22 0.0083226149 0.00000000 0.00000000
## 23 0.0131207287 0.00000000 0.00000000
## 24 0.0135341213 0.00000000 0.00000000
## 25 0.0263274164 0.00000000 0.00000000
## 26 0.0300519385 0.00000000 0.00000000
## 27 0.0301173304 0.00000000 0.00000000
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## 29 0.0345724127 0.00000000 0.00000000
## 30 0.0359044873 0.00000000 0.00000000
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## 32 0.0379039245 0.00000000 0.00000000
## 33 0.0400845352 0.00000000 0.00000000
## 34 0.0402361940 0.00000000 0.00000000
## 35 0.0403980175 0.00000000 0.00000000
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## 37 0.0410275891 0.00000000 0.00000000
## 38 0.0410467091 0.00000000 0.00000000
## 39 0.0411299994 0.00000000 0.00000000
## 40 0.0417099671 0.00000000 0.00000000
## 41 0.0423605683 0.00000000 0.00000000
## 42 0.0527304905 -0.01101182 0.00000000
## 43 0.0634719985 -0.02197491 0.00000000
## 44 0.0724278082 -0.03055766 0.00000000
## 45 0.0770347615 -0.03494831 0.00000000
## 46 0.0788593029 -0.03676929 0.00000000
## 47 0.0807418958 -0.03863720 0.00000000
## 48 0.0843503894 -0.04197461 0.00000000
## 49 0.0892999107 -0.04646745 0.00000000
## 50 0.0984503626 -0.05466915 0.00000000
## 51 0.1075257818 -0.06315158 0.00000000
## 52 0.1089368790 -0.06447961 0.00000000
## 53 0.1129868191 -0.06838828 0.00000000
## 54 0.1152063465 -0.07034811 0.00000000
## 55 0.1213096327 -0.07591823 0.00000000
## 56 0.1236065360 -0.07791406 0.00392099
## 57 0.1300354574 -0.08327863 0.01633562
## 58 0.1326985077 -0.08594647 0.02004832
## 59 0.1332033299 -0.08646782 0.02075268
## 60 0.1355748870 -0.08877398 0.02346878
## 61 0.1363635200 -0.08955472 0.02447231
## ManufacturingProcess43 ManufacturingProcess44 ManufacturingProcess45
## 0 0.000000000 0.000000000 0.000000000
## 1 0.000000000 0.000000000 0.000000000
## 2 0.000000000 0.000000000 0.000000000
## 3 0.000000000 0.000000000 0.000000000
## 4 0.000000000 0.000000000 0.000000000
## 5 0.000000000 0.000000000 0.000000000
## 6 0.000000000 0.000000000 0.000000000
## 7 0.000000000 0.000000000 0.000000000
## 8 0.000000000 0.000000000 0.000000000
## 9 0.000000000 0.000000000 0.006800248
## 10 0.000000000 0.000000000 0.020302104
## 11 0.000000000 0.000000000 0.021085607
## 12 0.000000000 0.000000000 0.042314212
## 13 0.000000000 0.000000000 0.048116214
## 14 0.000000000 0.000000000 0.049868567
## 15 0.000000000 0.000000000 0.054226068
## 16 0.000000000 0.000000000 0.057406429
## 17 0.000000000 0.000000000 0.062702692
## 18 0.000000000 0.000000000 0.069385824
## 19 0.000000000 0.000000000 0.070253095
## 20 0.000000000 0.000000000 0.070339739
## 21 0.000000000 0.000000000 0.070958622
## 22 0.000000000 0.000000000 0.073486872
## 23 0.000000000 0.000000000 0.071339393
## 24 0.000000000 0.000000000 0.071208823
## 25 0.000000000 0.000000000 0.068372630
## 26 0.000000000 0.000000000 0.070066978
## 27 0.000000000 0.000000000 0.070128495
## 28 0.000000000 0.000000000 0.073109408
## 29 0.000000000 0.000000000 0.075488024
## 30 0.000000000 0.000000000 0.076870416
## 31 0.000000000 0.000000000 0.077922320
## 32 0.000000000 0.000000000 0.079901340
## 33 0.000000000 0.000000000 0.081978483
## 34 0.000000000 0.000000000 0.082143744
## 35 0.000000000 0.000000000 0.082330435
## 36 0.000000000 0.000000000 0.082518656
## 37 0.000000000 0.000000000 0.083918147
## 38 0.000000000 0.000000000 0.083982391
## 39 0.000000000 0.000000000 0.084451920
## 40 0.000000000 0.000000000 0.089096955
## 41 0.009324276 0.000000000 0.092835520
## 42 0.017298599 0.000000000 0.095677869
## 43 0.022027276 0.000000000 0.098957161
## 44 0.027582209 0.000000000 0.101596053
## 45 0.030812274 0.000000000 0.103051442
## 46 0.031839268 -0.002191051 0.104645062
## 47 0.032933434 -0.004356527 0.106252676
## 48 0.035728532 -0.007704522 0.109697527
## 49 0.039705280 -0.012338347 0.114478907
## 50 0.047169969 -0.020898717 0.123278798
## 51 0.053933022 -0.028234044 0.131709105
## 52 0.055018068 -0.029409139 0.133016680
## 53 0.057727876 -0.032841455 0.136755639
## 54 0.059175621 -0.034731146 0.138491773
## 55 0.063111898 -0.039967521 0.143785873
## 56 0.064522024 -0.044462018 0.145372125
## 57 0.068832504 -0.058728629 0.150454488
## 58 0.070473353 -0.062633842 0.152289880
## 59 0.070713910 -0.063401346 0.152654053
## 60 0.071190888 -0.065951139 0.154481913
## 61 0.071344892 -0.066836942 0.155152062- 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?
ManufacturingProcess32 and Yield variables have a 0.60 correlation.
plot(df$ManufacturingProcess32, df$Yield)
temp <- df[,c('Yield','ManufacturingProcess32')]
cor(temp)## Yield ManufacturingProcess32
## Yield 1.0000000 0.6083321
## ManufacturingProcess32 0.6083321 1.0000000