DS 624: Homwork 9 (Trees and Rules)
Kuhn: 8.1, 8.2, 8.3, 8.7
Donny Lofland
Source Code: https://github.com/djlofland/DATA624_PredictiveAnalytics/tree/master/Homework_9
Problem 8.1
Recreate the simulated data from Exercise 7.2:
Load Data
Part (A)
Fit a random forest model to all of the predictors, then estimate the variable importance scores:
set.seed(200)
model1 <- randomForest(y ~ ., data = simulated,
importance = TRUE,
ntree = 1000)
(rfImp1 <- varImp(model1, scale = FALSE))## Overall
## V1 8.68879876
## V2 6.47488556
## V3 0.71801185
## V4 7.73791893
## V5 2.28677136
## V6 0.18577159
## V7 0.03371068
## V8 -0.06534861
## V9 -0.10124041
## V10 -0.10053684Did the random forest model significantly use the uninformative predictors (V6 – V10)?
RandomForest identified
V1-V5as the more important features, but foundV6-V10to not be significantly important.
Part (B)
Now add an additional predictor that is highly correlated with one of the informative predictors. For example:
set.seed(200)
simulated$duplicate1 <- simulated$V1 + rnorm(200) * .1
cor(simulated$duplicate1, simulated$V1)## [1] 0.9497025Fit another random forest model to these data. Did the importance score for V1 change?
set.seed(200)
model2 <- randomForest(y ~ ., data = simulated,
importance = TRUE,
ntree = 1000)
(rfImp1 <- varImp(model2, scale = FALSE))## Overall
## V1 6.106963692
## V2 6.202910805
## V3 0.628919280
## V4 7.019864830
## V5 2.239542012
## V6 0.106378124
## V7 -0.114253349
## V8 -0.090321828
## V9 0.009518246
## V10 -0.036864866
## duplicate1 4.039784189Yes, the importnce score for
V1decreased when we added a highly correlated featureduplicate1
What happens when you add another predictor that is also highly correlated with V1?
set.seed(200)
simulated$duplicate2 <- simulated$V1 + rnorm(200) * .1
cor(simulated$duplicate1, simulated$V1)## [1] 0.9497025set.seed(200)
model3 <- randomForest(y ~ ., data = simulated,
importance = TRUE,
ntree = 1000)
(rfImp1 <- varImp(model3, scale = FALSE))## Overall
## V1 5.10087370
## V2 6.43303576
## V3 0.46424167
## V4 7.09328937
## V5 2.07264067
## V6 0.17902427
## V7 0.02434474
## V8 -0.04353591
## V9 -0.04314904
## V10 -0.04931179
## duplicate1 2.93134491
## duplicate2 2.99805957The importance score for
V1decreases further when another highly correlated featureduplicate2is added.
Part (C)
Use the cforest function in the party package to fit a random forest model using conditional inference trees. The party package function varimp can calculate predictor importance. The conditional argument of that function toggles between the traditional importance measure and the modified version described in Strobl et al. (2007). Do these importances show the same pattern as the traditional random forest model?
library(party)
set.seed(200)
model4 <- cforest(y ~ ., data = simulated)
(rfImp2 <- varimp(model4, conditional = FALSE) %>%
sort(decreasing = T))## V4 V2 V1 duplicate1 V5 duplicate2
## 7.460033551 6.066271874 5.390384642 2.729868197 1.969226339 1.437291092
## V3 V6 V7 V9 V10 V8
## 0.021937627 0.007088557 0.005249178 -0.006778664 -0.008015955 -0.031046930## V4 V2 V1 V5 duplicate1 duplicate2
## 6.200117742 4.880955367 2.709403126 1.410084928 1.249186491 0.557887207
## V6 V3 V7 V9 V8 V10
## 0.019372783 0.010900359 0.010426508 0.005762708 0.001617468 -0.014948188## Length Class Mode
## 1 RandomForest S4Using the
party::cforestmodel andconditional=FALSE, we get the same feature importance scores as seen with therandomForestversion. Withconditional=TRUEwe get different scores. While the score differ, their order doesn’t.
Part (D)
Repeat this process with different tree models, such as boosted trees and Cubist. Does the same pattern occur?
Boosted Tree
#gbmModel <- gbm(y ~ ., data = simulated, distribution="gaussian")
gbmGrid <- expand.grid(
interaction.depth = seq(1, 7, by = 2),
n.trees = seq(100, 1000, by = 50),
shrinkage = c(0.01, 0.1),
n.minobsinnode=10)
metric <- "RMSE"
trainControl <- trainControl(method="cv", number=10)
set.seed(200)
trainX <- simulated %>%
dplyr::select(-y)
gbmTune <- train(trainX, simulated$y,
method = "gbm",
tuneGrid = gbmGrid,
trControl=trainControl,
metric=metric,
bag.fraction=0.75,
verbose = FALSE)
(gbmImp1 <- varImp(gbmTune, scale = FALSE))## gbm variable importance
##
## Overall
## V4 6372.43
## V2 5077.65
## V1 4551.08
## V5 2205.16
## V3 1989.64
## duplicate1 1169.49
## V6 183.91
## V7 121.26
## V8 103.89
## V10 84.19
## V9 63.97
## duplicate2 0.00
## var rel.inf
## V4 V4 29.0677568
## V2 V2 23.1616428
## V1 V1 20.7596935
## V5 V5 10.0588114
## V3 V3 9.0757175
## duplicate1 duplicate1 5.3346036
## V6 V6 0.8389177
## V7 V7 0.5531361
## V8 V8 0.4738926
## V10 V10 0.3840461
## V9 V9 0.2917816
## duplicate2 duplicate2 0.0000000Cubist
library(Cubist)
# cubistMod <- cubist(trainX, simulated$y)
cubistMod <- train(trainX, simulated$y, method="cubist")
(cubImp1 <- varImp(cubistMod, scale = FALSE))## cubist variable importance
##
## Overall
## V1 72.0
## V2 57.0
## V4 49.0
## V3 42.0
## V5 37.5
## V6 18.5
## V7 0.0
## duplicate1 0.0
## duplicate2 0.0
## V10 0.0
## V8 0.0
## V9 0.0Cubist definitely handles feature importance differently than randomForest. With cubist, the order of features switched.
Problem 8.2
Use a simulation to show tree bias with different granularities.
# Construct a simple dataset with a few features having different frequencies. Add copies of feature rows
# so some can be excluded from the target and we can create a simple linear model
rows <- list()
for (i in 1:1000) {
row <- list(i, floor(i/10), floor(i/100), i, floor(i/10), floor(i/100))
rows <- rbind(rows, row)
}
# Make sure everything is numeric
df <- as_tibble(rows)## Warning: The `x` argument of `as_tibble.matrix()` must have unique column names if `.name_repair` is omitted as of tibble 2.0.0.
## Using compatibility `.name_repair`.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_warnings()` to see where this warning was generated.df <- transform(df,
V1=as.numeric(V1),
V2=as.numeric(V2),
V3=as.numeric(V3),
V4=as.numeric(V4),
V5=as.numeric(V5),
V6=as.numeric(V6))
# Add a target variable, y, that is a simple linear combiation of V4, V5 and V6
df$y <- (2 * df$V4) + (2 * df$V5) + (2 * df$V6)
# Randomize row order
rows <- sample(nrow(df))
df <- df[rows, ]
# Run RandomForest
set.seed(200)
rfModel <- randomForest(y ~ ., data = df,
importance = TRUE,
ntree = 1000)
# Show Feature importance
(dfImp <- varImp(rfModel, scale = FALSE))## Overall
## V1 109427.41
## V2 56568.42
## V3 37698.98
## V4 115976.40
## V5 66579.70
## V6 31540.81In this simple dataset,
V1,V2andV3aren’t included in the linear formula fory; however, they are perfectly correlated withV4,V5, andV6so RandomForest incorrectly gives distribites the importance score across the irrelavant features since it cannot tell the difference. Next, the formula for y is a simple linear function, so each variableV4,V5andV6should contribute equal weight toyand have equal importance scores; however, due to bias, RF puts more importance on the features with more distinct values - in this caseV4has 1000 value whileV5has 100 value andV6only has 10 values.
Problem 8.3
In stochastic gradient boosting the bagging fraction and learning rate will govern the construction of the trees as they are guided by the gradient. Although the optimal values of these parameters should be obtained through the tuning process, it is helpful to understand how the magnitudes of these parameters affect magnitudes of variable importance. Figure 8.24 provides the variable importance plots for boosting using two extreme values for the bagging fraction (0.1 and 0.9) and the learning rate (0.1 and 0.9) for the solubility data. The left-hand plot has both parameters set to 0.1, and the right-hand plot has both set to 0.9:
Part (A)
Why does the model on the right focus its importance on just the first few of predictors, whereas the model on the left spreads importance across more predictors?
The bagged fraction governs how many sample will be used in each step to create a model and learning rate governs the percentage of the new prediction that will be added to the previous pass. The Figure on the right has learning rate = 0.9 and bagged fraction = 0.9. Since the bagged fraction is 0.9, 90% of sample will be drawn which represents most of the total available samples. As such, with each pass, our models will end up being fairly similar and each step will reinforce the previous steps. With a learning rate = 0.9, we are also reinforcing such that the models tend to be similar and inflate the most important features. The figure on the left, with learning rate = 0.1 and bagged fraction = 0.1, will generate tress with more diversity and thus lower down features have a chance to compete for attention - hence more importance given to lower down features.
Part (B)
Which model do you think would be more predictive of other samples?
The model on the right (0.9, 0.9) probably doesn’t generalize as well - as mentioned, by having high bagging fraction and learning rate, it hasn’t seen as many combinations of different trees so will overemphasize the few top features. The model on the LEFT (0.1, 0.1) has had a chance to weigh more combinations of different trees providing a better ensemble, lower error, and better generalization. The issue with too low a bagging fraction and/or learning rate is that a model might not have explored enough to learn all the patterns. However, from the text, we know that an ensemble with a bunch of weak learners can perform quite well. I think the LEFT is better, but it’s possible the rates are suboptimally low - we don’t know without some hyperparameter tuning.
Part (C)
How would increasing interaction depth affect the slope of predictor importance for either model in Fig. 8.24?
Interaction depth is the number of splits that need to be performed on a tree and increasing this increases the total number of nodes. If interactin depth is too low, we probably have very low accuracy (not enought resolution). As interaction depth increases, above a threshold, we probalky have too many nodes which wouild lead to overfitting and lack of generalization. Increasing interaction depth on the LEFT chart (0.1, 0.1) would probably provide more resolution, but with such a small learning rate, it might be counter productive. For the model on the RIGHT (0.9, 0.9), I would suspect increasing tree depth might actually hurt performance.
Problem 8.7
Refer to Exercises 6.3 and 7.5 which describe a chemical manufacturing process. Use the same data imputation, data splitting, and pre-processing steps as before and train several tree-based models:
Load & Clean Data
# NOTE: Code copied from my Homework #7
data("ChemicalManufacturingProcess")
cmp <- as_tibble(ChemicalManufacturingProcess)
x_raw <- cmp[,2:58]
y_raw <- as.matrix(cmp$Yield)
print(paste(nrow(x_raw), ncol(x_raw)))## [1] "176 57"## [1] "176 1"# Various NA plots to inspect data
knitr::kable(miss_var_summary(cmp) %>% filter(n_miss > 0),
caption = 'Missing Values',
format="html",
table.attr="style='width:50%;'") %>%
kableExtra::kable_styling()| variable | n_miss | pct_miss |
|---|---|---|
| ManufacturingProcess03 | 15 | 8.5227273 |
| ManufacturingProcess11 | 10 | 5.6818182 |
| ManufacturingProcess10 | 9 | 5.1136364 |
| ManufacturingProcess25 | 5 | 2.8409091 |
| ManufacturingProcess26 | 5 | 2.8409091 |
| ManufacturingProcess27 | 5 | 2.8409091 |
| ManufacturingProcess28 | 5 | 2.8409091 |
| ManufacturingProcess29 | 5 | 2.8409091 |
| ManufacturingProcess30 | 5 | 2.8409091 |
| ManufacturingProcess31 | 5 | 2.8409091 |
| ManufacturingProcess33 | 5 | 2.8409091 |
| ManufacturingProcess34 | 5 | 2.8409091 |
| ManufacturingProcess35 | 5 | 2.8409091 |
| ManufacturingProcess36 | 5 | 2.8409091 |
| ManufacturingProcess02 | 3 | 1.7045455 |
| ManufacturingProcess06 | 2 | 1.1363636 |
| ManufacturingProcess01 | 1 | 0.5681818 |
| ManufacturingProcess04 | 1 | 0.5681818 |
| ManufacturingProcess05 | 1 | 0.5681818 |
| ManufacturingProcess07 | 1 | 0.5681818 |
| ManufacturingProcess08 | 1 | 0.5681818 |
| ManufacturingProcess12 | 1 | 0.5681818 |
| ManufacturingProcess14 | 1 | 0.5681818 |
| ManufacturingProcess22 | 1 | 0.5681818 |
| ManufacturingProcess23 | 1 | 0.5681818 |
| ManufacturingProcess24 | 1 | 0.5681818 |
| ManufacturingProcess40 | 1 | 0.5681818 |
| ManufacturingProcess41 | 1 | 0.5681818 |
# Impute missing using KNN
x_imputed <- knn.impute(as.matrix(x_raw), k=10)
# Check for columns with little variance - candidate to drop
lowVariance <- nearZeroVar(x_imputed, names = TRUE)
head(lowVariance)## [1] "BiologicalMaterial07"lowVariance <- nearZeroVar(x_imputed)
x_lowvar <- x_imputed[,-lowVariance]
# Deal with outliers ... impute to median
x_outliers <- outlieR::impute(x_lowvar, fill='median')
# Find and drop high correlation features
correlations <- cor(x_outliers)
highCorr <- findCorrelation(correlations, names=TRUE, cutoff=0.9)
(highCorr)## [1] "BiologicalMaterial02" "ManufacturingProcess26" "BiologicalMaterial04"
## [4] "BiologicalMaterial12" "ManufacturingProcess11" "ManufacturingProcess27"
## [7] "ManufacturingProcess44" "ManufacturingProcess40"Split Training & Testing
# get training/test split
trainingRows <- createDataPartition(y_raw, p=0.8, list=FALSE)
# Build training datasets
trainX <- x_transf[trainingRows,]
trainY <- y_raw[trainingRows]
# put remaining rows into the test sets
testX <- x_transf[-trainingRows,]
testY <- y_raw[-trainingRows]
# Build a DF
trainingData <- as.data.frame(trainX)
trainingData$Yield <- trainYPart (A)
Which tree-based regression model gives the optimal resampling and test set performance?
RandomForest
set.seed(42424)
cl <- makePSOCKcluster(5)
registerDoParallel(cl)
## Create a specific candidate set of models to evaluate:
rfGrid <- expand.grid(
.mtry = c(2, 8, 14, 20, 26)
)
ctrl <- trainControl(method='cv', number=10)
rfTune <- train(trainX, trainY,
method = "rf",
tuneGrid = rfGrid,
trControl = ctrl)
stopCluster(cl)
# Model results
plot(rfTune)
## Length Class Mode
## call 4 -none- call
## type 1 -none- character
## predicted 144 -none- numeric
## mse 500 -none- numeric
## rsq 500 -none- numeric
## oob.times 144 -none- numeric
## importance 48 -none- numeric
## importanceSD 0 -none- NULL
## localImportance 0 -none- NULL
## proximity 0 -none- NULL
## ntree 1 -none- numeric
## mtry 1 -none- numeric
## forest 11 -none- list
## coefs 0 -none- NULL
## y 144 -none- numeric
## test 0 -none- NULL
## inbag 0 -none- NULL
## xNames 48 -none- character
## problemType 1 -none- character
## tuneValue 1 data.frame list
## obsLevels 1 -none- logical
## param 0 -none- list## rf variable importance
##
## only 20 most important variables shown (out of 48)
##
## Overall
## ManufacturingProcess32 100.000
## ManufacturingProcess13 22.699
## BiologicalMaterial06 17.613
## ManufacturingProcess36 13.810
## ManufacturingProcess06 13.066
## BiologicalMaterial03 12.956
## ManufacturingProcess17 12.704
## BiologicalMaterial11 10.211
## ManufacturingProcess09 9.384
## ManufacturingProcess31 8.052
## BiologicalMaterial01 7.057
## ManufacturingProcess15 4.963
## ManufacturingProcess28 4.756
## BiologicalMaterial08 4.597
## ManufacturingProcess21 4.181
## ManufacturingProcess30 3.816
## BiologicalMaterial09 3.782
## ManufacturingProcess39 3.420
## ManufacturingProcess24 3.321
## BiologicalMaterial10 3.141modelPred <- predict(rfTune, newdata=testX)
modelValues <- data.frame(obs = testY, pred=modelPred)
colnames(modelValues) = c('obs', 'pred')
(rf_values <- defaultSummary(modelValues))## RMSE Rsquared MAE
## 1.314611 0.564701 1.011440GBM
set.seed(42424)
cl <- makePSOCKcluster(5)
registerDoParallel(cl)
## Create a specific candidate set of models to evaluate:
gbmGrid <- expand.grid(
.interaction.depth = seq(1, 7, by = 2),
.n.trees = seq(100, 1000, by = 50),
.shrinkage = c(0.01, 0.1),
.n.minobsinnode = 10
)
ctrl <- trainControl(method='cv', number=10)
gbmTune <- train(trainX, trainY,
method = "gbm",
tuneGrid = gbmGrid,
trControl = ctrl,
verbose = FALSE)
stopCluster(cl)
# Model results
plot(gbmTune)
## var rel.inf
## ManufacturingProcess32 ManufacturingProcess32 29.44156537
## ManufacturingProcess13 ManufacturingProcess13 7.10962837
## ManufacturingProcess06 ManufacturingProcess06 5.48061730
## ManufacturingProcess17 ManufacturingProcess17 4.43533004
## BiologicalMaterial03 BiologicalMaterial03 3.54816389
## ManufacturingProcess09 ManufacturingProcess09 3.45464118
## ManufacturingProcess31 ManufacturingProcess31 3.10847311
## BiologicalMaterial06 BiologicalMaterial06 3.10328460
## ManufacturingProcess15 ManufacturingProcess15 3.07907842
## BiologicalMaterial11 BiologicalMaterial11 2.28273768
## BiologicalMaterial05 BiologicalMaterial05 2.20832881
## ManufacturingProcess36 ManufacturingProcess36 1.99751960
## ManufacturingProcess43 ManufacturingProcess43 1.89438624
## BiologicalMaterial09 BiologicalMaterial09 1.78256058
## ManufacturingProcess04 ManufacturingProcess04 1.73064022
## ManufacturingProcess05 ManufacturingProcess05 1.39865204
## ManufacturingProcess39 ManufacturingProcess39 1.38342492
## ManufacturingProcess18 ManufacturingProcess18 1.32249263
## ManufacturingProcess24 ManufacturingProcess24 1.30287458
## ManufacturingProcess20 ManufacturingProcess20 1.21963965
## BiologicalMaterial10 BiologicalMaterial10 1.21423432
## ManufacturingProcess30 ManufacturingProcess30 1.20948735
## ManufacturingProcess37 ManufacturingProcess37 1.17816723
## BiologicalMaterial01 BiologicalMaterial01 1.15879398
## BiologicalMaterial08 BiologicalMaterial08 1.02741630
## ManufacturingProcess21 ManufacturingProcess21 1.01617238
## ManufacturingProcess14 ManufacturingProcess14 1.00027002
## ManufacturingProcess01 ManufacturingProcess01 0.93775555
## ManufacturingProcess29 ManufacturingProcess29 0.88099138
## ManufacturingProcess45 ManufacturingProcess45 0.86580877
## ManufacturingProcess03 ManufacturingProcess03 0.84129183
## ManufacturingProcess16 ManufacturingProcess16 0.83916408
## ManufacturingProcess35 ManufacturingProcess35 0.80562454
## ManufacturingProcess19 ManufacturingProcess19 0.70792312
## ManufacturingProcess22 ManufacturingProcess22 0.68366881
## ManufacturingProcess25 ManufacturingProcess25 0.57619991
## ManufacturingProcess02 ManufacturingProcess02 0.57083886
## ManufacturingProcess23 ManufacturingProcess23 0.56506750
## ManufacturingProcess42 ManufacturingProcess42 0.51801931
## ManufacturingProcess28 ManufacturingProcess28 0.40754508
## ManufacturingProcess10 ManufacturingProcess10 0.39489666
## ManufacturingProcess33 ManufacturingProcess33 0.38088533
## ManufacturingProcess08 ManufacturingProcess08 0.23261377
## ManufacturingProcess07 ManufacturingProcess07 0.22501714
## ManufacturingProcess12 ManufacturingProcess12 0.20423852
## ManufacturingProcess38 ManufacturingProcess38 0.16941287
## ManufacturingProcess34 ManufacturingProcess34 0.05398256
## ManufacturingProcess41 ManufacturingProcess41 0.05047359## gbm variable importance
##
## only 20 most important variables shown (out of 48)
##
## Overall
## ManufacturingProcess32 100.000
## ManufacturingProcess13 24.018
## ManufacturingProcess06 18.475
## ManufacturingProcess17 14.919
## BiologicalMaterial03 11.901
## ManufacturingProcess09 11.582
## ManufacturingProcess31 10.405
## BiologicalMaterial06 10.387
## ManufacturingProcess15 10.304
## BiologicalMaterial11 7.595
## BiologicalMaterial05 7.342
## ManufacturingProcess36 6.625
## ManufacturingProcess43 6.274
## BiologicalMaterial09 5.893
## ManufacturingProcess04 5.717
## ManufacturingProcess05 4.587
## ManufacturingProcess39 4.535
## ManufacturingProcess18 4.328
## ManufacturingProcess24 4.261
## ManufacturingProcess20 3.978modelPred <- predict(gbmTune, newdata=testX)
modelValues <- data.frame(obs = testY, pred=modelPred)
colnames(modelValues) = c('obs', 'pred')
(gbm_values <- defaultSummary(modelValues))## RMSE Rsquared MAE
## 1.2592608 0.5920278 0.9807692Cubist
set.seed(42424)
cl <- makePSOCKcluster(5)
registerDoParallel(cl)
## Create a specific candidate set of models to evaluate:
cubGrid <- expand.grid(
.committees = c(1, 2, 4, 8, 16, 32, 64, 96),
.neighbors = c(0, 1, 5, 9)
)
ctrl <- trainControl(method='cv', number=10)
cubTune <- train(trainX, trainY,
method = "cubist",
tuneGrid = cubGrid)
stopCluster(cl)
# Model results
plot(cubTune)
##
## Call:
## cubist.default(x = x, y = y, committees = param$committees)
##
##
## Cubist [Release 2.07 GPL Edition] Wed Dec 2 22:06:05 2020
## ---------------------------------
##
## Target attribute `outcome'
##
## Read 144 cases (49 attributes) from undefined.data
##
## Model 1:
##
## Rule 1/1: [43 cases, mean 38.560, range 36.77 to 41.43, est err 0.583]
##
## if
## BiologicalMaterial06 <= -0.4236438
## ManufacturingProcess32 <= -0.04259344
## then
## outcome = 40.374 - 6.66 ManufacturingProcess39
## + 1.25 ManufacturingProcess42 - 0.78 ManufacturingProcess13
## + 0.51 ManufacturingProcess06 + 0.34 ManufacturingProcess32
## - 0.22 ManufacturingProcess33 + 0.15 ManufacturingProcess15
## - 0.05 ManufacturingProcess35
##
## Rule 1/2: [38 cases, mean 39.806, range 38.2 to 42.07, est err 0.545]
##
## if
## BiologicalMaterial06 > -0.4236438
## ManufacturingProcess32 <= -0.04259344
## then
## outcome = 40.144 + 0.59 ManufacturingProcess04
## + 0.54 ManufacturingProcess32 - 0.57 ManufacturingProcess17
## - 0.38 ManufacturingProcess31 + 0.25 ManufacturingProcess29
## - 0.24 ManufacturingProcess33 - 0.12 ManufacturingProcess20
## - 0.04 ManufacturingProcess13 + 0.02 ManufacturingProcess15
##
## Rule 1/3: [23 cases, mean 41.004, range 36.83 to 43.88, est err 0.784]
##
## if
## ManufacturingProcess13 > 0.3138531
## ManufacturingProcess32 > -0.04259344
## then
## outcome = 41.05 + 1.68 ManufacturingProcess32
## - 1.35 ManufacturingProcess13 + 0.46 ManufacturingProcess14
## + 0.39 ManufacturingProcess29 - 0.3 BiologicalMaterial01
## - 0.27 BiologicalMaterial06 + 0.25 BiologicalMaterial03
## - 0.24 ManufacturingProcess17 - 0.21 ManufacturingProcess33
## + 0.2 ManufacturingProcess04 - 0.15 BiologicalMaterial10
## - 0.12 ManufacturingProcess20 - 0.11 ManufacturingProcess18
## - 0.07 ManufacturingProcess24
##
## Rule 1/4: [40 cases, mean 41.869, range 38.99 to 46.34, est err 0.820]
##
## if
## ManufacturingProcess13 <= 0.3138531
## ManufacturingProcess32 > -0.04259344
## then
## outcome = 39.75 + 1.93 ManufacturingProcess32
## - 1.43 BiologicalMaterial06 + 1.35 BiologicalMaterial03
## - 0.82 BiologicalMaterial10 + 0.77 ManufacturingProcess29
## - 0.72 ManufacturingProcess13 - 0.58 ManufacturingProcess18
## + 0.36 ManufacturingProcess04 - 0.35 ManufacturingProcess24
## + 0.07 BiologicalMaterial11
##
## Model 2:
##
## Rule 2/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.007]
##
## outcome = 40.209 + 1.25 ManufacturingProcess32
## - 0.89 ManufacturingProcess13
##
## Model 3:
##
## Rule 3/1: [18 cases, mean 38.692, range 36.77 to 41.43, est err 1.436]
##
## if
## ManufacturingProcess32 <= -1.21499
## then
## outcome = 31.609 - 4.65 ManufacturingProcess32
## - 0.03 ManufacturingProcess36 + 0.02 ManufacturingProcess09
##
## Rule 3/2: [13 cases, mean 38.857, range 37.39 to 41.43, est err 2.315]
##
## if
## BiologicalMaterial10 <= -1.391486
## then
## outcome = 46.464 + 5.39 BiologicalMaterial10
## + 2.94 ManufacturingProcess05 - 3.09 ManufacturingProcess32
##
## Rule 3/3: [12 cases, mean 40.234, range 38.6 to 42.44, est err 3.495]
##
## if
## ManufacturingProcess01 <= -0.2871256
## ManufacturingProcess17 <= 0.5293865
## ManufacturingProcess32 > -1.21499
## then
## outcome = 36.82 - 2.13 ManufacturingProcess32
## - 1.36 ManufacturingProcess01 - 1.09 ManufacturingProcess17
## + 0.65 BiologicalMaterial01 + 0.54 ManufacturingProcess23
##
## Rule 3/4: [126 cases, mean 40.414, range 36.83 to 46.34, est err 1.071]
##
## if
## ManufacturingProcess32 > -1.21499
## then
## outcome = 40.468 + 1.4 ManufacturingProcess32
## + 0.89 ManufacturingProcess09 - 0.51 ManufacturingProcess28
## + 0.41 BiologicalMaterial08 - 0.23 ManufacturingProcess36
## + 0.17 ManufacturingProcess42 - 0.13 ManufacturingProcess24
## - 0.12 ManufacturingProcess21 + 0.1 ManufacturingProcess01
## + 0.04 ManufacturingProcess15
##
## Rule 3/5: [56 cases, mean 40.503, range 37.42 to 46.34, est err 1.268]
##
## if
## BiologicalMaterial09 > -0.6565034
## ManufacturingProcess01 > -0.2871256
## ManufacturingProcess17 <= 0.5293865
## ManufacturingProcess32 > -1.21499
## ManufacturingProcess42 > -0.1530976
## then
## outcome = 41.73 - 10.25 ManufacturingProcess42
## - 1.48 ManufacturingProcess24 + 1.57 ManufacturingProcess32
## - 1.31 ManufacturingProcess21 + 1.35 ManufacturingProcess09
## - 1.03 ManufacturingProcess36 - 0.7 ManufacturingProcess16
## - 0.59 BiologicalMaterial06 - 0.42 BiologicalMaterial09
## - 0.3 ManufacturingProcess01 - 0.3 ManufacturingProcess17
##
## Rule 3/6: [77 cases, mean 40.594, range 37.42 to 46.34, est err 1.480]
##
## if
## ManufacturingProcess17 <= 0.5293865
## ManufacturingProcess32 > -1.21499
## ManufacturingProcess42 > -0.1530976
## then
## outcome = 42.566 - 5.83 ManufacturingProcess42
## + 2.61 BiologicalMaterial03 - 2.01 BiologicalMaterial06
## - 1.44 BiologicalMaterial09 - 1.03 ManufacturingProcess01
## - 1.03 ManufacturingProcess17 - 0.95 ManufacturingProcess36
## - 0.74 ManufacturingProcess24
##
## Rule 3/7: [75 cases, mean 40.633, range 37.14 to 46.34, est err 1.293]
##
## if
## ManufacturingProcess01 > -0.2871256
## ManufacturingProcess17 <= 0.5293865
## ManufacturingProcess32 > -1.21499
## then
## outcome = 39.696 - 2.29 ManufacturingProcess01
## - 1.36 ManufacturingProcess36 - 1.38 ManufacturingProcess17
## + 0.13 ManufacturingProcess32 + 0.1 ManufacturingProcess09
## + 0.07 ManufacturingProcess42 - 0.05 ManufacturingProcess24
## - 0.05 ManufacturingProcess21
##
## Model 4:
##
## Rule 4/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.058]
##
## outcome = 39.901 + 1.34 ManufacturingProcess32
## - 1.02 ManufacturingProcess13 + 0.5 ManufacturingProcess04
##
## Model 5:
##
## Rule 5/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.090]
##
## outcome = 40.603 + 1.95 ManufacturingProcess32
## - 1.14 ManufacturingProcess33 - 1.06 ManufacturingProcess17
## + 0.79 ManufacturingProcess29
##
## Model 6:
##
## Rule 6/1: [43 cases, mean 38.560, range 36.77 to 41.43, est err 1.219]
##
## if
## BiologicalMaterial06 <= -0.4236438
## ManufacturingProcess32 <= -0.04259344
## then
## outcome = 36.874 - 0.78 ManufacturingProcess32
## + 0.1 ManufacturingProcess04 + 0.1 ManufacturingProcess30
## - 0.09 ManufacturingProcess16 + 0.09 ManufacturingProcess14
## - 0.09 ManufacturingProcess13 + 0.04 ManufacturingProcess18
##
## Rule 6/2: [81 cases, mean 39.144, range 36.77 to 42.07, est err 1.247]
##
## if
## ManufacturingProcess32 <= -0.04259344
## then
## outcome = 40.17 + 0.98 ManufacturingProcess04
## + 0.63 ManufacturingProcess32 + 0.43 ManufacturingProcess30
## - 0.4 ManufacturingProcess16 + 0.37 ManufacturingProcess14
## - 0.38 ManufacturingProcess13 + 0.19 ManufacturingProcess18
##
## Rule 6/3: [13 cases, mean 41.373, range 38.99 to 43.57, est err 2.732]
##
## if
## BiologicalMaterial03 <= -0.09240372
## ManufacturingProcess13 <= 0.3138531
## ManufacturingProcess32 > -0.04259344
## then
## outcome = 44.81 + 6.61 BiologicalMaterial03
## - 1.22 ManufacturingProcess24 - 0.79 ManufacturingProcess13
## + 0.07 ManufacturingProcess32 - 0.05 ManufacturingProcess05
## + 0.04 ManufacturingProcess04
##
## Rule 6/4: [63 cases, mean 41.554, range 36.83 to 46.34, est err 1.500]
##
## if
## ManufacturingProcess32 > -0.04259344
## then
## outcome = 41.662 - 1.81 ManufacturingProcess13
## + 1 ManufacturingProcess32 + 0.79 ManufacturingProcess04
## + 0.6 ManufacturingProcess14 + 0.22 ManufacturingProcess30
## - 0.2 ManufacturingProcess16 + 0.09 ManufacturingProcess18
##
## Rule 6/5: [40 cases, mean 41.869, range 38.99 to 46.34, est err 1.002]
##
## if
## ManufacturingProcess13 <= 0.3138531
## ManufacturingProcess32 > -0.04259344
## then
## outcome = 39.637 + 1.32 ManufacturingProcess32
## - 1.37 ManufacturingProcess13 - 1.11 ManufacturingProcess05
## - 0.9 ManufacturingProcess24 + 0.84 ManufacturingProcess04
##
## Rule 6/6: [21 cases, mean 42.182, range 39.4 to 46.34, est err 1.493]
##
## if
## BiologicalMaterial03 > -0.09240372
## BiologicalMaterial06 > 0.5418619
## ManufacturingProcess13 <= 0.3138531
## ManufacturingProcess32 > -0.04259344
## then
## outcome = 35.105 + 3.13 BiologicalMaterial06
## - 1.49 ManufacturingProcess13 + 0.62 BiologicalMaterial03
## + 0.42 ManufacturingProcess06
##
## Model 7:
##
## Rule 7/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.040]
##
## outcome = 39.988 + 1.98 ManufacturingProcess32
## - 1.18 ManufacturingProcess33 - 0.89 ManufacturingProcess17
## + 0.73 ManufacturingProcess29
##
## Model 8:
##
## Rule 8/1: [81 cases, mean 39.144, range 36.77 to 42.07, est err 1.192]
##
## if
## ManufacturingProcess32 <= -0.04259344
## then
## outcome = 38.262 + 1.21 ManufacturingProcess15
## - 0.51 ManufacturingProcess14 - 0.49 ManufacturingProcess32
## - 0.5 ManufacturingProcess13 - 0.31 ManufacturingProcess16
## - 0.28 ManufacturingProcess05
##
## Rule 8/2: [38 cases, mean 39.806, range 38.2 to 42.07, est err 1.018]
##
## if
## BiologicalMaterial06 > -0.4236438
## ManufacturingProcess32 <= -0.04259344
## then
## outcome = 40.806 - 0.85 BiologicalMaterial06
## + 0.63 ManufacturingProcess04 - 0.54 ManufacturingProcess22
## + 0.21 ManufacturingProcess15 - 0.1 ManufacturingProcess13
## - 0.09 ManufacturingProcess14 - 0.05 ManufacturingProcess05
## - 0.05 ManufacturingProcess16
##
## Rule 8/3: [23 cases, mean 41.004, range 36.83 to 43.88, est err 1.152]
##
## if
## ManufacturingProcess13 > 0.3138531
## ManufacturingProcess32 > -0.04259344
## then
## outcome = 43.08 - 2.53 ManufacturingProcess13
## + 0.74 ManufacturingProcess14 + 0.73 ManufacturingProcess32
## + 0.26 ManufacturingProcess04 - 0.22 BiologicalMaterial01
## + 0.16 BiologicalMaterial03
##
## Rule 8/4: [13 cases, mean 41.373, range 38.99 to 43.57, est err 2.543]
##
## if
## BiologicalMaterial03 <= -0.09240372
## ManufacturingProcess13 <= 0.3138531
## ManufacturingProcess32 > -0.04259344
## then
## outcome = 45.578 + 6.69 BiologicalMaterial03
## - 1.28 ManufacturingProcess24 - 0.77 ManufacturingProcess13
##
## Rule 8/5: [63 cases, mean 41.554, range 36.83 to 46.34, est err 1.282]
##
## if
## ManufacturingProcess32 > -0.04259344
## then
## outcome = 40.04 - 1.51 ManufacturingProcess13
## - 1.18 BiologicalMaterial01 + 1.09 ManufacturingProcess32
## + 1 BiologicalMaterial03 - 0.44 ManufacturingProcess24
## + 0.03 ManufacturingProcess04
##
## Model 9:
##
## Rule 9/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.003]
##
## outcome = 40.326 + 2.34 ManufacturingProcess32
## - 1.18 ManufacturingProcess33 + 0.57 ManufacturingProcess29
## - 0.59 ManufacturingProcess17 + 0.51 ManufacturingProcess04
## + 0.42 ManufacturingProcess30
##
## Model 10:
##
## Rule 10/1: [43 cases, mean 38.560, range 36.77 to 41.43, est err 1.107]
##
## if
## BiologicalMaterial06 <= -0.4236438
## ManufacturingProcess32 <= -0.04259344
## then
## outcome = 37.688 - 0.75 ManufacturingProcess33
## - 0.7 ManufacturingProcess03 + 0.1 ManufacturingProcess09
## - 0.08 ManufacturingProcess13 + 0.06 ManufacturingProcess32
## + 0.05 BiologicalMaterial03 - 0.04 BiologicalMaterial11
## + 0.04 ManufacturingProcess14 + 0.03 ManufacturingProcess06
##
## Rule 10/2: [38 cases, mean 39.806, range 38.2 to 42.07, est err 0.826]
##
## if
## BiologicalMaterial06 > -0.4236438
## ManufacturingProcess32 <= -0.04259344
## then
## outcome = 40.49 - 0.98 BiologicalMaterial08 + 0.88 BiologicalMaterial01
## - 0.75 BiologicalMaterial06 - 0.09 ManufacturingProcess13
## + 0.06 BiologicalMaterial03 + 0.06 ManufacturingProcess32
## + 0.05 ManufacturingProcess09 - 0.04 BiologicalMaterial11
## + 0.04 ManufacturingProcess14 + 0.03 ManufacturingProcess06
##
## Rule 10/3: [63 cases, mean 41.554, range 36.83 to 46.34, est err 1.161]
##
## if
## ManufacturingProcess32 > -0.04259344
## then
## outcome = 41.224 - 1.33 ManufacturingProcess28
## - 1.32 ManufacturingProcess13 + 1.15 ManufacturingProcess39
## + 0.71 BiologicalMaterial06 + 0.19 ManufacturingProcess32
## + 0.17 BiologicalMaterial03 + 0.12 ManufacturingProcess14
## - 0.11 BiologicalMaterial11 + 0.08 ManufacturingProcess06
##
## Model 11:
##
## Rule 11/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.105]
##
## outcome = 40.252 + 2.52 ManufacturingProcess30
## + 2.27 ManufacturingProcess25 + 1.42 ManufacturingProcess32
## - 0.92 ManufacturingProcess29 - 0.96 ManufacturingProcess17
## + 0.63 ManufacturingProcess04
##
## Model 12:
##
## Rule 12/1: [30 cases, mean 38.427, range 36.77 to 40.66, est err 1.360]
##
## if
## BiologicalMaterial06 <= -0.9291902
## then
## outcome = 37.7 - 15.95 ManufacturingProcess39
## - 2.78 BiologicalMaterial06 + 0.36 ManufacturingProcess24
## + 0.13 ManufacturingProcess32 + 0.1 ManufacturingProcess29
## + 0.08 BiologicalMaterial03 - 0.08 ManufacturingProcess33
## + 0.06 ManufacturingProcess02 - 0.06 ManufacturingProcess25
## - 0.05 BiologicalMaterial08
##
## Rule 12/2: [16 cases, mean 39.864, range 37.86 to 42.73, est err 2.843]
##
## if
## BiologicalMaterial06 > -0.9291902
## BiologicalMaterial06 <= -0.4236438
## ManufacturingProcess13 > -0.2913785
## then
## outcome = 30.949 - 14.66 BiologicalMaterial06
## - 1.79 ManufacturingProcess33 - 1.47 ManufacturingProcess05
## + 1.01 ManufacturingProcess32 - 0.9 ManufacturingProcess24
##
## Rule 12/3: [70 cases, mean 40.327, range 36.83 to 43.88, est err 1.159]
##
## if
## BiologicalMaterial06 > -0.9291902
## ManufacturingProcess13 > -0.2913785
## then
## outcome = 41.228 + 1.78 ManufacturingProcess29
## + 1.07 ManufacturingProcess02 - 1.05 ManufacturingProcess19
## + 0.89 ManufacturingProcess32 - 0.61 BiologicalMaterial08
## - 0.28 ManufacturingProcess25 - 0.24 ManufacturingProcess33
## + 0.16 BiologicalMaterial03 - 0.13 ManufacturingProcess30
##
## Rule 12/4: [48 cases, mean 41.076, range 38.13 to 46.34, est err 1.048]
##
## if
## ManufacturingProcess13 <= -0.2913785
## then
## outcome = 38.84 - 1.58 ManufacturingProcess13
## + 0.74 ManufacturingProcess32 + 0.68 BiologicalMaterial06
## + 0.61 ManufacturingProcess29 - 0.63 ManufacturingProcess25
## - 0.4 ManufacturingProcess33 - 0.35 ManufacturingProcess30
## + 0.26 BiologicalMaterial03 + 0.22 ManufacturingProcess02
## - 0.17 BiologicalMaterial08
##
## Model 13:
##
## Rule 13/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.106]
##
## outcome = 40.248 + 2.14 ManufacturingProcess30
## + 1.6 ManufacturingProcess25 + 1.41 ManufacturingProcess32
## - 1.21 ManufacturingProcess17 - 0.99 ManufacturingProcess15
## + 0.8 ManufacturingProcess14 + 0.64 ManufacturingProcess04
##
## Model 14:
##
## Rule 14/1: [43 cases, mean 38.560, range 36.77 to 41.43, est err 1.212]
##
## if
## BiologicalMaterial06 <= -0.4236438
## ManufacturingProcess32 <= -0.04259344
## then
## outcome = 42.213 - 16.53 ManufacturingProcess39
## - 1.31 ManufacturingProcess13 + 0.1 ManufacturingProcess15
## + 0.08 BiologicalMaterial06 + 0.08 ManufacturingProcess10
## + 0.07 ManufacturingProcess02 - 0.06 ManufacturingProcess05
##
## Rule 14/2: [38 cases, mean 39.806, range 38.2 to 42.07, est err 1.108]
##
## if
## BiologicalMaterial06 > -0.4236438
## ManufacturingProcess32 <= -0.04259344
## then
## outcome = 40.967 - 1.14 BiologicalMaterial08 + 0.88 BiologicalMaterial01
## - 0.76 BiologicalMaterial06 - 0.24 ManufacturingProcess37
## + 0.19 ManufacturingProcess45 + 0.04 ManufacturingProcess15
## - 0.03 ManufacturingProcess05 + 0.03 ManufacturingProcess10
## + 0.02 ManufacturingProcess02
##
## Rule 14/3: [63 cases, mean 41.554, range 36.83 to 46.34, est err 1.202]
##
## if
## ManufacturingProcess32 > -0.04259344
## then
## outcome = 41.104 + 0.41 ManufacturingProcess32
## - 0.4 ManufacturingProcess13 - 0.33 BiologicalMaterial10
## + 0.33 BiologicalMaterial06 + 0.28 ManufacturingProcess02
## + 0.31 ManufacturingProcess06
##
## Model 15:
##
## Rule 15/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.057]
##
## outcome = 40.255 + 1.97 ManufacturingProcess32
## - 1.05 ManufacturingProcess13 + 0.84 ManufacturingProcess04
## - 0.61 ManufacturingProcess33 + 0.58 ManufacturingProcess15
## + 0.54 ManufacturingProcess30
##
## Model 16:
##
## Rule 16/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.159]
##
## outcome = 40.141 + 1.66 ManufacturingProcess32
## - 0.79 ManufacturingProcess33 + 0.5 BiologicalMaterial03
##
## Model 17:
##
## Rule 17/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.290]
##
## outcome = 40.114 - 2.01 ManufacturingProcess13
## + 1.32 ManufacturingProcess32 + 1.11 ManufacturingProcess29
## - 0.94 ManufacturingProcess21 + 0.87 ManufacturingProcess04
## + 0.53 ManufacturingProcess17 - 0.51 ManufacturingProcess25
##
## Model 18:
##
## Rule 18/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.152]
##
## outcome = 40.298 + 1.25 ManufacturingProcess32
##
## Model 19:
##
## Rule 19/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.307]
##
## outcome = 40.071 - 4.02 ManufacturingProcess13
## + 2.6 ManufacturingProcess17 + 2.01 ManufacturingProcess32
## - 1.51 ManufacturingProcess21 - 1.41 ManufacturingProcess33
## + 1.12 ManufacturingProcess15 - 0.55 BiologicalMaterial08
## - 0.49 ManufacturingProcess35 + 0.47 BiologicalMaterial03
##
## Model 20:
##
## Rule 20/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.218]
##
## outcome = 40.257 + 1.26 ManufacturingProcess32
## + 0.66 ManufacturingProcess04 + 0.58 ManufacturingProcess29
## - 0.38 ManufacturingProcess16
##
## Model 21:
##
## Rule 21/1: [39 cases, mean 40.048, range 36.83 to 43.44, est err 1.038]
##
## if
## ManufacturingProcess17 > 0.5293865
## then
## outcome = 40.959 - 1.98 ManufacturingProcess17
## + 1.66 ManufacturingProcess32 + 0.61 BiologicalMaterial08
## - 0.21 ManufacturingProcess13 - 0.11 ManufacturingProcess21
## + 0.1 ManufacturingProcess30 - 0.1 ManufacturingProcess36
##
## Rule 21/2: [105 cases, mean 40.254, range 36.77 to 46.34, est err 1.147]
##
## if
## ManufacturingProcess17 <= 0.5293865
## then
## outcome = 39.635 - 1.16 ManufacturingProcess17
## - 0.9 ManufacturingProcess36 - 0.64 ManufacturingProcess13
## + 0.5 ManufacturingProcess06 + 0.38 ManufacturingProcess32
## - 0.33 ManufacturingProcess21 + 0.29 ManufacturingProcess30
##
## Model 22:
##
## Rule 22/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.172]
##
## outcome = 40.463 + 2.01 ManufacturingProcess32
## - 0.91 ManufacturingProcess33
##
## Model 23:
##
## Rule 23/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.237]
##
## outcome = 39.858 - 2.72 ManufacturingProcess13
## - 1.54 ManufacturingProcess21 + 1.26 ManufacturingProcess17
## + 0.98 ManufacturingProcess32 + 0.7 ManufacturingProcess29
##
## Model 24:
##
## Rule 24/1: [18 cases, mean 38.692, range 36.77 to 41.43, est err 1.540]
##
## if
## ManufacturingProcess32 <= -1.21499
## then
## outcome = 38.398 - 1.05 BiologicalMaterial01
## - 0.95 ManufacturingProcess35 + 0.21 ManufacturingProcess32
## - 0.13 ManufacturingProcess33 - 0.09 ManufacturingProcess36
##
## Rule 24/2: [126 cases, mean 40.414, range 36.83 to 46.34, est err 1.161]
##
## if
## ManufacturingProcess32 > -1.21499
## then
## outcome = 40.669 + 1.49 ManufacturingProcess32
## - 0.71 ManufacturingProcess33 + 0.44 BiologicalMaterial03
## - 0.45 ManufacturingProcess36 + 0.41 ManufacturingProcess09
## + 0.39 ManufacturingProcess39 + 0.39 ManufacturingProcess13
## + 0.29 ManufacturingProcess01 - 0.3 BiologicalMaterial11
##
## Rule 24/3: [40 cases, mean 41.213, range 38.65 to 46.34, est err 1.705]
##
## if
## BiologicalMaterial03 > -0.2606128
## ManufacturingProcess01 > 0.04361184
## then
## outcome = 42.044 + 2.2 ManufacturingProcess32
## - 1.25 BiologicalMaterial09 + 1.09 ManufacturingProcess39
## - 0.5 ManufacturingProcess19 - 0.24 ManufacturingProcess01
## + 0.12 BiologicalMaterial03
##
## Model 25:
##
## Rule 25/1: [23 cases, mean 38.401, range 36.77 to 42.58, est err 2.034]
##
## if
## BiologicalMaterial03 <= -0.3512033
## ManufacturingProcess13 > 0.1156042
## then
## outcome = 40.532 - 11.37 ManufacturingProcess39
## - 1.64 ManufacturingProcess17 - 0.51 BiologicalMaterial09
## + 0.36 ManufacturingProcess31 + 0.4 ManufacturingProcess09
## + 0.35 BiologicalMaterial08 + 0.32 BiologicalMaterial10
## - 0.29 BiologicalMaterial01 + 0.19 BiologicalMaterial03
##
## Rule 25/2: [72 cases, mean 39.814, range 36.77 to 43.88, est err 1.216]
##
## if
## ManufacturingProcess13 > 0.1156042
## then
## outcome = 40.587 - 1.48 ManufacturingProcess13
## - 0.78 BiologicalMaterial09 + 0.5 ManufacturingProcess32
## + 0.43 BiologicalMaterial10 + 0.37 ManufacturingProcess29
## - 0.29 ManufacturingProcess21 + 0.21 ManufacturingProcess04
## + 0.13 ManufacturingProcess09 + 0.11 ManufacturingProcess31
## + 0.11 BiologicalMaterial08 - 0.09 BiologicalMaterial01
## + 0.06 BiologicalMaterial03
##
## Rule 25/3: [72 cases, mean 40.583, range 37.39 to 46.34, est err 1.303]
##
## if
## ManufacturingProcess13 <= 0.1156042
## then
## outcome = 38.888 - 4.47 ManufacturingProcess17
## + 1.98 ManufacturingProcess21 + 1.37 ManufacturingProcess13
## + 1.18 ManufacturingProcess29 - 0.71 ManufacturingProcess24
## + 0.11 ManufacturingProcess32 + 0.05 ManufacturingProcess04
##
## Model 26:
##
## Rule 26/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.221]
##
## outcome = 40.657 + 2.32 ManufacturingProcess32
## - 1.09 ManufacturingProcess33 + 0.69 ManufacturingProcess39
## - 0.62 ManufacturingProcess28 + 0.43 ManufacturingProcess09
## + 0.37 BiologicalMaterial03
##
## Model 27:
##
## Rule 27/1: [48 cases, mean 39.222, range 36.77 to 44.16, est err 1.580]
##
## if
## BiologicalMaterial11 > -0.7828298
## ManufacturingProcess17 <= 0.6095197
## ManufacturingProcess36 > 0.1941933
## then
## outcome = 37.921 - 1.86 ManufacturingProcess17
## + 0.79 ManufacturingProcess12 - 0.34 ManufacturingProcess03
## + 0.22 ManufacturingProcess29 - 0.2 BiologicalMaterial11
## + 0.16 BiologicalMaterial03 - 0.17 ManufacturingProcess36
## + 0.03 ManufacturingProcess10 + 0.03 ManufacturingProcess04
## + 0.03 ManufacturingProcess32
##
## Rule 27/2: [63 cases, mean 39.294, range 36.77 to 44.16, est err 1.517]
##
## if
## ManufacturingProcess17 <= 0.6095197
## ManufacturingProcess36 > 0.1941933
## then
## outcome = 41.063 - 1.78 ManufacturingProcess17
## + 0.78 ManufacturingProcess29 - 0.77 BiologicalMaterial11
## + 0.58 BiologicalMaterial03 - 0.6 ManufacturingProcess36
## + 0.23 ManufacturingProcess12 + 0.11 ManufacturingProcess04
## + 0.09 ManufacturingProcess32 + 0.08 ManufacturingProcess10
## + 0.06 ManufacturingProcess15
##
## Rule 27/3: [34 cases, mean 40.118, range 36.83 to 43.44, est err 1.043]
##
## if
## ManufacturingProcess17 > 0.6095197
## then
## outcome = 40.75 - 1.58 ManufacturingProcess17
## + 1.07 ManufacturingProcess32 + 0.62 ManufacturingProcess29
## + 0.46 ManufacturingProcess04 + 0.34 ManufacturingProcess10
## - 0.35 ManufacturingProcess36 + 0.31 ManufacturingProcess12
## + 0.25 ManufacturingProcess15
##
## Rule 27/4: [110 cases, mean 40.223, range 36.77 to 46.34, est err 1.078]
##
## if
## ManufacturingProcess17 <= 0.6095197
## then
## outcome = 39.871 - 1.5 ManufacturingProcess17
## + 0.58 ManufacturingProcess29 + 0.55 ManufacturingProcess04
## - 0.59 ManufacturingProcess36 + 0.46 ManufacturingProcess32
## + 0.41 ManufacturingProcess10 + 0.38 ManufacturingProcess12
## + 0.3 ManufacturingProcess15 - 0.21 BiologicalMaterial11
## + 0.17 BiologicalMaterial03
##
## Model 28:
##
## Rule 28/1: [27 cases, mean 38.237, range 36.77 to 39.84, est err 1.089]
##
## if
## BiologicalMaterial06 <= -0.9291902
## ManufacturingProcess32 > -1.84024
## then
## outcome = 35.065 - 1.77 BiologicalMaterial06
## - 0.97 ManufacturingProcess05 + 0.09 ManufacturingProcess32
## - 0.03 ManufacturingProcess29 + 0.03 ManufacturingProcess39
## + 0.03 ManufacturingProcess06
##
## Rule 28/2: [4 cases, mean 39.702, range 38.42 to 40.66, est err 1.538]
##
## if
## ManufacturingProcess32 <= -1.84024
## then
## outcome = 40.343
##
## Rule 28/3: [140 cases, mean 40.213, range 36.77 to 46.34, est err 1.074]
##
## if
## ManufacturingProcess32 > -1.84024
## then
## outcome = 40.554 + 1.64 ManufacturingProcess32
## - 0.56 ManufacturingProcess29 + 0.51 ManufacturingProcess42
## + 0.46 ManufacturingProcess06 + 0.41 ManufacturingProcess09
## + 0.35 BiologicalMaterial05 + 0.11 ManufacturingProcess39
## + 0.1 BiologicalMaterial06
##
## Model 29:
##
## Rule 29/1: [34 cases, mean 40.118, range 36.83 to 43.44, est err 0.899]
##
## if
## ManufacturingProcess17 > 0.6095197
## then
## outcome = 40.762 - 1.32 ManufacturingProcess13
## + 1.2 ManufacturingProcess32 + 0.78 ManufacturingProcess29
## - 0.69 BiologicalMaterial06 - 0.7 ManufacturingProcess33
## + 0.65 BiologicalMaterial03 + 0.55 ManufacturingProcess14
## - 0.42 ManufacturingProcess28 - 0.32 ManufacturingProcess17
## + 0.13 ManufacturingProcess19
##
## Rule 29/2: [110 cases, mean 40.223, range 36.77 to 46.34, est err 1.061]
##
## if
## ManufacturingProcess17 <= 0.6095197
## then
## outcome = 39.523 + 1.2 ManufacturingProcess32
## - 1.12 ManufacturingProcess17 + 0.78 ManufacturingProcess29
## - 0.71 ManufacturingProcess33 - 0.63 ManufacturingProcess13
## - 0.33 BiologicalMaterial06 + 0.31 BiologicalMaterial03
## + 0.26 ManufacturingProcess14 - 0.2 ManufacturingProcess28
##
## Model 30:
##
## Rule 30/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.101]
##
## outcome = 40.494 + 1.07 ManufacturingProcess32
## + 0.76 ManufacturingProcess09 + 0.6 ManufacturingProcess04
## - 0.64 ManufacturingProcess36 - 0.41 ManufacturingProcess37
## + 0.41 ManufacturingProcess06
##
## Model 31:
##
## Rule 31/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.075]
##
## outcome = 39.886 + 1.69 ManufacturingProcess32
## - 1.13 ManufacturingProcess33 - 1.21 ManufacturingProcess17
## + 0.76 ManufacturingProcess29
##
## Model 32:
##
## Rule 32/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.098]
##
## outcome = 40.469 + 1.73 ManufacturingProcess32
## + 0.89 ManufacturingProcess09 + 0.75 ManufacturingProcess04
##
## Model 33:
##
## Rule 33/1: [34 cases, mean 40.118, range 36.83 to 43.44, est err 0.974]
##
## if
## ManufacturingProcess17 > 0.6095197
## then
## outcome = 40.541 + 1.33 ManufacturingProcess32
## - 0.95 ManufacturingProcess33 - 0.97 ManufacturingProcess17
## + 0.67 ManufacturingProcess29 + 0.19 BiologicalMaterial06
##
## Rule 33/2: [99 cases, mean 40.176, range 36.77 to 46.34, est err 1.182]
##
## if
## ManufacturingProcess17 <= 0.6095197
## ManufacturingProcess39 > -0.02781602
## then
## outcome = 42.424 - 12.62 ManufacturingProcess39
## - 2.54 ManufacturingProcess17 + 1.56 ManufacturingProcess29
## + 1.38 BiologicalMaterial06 - 1.12 BiologicalMaterial11
## - 0.81 ManufacturingProcess19 - 0.84 ManufacturingProcess33
## + 0.83 ManufacturingProcess32 - 0.75 ManufacturingProcess09
##
## Rule 33/3: [110 cases, mean 40.223, range 36.77 to 46.34, est err 1.882]
##
## if
## ManufacturingProcess17 <= 0.6095197
## then
## outcome = 41.445 + 0.67 ManufacturingProcess39
## - 0.37 ManufacturingProcess17 + 0.33 ManufacturingProcess32
## - 0.27 ManufacturingProcess33 + 0.2 ManufacturingProcess29
##
## Rule 33/4: [14 cases, mean 42.004, range 38.6 to 46.34, est err 1.043]
##
## if
## ManufacturingProcess02 <= 0.1966117
## ManufacturingProcess17 <= 0.6095197
## ManufacturingProcess39 > -0.02781602
## then
## outcome = 42.133 - 5.47 ManufacturingProcess39
## - 2.82 ManufacturingProcess17 + 0.76 ManufacturingProcess29
## + 0.69 BiologicalMaterial06 - 0.56 BiologicalMaterial11
## - 0.41 ManufacturingProcess19 - 0.39 ManufacturingProcess33
## + 0.38 ManufacturingProcess32 - 0.38 ManufacturingProcess09
##
## Model 34:
##
## Rule 34/1: [43 cases, mean 38.560, range 36.77 to 41.43, est err 1.323]
##
## if
## BiologicalMaterial06 <= -0.4236438
## ManufacturingProcess32 <= -0.04259344
## then
## outcome = 37.753 + 0.89 BiologicalMaterial06 - 0.53 BiologicalMaterial03
## + 0.6 ManufacturingProcess06 - 0.36 BiologicalMaterial11
## + 0.31 BiologicalMaterial09 - 0.27 ManufacturingProcess31
## + 0.19 ManufacturingProcess04 - 0.16 ManufacturingProcess05
##
## Rule 34/2: [81 cases, mean 39.144, range 36.77 to 42.07, est err 1.076]
##
## if
## ManufacturingProcess32 <= -0.04259344
## then
## outcome = 39.978 + 0.91 ManufacturingProcess04
## + 0.78 BiologicalMaterial06 + 0.81 ManufacturingProcess32
## - 0.46 BiologicalMaterial03 - 0.39 ManufacturingProcess13
## - 0.32 BiologicalMaterial11 + 0.27 BiologicalMaterial09
## - 0.24 ManufacturingProcess31 - 0.14 ManufacturingProcess05
##
## Rule 34/3: [63 cases, mean 41.554, range 36.83 to 46.34, est err 1.341]
##
## if
## ManufacturingProcess32 > -0.04259344
## then
## outcome = 40.245 + 2.37 ManufacturingProcess32
## - 1.23 ManufacturingProcess13 + 0.93 ManufacturingProcess04
## - 0.71 ManufacturingProcess28
##
## Model 35:
##
## Rule 35/1: [98 cases, mean 39.618, range 36.77 to 44.35, est err 1.140]
##
## if
## ManufacturingProcess31 > -0.1850009
## then
## outcome = 40.001 + 1.11 ManufacturingProcess32
## - 1.02 ManufacturingProcess33 + 0.61 ManufacturingProcess29
## - 0.69 ManufacturingProcess13 + 0.51 ManufacturingProcess14
## - 0.52 ManufacturingProcess36 - 0.44 ManufacturingProcess25
## - 0.25 ManufacturingProcess31
##
## Rule 35/2: [46 cases, mean 41.436, range 38 to 46.34, est err 0.968]
##
## if
## ManufacturingProcess31 <= -0.1850009
## then
## outcome = 40.447 - 0.73 ManufacturingProcess33
## + 0.67 ManufacturingProcess32 + 0.52 ManufacturingProcess09
## - 0.5 ManufacturingProcess13 + 0.43 ManufacturingProcess29
## + 0.36 ManufacturingProcess14 - 0.37 ManufacturingProcess36
## - 0.31 ManufacturingProcess25 + 0.19 ManufacturingProcess19
##
## Model 36:
##
## Rule 36/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.142]
##
## outcome = 40.284 + 1.74 ManufacturingProcess32
## - 0.97 ManufacturingProcess17 + 0.85 ManufacturingProcess04
## - 0.46 ManufacturingProcess16 + 0.41 ManufacturingProcess29
## + 0.27 BiologicalMaterial03
##
## Model 37:
##
## Rule 37/1: [88 cases, mean 39.571, range 36.77 to 44.35, est err 1.245]
##
## if
## ManufacturingProcess31 > -0.1054403
## ManufacturingProcess39 > -0.07991989
## then
## outcome = 41.61 - 9.82 ManufacturingProcess39
## - 1.98 ManufacturingProcess10 - 1.76 ManufacturingProcess16
## - 1.82 ManufacturingProcess13 + 1.53 BiologicalMaterial05
## - 1.37 BiologicalMaterial11 + 0.8 ManufacturingProcess09
## + 0.96 ManufacturingProcess43 + 0.19 ManufacturingProcess32
## - 0.16 ManufacturingProcess33 + 0.1 ManufacturingProcess15
## - 0.08 ManufacturingProcess01
##
## Rule 37/2: [9 cases, mean 40.151, range 38.9 to 42.23, est err 1.668]
##
## if
## ManufacturingProcess31 > -0.1054403
## ManufacturingProcess39 <= -0.07991989
## then
## outcome = 40.834 + 0.49 ManufacturingProcess39
## - 0.44 ManufacturingProcess10 - 0.37 ManufacturingProcess16
## - 0.38 ManufacturingProcess13 + 0.32 BiologicalMaterial05
## - 0.24 ManufacturingProcess01 - 0.22 BiologicalMaterial11
##
## Rule 37/3: [47 cases, mean 41.383, range 38 to 46.34, est err 1.114]
##
## if
## ManufacturingProcess31 <= -0.1054403
## then
## outcome = 40.966 + 1.31 ManufacturingProcess32
## - 1.11 ManufacturingProcess33 - 0.83 ManufacturingProcess13
## + 0.69 ManufacturingProcess15
##
## Model 38:
##
## Rule 38/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.191]
##
## outcome = 40.268 + 2.04 ManufacturingProcess32
## - 1.22 ManufacturingProcess17 + 1.03 ManufacturingProcess04
## + 0.59 ManufacturingProcess29 - 0.5 ManufacturingProcess15
##
## Model 39:
##
## Rule 39/1: [30 cases, mean 38.427, range 36.77 to 40.66, est err 1.748]
##
## if
## BiologicalMaterial06 <= -0.9291902
## then
## outcome = 37.99 - 13.41 ManufacturingProcess39
## - 1.65 BiologicalMaterial03 - 1.36 ManufacturingProcess33
##
## Rule 39/2: [123 cases, mean 39.976, range 36.77 to 46.34, est err 1.116]
##
## if
## ManufacturingProcess31 > -0.8959645
## then
## outcome = 40.517 + 1.16 ManufacturingProcess32
## - 1.1 ManufacturingProcess33 + 0.66 ManufacturingProcess15
## + 0.56 ManufacturingProcess29 - 0.53 ManufacturingProcess16
## - 0.56 ManufacturingProcess25 - 0.56 ManufacturingProcess36
## - 0.35 ManufacturingProcess31
##
## Rule 39/3: [20 cases, mean 41.679, range 39.3 to 43.57, est err 1.114]
##
## if
## BiologicalMaterial06 > -0.9291902
## ManufacturingProcess31 <= -0.8959645
## then
## outcome = 41.77 + 0.75 ManufacturingProcess09
## - 0.1 ManufacturingProcess33 + 0.08 ManufacturingProcess15
## + 0.08 ManufacturingProcess32 + 0.06 ManufacturingProcess29
## - 0.06 ManufacturingProcess16 - 0.06 ManufacturingProcess25
## - 0.06 ManufacturingProcess36
##
## Model 40:
##
## Rule 40/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.147]
##
## outcome = 40.091 + 1.96 ManufacturingProcess32
## - 1.25 ManufacturingProcess13 + 0.84 ManufacturingProcess04
##
## Model 41:
##
## Rule 41/1: [30 cases, mean 38.427, range 36.77 to 40.66, est err 1.201]
##
## if
## BiologicalMaterial06 <= -0.9291902
## then
## outcome = 38.915 - 16.62 ManufacturingProcess39
## - 2.25 BiologicalMaterial06 + 0.25 ManufacturingProcess29
## + 0.22 ManufacturingProcess02 + 0.2 ManufacturingProcess30
## - 0.19 BiologicalMaterial11 + 0.13 ManufacturingProcess14
## + 0.1 ManufacturingProcess34 - 0.1 ManufacturingProcess15
## - 0.08 ManufacturingProcess21 + 0.06 ManufacturingProcess31
## - 0.06 ManufacturingProcess35
##
## Rule 41/2: [114 cases, mean 40.665, range 36.83 to 46.34, est err 1.235]
##
## if
## BiologicalMaterial06 > -0.9291902
## then
## outcome = 40.527 + 1.71 BiologicalMaterial06
## + 1.36 ManufacturingProcess29 + 1.04 ManufacturingProcess02
## + 1.03 ManufacturingProcess30 - 0.88 BiologicalMaterial11
## + 0.6 ManufacturingProcess14 + 0.56 ManufacturingProcess39
## - 0.53 ManufacturingProcess21 + 0.48 ManufacturingProcess34
## - 0.48 ManufacturingProcess15 + 0.29 ManufacturingProcess31
## - 0.28 ManufacturingProcess35
##
## Model 42:
##
## Rule 42/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.192]
##
## outcome = 40.139 + 2.02 ManufacturingProcess32
## - 1.33 ManufacturingProcess13 + 0.94 ManufacturingProcess04
##
## Model 43:
##
## Rule 43/1: [30 cases, mean 38.427, range 36.77 to 40.66, est err 1.599]
##
## if
## BiologicalMaterial06 <= -0.9291902
## then
## outcome = 37.965 - 18.88 ManufacturingProcess39
## - 3.42 BiologicalMaterial06 - 0.75 ManufacturingProcess21
## - 0.09 ManufacturingProcess33 + 0.08 ManufacturingProcess32
## + 0.06 ManufacturingProcess29 - 0.05 ManufacturingProcess20
## + 0.04 ManufacturingProcess15
##
## Rule 43/2: [52 cases, mean 39.913, range 36.77 to 44.16, est err 0.942]
##
## if
## ManufacturingProcess21 > -0.1372423
## ManufacturingProcess31 > -0.8959645
## then
## outcome = 41.099 - 1.18 ManufacturingProcess31
## + 1.27 ManufacturingProcess32 + 0.82 ManufacturingProcess14
## - 0.79 ManufacturingProcess15 - 0.8 ManufacturingProcess33
## - 0.54 ManufacturingProcess21 + 0.33 ManufacturingProcess29
## - 0.36 ManufacturingProcess17 - 0.15 ManufacturingProcess20
## - 0.08 ManufacturingProcess35
##
## Rule 43/3: [71 cases, mean 40.022, range 37.14 to 46.34, est err 1.398]
##
## if
## ManufacturingProcess21 <= -0.1372423
## ManufacturingProcess31 > -0.8959645
## then
## outcome = 39.697 - 2.39 ManufacturingProcess31
## + 2.57 ManufacturingProcess32 - 1.68 ManufacturingProcess33
## - 1.38 ManufacturingProcess21 + 1.33 ManufacturingProcess14
## - 0.2 ManufacturingProcess15 + 0.03 ManufacturingProcess29
##
## Rule 43/4: [20 cases, mean 41.679, range 39.3 to 43.57, est err 1.278]
##
## if
## BiologicalMaterial06 > -0.9291902
## ManufacturingProcess31 <= -0.8959645
## then
## outcome = 41.696 + 0.45 ManufacturingProcess29
## + 0.43 ManufacturingProcess32 - 0.39 ManufacturingProcess33
## - 0.26 ManufacturingProcess21 - 0.2 ManufacturingProcess20
## - 0.11 ManufacturingProcess35
##
## Model 44:
##
## Rule 44/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.196]
##
## outcome = 40.001 + 1.92 ManufacturingProcess32
## - 1.37 ManufacturingProcess13 + 0.97 ManufacturingProcess04
##
## Model 45:
##
## Rule 45/1: [30 cases, mean 38.427, range 36.77 to 40.66, est err 1.254]
##
## if
## BiologicalMaterial06 <= -0.9291902
## then
## outcome = 39.009 - 18.35 ManufacturingProcess39
## - 2.7 BiologicalMaterial06 + 0.17 ManufacturingProcess29
## + 0.15 ManufacturingProcess32 - 0.14 ManufacturingProcess33
## - 0.09 ManufacturingProcess20 - 0.08 ManufacturingProcess21
##
## Rule 45/2: [114 cases, mean 40.665, range 36.83 to 46.34, est err 1.307]
##
## if
## BiologicalMaterial06 > -0.9291902
## then
## outcome = 40.701 + 1.54 ManufacturingProcess29
## + 1.49 ManufacturingProcess32 - 1.36 ManufacturingProcess33
## - 0.78 ManufacturingProcess21 - 0.67 ManufacturingProcess20
##
## Model 46:
##
## Rule 46/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.249]
##
## outcome = 39.974 + 1.83 ManufacturingProcess32
## - 1.5 ManufacturingProcess13 + 1.12 ManufacturingProcess04
##
## Model 47:
##
## Rule 47/1: [30 cases, mean 38.427, range 36.77 to 40.66, est err 1.349]
##
## if
## BiologicalMaterial06 <= -0.9291902
## then
## outcome = 39.192 - 20 ManufacturingProcess39 - 2.69 BiologicalMaterial06
## + 0.03 ManufacturingProcess42 + 0.03 ManufacturingProcess32
## + 0.03 ManufacturingProcess09 + 0.03 ManufacturingProcess13
## - 0.03 ManufacturingProcess17 - 0.02 BiologicalMaterial03
##
## Rule 47/2: [114 cases, mean 40.665, range 36.83 to 46.34, est err 1.186]
##
## if
## BiologicalMaterial06 > -0.9291902
## then
## outcome = 40.558 + 0.94 BiologicalMaterial06
## + 0.8 ManufacturingProcess32 + 0.74 ManufacturingProcess42
## - 0.81 ManufacturingProcess17 + 0.73 ManufacturingProcess09
## - 0.63 BiologicalMaterial03 + 0.67 ManufacturingProcess13
## + 0.47 BiologicalMaterial05
##
## Model 48:
##
## Rule 48/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.186]
##
## outcome = 39.939 + 1.69 ManufacturingProcess32
## - 1.4 ManufacturingProcess13 + 0.98 ManufacturingProcess04
##
## Model 49:
##
## Rule 49/1: [30 cases, mean 38.427, range 36.77 to 40.66, est err 1.577]
##
## if
## BiologicalMaterial06 <= -0.9291902
## then
## outcome = 38.509 - 19.35 ManufacturingProcess39
## - 3.25 BiologicalMaterial06 + 0.6 ManufacturingProcess14
## + 0.04 ManufacturingProcess15 - 0.03 ManufacturingProcess16
##
## Rule 49/2: [114 cases, mean 40.665, range 36.83 to 46.34, est err 1.325]
##
## if
## BiologicalMaterial06 > -0.9291902
## then
## outcome = 40.714 + 1.56 ManufacturingProcess15
## - 1.2 ManufacturingProcess16 + 0.62 BiologicalMaterial05
## - 0.39 ManufacturingProcess04 + 0.43 ManufacturingProcess06
##
## Model 50:
##
## Rule 50/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.069]
##
## outcome = 39.933 + 1.39 ManufacturingProcess32
## - 1.18 ManufacturingProcess13
##
## Model 51:
##
## Rule 51/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.306]
##
## outcome = 40.452 + 1.62 ManufacturingProcess15
## + 1.65 ManufacturingProcess32 - 1.36 ManufacturingProcess33
## - 0.93 ManufacturingProcess16
##
## Model 52:
##
## Rule 52/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.305]
##
## outcome = 39.898 - 3.04 ManufacturingProcess13
## + 1.61 ManufacturingProcess32 + 1.47 ManufacturingProcess17
## - 0.86 ManufacturingProcess21 + 0.59 ManufacturingProcess04
##
## Model 53:
##
## Rule 53/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.352]
##
## outcome = 40.494 + 1.71 ManufacturingProcess32
## - 1.46 ManufacturingProcess33 + 1.26 ManufacturingProcess14
## + 0.96 ManufacturingProcess30 - 0.69 ManufacturingProcess16
## + 0.6 ManufacturingProcess19 + 0.28 BiologicalMaterial03
##
## Model 54:
##
## Rule 54/1: [72 cases, mean 39.814, range 36.77 to 43.88, est err 1.159]
##
## if
## ManufacturingProcess13 > 0.1156042
## then
## outcome = 39.857 + 1.76 ManufacturingProcess32
## + 1.13 ManufacturingProcess09 - 0.87 BiologicalMaterial11
## - 0.61 ManufacturingProcess20 - 0.21 ManufacturingProcess15
## - 0.17 ManufacturingProcess17 + 0.14 ManufacturingProcess29
## - 0.11 ManufacturingProcess10 + 0.09 ManufacturingProcess01
## + 0.07 BiologicalMaterial05 + 0.08 ManufacturingProcess06
##
## Rule 54/2: [72 cases, mean 40.583, range 37.39 to 46.34, est err 1.113]
##
## if
## ManufacturingProcess13 <= 0.1156042
## then
## outcome = 39.196 - 1.59 ManufacturingProcess13
## + 0.63 BiologicalMaterial05 + 0.64 ManufacturingProcess32
## - 0.5 ManufacturingProcess15 - 0.46 ManufacturingProcess24
## - 0.39 ManufacturingProcess17 + 0.32 ManufacturingProcess29
## - 0.27 ManufacturingProcess10 + 0.28 ManufacturingProcess09
## + 0.21 ManufacturingProcess01 - 0.22 BiologicalMaterial11
## + 0.18 ManufacturingProcess06
##
## Model 55:
##
## Rule 55/1: [65 cases, mean 39.586, range 36.77 to 44.16, est err 0.927]
##
## if
## ManufacturingProcess15 <= -0.1704276
## then
## outcome = 39.79 + 1.48 ManufacturingProcess32
## - 0.81 ManufacturingProcess01 - 0.6 ManufacturingProcess25
## + 0.1 ManufacturingProcess42 + 0.09 ManufacturingProcess15
## + 0.08 ManufacturingProcess09 + 0.05 BiologicalMaterial05
##
## Rule 55/2: [79 cases, mean 40.702, range 37.3 to 46.34, est err 1.695]
##
## if
## ManufacturingProcess15 > -0.1704276
## then
## outcome = 40.677 + 1.25 ManufacturingProcess42
## + 1.14 ManufacturingProcess29 - 0.94 ManufacturingProcess28
## + 0.89 BiologicalMaterial05 - 0.8 ManufacturingProcess20
## + 0.53 BiologicalMaterial03 + 0.51 ManufacturingProcess15
## + 0.04 ManufacturingProcess32 + 0.03 ManufacturingProcess09
##
## Model 56:
##
## Rule 56/1: [66 cases, mean 39.804, range 36.77 to 43.88, est err 1.277]
##
## if
## ManufacturingProcess13 > 0.2151572
## then
## outcome = 39.965 + 1.82 ManufacturingProcess32
## + 1.33 ManufacturingProcess02 - 1.15 ManufacturingProcess31
## + 0.92 BiologicalMaterial06 - 0.82 BiologicalMaterial11
## - 0.54 ManufacturingProcess01 - 0.48 ManufacturingProcess18
## + 0.4 ManufacturingProcess09 - 0.29 ManufacturingProcess15
## - 0.25 ManufacturingProcess37 - 0.1 ManufacturingProcess13
## - 0.04 ManufacturingProcess33
##
## Rule 56/2: [78 cases, mean 40.532, range 37.39 to 46.34, est err 1.234]
##
## if
## ManufacturingProcess13 <= 0.2151572
## then
## outcome = 39.205 - 2.2 ManufacturingProcess13
## + 1.32 ManufacturingProcess32 - 0.26 ManufacturingProcess33
## - 0.21 BiologicalMaterial11
##
## Rule 56/3: [15 cases, mean 41.697, range 40.38 to 43.88, est err 1.404]
##
## if
## ManufacturingProcess13 > 0.2151572
## ManufacturingProcess32 > 0.5076501
## then
## outcome = 43.814 - 2.91 ManufacturingProcess13
## - 1.39 BiologicalMaterial11 + 0.39 ManufacturingProcess02
## - 0.34 ManufacturingProcess31 + 0.3 ManufacturingProcess32
## + 0.27 BiologicalMaterial06 + 0.12 ManufacturingProcess09
## - 0.09 ManufacturingProcess15 - 0.07 ManufacturingProcess37
##
## Model 57:
##
## Rule 57/1: [65 cases, mean 39.586, range 36.77 to 44.16, est err 1.049]
##
## if
## ManufacturingProcess15 <= -0.1704276
## then
## outcome = 39.82 + 1.35 ManufacturingProcess32
## + 0.41 ManufacturingProcess15 - 0.39 ManufacturingProcess33
## - 0.22 ManufacturingProcess16 + 0.22 ManufacturingProcess04
## + 0.2 ManufacturingProcess29 + 0.14 BiologicalMaterial11
##
## Rule 57/2: [79 cases, mean 40.702, range 37.3 to 46.34, est err 1.598]
##
## if
## ManufacturingProcess15 > -0.1704276
## then
## outcome = 41.379 - 1.46 ManufacturingProcess31
## - 0.87 ManufacturingProcess30 + 0.7 ManufacturingProcess04
## + 0.57 BiologicalMaterial05 + 0.58 ManufacturingProcess32
## - 0.53 ManufacturingProcess20 + 0.54 ManufacturingProcess15
## - 0.52 ManufacturingProcess33 - 0.29 ManufacturingProcess16
## + 0.27 ManufacturingProcess29 + 0.19 BiologicalMaterial11
##
## Model 58:
##
## Rule 58/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.378]
##
## outcome = 39.809 + 2.05 ManufacturingProcess32
## - 1.74 ManufacturingProcess13 - 0.72 ManufacturingProcess33
## - 0.64 BiologicalMaterial11 + 0.35 BiologicalMaterial06
##
## Model 59:
##
## Rule 59/1: [65 cases, mean 39.586, range 36.77 to 44.16, est err 1.157]
##
## if
## ManufacturingProcess15 <= -0.1704276
## then
## outcome = 39.868 + 1 ManufacturingProcess32
## - 0.76 ManufacturingProcess01 + 0.45 ManufacturingProcess17
## - 0.39 ManufacturingProcess19 - 0.31 ManufacturingProcess21
## - 0.32 ManufacturingProcess13 + 0.19 ManufacturingProcess15
## - 0.2 ManufacturingProcess36 + 0.18 ManufacturingProcess42
## + 0.12 ManufacturingProcess09 + 0.11 BiologicalMaterial06
## + 0.1 ManufacturingProcess02 + 0.09 BiologicalMaterial05
##
## Rule 59/2: [79 cases, mean 40.702, range 37.3 to 46.34, est err 1.776]
##
## if
## ManufacturingProcess15 > -0.1704276
## then
## outcome = 40.484 + 1.19 ManufacturingProcess15
## + 1.03 BiologicalMaterial06 + 0.65 ManufacturingProcess09
## - 0.58 BiologicalMaterial05 + 0.14 ManufacturingProcess17
## - 0.1 ManufacturingProcess21 - 0.1 ManufacturingProcess13
## - 0.07 ManufacturingProcess36 + 0.06 ManufacturingProcess42
## + 0.03 ManufacturingProcess02
##
## Rule 59/3: [57 cases, mean 40.899, range 37.89 to 46.34, est err 1.640]
##
## if
## BiologicalMaterial08 > -0.3356996
## ManufacturingProcess15 > -0.1704276
## then
## outcome = 41.176 + 1.32 ManufacturingProcess45
## + 1.2 BiologicalMaterial05 + 0.57 ManufacturingProcess29
## + 0.03 BiologicalMaterial06
##
## Rule 59/4: [11 cases, mean 41.827, range 39.58 to 43.88, est err 2.910]
##
## if
## BiologicalMaterial05 > -1.381866
## BiologicalMaterial08 <= -0.3356996
## ManufacturingProcess15 > -0.1704276
## ManufacturingProcess45 <= 0.1604411
## then
## outcome = 44.252
##
## Model 60:
##
## Rule 60/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.349]
##
## outcome = 39.708 - 1.96 ManufacturingProcess13
## + 1.51 ManufacturingProcess32 + 0.63 ManufacturingProcess04
##
## Model 61:
##
## Rule 61/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.410]
##
## outcome = 40.736 + 2.03 ManufacturingProcess32
## - 1.4 ManufacturingProcess33 + 0.97 ManufacturingProcess15
##
## Model 62:
##
## Rule 62/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.387]
##
## outcome = 39.699 - 2.04 ManufacturingProcess13
## + 1.51 ManufacturingProcess32 + 0.65 ManufacturingProcess04
##
## Model 63:
##
## Rule 63/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.403]
##
## outcome = 40.545 + 1.77 ManufacturingProcess32
## - 1.4 ManufacturingProcess33 - 0.94 ManufacturingProcess10
## + 0.74 ManufacturingProcess29 + 0.73 ManufacturingProcess30
## + 0.37 BiologicalMaterial03
##
## Model 64:
##
## Rule 64/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.357]
##
## outcome = 39.743 - 1.96 ManufacturingProcess13
## + 1.6 ManufacturingProcess32 + 0.84 ManufacturingProcess04
##
## Model 65:
##
## Rule 65/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.318]
##
## outcome = 40.514 + 1.09 ManufacturingProcess29
## - 0.8 ManufacturingProcess36 - 0.77 ManufacturingProcess25
## - 0.66 ManufacturingProcess10 + 0.38 BiologicalMaterial03
##
## Model 66:
##
## Rule 66/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.318]
##
## outcome = 39.882 + 2.86 ManufacturingProcess32
## - 1.78 ManufacturingProcess13 - 1.37 ManufacturingProcess33
## + 0.87 ManufacturingProcess04
##
## Model 67:
##
## Rule 67/1: [24 cases, mean 38.293, range 36.77 to 40.66, est err 1.522]
##
## if
## BiologicalMaterial06 <= -0.9291902
## ManufacturingProcess15 > -0.8591353
## then
## outcome = 41.592 - 16.98 ManufacturingProcess39
## + 1.54 ManufacturingProcess15 - 1.33 BiologicalMaterial01
##
## Rule 67/2: [20 cases, mean 39.674, range 37.86 to 42.73, est err 1.610]
##
## if
## BiologicalMaterial06 > -0.9291902
## BiologicalMaterial06 <= -0.4236438
## ManufacturingProcess15 > -0.8591353
## then
## outcome = 30.109 - 15.38 BiologicalMaterial06
## - 0.93 ManufacturingProcess36 - 0.64 BiologicalMaterial05
## + 0.11 ManufacturingProcess15 - 0.06 BiologicalMaterial11
## - 0.05 ManufacturingProcess16 + 0.04 ManufacturingProcess45
## + 0.02 ManufacturingProcess30
##
## Rule 67/3: [22 cases, mean 39.955, range 36.83 to 42.07, est err 1.390]
##
## if
## ManufacturingProcess15 <= -0.8591353
## then
## outcome = 40.846 + 0.63 BiologicalMaterial06
## - 0.55 ManufacturingProcess21 + 0.4 ManufacturingProcess30
## - 0.34 BiologicalMaterial11 + 0.33 ManufacturingProcess15
## + 0.29 ManufacturingProcess39 - 0.31 ManufacturingProcess36
## + 0.23 ManufacturingProcess18 - 0.16 ManufacturingProcess02
##
## Rule 67/4: [98 cases, mean 40.720, range 37.86 to 46.34, est err 1.335]
##
## if
## BiologicalMaterial06 > -0.9291902
## ManufacturingProcess15 > -0.8591353
## then
## outcome = 41.038 + 1.52 ManufacturingProcess15
## - 0.73 BiologicalMaterial11 + 0.65 BiologicalMaterial05
## - 0.56 ManufacturingProcess16 + 0.55 ManufacturingProcess45
## - 0.58 ManufacturingProcess36 + 0.28 BiologicalMaterial06
## + 0.18 ManufacturingProcess30 + 0.14 ManufacturingProcess02
## + 0.13 ManufacturingProcess39 + 0.1 ManufacturingProcess18
##
## Model 68:
##
## Rule 68/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.272]
##
## outcome = 39.929 - 1.82 ManufacturingProcess13
## + 1.59 ManufacturingProcess32 + 0.68 ManufacturingProcess04
##
## Model 69:
##
## Rule 69/1: [18 cases, mean 38.692, range 36.77 to 41.43, est err 1.248]
##
## if
## ManufacturingProcess32 <= -1.21499
## then
## outcome = 37.212 - 0.87 ManufacturingProcess32
## - 0.69 ManufacturingProcess33 - 0.41 ManufacturingProcess02
## - 0.39 ManufacturingProcess21 - 0.22 ManufacturingProcess35
##
## Rule 69/2: [69 cases, mean 40.315, range 37.14 to 46.34, est err 1.987]
##
## if
## ManufacturingProcess21 <= 0.1505547
## ManufacturingProcess32 > -1.21499
## then
## outcome = 39.81 - 3.17 ManufacturingProcess01
## - 2.37 ManufacturingProcess21 + 2.19 BiologicalMaterial03
## - 1.52 BiologicalMaterial09 + 0.23 ManufacturingProcess32
## - 0.12 ManufacturingProcess33 + 0.05 BiologicalMaterial05
##
## Rule 69/3: [126 cases, mean 40.414, range 36.83 to 46.34, est err 1.335]
##
## if
## ManufacturingProcess32 > -1.21499
## then
## outcome = 40.965 + 1.44 ManufacturingProcess32
## - 0.7 ManufacturingProcess21 - 0.51 ManufacturingProcess31
## - 0.42 ManufacturingProcess33 - 0.28 ManufacturingProcess02
## - 0.1 ManufacturingProcess35
##
## Rule 69/4: [32 cases, mean 40.892, range 38.37 to 44.35, est err 2.193]
##
## if
## ManufacturingProcess01 <= 0.1125761
## ManufacturingProcess21 <= 0.1505547
## ManufacturingProcess32 > -1.21499
## then
## outcome = 41.607 - 1.26 ManufacturingProcess21
## - 1.05 ManufacturingProcess24 - 0.98 BiologicalMaterial03
## + 0.5 ManufacturingProcess32 - 0.3 ManufacturingProcess01
## - 0.26 ManufacturingProcess33 + 0.1 BiologicalMaterial05
## - 0.03 ManufacturingProcess02
##
## Model 70:
##
## Rule 70/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.354]
##
## outcome = 39.534 + 2.1 ManufacturingProcess32
## - 1.81 ManufacturingProcess13 + 0.89 ManufacturingProcess04
## - 0.56 ManufacturingProcess33
##
## Model 71:
##
## Rule 71/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.339]
##
## outcome = 40.652 + 0.81 ManufacturingProcess30
## - 0.67 ManufacturingProcess10 + 0.65 ManufacturingProcess29
## + 0.63 ManufacturingProcess32 + 0.44 BiologicalMaterial03
##
## Model 72:
##
## Rule 72/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.392]
##
## outcome = 39.574 + 2.82 ManufacturingProcess32
## - 1.77 ManufacturingProcess13 - 1.4 ManufacturingProcess33
## + 0.89 ManufacturingProcess04
##
## Model 73:
##
## Rule 73/1: [24 cases, mean 38.293, range 36.77 to 40.66, est err 1.789]
##
## if
## BiologicalMaterial06 <= -0.9291902
## ManufacturingProcess15 > -0.8591353
## then
## outcome = 40.57 - 17.52 ManufacturingProcess39
## - 1.39 BiologicalMaterial03 + 1.2 ManufacturingProcess15
## + 0.96 ManufacturingProcess36
##
## Rule 73/2: [8 cases, mean 39.524, range 38.13 to 42.58, est err 3.032]
##
## if
## BiologicalMaterial05 > -0.1509527
## BiologicalMaterial06 > -0.9291902
## BiologicalMaterial06 <= -0.4236438
## then
## outcome = 35.884 + 12.78 BiologicalMaterial05
## + 8.6 ManufacturingProcess15 - 6.03 BiologicalMaterial11
## - 0.71 BiologicalMaterial06 - 0.04 ManufacturingProcess36
##
## Rule 73/3: [22 cases, mean 39.955, range 36.83 to 42.07, est err 1.344]
##
## if
## ManufacturingProcess15 <= -0.8591353
## then
## outcome = 41.178 + 0.71 BiologicalMaterial06
## - 0.51 ManufacturingProcess21 + 0.44 ManufacturingProcess30
## - 0.37 BiologicalMaterial11 + 0.36 ManufacturingProcess15
## - 0.36 ManufacturingProcess36 + 0.32 ManufacturingProcess39
## + 0.26 ManufacturingProcess18 - 0.12 ManufacturingProcess02
##
## Rule 73/4: [54 cases, mean 40.068, range 36.77 to 46.34, est err 2.049]
##
## if
## ManufacturingProcess01 > 0.1538577
## ManufacturingProcess15 > -0.8591353
## then
## outcome = 43.262 - 3 ManufacturingProcess01
## + 1.95 ManufacturingProcess42 - 1.83 ManufacturingProcess45
## + 1.57 BiologicalMaterial06 + 0.28 ManufacturingProcess30
## + 0.25 ManufacturingProcess15 - 0.23 BiologicalMaterial11
## + 0.22 ManufacturingProcess02 - 0.24 ManufacturingProcess36
## + 0.2 ManufacturingProcess39 + 0.16 ManufacturingProcess18
##
## Rule 73/5: [17 cases, mean 40.077, range 37.86 to 42.73, est err 1.807]
##
## if
## BiologicalMaterial05 <= -0.1509527
## BiologicalMaterial06 > -0.9291902
## BiologicalMaterial06 <= -0.4236438
## then
## outcome = 31.657 - 15.72 BiologicalMaterial06
## - 1.16 ManufacturingProcess36 + 0.03 ManufacturingProcess15
##
## Rule 73/6: [78 cases, mean 40.988, range 38.35 to 46.34, est err 1.942]
##
## if
## BiologicalMaterial06 > -0.4236438
## ManufacturingProcess15 > -0.8591353
## then
## outcome = 42.023 - 2.54 BiologicalMaterial11
## + 0.46 ManufacturingProcess15 + 0.24 ManufacturingProcess19
## - 0.18 ManufacturingProcess18 - 0.12 ManufacturingProcess36
## + 0.09 BiologicalMaterial05 + 0.09 ManufacturingProcess45
##
## Rule 73/7: [16 cases, mean 41.686, range 38.35 to 44.35, est err 2.247]
##
## if
## BiologicalMaterial11 > 0.9264525
## ManufacturingProcess01 <= 0.1538577
## then
## outcome = 47.928 - 3.43 BiologicalMaterial11 - 0.92 BiologicalMaterial06
## + 0.57 ManufacturingProcess15
##
## Model 74:
##
## Rule 74/1: [27 cases, mean 38.442, range 36.77 to 40.19, est err 1.755]
##
## if
## ManufacturingProcess09 <= -0.4686664
## ManufacturingProcess32 <= -0.04259344
## then
## outcome = 38.346 + 1.28 ManufacturingProcess32
## - 0.83 ManufacturingProcess33 - 0.66 ManufacturingProcess31
## - 0.38 ManufacturingProcess20 + 0.33 ManufacturingProcess19
## + 0.27 ManufacturingProcess04 + 0.26 BiologicalMaterial08
## + 0.27 ManufacturingProcess09 + 0.23 ManufacturingProcess06
##
## Rule 74/2: [105 cases, mean 40.642, range 37.39 to 46.34, est err 1.093]
##
## if
## ManufacturingProcess09 > -0.4686664
## then
## outcome = 39.451 + 1.89 ManufacturingProcess32
## - 1.1 ManufacturingProcess33 - 0.81 ManufacturingProcess13
## - 0.46 ManufacturingProcess31 + 0.41 ManufacturingProcess14
## + 0.38 ManufacturingProcess04 + 0.31 ManufacturingProcess10
## - 0.27 ManufacturingProcess20 + 0.23 ManufacturingProcess45
## + 0.23 ManufacturingProcess19 + 0.19 ManufacturingProcess09
## + 0.16 ManufacturingProcess06
##
## Rule 74/3: [63 cases, mean 41.554, range 36.83 to 46.34, est err 1.510]
##
## if
## ManufacturingProcess32 > -0.04259344
## then
## outcome = 39.746 + 2.4 ManufacturingProcess32
## - 2.08 ManufacturingProcess13 - 0.68 ManufacturingProcess33
## + 0.54 ManufacturingProcess14 + 0.43 ManufacturingProcess42
## + 0.41 ManufacturingProcess10 - 0.38 ManufacturingProcess28
## + 0.3 ManufacturingProcess45 + 0.25 ManufacturingProcess04
##
## Model 75:
##
## Rule 75/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.354]
##
## outcome = 40.958 - 1.11 ManufacturingProcess36
##
## Model 76:
##
## Rule 76/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.520]
##
## outcome = 39.459 + 2.58 ManufacturingProcess32
## - 1.87 ManufacturingProcess13 - 1.53 ManufacturingProcess33
## + 1.42 ManufacturingProcess15 + 0.76 ManufacturingProcess04
## - 0.74 ManufacturingProcess16 + 0.34 ManufacturingProcess29
##
## Model 77:
##
## Rule 77/1: [17 cases, mean 38.756, range 36.77 to 40.66, est err 1.484]
##
## if
## ManufacturingProcess36 > 0.5004068
## then
## outcome = 38.192 - 1.23 ManufacturingProcess32
##
## Rule 77/2: [127 cases, mean 40.392, range 36.83 to 46.34, est err 1.849]
##
## if
## ManufacturingProcess36 <= 0.5004068
## then
## outcome = 39.299 - 1.29 ManufacturingProcess31
## - 1.3 BiologicalMaterial10 - 1.37 ManufacturingProcess36
##
## Rule 77/3: [93 cases, mean 40.787, range 38.05 to 46.34, est err 1.179]
##
## if
## BiologicalMaterial03 > -0.3512033
## then
## outcome = 41.494 - 0.83 ManufacturingProcess36
## - 0.68 BiologicalMaterial08 + 0.56 ManufacturingProcess30
## + 0.54 ManufacturingProcess25
##
## Rule 77/4: [7 cases, mean 42.563, range 41.62 to 43.88, est err 2.683]
##
## if
## BiologicalMaterial03 > -0.3512033
## BiologicalMaterial08 <= -0.6640892
## ManufacturingProcess36 <= 0.5004068
## then
## outcome = 44.27 - 0.9 ManufacturingProcess36
##
## Model 78:
##
## Rule 78/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.373]
##
## outcome = 40.292 + 2.46 ManufacturingProcess32
## - 1.64 ManufacturingProcess13 - 1.43 ManufacturingProcess33
## + 1.3 ManufacturingProcess15 + 0.57 ManufacturingProcess31
## + 0.55 BiologicalMaterial10 - 0.54 ManufacturingProcess16
##
## Model 79:
##
## Rule 79/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.386]
##
## outcome = 40.149 - 0.99 ManufacturingProcess31
## + 1.08 ManufacturingProcess32 - 0.78 BiologicalMaterial10
## + 0.72 ManufacturingProcess04
##
## Model 80:
##
## Rule 80/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.468]
##
## outcome = 40.219 + 2.28 ManufacturingProcess32
## - 1.66 ManufacturingProcess17 - 1.41 ManufacturingProcess33
## + 1.08 ManufacturingProcess29 - 0.98 ManufacturingProcess16
## + 0.7 ManufacturingProcess31 + 0.69 ManufacturingProcess15
## + 0.62 BiologicalMaterial10
##
## Model 81:
##
## Rule 81/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.388]
##
## outcome = 40.348 - 1.03 BiologicalMaterial08
## + 1.02 ManufacturingProcess30 + 0.95 ManufacturingProcess32
## + 0.84 BiologicalMaterial06 + 0.64 ManufacturingProcess04
## + 0.24 ManufacturingProcess17
##
## Model 82:
##
## Rule 82/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.355]
##
## outcome = 40.159 - 1.47 ManufacturingProcess16
## - 1.65 ManufacturingProcess17 + 1.34 ManufacturingProcess32
## + 0.89 ManufacturingProcess20 + 0.79 ManufacturingProcess15
## + 0.68 BiologicalMaterial08
##
## Model 83:
##
## Rule 83/1: [81 cases, mean 39.144, range 36.77 to 42.07, est err 1.186]
##
## if
## ManufacturingProcess32 <= -0.04259344
## then
## outcome = 39.076 - 1.15 ManufacturingProcess33
## + 0.18 ManufacturingProcess32
##
## Rule 83/2: [63 cases, mean 41.554, range 36.83 to 46.34, est err 1.614]
##
## if
## ManufacturingProcess32 > -0.04259344
## then
## outcome = 40.35 - 0.81 ManufacturingProcess24
##
## Rule 83/3: [26 cases, mean 42.078, range 36.83 to 44.35, est err 2.152]
##
## if
## ManufacturingProcess32 > -0.04259344
## ManufacturingProcess43 <= -0.1283031
## then
## outcome = 43.459 + 1.24 ManufacturingProcess39
## - 1.05 ManufacturingProcess19 + 0.05 ManufacturingProcess32
## - 0.03 ManufacturingProcess33
##
## Model 84:
##
## Rule 84/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.316]
##
## outcome = 40.342 + 2.08 ManufacturingProcess32
## - 1.33 ManufacturingProcess17 + 0.74 ManufacturingProcess29
## + 0.69 ManufacturingProcess04 + 0.56 ManufacturingProcess09
## - 0.41 ManufacturingProcess03
##
## Model 85:
##
## Rule 85/1: [6 cases, mean 39.450, range 38.82 to 40.66, est err 7.124]
##
## if
## BiologicalMaterial06 <= -1.560284
## then
## outcome = 41.373 + 2.32 ManufacturingProcess29
## - 1.16 BiologicalMaterial06 - 0.73 ManufacturingProcess39
##
## Rule 85/2: [33 cases, mean 40.171, range 36.83 to 43.44, est err 1.503]
##
## if
## ManufacturingProcess17 > 0.6095197
## ManufacturingProcess39 > -0.02781602
## then
## outcome = 41.978 + 1.48 ManufacturingProcess31
## - 1.46 ManufacturingProcess17 + 1.23 BiologicalMaterial06
## - 0.76 ManufacturingProcess02 - 0.61 ManufacturingProcess39
##
## Rule 85/3: [132 cases, mean 40.175, range 36.77 to 46.34, est err 1.329]
##
## if
## ManufacturingProcess39 > -0.02781602
## then
## outcome = 42.214 - 11.8 ManufacturingProcess39
## - 1.01 ManufacturingProcess17 + 0.79 BiologicalMaterial06
##
## Rule 85/4: [12 cases, mean 40.459, range 38.35 to 43.84, est err 2.084]
##
## if
## ManufacturingProcess39 <= -0.02781602
## then
## outcome = 41.333 + 0.65 ManufacturingProcess39
##
## Model 86:
##
## Rule 86/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.359]
##
## outcome = 40.635 + 2.08 ManufacturingProcess32
## + 1.3 ManufacturingProcess29 + 0.93 ManufacturingProcess04
## - 0.87 ManufacturingProcess17 - 0.69 ManufacturingProcess19
## - 0.64 ManufacturingProcess13
##
## Model 87:
##
## Rule 87/1: [30 cases, mean 38.427, range 36.77 to 40.66, est err 1.754]
##
## if
## BiologicalMaterial06 <= -0.9291902
## then
## outcome = 38.775 - 20.77 ManufacturingProcess39
## - 2.48 BiologicalMaterial06 + 0.94 ManufacturingProcess36
## + 0.26 ManufacturingProcess24 - 0.06 ManufacturingProcess33
## + 0.03 ManufacturingProcess02 + 0.03 ManufacturingProcess19
## - 0.03 BiologicalMaterial11 + 0.03 ManufacturingProcess32
## - 0.03 ManufacturingProcess25
##
## Rule 87/2: [132 cases, mean 40.175, range 36.77 to 46.34, est err 1.212]
##
## if
## ManufacturingProcess39 > -0.02781602
## then
## outcome = 40.427 - 1.8 ManufacturingProcess39
## + 1.29 BiologicalMaterial06 - 0.98 ManufacturingProcess33
## - 0.58 BiologicalMaterial11 + 0.57 ManufacturingProcess19
## + 0.53 ManufacturingProcess02 + 0.57 ManufacturingProcess32
## - 0.56 ManufacturingProcess25 - 0.45 ManufacturingProcess36
##
## Rule 87/3: [12 cases, mean 40.459, range 38.35 to 43.84, est err 2.178]
##
## if
## ManufacturingProcess39 <= -0.02781602
## then
## outcome = 41.471 + 0.7 ManufacturingProcess39
##
## Model 88:
##
## Rule 88/1: [75 cases, mean 39.779, range 36.77 to 43.88, est err 1.792]
##
## if
## ManufacturingProcess17 > 0.03377622
## then
## outcome = 38.336 + 0.73 BiologicalMaterial10
## + 0.46 ManufacturingProcess38 + 0.12 ManufacturingProcess31
## + 0.08 ManufacturingProcess29 + 0.07 ManufacturingProcess30
## - 0.06 ManufacturingProcess17 + 0.05 ManufacturingProcess32
##
## Rule 88/2: [69 cases, mean 40.654, range 37.39 to 46.34, est err 1.372]
##
## if
## ManufacturingProcess17 <= 0.03377622
## then
## outcome = 38.819 - 2.26 ManufacturingProcess17
## + 0.63 ManufacturingProcess31 + 0.46 ManufacturingProcess29
## + 0.38 ManufacturingProcess30 + 0.38 ManufacturingProcess32
## + 0.36 ManufacturingProcess33 - 0.28 ManufacturingProcess03
## - 0.23 ManufacturingProcess13 - 0.14 ManufacturingProcess21
## + 0.1 BiologicalMaterial10
##
## Rule 88/3: [63 cases, mean 41.554, range 36.83 to 46.34, est err 1.125]
##
## if
## ManufacturingProcess32 > -0.04259344
## then
## outcome = 39.856 + 2.27 ManufacturingProcess32
## - 0.6 ManufacturingProcess31 - 0.49 ManufacturingProcess28
## + 0.43 ManufacturingProcess09 - 0.4 ManufacturingProcess13
## - 0.2 ManufacturingProcess20 - 0.2 ManufacturingProcess21
## + 0.15 ManufacturingProcess01 + 0.18 ManufacturingProcess17
## - 0.13 BiologicalMaterial11 + 0.1 ManufacturingProcess14
## + 0.07 ManufacturingProcess45 + 0.06 ManufacturingProcess29
##
## Rule 88/4: [21 cases, mean 41.962, range 36.83 to 43.88, est err 3.132]
##
## if
## ManufacturingProcess17 > -1.039519
## ManufacturingProcess32 > -0.04259344
## ManufacturingProcess43 <= -0.1283031
## then
## outcome = 42.557 + 2.78 ManufacturingProcess32
## + 4.96 ManufacturingProcess43 - 2.1 ManufacturingProcess28
## + 1.67 ManufacturingProcess09 - 0.33 ManufacturingProcess31
## - 0.28 ManufacturingProcess20 - 0.19 BiologicalMaterial11
## + 0.17 ManufacturingProcess01 + 0.09 ManufacturingProcess14
##
## Rule 88/5: [12 cases, mean 42.535, range 39.49 to 46.34, est err 3.143]
##
## if
## ManufacturingProcess17 <= -1.039519
## ManufacturingProcess32 > -0.04259344
## then
## outcome = 34.656 - 4.26 ManufacturingProcess13
## + 2.93 ManufacturingProcess32 - 0.21 ManufacturingProcess28
## + 0.18 ManufacturingProcess09 + 0.14 ManufacturingProcess45
## + 0.09 ManufacturingProcess14 + 0.06 ManufacturingProcess01
##
## Model 89:
##
## Rule 89/1: [13 cases, mean 39.015, range 37.3 to 41.43, est err 1.463]
##
## if
## ManufacturingProcess32 <= -1.420371
## then
## outcome = 52.977 - 29 ManufacturingProcess02
## + 4.62 ManufacturingProcess01
##
## Rule 89/2: [101 cases, mean 39.744, range 36.77 to 44.35, est err 1.436]
##
## if
## BiologicalMaterial06 <= 0.5418619
## then
## outcome = 40.266 + 1.64 ManufacturingProcess09
## - 1.44 ManufacturingProcess05 + 1.36 ManufacturingProcess32
## - 1 BiologicalMaterial10 + 0.76 BiologicalMaterial06
## - 0.06 ManufacturingProcess36 + 0.04 ManufacturingProcess06
##
## Rule 89/3: [131 cases, mean 40.316, range 36.77 to 46.34, est err 1.082]
##
## if
## ManufacturingProcess32 > -1.420371
## then
## outcome = 39.532 + 1.15 ManufacturingProcess32
## + 0.7 BiologicalMaterial06 + 0.51 ManufacturingProcess39
## - 0.39 BiologicalMaterial10 + 0.41 ManufacturingProcess09
## + 0.39 ManufacturingProcess04 - 0.39 ManufacturingProcess36
## + 0.29 ManufacturingProcess06 + 0.1 ManufacturingProcess30
##
## Rule 89/4: [49 cases, mean 40.487, range 37.64 to 44.35, est err 1.529]
##
## if
## BiologicalMaterial06 <= 0.5418619
## ManufacturingProcess01 <= 0.1125761
## ManufacturingProcess32 > -1.420371
## then
## outcome = 41.759 + 2.87 ManufacturingProcess31
## + 1.69 ManufacturingProcess01 + 1.54 BiologicalMaterial05
## - 1.52 ManufacturingProcess13 + 1.08 ManufacturingProcess32
## + 0.51 ManufacturingProcess06 + 0.02 BiologicalMaterial06
##
## Model 90:
##
## Rule 90/1: [81 cases, mean 39.144, range 36.77 to 42.07, est err 1.032]
##
## if
## ManufacturingProcess32 <= -0.04259344
## then
## outcome = 39.998 - 1.14 ManufacturingProcess17
## + 0.85 BiologicalMaterial10 + 0.55 ManufacturingProcess32
## - 0.36 BiologicalMaterial09 + 0.3 ManufacturingProcess29
## - 0.28 ManufacturingProcess33 + 0.23 ManufacturingProcess04
## - 0.2 BiologicalMaterial11 + 0.19 BiologicalMaterial06
## - 0.11 ManufacturingProcess37
##
## Rule 90/2: [63 cases, mean 41.554, range 36.83 to 46.34, est err 1.036]
##
## if
## ManufacturingProcess32 > -0.04259344
## then
## outcome = 40.448 + 1.45 ManufacturingProcess32
## - 1.38 ManufacturingProcess17 + 0.63 ManufacturingProcess29
## - 0.57 ManufacturingProcess33 + 0.48 ManufacturingProcess04
## - 0.42 BiologicalMaterial11 + 0.39 BiologicalMaterial06
## + 0.28 BiologicalMaterial10 - 0.23 ManufacturingProcess37
##
## Model 91:
##
## Rule 91/1: [13 cases, mean 39.015, range 37.3 to 41.43, est err 1.222]
##
## if
## ManufacturingProcess32 <= -1.420371
## then
## outcome = 39.183
##
## Rule 91/2: [131 cases, mean 40.316, range 36.77 to 46.34, est err 1.099]
##
## if
## ManufacturingProcess32 > -1.420371
## then
## outcome = 39.887 + 2.23 ManufacturingProcess32
## + 0.93 ManufacturingProcess30 - 0.82 ManufacturingProcess33
## - 0.71 BiologicalMaterial10 + 0.71 BiologicalMaterial06
## + 0.57 ManufacturingProcess04 + 0.61 ManufacturingProcess25
## + 0.43 ManufacturingProcess09 - 0.39 ManufacturingProcess20
## + 0.37 ManufacturingProcess39 + 0.32 ManufacturingProcess18
## + 0.29 ManufacturingProcess02 + 0.2 ManufacturingProcess06
##
## Model 92:
##
## Rule 92/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.166]
##
## outcome = 40.412 - 1.35 ManufacturingProcess17
## - 0.86 ManufacturingProcess36 + 0.69 BiologicalMaterial10
## + 0.38 ManufacturingProcess19
##
## Model 93:
##
## Rule 93/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.133]
##
## outcome = 39.947 + 1.88 ManufacturingProcess32
## + 0.93 ManufacturingProcess09 - 0.7 BiologicalMaterial10
## + 0.43 ManufacturingProcess04
##
## Model 94:
##
## Rule 94/1: [32 cases, mean 40.071, range 36.83 to 43.44, est err 1.311]
##
## if
## BiologicalMaterial06 <= 1.740615
## ManufacturingProcess17 > 0.6095197
## then
## outcome = 41.7 + 0.73 BiologicalMaterial03 - 0.72 ManufacturingProcess17
## + 0.45 ManufacturingProcess15 + 0.44 ManufacturingProcess32
## - 0.36 ManufacturingProcess33 + 0.22 ManufacturingProcess29
## - 0.24 ManufacturingProcess13 - 0.18 ManufacturingProcess21
## + 0.12 BiologicalMaterial10
##
## Rule 94/2: [132 cases, mean 40.175, range 36.77 to 46.34, est err 1.633]
##
## if
## ManufacturingProcess39 > -0.02781602
## then
## outcome = 42.413 - 10.82 ManufacturingProcess39
## - 4.39 ManufacturingProcess17 - 3.08 BiologicalMaterial11
## + 2.48 ManufacturingProcess13 + 1.98 BiologicalMaterial06
## + 1.82 ManufacturingProcess21 + 1.04 BiologicalMaterial08
## + 0.85 BiologicalMaterial05 - 0.48 ManufacturingProcess33
## + 0.38 ManufacturingProcess14 + 0.39 ManufacturingProcess32
## + 0.29 BiologicalMaterial10 - 0.26 ManufacturingProcess16
## + 0.21 ManufacturingProcess42 + 0.17 ManufacturingProcess06
##
## Rule 94/3: [12 cases, mean 40.459, range 38.35 to 43.84, est err 1.894]
##
## if
## ManufacturingProcess39 <= -0.02781602
## then
## outcome = 42.112 - 0.81 ManufacturingProcess17
## + 0.68 ManufacturingProcess39 - 0.24 BiologicalMaterial11
## + 0.21 ManufacturingProcess14 - 0.2 ManufacturingProcess33
## + 0.17 BiologicalMaterial05 + 0.17 BiologicalMaterial06
## - 0.15 ManufacturingProcess16 + 0.15 ManufacturingProcess32
## + 0.13 ManufacturingProcess21 + 0.12 ManufacturingProcess42
## + 0.11 BiologicalMaterial10 + 0.1 ManufacturingProcess06
##
## Rule 94/4: [6 cases, mean 41.712, range 38.35 to 46.34, est err 5.518]
##
## if
## BiologicalMaterial06 > 1.740615
## then
## outcome = 84.405 - 20.31 BiologicalMaterial06
## - 1.93 ManufacturingProcess37
##
## Rule 94/5: [21 cases, mean 41.794, range 39.3 to 44.35, est err 1.079]
##
## if
## BiologicalMaterial06 <= 1.740615
## BiologicalMaterial11 > 0.9264525
## ManufacturingProcess39 > -0.02781602
## then
## outcome = 42.148 - 1.61 ManufacturingProcess17
## - 0.77 ManufacturingProcess39 - 0.39 ManufacturingProcess33
## + 0.38 ManufacturingProcess32 - 0.35 BiologicalMaterial11
## + 0.29 BiologicalMaterial06 + 0.28 ManufacturingProcess14
## + 0.21 BiologicalMaterial05 + 0.16 BiologicalMaterial10
## - 0.14 ManufacturingProcess16 + 0.12 ManufacturingProcess21
## - 0.13 ManufacturingProcess13 + 0.11 ManufacturingProcess42
## + 0.09 ManufacturingProcess06 + 0.06 ManufacturingProcess29
##
## Model 95:
##
## Rule 95/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.086]
##
## outcome = 40.314 + 2.03 ManufacturingProcess32
## + 1.04 ManufacturingProcess09 + 0.54 ManufacturingProcess04
## - 0.53 BiologicalMaterial01
##
## Model 96:
##
## Rule 96/1: [144 cases, mean 40.198, range 36.77 to 46.34, est err 1.097]
##
## outcome = 40.07 + 1.39 ManufacturingProcess32
## - 1.13 ManufacturingProcess33 - 1.14 ManufacturingProcess17
## + 0.78 ManufacturingProcess29 + 0.36 BiologicalMaterial06
##
##
## Evaluation on training data (144 cases):
##
## Average |error| 0.644
## Relative |error| 0.44
## Correlation coefficient 0.88
##
##
## Attribute usage:
## Conds Model
##
## 19% 86% ManufacturingProcess32
## 11% 23% BiologicalMaterial06
## 8% 33% ManufacturingProcess17
## 5% 25% ManufacturingProcess15
## 5% 41% ManufacturingProcess13
## 4% 15% ManufacturingProcess39
## 4% 13% ManufacturingProcess31
## 2% 8% ManufacturingProcess01
## 2% 18% ManufacturingProcess36
## 1% 15% ManufacturingProcess21
## 1% 19% BiologicalMaterial03
## 8% ManufacturingProcess42
## 20% ManufacturingProcess09
## 16% BiologicalMaterial11
## 8% BiologicalMaterial08
## 3% BiologicalMaterial09
## 10% BiologicalMaterial05
## 9% ManufacturingProcess02
## 12% BiologicalMaterial10
## 4% ManufacturingProcess45
## 41% ManufacturingProcess04
## 40% ManufacturingProcess33
## 35% ManufacturingProcess29
## 16% ManufacturingProcess30
## 15% ManufacturingProcess16
## 12% ManufacturingProcess14
## 11% ManufacturingProcess06
## 9% ManufacturingProcess25
## 8% ManufacturingProcess19
## 8% ManufacturingProcess10
## 7% ManufacturingProcess20
## 5% ManufacturingProcess24
## 5% ManufacturingProcess28
## 5% ManufacturingProcess18
## 4% ManufacturingProcess35
## 3% ManufacturingProcess05
## 3% BiologicalMaterial01
## 3% ManufacturingProcess37
## 2% ManufacturingProcess03
## 2% ManufacturingProcess12
##
##
## Time: 0.3 secs## cubist variable importance
##
## only 20 most important variables shown (out of 48)
##
## Overall
## ManufacturingProcess32 100.00
## ManufacturingProcess13 43.81
## ManufacturingProcess17 39.05
## ManufacturingProcess04 39.05
## ManufacturingProcess33 38.10
## ManufacturingProcess29 33.33
## BiologicalMaterial06 32.38
## ManufacturingProcess15 28.57
## ManufacturingProcess36 19.05
## ManufacturingProcess09 19.05
## BiologicalMaterial03 19.05
## ManufacturingProcess39 18.10
## ManufacturingProcess31 16.19
## BiologicalMaterial11 15.24
## ManufacturingProcess21 15.24
## ManufacturingProcess30 15.24
## ManufacturingProcess16 14.29
## ManufacturingProcess14 11.43
## BiologicalMaterial10 11.43
## ManufacturingProcess06 10.48modelPred <- predict(cubTune, newdata=testX)
modelValues <- data.frame(obs = testY, pred=modelPred)
colnames(modelValues) = c('obs', 'pred')
(cub_values <- defaultSummary(modelValues))## RMSE Rsquared MAE
## 0.7674541 0.8651562 0.6235312Part (B)
Which predictors are most important in the optimal tree-based regression model? Do either the biological or process variables dominate the list? How do the top 10 important predictors compare to the top 10 predictors from the optimal linear and nonlinear models?
The optimal tree-base regression was Cubist (RMSE=11.12429 and \(R^2\) = 0.6610). There was a number of overlaps between the tree-based top features and those seen in Linear Regression and Nonlinear Regression, including:
ManufacturingProcess32,ManufacturingProcess17,BiologicalMaterial06,ManufacturingProcess13,ManufacturingProcess31,BiologicalMaterial03,ManufacturingProcess33. Note that the order of importance difference between the features found here vs the other approaches.
Part (C)
Plot the optimal single tree with the distribution of yield in the terminal nodes. Does this view of the data provide additional knowledge about the biological or process predictors and their relationship with yield?
Note that Cubist was my winner which doesn’t lend it’s to printing a “tree” with terminal nodes. After a bunch of fails, I gave up trying to print a pretty decision tree for my GBM model. Instead, I’m going to train a simple CART model using rpart2 since I do know how to print a nice decision tree from that model.
## Loading required package: libcoin##
## Attaching package: 'partykit'## The following objects are masked from 'package:party':
##
## cforest, ctree, ctree_control, edge_simple, mob, mob_control,
## node_barplot, node_bivplot, node_boxplot, node_inner, node_surv,
## node_terminal, varimp## Rattle: A free graphical interface for data science with R.
## Version 5.4.0 Copyright (c) 2006-2020 Togaware Pty Ltd.
## Type 'rattle()' to shake, rattle, and roll your data.##
## Attaching package: 'rattle'## The following object is masked from 'package:randomForest':
##
## importanceset.seed(42424)
cl <- makePSOCKcluster(5)
registerDoParallel(cl)
rpartControl <- trainControl(
method= "cv",
number=10
)
model <- train(trainX, trainY,
method="rpart2",
trControl = rpartControl,
tuneLength=10)
stopCluster(cl)
(model)## CART
##
## 144 samples
## 48 predictor
##
## No pre-processing
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 128, 130, 130, 131, 129, 129, ...
## Resampling results across tuning parameters:
##
## maxdepth RMSE Rsquared MAE
## 1 1.420425 0.4139289 1.148394
## 2 1.432901 0.4105528 1.139213
## 3 1.401456 0.4503310 1.084805
## 4 1.433047 0.4414313 1.092505
## 5 1.443769 0.4476999 1.115953
## 6 1.416983 0.4663819 1.101035
## 7 1.461927 0.4258692 1.138774
## 8 1.443897 0.4303523 1.123700
## 9 1.429911 0.4310018 1.107420
## 10 1.423474 0.4387595 1.107968
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was maxdepth = 3.
From this chart, we can see the paths that lead to the highest (node #8, followed by node #10) and lowest yields (node #9 or node # 11). This offers a simple way to identify optimal conditions based on the model. Since we have no control over the Biological features, if we know those in advance, we can work backwards to identify which manufacturing settings (under our control), might lead to the best yield.