BrianSingh_data624_HW7
2024-04-12
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:
(a) Start R and use these commands to load the data:
library(AppliedPredictiveModeling)## Warning: package 'AppliedPredictiveModeling' was built under R version 4.2.3data(permeability)b. 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?
library(caret)## Warning: package 'caret' was built under R version 4.2.3## Loading required package: ggplot2## Warning: package 'ggplot2' was built under R version 4.2.3## Loading required package: lattice## Warning: package 'lattice' was built under R version 4.2.3fingerprints_filtered <- fingerprints[, -nearZeroVar(fingerprints)]
dim(fingerprints_filtered)## [1] 165 388388 predictors are left for modeling.
c. 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?
set.seed(1234)
train_selection <- createDataPartition(permeability, p = .8, list = FALSE)
train_x <- fingerprints_filtered[train_selection, ]
test_x <- fingerprints_filtered[-train_selection, ]
train_y <- permeability[train_selection, ]
test_y <- permeability[-train_selection, ]
PLS <- train(x = train_x, y = train_y,method = "pls",metric = "Rsquared", tuneLength = 10, trControl = trainControl(method = "cv"), preProcess = c('center', 'scale'))
PLS_result <- PLS$results
PLS## Partial Least Squares
##
## 133 samples
## 388 predictors
##
## Pre-processing: centered (388), scaled (388)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 119, 119, 120, 120, 120, 121, ...
## Resampling results across tuning parameters:
##
## ncomp RMSE Rsquared MAE
## 1 12.76548 0.3949848 9.782056
## 2 11.08419 0.5662412 7.827891
## 3 11.02409 0.5704308 8.285652
## 4 11.16727 0.5556966 8.423255
## 5 11.09218 0.5573860 8.252132
## 6 10.96320 0.5653475 8.090110
## 7 11.06634 0.5592164 8.455477
## 8 11.21343 0.5559115 8.601945
## 9 11.24153 0.5635851 8.559953
## 10 11.63386 0.5463035 8.841897
##
## Rsquared was used to select the optimal model using the largest value.
## The final value used for the model was ncomp = 3.The final value used for the model was ncomp = 3 with an rsquares of 0.5606977
d. Predict the response for the test set. What is the test set estimate of R2?
fingerprint_predict <- predict(PLS, test_x)
postResample(fingerprint_predict, test_y)## RMSE Rsquared MAE
## 14.033165 0.138877 9.495030The test set estimated of Rsquared is 0.2440012
e. Try building other models discussed in this chapter. Do any have better predictive performance?
set.seed(5678)
ridge_train <- train(x=train_x, y=train_y,method='ridge', metric='Rsquared',tuneGrid=data.frame(.lambda = seq(0, 1, by=0.1)),trControl=trainControl(method='cv'),preProcess=c('center','scale'))## Warning: model fit failed for Fold10: lambda=0.0 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.ridge_train## Ridge Regression
##
## 133 samples
## 388 predictors
##
## Pre-processing: centered (388), scaled (388)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 119, 119, 120, 119, 120, 120, ...
## Resampling results across tuning parameters:
##
## lambda RMSE Rsquared MAE
## 0.0 13.49126 0.4365961 9.679907
## 0.1 11.50897 0.5413120 8.507836
## 0.2 11.69481 0.5387242 8.743099
## 0.3 12.07012 0.5403318 9.074433
## 0.4 12.55911 0.5419691 9.475287
## 0.5 13.13064 0.5434704 9.925781
## 0.6 13.77109 0.5440621 10.459382
## 0.7 14.46238 0.5446213 11.039901
## 0.8 15.19632 0.5449756 11.644364
## 0.9 15.96540 0.5450875 12.263755
## 1.0 16.75702 0.5452463 12.888947
##
## Rsquared was used to select the optimal model using the largest value.
## The final value used for the model was lambda = 1.Ridge regression’s optimal lambda is 0.4, with an rsquared of 0.5382022, which is a better performance that PLS.
set.seed(789)
lars_train <- train(train_x, train_y, method = "lars", metric = "Rsquared",tuneLength = 10, trControl=trainControl(method='cv'), preProc = c("center", "scale"))
lars_train## Least Angle Regression
##
## 133 samples
## 388 predictors
##
## Pre-processing: centered (388), scaled (388)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 120, 119, 120, 119, 120, 119, ...
## Resampling results across tuning parameters:
##
## fraction RMSE Rsquared MAE
## 0.0500000 11.20680 0.5827230 7.887273
## 0.1555556 11.36698 0.5654115 8.342067
## 0.2611111 11.99233 0.5360780 8.742474
## 0.3666667 12.39335 0.5121641 8.931486
## 0.4722222 12.65635 0.4940958 9.037095
## 0.5777778 13.04394 0.4761195 9.296571
## 0.6833333 13.13094 0.4696574 9.386220
## 0.7888889 13.33400 0.4756693 9.433763
## 0.8944444 13.68104 0.4711790 9.704378
## 1.0000000 14.39200 0.4531616 10.183606
##
## Rsquared was used to select the optimal model using the largest value.
## The final value used for the model was fraction = 0.05.The final value used for the model was fraction = 0.05 with an rsquared of 0.4924561 which is a better performance that PLS but not than Lars.
e. Would you recommend any of your models to replace the permeability laboratory experiment?
The Lars model has a higher Rsquared and lower RMSE than the others
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:
(a) Start R and use these commands to load the data:
library(AppliedPredictiveModeling)
data(ChemicalManufacturingProcess)b. 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).
summary(ChemicalManufacturingProcess)## Yield BiologicalMaterial01 BiologicalMaterial02 BiologicalMaterial03
## Min. :35.25 Min. :4.580 Min. :46.87 Min. :56.97
## 1st Qu.:38.75 1st Qu.:5.978 1st Qu.:52.68 1st Qu.:64.98
## Median :39.97 Median :6.305 Median :55.09 Median :67.22
## Mean :40.18 Mean :6.411 Mean :55.69 Mean :67.70
## 3rd Qu.:41.48 3rd Qu.:6.870 3rd Qu.:58.74 3rd Qu.:70.43
## Max. :46.34 Max. :8.810 Max. :64.75 Max. :78.25
##
## BiologicalMaterial04 BiologicalMaterial05 BiologicalMaterial06
## Min. : 9.38 Min. :13.24 Min. :40.60
## 1st Qu.:11.24 1st Qu.:17.23 1st Qu.:46.05
## Median :12.10 Median :18.49 Median :48.46
## Mean :12.35 Mean :18.60 Mean :48.91
## 3rd Qu.:13.22 3rd Qu.:19.90 3rd Qu.:51.34
## Max. :23.09 Max. :24.85 Max. :59.38
##
## BiologicalMaterial07 BiologicalMaterial08 BiologicalMaterial09
## Min. :100.0 Min. :15.88 Min. :11.44
## 1st Qu.:100.0 1st Qu.:17.06 1st Qu.:12.60
## Median :100.0 Median :17.51 Median :12.84
## Mean :100.0 Mean :17.49 Mean :12.85
## 3rd Qu.:100.0 3rd Qu.:17.88 3rd Qu.:13.13
## Max. :100.8 Max. :19.14 Max. :14.08
##
## BiologicalMaterial10 BiologicalMaterial11 BiologicalMaterial12
## Min. :1.770 Min. :135.8 Min. :18.35
## 1st Qu.:2.460 1st Qu.:143.8 1st Qu.:19.73
## Median :2.710 Median :146.1 Median :20.12
## Mean :2.801 Mean :147.0 Mean :20.20
## 3rd Qu.:2.990 3rd Qu.:149.6 3rd Qu.:20.75
## Max. :6.870 Max. :158.7 Max. :22.21
##
## ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03
## Min. : 0.00 Min. : 0.00 Min. :1.47
## 1st Qu.:10.80 1st Qu.:19.30 1st Qu.:1.53
## Median :11.40 Median :21.00 Median :1.54
## Mean :11.21 Mean :16.68 Mean :1.54
## 3rd Qu.:12.15 3rd Qu.:21.50 3rd Qu.:1.55
## Max. :14.10 Max. :22.50 Max. :1.60
## NA's :1 NA's :3 NA's :15
## ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06
## Min. :911.0 Min. : 923.0 Min. :203.0
## 1st Qu.:928.0 1st Qu.: 986.8 1st Qu.:205.7
## Median :934.0 Median : 999.2 Median :206.8
## Mean :931.9 Mean :1001.7 Mean :207.4
## 3rd Qu.:936.0 3rd Qu.:1008.9 3rd Qu.:208.7
## Max. :946.0 Max. :1175.3 Max. :227.4
## NA's :1 NA's :1 NA's :2
## ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess09
## Min. :177.0 Min. :177.0 Min. :38.89
## 1st Qu.:177.0 1st Qu.:177.0 1st Qu.:44.89
## Median :177.0 Median :178.0 Median :45.73
## Mean :177.5 Mean :177.6 Mean :45.66
## 3rd Qu.:178.0 3rd Qu.:178.0 3rd Qu.:46.52
## Max. :178.0 Max. :178.0 Max. :49.36
## NA's :1 NA's :1
## ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12
## Min. : 7.500 Min. : 7.500 Min. : 0.0
## 1st Qu.: 8.700 1st Qu.: 9.000 1st Qu.: 0.0
## Median : 9.100 Median : 9.400 Median : 0.0
## Mean : 9.179 Mean : 9.386 Mean : 857.8
## 3rd Qu.: 9.550 3rd Qu.: 9.900 3rd Qu.: 0.0
## Max. :11.600 Max. :11.500 Max. :4549.0
## NA's :9 NA's :10 NA's :1
## ManufacturingProcess13 ManufacturingProcess14 ManufacturingProcess15
## Min. :32.10 Min. :4701 Min. :5904
## 1st Qu.:33.90 1st Qu.:4828 1st Qu.:6010
## Median :34.60 Median :4856 Median :6032
## Mean :34.51 Mean :4854 Mean :6039
## 3rd Qu.:35.20 3rd Qu.:4882 3rd Qu.:6061
## Max. :38.60 Max. :5055 Max. :6233
## NA's :1
## ManufacturingProcess16 ManufacturingProcess17 ManufacturingProcess18
## Min. : 0 Min. :31.30 Min. : 0
## 1st Qu.:4561 1st Qu.:33.50 1st Qu.:4813
## Median :4588 Median :34.40 Median :4835
## Mean :4566 Mean :34.34 Mean :4810
## 3rd Qu.:4619 3rd Qu.:35.10 3rd Qu.:4862
## Max. :4852 Max. :40.00 Max. :4971
##
## ManufacturingProcess19 ManufacturingProcess20 ManufacturingProcess21
## Min. :5890 Min. : 0 Min. :-1.8000
## 1st Qu.:6001 1st Qu.:4553 1st Qu.:-0.6000
## Median :6022 Median :4582 Median :-0.3000
## Mean :6028 Mean :4556 Mean :-0.1642
## 3rd Qu.:6050 3rd Qu.:4610 3rd Qu.: 0.0000
## Max. :6146 Max. :4759 Max. : 3.6000
##
## ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24
## Min. : 0.000 Min. :0.000 Min. : 0.000
## 1st Qu.: 3.000 1st Qu.:2.000 1st Qu.: 4.000
## Median : 5.000 Median :3.000 Median : 8.000
## Mean : 5.406 Mean :3.017 Mean : 8.834
## 3rd Qu.: 8.000 3rd Qu.:4.000 3rd Qu.:14.000
## Max. :12.000 Max. :6.000 Max. :23.000
## NA's :1 NA's :1 NA's :1
## ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27
## Min. : 0 Min. : 0 Min. : 0
## 1st Qu.:4832 1st Qu.:6020 1st Qu.:4560
## Median :4855 Median :6047 Median :4587
## Mean :4828 Mean :6016 Mean :4563
## 3rd Qu.:4877 3rd Qu.:6070 3rd Qu.:4609
## Max. :4990 Max. :6161 Max. :4710
## NA's :5 NA's :5 NA's :5
## ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30
## Min. : 0.000 Min. : 0.00 Min. : 0.000
## 1st Qu.: 0.000 1st Qu.:19.70 1st Qu.: 8.800
## Median :10.400 Median :19.90 Median : 9.100
## Mean : 6.592 Mean :20.01 Mean : 9.161
## 3rd Qu.:10.750 3rd Qu.:20.40 3rd Qu.: 9.700
## Max. :11.500 Max. :22.00 Max. :11.200
## NA's :5 NA's :5 NA's :5
## ManufacturingProcess31 ManufacturingProcess32 ManufacturingProcess33
## Min. : 0.00 Min. :143.0 Min. :56.00
## 1st Qu.:70.10 1st Qu.:155.0 1st Qu.:62.00
## Median :70.80 Median :158.0 Median :64.00
## Mean :70.18 Mean :158.5 Mean :63.54
## 3rd Qu.:71.40 3rd Qu.:162.0 3rd Qu.:65.00
## Max. :72.50 Max. :173.0 Max. :70.00
## NA's :5 NA's :5
## ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36
## Min. :2.300 Min. :463.0 Min. :0.01700
## 1st Qu.:2.500 1st Qu.:490.0 1st Qu.:0.01900
## Median :2.500 Median :495.0 Median :0.02000
## Mean :2.494 Mean :495.6 Mean :0.01957
## 3rd Qu.:2.500 3rd Qu.:501.5 3rd Qu.:0.02000
## Max. :2.600 Max. :522.0 Max. :0.02200
## NA's :5 NA's :5 NA's :5
## ManufacturingProcess37 ManufacturingProcess38 ManufacturingProcess39
## Min. :0.000 Min. :0.000 Min. :0.000
## 1st Qu.:0.700 1st Qu.:2.000 1st Qu.:7.100
## Median :1.000 Median :3.000 Median :7.200
## Mean :1.014 Mean :2.534 Mean :6.851
## 3rd Qu.:1.300 3rd Qu.:3.000 3rd Qu.:7.300
## Max. :2.300 Max. :3.000 Max. :7.500
##
## ManufacturingProcess40 ManufacturingProcess41 ManufacturingProcess42
## Min. :0.00000 Min. :0.00000 Min. : 0.00
## 1st Qu.:0.00000 1st Qu.:0.00000 1st Qu.:11.40
## Median :0.00000 Median :0.00000 Median :11.60
## Mean :0.01771 Mean :0.02371 Mean :11.21
## 3rd Qu.:0.00000 3rd Qu.:0.00000 3rd Qu.:11.70
## Max. :0.10000 Max. :0.20000 Max. :12.10
## NA's :1 NA's :1
## ManufacturingProcess43 ManufacturingProcess44 ManufacturingProcess45
## Min. : 0.0000 Min. :0.000 Min. :0.000
## 1st Qu.: 0.6000 1st Qu.:1.800 1st Qu.:2.100
## Median : 0.8000 Median :1.900 Median :2.200
## Mean : 0.9119 Mean :1.805 Mean :2.138
## 3rd Qu.: 1.0250 3rd Qu.:1.900 3rd Qu.:2.300
## Max. :11.0000 Max. :2.100 Max. :2.600
## sum(is.na(ChemicalManufacturingProcess))## [1] 106We have 106 NAs across different variables.
chemical_missing <- preProcess(ChemicalManufacturingProcess, method = "bagImpute")
chemical_imputed <- predict(chemical_missing, ChemicalManufacturingProcess)Bag imputing creates multiple imputed datasets by sampling with replacement from the original dataset.
c. 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?
set.seed(1357)
index <- createDataPartition(chemical_imputed$Yield, p = .8, list = FALSE)
train_chemical <- chemical_imputed[index, ]
test_chemical <- chemical_imputed[-index, ]
lm_model <- lm(Yield ~ ., chemical_imputed)
summary(lm_model)##
## Call:
## lm(formula = Yield ~ ., data = chemical_imputed)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.14184 -0.52928 -0.05022 0.48100 2.04082
##
## Coefficients: (1 not defined because of singularities)
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.443e+02 1.304e+02 1.107 0.27074
## BiologicalMaterial01 2.374e-01 3.351e-01 0.708 0.48011
## BiologicalMaterial02 -1.166e-01 1.254e-01 -0.929 0.35470
## BiologicalMaterial03 2.389e-01 2.326e-01 1.027 0.30653
## BiologicalMaterial04 -1.709e-01 5.229e-01 -0.327 0.74433
## BiologicalMaterial05 1.617e-01 1.041e-01 1.553 0.12310
## BiologicalMaterial06 -8.433e-02 2.970e-01 -0.284 0.77695
## BiologicalMaterial07 -1.460e+00 9.556e-01 -1.528 0.12928
## BiologicalMaterial08 6.953e-01 6.429e-01 1.081 0.28167
## BiologicalMaterial09 -1.360e+00 1.354e+00 -1.004 0.31724
## BiologicalMaterial10 1.998e-01 1.370e+00 0.146 0.88429
## BiologicalMaterial11 -8.302e-02 8.057e-02 -1.030 0.30494
## BiologicalMaterial12 3.457e-01 6.254e-01 0.553 0.58145
## ManufacturingProcess01 6.930e-02 9.338e-02 0.742 0.45949
## ManufacturingProcess02 2.978e-03 4.579e-02 0.065 0.94825
## ManufacturingProcess03 -4.229e+00 5.106e+00 -0.828 0.40923
## ManufacturingProcess04 6.193e-02 2.925e-02 2.117 0.03634 *
## ManufacturingProcess05 1.017e-03 3.804e-03 0.267 0.78974
## ManufacturingProcess06 3.489e-02 4.229e-02 0.825 0.41100
## ManufacturingProcess07 -1.776e-01 2.084e-01 -0.852 0.39580
## ManufacturingProcess08 -1.350e-01 2.506e-01 -0.539 0.59115
## ManufacturingProcess09 3.529e-01 1.777e-01 1.987 0.04927 *
## ManufacturingProcess10 -2.360e-02 5.568e-01 -0.042 0.96627
## ManufacturingProcess11 4.518e-01 7.323e-01 0.617 0.53840
## ManufacturingProcess12 8.256e-05 1.067e-04 0.774 0.44043
## ManufacturingProcess13 -1.906e-01 3.701e-01 -0.515 0.60746
## ManufacturingProcess14 -4.991e-04 1.072e-02 -0.047 0.96294
## ManufacturingProcess15 3.285e-03 8.596e-03 0.382 0.70299
## ManufacturingProcess16 -8.787e-05 3.346e-04 -0.263 0.79332
## ManufacturingProcess17 -1.532e-01 2.905e-01 -0.527 0.59887
## ManufacturingProcess18 4.710e-03 4.312e-03 1.092 0.27695
## ManufacturingProcess19 -1.100e-03 7.254e-03 -0.152 0.87975
## ManufacturingProcess20 -4.969e-03 4.574e-03 -1.086 0.27956
## ManufacturingProcess21 NA NA NA NA
## ManufacturingProcess22 -1.243e-02 4.115e-02 -0.302 0.76317
## ManufacturingProcess23 -4.783e-02 8.166e-02 -0.586 0.55916
## ManufacturingProcess24 -2.537e-02 2.302e-02 -1.102 0.27260
## ManufacturingProcess25 -1.906e-03 2.283e-03 -0.835 0.40538
## ManufacturingProcess26 2.883e-03 6.057e-03 0.476 0.63502
## ManufacturingProcess27 -6.446e-03 6.794e-03 -0.949 0.34462
## ManufacturingProcess28 -8.247e-02 3.070e-02 -2.687 0.00825 **
## ManufacturingProcess29 1.188e+00 9.069e-01 1.310 0.19263
## ManufacturingProcess30 -6.555e-01 5.903e-01 -1.110 0.26907
## ManufacturingProcess31 6.274e-02 1.155e-01 0.543 0.58790
## ManufacturingProcess32 3.237e-01 6.827e-02 4.741 5.96e-06 ***
## ManufacturingProcess33 -3.868e-01 1.274e-01 -3.036 0.00295 **
## ManufacturingProcess34 -1.251e+00 2.735e+00 -0.458 0.64813
## ManufacturingProcess35 -2.107e-02 1.724e-02 -1.222 0.22395
## ManufacturingProcess36 3.452e+02 3.079e+02 1.121 0.26449
## ManufacturingProcess37 -8.166e-01 2.889e-01 -2.826 0.00552 **
## ManufacturingProcess38 -2.175e-01 2.378e-01 -0.914 0.36232
## ManufacturingProcess39 8.136e-02 1.283e-01 0.634 0.52708
## ManufacturingProcess40 1.080e+00 6.466e+00 0.167 0.86761
## ManufacturingProcess41 -3.648e-01 4.690e+00 -0.078 0.93813
## ManufacturingProcess42 5.257e-02 2.062e-01 0.255 0.79923
## ManufacturingProcess43 1.957e-01 1.159e-01 1.689 0.09393 .
## ManufacturingProcess44 -8.385e-01 1.181e+00 -0.710 0.47906
## ManufacturingProcess45 9.891e-01 5.347e-01 1.850 0.06679 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.022 on 119 degrees of freedom
## Multiple R-squared: 0.7914, Adjusted R-squared: 0.6932
## F-statistic: 8.06 on 56 and 119 DF, p-value: < 2.2e-16the linear regression has an r sqared of 0.7858.
d. 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?
lm_predict <- predict(lm_model, test_chemical[ ,-1])## Warning in predict.lm(lm_model, test_chemical[, -1]): prediction from a
## rank-deficient fit may be misleadingpostResample(lm_predict, test_chemical[ ,1])## RMSE Rsquared MAE
## 0.8443454 0.8338351 0.6445676The Rsquared on the predicted test set is 0.7812, slightly lower, but just about the same as the training set.
e. Which predictors are most important in the model you have trained? Do either the biological or process predictors dominate the list?
Based on the model above, ManufacturingProcess32, 28, 33, 37 has the highest significance based on pvalues.
f. 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?
library(tidyverse)## Warning: package 'tidyverse' was built under R version 4.2.3## Warning: package 'tibble' was built under R version 4.2.3## Warning: package 'tidyr' was built under R version 4.2.3## Warning: package 'readr' was built under R version 4.2.3## Warning: package 'purrr' was built under R version 4.2.3## Warning: package 'dplyr' was built under R version 4.2.3## Warning: package 'stringr' was built under R version 4.2.3## Warning: package 'forcats' was built under R version 4.2.3## Warning: package 'lubridate' was built under R version 4.2.3## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
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## ✔ purrr 1.0.2 ✔ tidyr 1.3.0
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ✖ purrr::lift() masks caret::lift()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorslibrary(corrplot)## Warning: package 'corrplot' was built under R version 4.2.3## corrplot 0.92 loadedcorrelation <- cor(select(chemical_imputed, 'ManufacturingProcess32','ManufacturingProcess28','ManufacturingProcess33','ManufacturingProcess37','Yield'))
corrplot(correlation,)
The highest correlation, which is positive, appears to be between 32 and
33 and there are some negative correlations noted as well. The company
would want to improve their yield based on predictors, more so focusing
on process32. Maximizing that performance measure can potentially
increase results.