DATA624 Project 2

Executive summary

This project aimed to develop a predictive model, and identify important factors, of the pH values in four beverage brands produced by ABC Beverage. This information will help company leaders comply with new manufacturing regulations.

Historical datasets from two data files were used to develop models. ‘StudentData’ was used for model development, while ‘StudentEvaluation’ was held out for making predictions with the final selected model. First, I performed exploratory data analysis of ‘StudentData’ to understand the distribution of variables (e.g., shape, skew, presence of outliers) using histograms, boxplots, and correlation analysis.

In addition, statistical tests revealed a significant relationship between brand codes and pH values, which was the target variable. This relationship motivated a detailed investigation of how missing data varied by brand. This analysis revealed that the mechanism of missing data was “missing at random”, which is most appropriately imputed using random forest (RF) imputation or multiple imputation by chained equations (MICE). Due to difficulties implementing MICE, I imputed missing data using RF imputation.

Other data processing techniques included splitting the ‘StudentData’ dataset into training and test sets (70:30 ratio), dummy encoding the categorical brand code, and applying Box-Cox transformations to normalize the distributions of numeric variables. Several variables had bimodal distributions, which were not amenable to Box-Cox transformation, so I engineered new features to collapse their bimodal distributions into unimodal ones. I performed this statistical “legerdemain” by deconvoluting the bimodal distributions using Gaussian mixture models and then scaling data values by Z-scores weighted by the posterior probabilities.

After data preparation was completed, I trained and tested 11 models, including four linear models and seven nonlinear models, using the training and test datasets, respectively. I compared their performance using three common metrics, namely, RMSE, MAE, and \(R^2\). A rule-based model (Cubist) and random forest model were the best models and had nearly identical performance metrics (\(RMSE=0.10\) and \(R^2 = 0.64\)). I selected the Cubist model as the final model because it is more interpretable than random forest, and because I think it would be more useful to management and other non-technical stakeholders.

The most important predictive factors in the Cubist model was Mnf.Flow, followed by Balling.Lvl, Alch.Rel, Balling, and Oxygen.Filter. Lastly, I used the Cubist model to predict pH values using the holdout evaluation dataset and saved the predictions to an Excel file.

Data input

filename1 = 'StudentData.xlsx'
url1 <- paste0(domain, path, filename1)
beverages_data_df <- read.xlsx(url1, sheet = 1)

filename2 = 'StudentEvaluation.xlsx'
url2 <- paste0(domain, path, filename2)
beverages_eval_df <- read.xlsx(url2, sheet = 1)

Initial data checks

I checked for consistent data types, duplicate observations, and missing data.

Data types

“StudentData” dataset

This dataset has 2571 rows (observations) and 33 columns (features), and the data appear to be tidy. Of note, some features have missing values (NAs); this will be investigated and handled in more detail later.

glimpse(beverages_data_df)

The data types appear to be appropriate; however, I changed the Brand.Code variable from character type to factor since it is categorical.

beverages_data_df$Brand.Code <- as.factor(beverages_data_df$Brand.Code)

Hereafter, I will refer to this dataset as the “model development” dataset.

“StudentEvaluation” dataset

This dataset has 267 rows (observations) and 33 columns (features), and the data appear to be tidy. Some features have missing values (NAs). The target variable, PH, appears to be completely missing, which is expected since this is the dataset that will be used to make predictions.

glimpse(beverages_eval_df)

To facilitate analysis, I changed the categorical Brand.Code variable from character type to factor.

beverages_eval_df$Brand.Code <- as.factor(beverages_eval_df$Brand.Code)

Hereafter, I will refer to this dataset as the “holdout evaluation” dataset.

Duplicate rows

There were no duplicate rows in either dataset.

sprintf('Duplicate rows in StudentData dataset: %d', count_duplicate_rows(beverages_data_df))

## [1] "Duplicate rows in StudentData dataset: 0"

sprintf('Duplicate rows in StudentEvaluation dataset: %d', count_duplicate_rows(beverages_eval_df))

## [1] "Duplicate rows in StudentEvaluation dataset: 0"

Missing data (analysis part 1)

Overall, 1% of the model development dataset and 4.2% of the holdout evaluation dataset were missing data. In both datasets, most variables had at least one missing value, and the MFR variable has the most missing data.

Of note, four samples in the model development dataset were missing pH values. Since this is the target variable, these samples are not useful for training and should be removed.

Missing data patterns will be further investigated in the EDA section.

# Count number of missing values for each variable (column)
StudentData_miss_vec <- purrr::map_dbl(beverages_data_df, ~ { n_miss(.x) })

# Convert results vector to dataframe and format
StudentData_miss_df <- as.data.frame(StudentData_miss_vec)
StudentData_miss_df$variable <- rownames(StudentData_miss_df)
rownames(StudentData_miss_df) <- NULL
StudentData_miss_df %>%
  select(variable, 'n_miss' = 'StudentData_miss_vec') %>%
  arrange(desc(n_miss)) %>%
  kbl() %>%
  add_header_above(header = c('Number of missing values by variable in StudentData dataset' = 2), bold = TRUE) %>%
  kable_minimal() %>%
  row_spec(25, background = 'lightgray')

Number of missing values by variable in StudentData dataset
variable	n_miss
MFR	212
Brand.Code	120
Filler.Speed	57
PC.Volume	39
PSC.CO2	39
Fill.Ounces	38
PSC	33
Carb.Pressure1	32
Hyd.Pressure4	30
Carb.Pressure	27
Carb.Temp	26
PSC.Fill	23
Fill.Pressure	22
Filler.Level	20
Hyd.Pressure2	15
Hyd.Pressure3	15
Temperature	14
Oxygen.Filler	12
Pressure.Setpoint	12
Hyd.Pressure1	11
Carb.Volume	10
Carb.Rel	10
Alch.Rel	9
Usage.cont	5
PH	4
Mnf.Flow	2
Carb.Flow	2
Bowl.Setpoint	2
Density	1
Balling	1
Balling.Lvl	1
Pressure.Vacuum	0
Air.Pressurer	0

# Count number of missing values for each variable (column),
# excluding target variable (PH)
StudentEval_miss_vec <- purrr::map_dbl(select(beverages_eval_df, -c(PH)), ~ { n_miss(.x) })

# Convert results vector to dataframe and format
StudentEval_miss_df <- as.data.frame(StudentEval_miss_vec)
StudentEval_miss_df$variable <- rownames(StudentEval_miss_df)
rownames(StudentEval_miss_df) <- NULL
StudentEval_miss_df %>%
  select(variable, 'n_miss' = 'StudentEval_miss_vec') %>%
  arrange(desc(n_miss)) %>%
  kbl() %>%
  add_header_above(header = c('Number of missing values by variable in StudentEval dataset' = 2), bold = TRUE) %>%  
  kable_minimal()

Number of missing values by variable in StudentEval dataset
variable	n_miss
MFR	31
Filler.Speed	10
Brand.Code	8
Fill.Ounces	6
PSC	5
PSC.CO2	5
PC.Volume	4
Carb.Pressure1	4
Hyd.Pressure4	4
PSC.Fill	3
Oxygen.Filler	3
Alch.Rel	3
Fill.Pressure	2
Filler.Level	2
Temperature	2
Usage.cont	2
Pressure.Setpoint	2
Carb.Rel	2
Carb.Volume	1
Carb.Temp	1
Hyd.Pressure2	1
Hyd.Pressure3	1
Density	1
Balling	1
Pressure.Vacuum	1
Bowl.Setpoint	1
Air.Pressurer	1
Carb.Pressure	0
Mnf.Flow	0
Hyd.Pressure1	0
Carb.Flow	0
Balling.Lvl	0

vis_miss(beverages_data_df) +
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust = 1),
        plot.title = element_text(face = 'bold')) +
  ggtitle('Plot of Missing Values in StudentData dataset')

vis_miss(beverages_eval_df) +
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust = 1),
        plot.title = element_text(face = 'bold')) +
  ggtitle('Plot of Missing Values in StudentEval dataset')

Exploratory data analysis

For EDA, I focused on the model development dataset to guide data preparation and model development.

Frequency distribution of brand codes

There were four brand codes and some missing brand codes. Of note, the classes are imbalanced, with brand B having twice as many samples as brand D and four times as many samples as brands A and C. Since the frequency of the minority classes (A and C) are >5%, there should not be concerns with incomplete representation in cross-validation folds.

This class imbalance may affect patterns in missing data, which will be explored in a later section.

# Calculate proportion of brand codes
cat('Frequency distribution of brand codes')

## Frequency distribution of brand codes

round(table(beverages_data_df$Brand.Code, useNA = 'always') / (nrow(beverages_data_df)), 2)

## 
##    A    B    C    D <NA> 
## 0.11 0.48 0.12 0.24 0.05

Distribution of pH (target) by brand

To determine whether brand codes are related to pH values, I compared the distribution of pH values by brand using box plots and statistical tests. Although the medians appear visually close, the Kruskal-Wallis test showed that there is a significant difference in median pH values in at least two category levels of Brand.Code. Post-hoc analysis with Dunn’s test further showed that there are significant differences between all pairs of brand codes (all P<0.001).

Together, these tests suggest that the brand code is an important variable with predictive value. As a result, observations that are missing brand codes will need to be investigated in detail and imputed appropriately. The importance of brand code also suggests that engineering a new feature with the mean pH value for each brand code (i.e., target encoding) may be helpful.

beverages_data_df %>%
  drop_na(PH) %>%  # Omit observations with missing pH values
  ggplot(aes(x = PH)) +
    geom_boxplot() +
    xlim(7, 10) +
    facet_wrap(~ Brand.Code, ncol = 1) +
    ggtitle('Distribution of pH Values by Brand Code') +
    theme(
      panel.border = element_rect(color = 'darkgrey'),
      panel.background = element_blank(),
      axis.text.y = element_blank(),
      axis.ticks.y = element_blank(),
      plot.title = element_text(face = 'bold')
    )  

# Kruskal-Wallis test to determine whether median pH values are significantly different across brand codes
kruskal.test(PH ~ Brand.Code, data = beverages_data_df)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  PH by Brand.Code
## Kruskal-Wallis chi-squared = 256.99, df = 3, p-value < 2.2e-16

# Post-hoc Dunn test to determine which groups (brand codes) have signficantly different median pH values
# p-values are adjusted for multiple comparisons using Holm method
dunnTest(PH ~ Brand.Code, data = beverages_data_df, method = 'holm')

## Warning: Some rows deleted from 'x' and 'g' because missing data.

##   Kruskal-Wallis rank sum test
## 
## data: x and g
## Kruskal-Wallis chi-squared = 256.9912, df = 3, p-value = 0
## 
## 
##                      Dunn's Pairwise Comparison of x by g                     
##                                     (Holm)                                    
## Col Mean-│
## Row Mean │          A          B          C
## ─────────┼─────────────────────────────────
##        B │  -5.718955
##          │     0.0000*
##          │
##        C │   5.629699   13.00314
##          │     0.0000*    0.0000*
##          │
##        D │  -8.225602  -4.301059  -14.90211
##          │     0.0000*    0.0000*    0.0000*
## 
## FWER = 0.05
## Reject Ho if p ≤ FWER with stopping rule, where p = Pr(|Z| ≥ |z|)
## Dunn (1964) Kruskal-Wallis multiple comparison
## 
##   p-values adjusted with the Holm method.

##   Comparison          Z      P.unadj        P.adj
## 1      A - B  -5.718955 1.071810e-08 3.215430e-08
## 2      A - C   5.629700 1.805234e-08 3.610468e-08
## 3      B - C  13.003141 1.174190e-38 5.870950e-38
## 4      A - D  -8.225603 1.942120e-16 7.768481e-16
## 5      B - D  -4.301059 1.699835e-05 1.699835e-05
## 6      C - D -14.902120 3.192874e-50 1.915725e-49

Distribution of numeric variables

I characterized the overall shape and skewness of the distribution of variables and checked for outliers.

Variables with unimodal distribution

Most variables had a unimodal distribution. Some appeared to be approximately normal (e.g., Carb.Temp, PC.Volume), while others were skewed (e.g., MFR, Oxygen.Filler). For linear models (e.g., OLS) and distance-based models (e.g., kNN, SVM), variables that are not normally distributed may need to be transformed. Tree-based models, such as random forest, would not benefit from transformation, but it would not hurt either.

# Create facet plot of histograms
beverages_data_df %>%
  select(Alch.Rel, Carb.Pressure, Carb.Pressure1, Carb.Rel, Carb.Temp, 
         Carb.Volume, Fill.Ounces, Fill.Pressure, Filler.Level, Filler.Speed, 
         Hyd.Pressure1, Hyd.Pressure2, Hyd.Pressure3, Hyd.Pressure4, MFR, 
         Mnf.Flow, Oxygen.Filler, PC.Volume, PH, Pressure.Vacuum, PSC, PSC.CO2,
         PSC.Fill, Temperature, Usage.cont) %>%
  pivot_longer(cols = everything(), names_to = 'variable', values_to = 'value') %>%
  ggplot(aes(x = value)) +
    geom_histogram(bins = 30, fill = 'steelblue', na.rm = TRUE) +
    facet_wrap(~ variable, scales = 'free', ncol = 4) +
    labs(x = 'Value', y = 'Count') +
    ggtitle('Variables with unimodal distribution') +
    theme(
      panel.border = element_rect(color = 'darkgrey'),
      panel.background = element_rect(fill = 'white'),
      panel.grid = element_blank(),
      axis.title = element_text(face = 'bold'),
      plot.title = element_text(face = 'bold')
    )

Other variables

Five variables (Air.Pressurer, Balling, Balling.Lvl, Density, and Carb.Flow ) had a bimodal distribution. In addition, two set point variables, Bowl.Setpoint and Pressure.Setpoint, only had a few discrete values.

Because multimodal distributions indicate the presence of distinct subgroups of values and cannot be normalized using standard transformations (e.g., Box-Cox), it may be helpful to engineer new features for these variables (e.g., by deconvoluting the subgroup distributions), particularly for linear models.

For the set point variables, I assume the values are settings for a manufacturing control system, which implies that they are ordinal (i.e., ordered). This suggests that they should be treated as numeric variables rather than as categorical variables.

beverages_data_df %>%
  select(Air.Pressurer, Balling, Balling.Lvl, Bowl.Setpoint, 
         Carb.Flow, Density, Pressure.Setpoint) %>%
  pivot_longer(cols = everything(), names_to = 'variable', values_to = 'value') %>%
  ggplot(aes(x = value)) +
    geom_histogram(bins = 30, fill = 'steelblue', na.rm = TRUE) +
    facet_wrap(~ variable, scales = 'free', ncol = 4) +
    labs(x = 'Value', y = 'Count') +
    ggtitle('Variables with multimodal distribution') +  
    theme(
      panel.border = element_rect(color = 'darkgrey'),
      panel.background = element_rect(fill = 'white'),
      panel.grid = element_blank(),
      axis.title = element_text(face = 'bold'),
      plot.title = element_text(face = 'bold')      
    )

Skewness

Six variables were higly skewed. Specifically, Oxygen.Filler, Temperature, Air.Pressurer, and PSC.CO2 were highly positively skewed ( \(skewness \ge 1\)), while Filler.Speed and MFR were highly negatively skewed (\(skewness \le 1\)). For linear regression and distance-based machine learning models (e.g., kNN, SVM), these variables may benefit from transformation to stabilize variance. Of the remaining variables, 15 were moderately skewed (\(0.5 \le skewness < 1\)), and 11 were approximately symmetric (\(0 \le skewness < 1\)).

Of note, the skewness of the target variable, PH, was -0.29, which was assessed as approximately symmetric. This suggests that transformation is not needed. In addition, I do not think transforming the dependent variable would be advisable because transformed pH values would be difficult to interpret.

skewness_vec <- beverages_data_df %>%
  select(-c(Brand.Code)) %>%
  purrr::map_dbl(~ { e1071::skewness(.x, na.rm = TRUE) })

# Convert results vector to dataframe and format
skewness_df <- as.data.frame(skewness_vec)
skewness_df$variable <- rownames(skewness_df)
rownames(skewness_df) <- NULL
skewness_df %>%
  select(variable, 'skewness' = 'skewness_vec') %>%
  mutate(
    skewness = round(skewness, 3)
  ) %>%
  arrange(desc(skewness)) %>%
  kbl() %>%
  kable_minimal()

variable	skewness
Oxygen.Filler	2.660
Temperature	2.387
Air.Pressurer	2.252
PSC.CO2	1.729
PSC.Fill	0.933
Alch.Rel	0.884
PSC	0.849
Hyd.Pressure1	0.780
Balling	0.594
Balling.Lvl	0.586
Fill.Pressure	0.547
Hyd.Pressure4	0.546
Density	0.526
Pressure.Vacuum	0.526
Carb.Rel	0.503
Carb.Volume	0.392
PC.Volume	0.340
Carb.Temp	0.247
Pressure.Setpoint	0.203
Carb.Pressure	0.182
Carb.Pressure1	0.054
Mnf.Flow	0.004
Fill.Ounces	-0.022
PH	-0.291
Hyd.Pressure2	-0.302
Hyd.Pressure3	-0.319
Usage.cont	-0.535
Filler.Level	-0.848
Bowl.Setpoint	-0.974
Carb.Flow	-0.988
Filler.Speed	-2.870
MFR	-5.092

sprintf('%d variables were highly skewed (|skewness| >= 1)', 
        sum(abs(skewness_vec) >= 1))

## [1] "6 variables were highly skewed (|skewness| >= 1)"

sprintf('%d variables were moderately skewed (0.5 <= |skewness| < 1)', 
        sum(abs(skewness_vec) >= 0.5 & abs(skewness_vec) < 1))

## [1] "15 variables were moderately skewed (0.5 <= |skewness| < 1)"

sprintf('%d variables were approximately symmetric (0 <=|skewness| < 0.5)', 
        sum(abs(skewness_vec) >= 0 & abs(skewness_vec) < 0.5))

## [1] "11 variables were approximately symmetric (0 <=|skewness| < 0.5)"

Outliers

The box plots below show that most variables have outliers.

beverages_data_df %>%
  select(-c(Brand.Code)) %>%
  pivot_longer(cols = everything(), names_to = 'variable', values_to = 'value') %>%
  ggplot(aes(x = value)) +
    geom_boxplot(na.rm = TRUE) +
    facet_wrap(~ variable, scales = 'free', ncol = 4) +
    theme(
      panel.border = element_rect(color = 'darkgrey'),
      panel.background = element_blank(),
      axis.text.y = element_blank(),
      axis.ticks.y = element_blank()
    )

Variables with negative or zero values

Nine variables had a minimum value less than or equal to zero. These variables are important because Box-Cox transformation can only be performed with positive definite values. If these variables need to be transformed, a constant can be added to make their values positive.

min_vec <- beverages_data_df %>%
  select(-c(Brand.Code)) %>%
  purrr::map_dbl(~ { min(.x, na.rm = TRUE) })

# Convert results vector to dataframe and format
min_df <- as.data.frame(min_vec)
min_df$variable <- rownames(min_df)
rownames(min_df) <- NULL
min_df <- min_df %>%
  select(variable, 'min_value' = 'min_vec') %>%
  filter(min_value <= 0)

min_df %>%
  arrange(min_value) %>%
  kbl() %>%
  kable_minimal()

variable	min_value
Mnf.Flow	-100.20
Pressure.Vacuum	-6.60
Hyd.Pressure3	-1.20
Hyd.Pressure1	-0.80
Balling	-0.17
PSC.Fill	0.00
PSC.CO2	0.00
Hyd.Pressure2	0.00
Balling.Lvl	0.00

sprintf('%d variables have a minimum <= 0', nrow(min_df))

## [1] "9 variables have a minimum <= 0"

Range of pH values

I also confirmed that all pH values were scientifically plausible (i.e., between 0 and 14). Based on published tables of pH values of common foods,¹ the pH range from 7.88 to 9.36 in the provided datasets suggests that the beverages are dairy products.

sprintf('pH values range from %.2f to %.2f', 
        min(beverages_data_df$PH, na.rm = TRUE), max(beverages_data_df$PH, na.rm = TRUE))

## [1] "pH values range from 7.88 to 9.36"

Correlation analysis

The correlation plot below provides several useful insights about the relationships among pairs of variables:

• A total of 16 variables had strong positive correlations, such as Balling-Balling.Lvl (Pearson r=0.98) and Density-Balling (r=0.96). These variables may be redundant in linear models.

• Variables that have very weak correlations with the target variable PH (i.e., white squares in the correlation correspond to variables with r<0.1) are unlikely to have predictive value in linear models and could be omitted. These variables are encoded below.

  weak_corr_vars <- c('Air.Pressurer', 'Carb.Volume', 'Carb.Pressure', 'Carb.Pressure1', 'Carb.Temp', 'Density', 'Fill.Ounces', 'Filler.Speed', 'Hyd.Pressure1', 'MFR', 'PC.Volume', 'PSC.CO2', 'PSC', 'PSC.Fill')

• No variables were strongly correlated with the target variable PH, and only one (Mnf.Flow) had a moderate correlation (r=0.45). This suggests that multivariate linear or nonlinear models will be needed to capture complex relationships and predict pH values. In addition, I would expect accurate models of pH to include Mnf.Flow.

# Calculate correlation matrix
# Default method of cor() is Pearson correlation
beverages_data_cor_mat <- beverages_data_df %>%
  select(-c(Brand.Code)) %>%
  cor(use = "pairwise.complete.obs")  # omit observations with missing values

# Suppress small correlation coefficients in plot
beverages_data_cor_mat[abs(beverages_data_cor_mat) < 0.1] <- NA

# Generate correlation plot
corrplot(beverages_data_cor_mat, 
         method = 'square', 
         type = 'upper', 
         diag = FALSE,  # do not show correlations on diagonal
         tl.cex = 0.5,  # font size of variable label
         insig = 'blank',  # do not show insignificant correlation coefficients
         na.label = ' ', 
         na.label.col = 'white',
         addCoef.col = NULL,  # do not show coefficients 
         number.cex = 0.4, # font size of numbers
         tl.srt = 45)  # text rotation angle

Combining information about redundant variables from the correlation plot with the vis_miss() plot of missing data in the model development dataset (i.e., variables that are redundant and missing a lot of data may not worth keeping) suggested that the following variables could be omitted from linear models:

# Potentially redudant variables
redundant_vars <- c('Alch.Rel', 'Balling', 'Carb.Temp', 'Filler.Level', 'Hyd.Pressure2', 'MFR')

# List variables wtih strong correlations (abs(r) >= 0.7)
vars_strong_cor_df <- beverages_data_cor_mat %>%
  as.table() %>%
  as.data.frame() %>%
  rename('r' = 'Freq') %>%
  arrange(desc(r)) %>%  
  filter(
    # Omit self correlations
    (Var1 != Var2) &
    # Omit identical pairs (ie, cor(A,B) = cor(B,A))
    # After sorting correlation coefficient, these pairs will be in adjacent rows,
    # so just filter for even row numbers
    (row_number() %% 2 == 0) &
    # Threshold for strong correlation
    (abs(r) >= 0.7)
  )  

vars_strong_cor_df %>%
  mutate(
    r = round(r, 3)
  ) %>%
  kbl() %>%
  add_header_above(header = c('Strongly Correlated Variables in StudentData Dataset' = 3), bold = TRUE) %>%  
  kable_minimal() 

Strongly Correlated Variables in StudentData Dataset
Var1	Var2	r
Balling	Balling.Lvl	0.978
Density	Balling	0.955
Filler.Level	Bowl.Setpoint	0.949
Density	Balling.Lvl	0.948
Filler.Speed	MFR	0.930
Alch.Rel	Balling.Lvl	0.926
Hyd.Pressure2	Hyd.Pressure3	0.925
Balling	Alch.Rel	0.925
Density	Alch.Rel	0.903
Carb.Rel	Balling.Lvl	0.845
Alch.Rel	Carb.Rel	0.844
Density	Carb.Rel	0.824
Balling	Carb.Rel	0.822
Carb.Pressure	Carb.Temp	0.814
Carb.Volume	Carb.Rel	0.793
Carb.Volume	Balling	0.783
Carb.Volume	Alch.Rel	0.781
Carb.Volume	Balling.Lvl	0.779
Carb.Volume	Density	0.762
Mnf.Flow	Hyd.Pressure3	0.759
Hyd.Pressure1	Hyd.Pressure2	0.723

sprintf('%d variable pairs involving %d unique variables are strongly correlated (abs(r) >= 0.7)', 
        nrow(vars_strong_cor_df), 
        # Number of unique variables in pairs with strong correlations
        n_distinct(union(vars_strong_cor_df$Var1, vars_strong_cor_df$Var2)))

## [1] "21 variable pairs involving 16 unique variables are strongly correlated (abs(r) >= 0.7)"

Mnf.Flow_PH_cor <- cor(beverages_data_df$Mnf.Flow, beverages_data_df$PH, use = "pairwise.complete.obs") %>% round(3)
sprintf('The correlation coefficient between Mnf.Flow and pH is %.3f', Mnf.Flow_PH_cor)

## [1] "The correlation coefficient between Mnf.Flow and pH is -0.447"

Variables with near-zero variance

One variable (Fill.Pressure) had near-zero variance. This variable is unlikely to be informative for modeling and should be removed.

nzv_col_idx <- beverages_data_df %>%
  select(-c(Brand.Code)) %>%  # omit non-numeric variable
  caret::nearZeroVar(.)

sprintf('There are %d near-zero variance columns in StudentData dataset', length(nzv_col_idx))

## [1] "There are 1 near-zero variance columns in StudentData dataset"

# Affected variables
colnames(beverages_data_df)[nzv_col_idx]

## [1] "Fill.Pressure"

Comparison of missing data by brand (Missing data analysis part 2)

Analyses of missing data by brand provided insight into the mechanism of missing data, which informed the selection of an appropriate data imputation method.

Brand A

For Brand A, MFR was missing the most values, and 10 variables were not missing any values.

# Count number of missing values for each variable (column)
BrandA_miss_vec <- beverages_data_df %>%
  filter(Brand.Code == 'A') %>%
  purrr::map_dbl(~ { n_miss(.x) })

# Convert results vector to dataframe and format
BrandA_miss_df <- as.data.frame(BrandA_miss_vec)
BrandA_miss_df$variable <- rownames(BrandA_miss_df)
rownames(BrandA_miss_df) <- NULL
BrandA_miss_df %>%
  select(variable, 'n_miss' = 'BrandA_miss_vec') %>%
  arrange(desc(n_miss)) %>%
  kbl() %>%
  kable_minimal() %>%
  scroll_box('300px') 

variable	n_miss
MFR	36
Hyd.Pressure4	11
Fill.Ounces	8
Filler.Speed	8
PC.Volume	7
PSC	6
PSC.CO2	3
Carb.Pressure1	3
Carb.Pressure	2
PSC.Fill	2
Temperature	2
Carb.Flow	2
Oxygen.Filler	2
Bowl.Setpoint	2
Pressure.Setpoint	2
Carb.Temp	1
Fill.Pressure	1
Hyd.Pressure2	1
Hyd.Pressure3	1
Filler.Level	1
Usage.cont	1
Alch.Rel	1
Carb.Rel	1
Brand.Code	0
Carb.Volume	0
Mnf.Flow	0
Hyd.Pressure1	0
Density	0
Balling	0
Pressure.Vacuum	0
PH	0
Air.Pressurer	0
Balling.Lvl	0

beverages_data_df %>%
  filter(Brand.Code == 'A') %>%
  vis_miss() +
    theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust = 1))

Brand B

For Brand B, MFR was missing the most values, and 7 variables were not missing any values.

# Count number of missing values for each variable (column)
BrandB_miss_vec <- beverages_data_df %>%
  filter(Brand.Code == 'B') %>%
  purrr::map_dbl(~ { n_miss(.x) })

# Convert results vector to dataframe and format
BrandB_miss_df <- as.data.frame(BrandB_miss_vec)
BrandB_miss_df$variable <- rownames(BrandB_miss_df)
rownames(BrandB_miss_df) <- NULL
BrandB_miss_df %>%
  select(variable, 'n_miss' = 'BrandB_miss_vec') %>%
  arrange(desc(n_miss)) %>%
  kbl() %>%
  kable_minimal() %>%
  scroll_box('300px') 

variable	n_miss
MFR	85
Filler.Speed	25
PSC.CO2	21
PC.Volume	17
Fill.Ounces	16
Carb.Temp	15
PSC	15
Carb.Pressure1	15
Filler.Level	11
Carb.Pressure	10
PSC.Fill	10
Hyd.Pressure4	10
Fill.Pressure	8
Hyd.Pressure2	6
Hyd.Pressure3	6
Temperature	6
Alch.Rel	6
Carb.Volume	5
Oxygen.Filler	5
Hyd.Pressure1	4
Usage.cont	4
PH	4
Carb.Rel	4
Mnf.Flow	2
Density	1
Balling	1
Brand.Code	0
Carb.Flow	0
Pressure.Vacuum	0
Bowl.Setpoint	0
Pressure.Setpoint	0
Air.Pressurer	0
Balling.Lvl	0

beverages_data_df %>%
  filter(Brand.Code == 'B') %>%
  vis_miss() +
    theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust = 1))

Brand C

For Brand C. MFR was missing the most values, and 14 variables were not missing any values.

# Count number of missing values for each variable (column)
BrandC_miss_vec <- beverages_data_df %>%
  filter(Brand.Code == 'C') %>%
  purrr::map_dbl(~ { n_miss(.x) })

# Convert results vector to dataframe and format
BrandC_miss_df <- as.data.frame(BrandC_miss_vec)
BrandC_miss_df$variable <- rownames(BrandC_miss_df)
rownames(BrandC_miss_df) <- NULL
BrandC_miss_df %>%
  select(variable, 'n_miss' = 'BrandC_miss_vec') %>%
  arrange(desc(n_miss)) %>%
  kbl() %>%
  kable_minimal() %>%
  scroll_box('300px') 

variable	n_miss
MFR	28
Filler.Speed	8
Pressure.Setpoint	7
PSC.CO2	6
Fill.Ounces	4
PC.Volume	4
Fill.Pressure	4
Hyd.Pressure4	4
Carb.Pressure1	3
Oxygen.Filler	3
Carb.Rel	3
Carb.Pressure	2
Carb.Temp	2
PSC	2
PSC.Fill	2
Temperature	2
Carb.Volume	1
Filler.Level	1
Alch.Rel	1
Brand.Code	0
Mnf.Flow	0
Hyd.Pressure1	0
Hyd.Pressure2	0
Hyd.Pressure3	0
Usage.cont	0
Carb.Flow	0
Density	0
Balling	0
Pressure.Vacuum	0
PH	0
Bowl.Setpoint	0
Air.Pressurer	0
Balling.Lvl	0

beverages_data_df %>%
  filter(Brand.Code == 'C') %>%
  vis_miss() +
    theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust = 1))

Brand D

For Brand D. MFR was missing the most values, and 13 variables were not missing any values.

# Count number of missing values for each variable (column)
BrandD_miss_vec <- beverages_data_df %>%
  filter(Brand.Code == 'D') %>%
  purrr::map_dbl(~ { n_miss(.x) })

# Convert results vector to dataframe and format
BrandD_miss_df <- as.data.frame(BrandD_miss_vec)
BrandD_miss_df$variable <- rownames(BrandD_miss_df)
rownames(BrandD_miss_df) <- NULL
BrandD_miss_df %>%
  select(variable, 'n_miss' = 'BrandD_miss_vec') %>%
  arrange(desc(n_miss)) %>%
  kbl() %>%
  kable_minimal() %>%
  scroll_box('300px') 

variable	n_miss
MFR	50
Filler.Speed	13
Carb.Pressure	12
Carb.Pressure1	10
Hyd.Pressure2	8
Hyd.Pressure3	8
PC.Volume	7
PSC	7
PSC.CO2	7
Hyd.Pressure1	7
Fill.Ounces	6
Fill.Pressure	6
Carb.Temp	5
PSC.Fill	5
Filler.Level	5
Carb.Volume	4
Temperature	3
Pressure.Setpoint	2
Hyd.Pressure4	1
Oxygen.Filler	1
Brand.Code	0
Mnf.Flow	0
Usage.cont	0
Carb.Flow	0
Density	0
Balling	0
Pressure.Vacuum	0
PH	0
Bowl.Setpoint	0
Air.Pressurer	0
Alch.Rel	0
Carb.Rel	0
Balling.Lvl	0

beverages_data_df %>%
  filter(Brand.Code == 'D') %>%
  vis_miss() +
    theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust = 1))

Brand unknown

For samples with missing brand code. MFR was missing the most values, and 13 variables were not missing any values.

# Count number of missing values for each variable (column)
BrandNA_miss_vec <- beverages_data_df %>%
  filter(is.na(Brand.Code)) %>%
  purrr::map_dbl(~ { n_miss(.x) })

# Convert results vector to dataframe and format
BrandNA_miss_df <- as.data.frame(BrandNA_miss_vec)
BrandNA_miss_df$variable <- rownames(BrandNA_miss_df)
rownames(BrandNA_miss_df) <- NULL
BrandNA_miss_df %>%
  select(variable, 'n_miss' = 'BrandNA_miss_vec') %>%
  arrange(desc(n_miss)) %>%
  kbl() %>%
  kable_minimal() %>%
  scroll_box('300px')

variable	n_miss
Brand.Code	120
MFR	13
Fill.Ounces	4
PC.Volume	4
PSC.Fill	4
Hyd.Pressure4	4
Carb.Temp	3
PSC	3
Fill.Pressure	3
Filler.Speed	3
PSC.CO2	2
Filler.Level	2
Carb.Rel	2
Carb.Pressure	1
Carb.Pressure1	1
Temperature	1
Oxygen.Filler	1
Pressure.Setpoint	1
Alch.Rel	1
Balling.Lvl	1
Carb.Volume	0
Mnf.Flow	0
Hyd.Pressure1	0
Hyd.Pressure2	0
Hyd.Pressure3	0
Usage.cont	0
Carb.Flow	0
Density	0
Balling	0
Pressure.Vacuum	0
PH	0
Bowl.Setpoint	0
Air.Pressurer	0

beverages_data_df %>%
  filter(is.na(Brand.Code)) %>%
  vis_miss() +
    theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust = 1))

Implications for data imputation

As shown in the summary table below, data missingness is not uniform across all brands and not completely random. For example, Carb.Flow and Bowl.Setpoint are only missing in Brand A samples, and Mnf.Flow, Density, and Balling are only missing in Brand B samples. In addition, some variables are missing values from more brands than others. These findings indicate there are patterns in the missing data, which suggest that the mechanism of missing data is “missing at random” (MAR) rather than “missing completely at random” (MCAR).²

As an additional check, I performed Little’s test for MCAR.³ The test P<0.05, so the null hypothesis of MCAR is rejected. However, the test is limited to 30 variables, so I had to omit a few variables (I chose ones with no or very few missing values), which may affect the reliability of the test result. Nevertheless, the analysis of data missingness by brand suggests that the missing data mechanism is not MCAR.

For MAR, valid imputation methods include multiple imputation using chained equations (MICE) and random forest (RF) imputation models (implemented in missForest package). Both of these imputation methods can handle categorical and numeric variables, so they are both suitable for the ABC Beverages dataset. Unlike MICE, RF imputation is a non-parametric tree-based method, so it can handle skewed variables and multimodal distributions without pre-processing. However, RF imputation results in a single imputed dataset, whereas MICE produces multiple imputed datasets and is considered more statistically robust because it accounts for uncertainty.

I initially intended to compare RF vs MICE imputation; however, I ran into problems with NAs persisting after MICE imputation and was not able to resolve the issue in the time I had available. As a result, I resorted to using RF imputation.

# Combine missingness by brand into single dataframe
na_vars_all_brands_list <- list(BrandA_miss_df, BrandB_miss_df, BrandC_miss_df, 
                                BrandD_miss_df, BrandNA_miss_df)
na_vars_all_brands_df <- purrr::reduce(na_vars_all_brands_list, 
                                       full_join, by = 'variable') %>%
  select(variable, 
         'BrandA_miss' = 'BrandA_miss_vec',
         'BrandB_miss' = 'BrandB_miss_vec',
         'BrandC_miss' = 'BrandC_miss_vec',
         'BrandD_miss' = 'BrandD_miss_vec',
         'BrandNA_miss' = 'BrandNA_miss_vec') %>%
  filter(variable != 'Brand.Code')

na_vars_all_brands_df %>%
  # Calculate number of brands with missing data for each variable
  mutate(
    n_brands_miss = ifelse(BrandA_miss > 0, 1, 0) + 
                    ifelse(BrandB_miss > 0, 1, 0) +
                    ifelse(BrandC_miss > 0, 1, 0) + 
                    ifelse(BrandD_miss > 0, 1, 0) + 
                    ifelse(BrandNA_miss > 0, 1, 0),
    .after = 'variable'
  ) %>%
  arrange(desc(n_brands_miss)) %>%
  kbl() %>%
  kable_minimal() %>%
  scroll_box('500px')

variable	n_brands_miss	BrandA_miss	BrandB_miss	BrandC_miss	BrandD_miss	BrandNA_miss
Fill.Ounces	5	8	16	4	6	4
PC.Volume	5	7	17	4	7	4
Carb.Pressure	5	2	10	2	12	1
Carb.Temp	5	1	15	2	5	3
PSC	5	6	15	2	7	3
PSC.Fill	5	2	10	2	5	4
PSC.CO2	5	3	21	6	7	2
Carb.Pressure1	5	3	15	3	10	1
Fill.Pressure	5	1	8	4	6	3
Hyd.Pressure4	5	11	10	4	1	4
Filler.Level	5	1	11	1	5	2
Filler.Speed	5	8	25	8	13	3
Temperature	5	2	6	2	3	1
MFR	5	36	85	28	50	13
Oxygen.Filler	5	2	5	3	1	1
Pressure.Setpoint	4	2	0	7	2	1
Alch.Rel	4	1	6	1	0	1
Carb.Rel	4	1	4	3	0	2
Carb.Volume	3	0	5	1	4	0
Hyd.Pressure2	3	1	6	0	8	0
Hyd.Pressure3	3	1	6	0	8	0
Hyd.Pressure1	2	0	4	0	7	0
Usage.cont	2	1	4	0	0	0
Mnf.Flow	1	0	2	0	0	0
Carb.Flow	1	2	0	0	0	0
Density	1	0	1	0	0	0
Balling	1	0	1	0	0	0
PH	1	0	4	0	0	0
Bowl.Setpoint	1	2	0	0	0	0
Balling.Lvl	1	0	0	0	0	1
Pressure.Vacuum	0	0	0	0	0	0
Air.Pressurer	0	0	0	0	0	0

cat('Variables missing in only Brand A\n')

## Variables missing in only Brand A

na_vars_all_brands_df %>%
  filter(BrandA_miss > 0 & 
         BrandB_miss == 0 &
         BrandC_miss == 0 & 
         BrandD_miss == 0 &
         BrandNA_miss == 0) %>%
  pull(variable)

## [1] "Carb.Flow"     "Bowl.Setpoint"

cat('Variables missing in only Brand B\n')

## Variables missing in only Brand B

na_vars_all_brands_df %>%
  filter(BrandA_miss == 0 & 
         BrandB_miss > 0 & 
         BrandC_miss == 0 & 
         BrandD_miss == 0 & 
         BrandNA_miss == 0) %>%
  pull(variable)

## [1] "Mnf.Flow" "Density"  "Balling"  "PH"

# Little's test for "missing completely at random" (MCAR)
# The implementation of this test is limited to <30 variables for reliable p-values, 
# so I removed a few variables with no or very few missing values
mcar_test(select(beverages_data_df, -c(Air.Pressurer, Pressure.Vacuum, Balling.Lvl, Bowl.Setpoint)))

## # A tibble: 1 × 4
##   statistic    df p.value missing.patterns
##       <dbl> <dbl>   <dbl>            <int>
## 1     9786.  2968       0              114

Data preparation

For RF imputation, data preparation is relatively simple because it is a non-parametric, tree-based method and can handle skewed and multimodal variables without transformation. As a result, I only omitted uninformative observations/features before splitting the data into training and test sets and imputing the missing data.

However, additional preparation is needed prior to predictive modeling, such as transforming variables to normalize distributions and engineering new features. To maintain feature consistency between datasets and avoid target leakage, these operations are first performed on the training dataset to determine the “rules” or specific parameters, and then the same methodology is applied to both the test and holdout evaluation datasets.

Omitted data

First, I removed the four observations in the model development dataset that did not have a pH value (target).

beverages_data_df <- beverages_data_df %>%
  drop_na(PH)

Data split

Then I split the data 70:30 into training and test datasets.

set.seed(144)

train_idx <- caret::createDataPartition(beverages_data_df$PH, p = 0.7, list = FALSE)
trainX <- subset(beverages_data_df[train_idx, ], select = -PH)
trainY <- beverages_data_df[train_idx, 'PH']
testX <- subset(beverages_data_df[-train_idx, ], select = -PH)
testY <- beverages_data_df[-train_idx, 'PH']

For consistency, I also removed the PH (target) variable from the holdout evaluation dataset, even though it does not have any values except NA.

evalX <- select(beverages_eval_df, -c(PH))

Remove near-zero variance variable

I removed the near-zero variance variable that was identified during EDA from the training, test, and holdout evaluaton datasets. Of note, I did this before dummy encoding, which adds variables and changes column indexes.

trainX <- trainX[, -nzv_col_idx]
testX <- testX[, -nzv_col_idx]
evalX <- evalX[, -nzv_col_idx]

Data imputation

Next, I imputed missing data using random forest (RF) imputation. To avoid target leakage, the same RF model that is used to impute the training dataset is also used to impute the test and holdout evaluaton datasets. Doing this requires using the missForest() function from the missForestPredict package rather than the missForest package.

Also of note, data imputation is performed before dummy encoding so that missing brand codes are imputed as categorical variables rather than as dummy variables, which are numeric (0s and 1s).

# This block may take a minute or two to run
set.seed(144)

# Training dataset
# missForestPredict::missForest "remembers" the model so it can be reused for the test dataset
trainX_RF_model <- missForestPredict::missForest(xmis = trainX, verbose = FALSE)
trainX <- trainX_RF_model$ximp

set.seed(144)

# Use the same model that was used to impute the test and evaluation datasets 
testX <- missForestPredict(trainX_RF_model, newdata = testX)
evalX <- missForestPredict(trainX_RF_model, newdata = evalX)

Dummy encoding

Because some models cannot handle categorical variables, I dummy encoded Brand.Code in the training, test, and holdout evaluation datasets. However, before doing this, I created variables to store the original values of Brand.Code, because I needed them for target encoding (Feature engineering section), and dummy encoding removes the original variable after encoding.

trainX_brand_code <- trainX$Brand.Code
testX_brand_code <- testX$Brand.Code

dummy_encoder_train <- dummyVars(~ Brand.Code, data = trainX)
dummy_vars_train <- data.frame(predict(dummy_encoder_train, newdata = trainX))
# recreate training dataset
trainX <- bind_cols(dummy_vars_train, select(trainX, -c(Brand.Code)))

dummy_encoder_test <- dummyVars(~ Brand.Code, data = testX)
dummy_vars_test <- data.frame(predict(dummy_encoder_test, newdata = testX))
# recreate test dataset
testX <- bind_cols(dummy_vars_test, select(testX, -c(Brand.Code)))

dummy_encoder_eval <- dummyVars(~ Brand.Code, data = evalX)
dummy_vars_eval <- data.frame(predict(dummy_encoder_eval, newdata = evalX))
# recreate eval dataset
evalX <- bind_cols(dummy_vars_eval, select(evalX, -c(Brand.Code)))

Transformations

Because Box-Cox transformation requires positive definite values, I added a constant to all unimodal variables with negative or zero values in the training, test, and holdout evaluation datasets.

# Variables with min <= 0 were identified in EDA section
# Only unimodal variables are shifted here because Box-Cox transformation
# cannot normalize multimodal distributions
Hyd_Pressure1_shift <- abs(min(beverages_data_df$Hyd.Pressure1, na.rm = TRUE)) + 1
Hyd_Pressure2_shift <- abs(min(beverages_data_df$Hyd.Pressure2, na.rm = TRUE)) + 1
Hyd_Pressure3_shift <- abs(min(beverages_data_df$Hyd.Pressure3, na.rm = TRUE)) + 1
Mnf_Flow_shift <- abs(min(beverages_data_df$Mnf.Flow, na.rm = TRUE)) + 1
Pressure_Vacuum_shift <- abs(min(beverages_data_df$Pressure.Vacuum, na.rm = TRUE)) + 1
PSC_CO2_shift <- abs(min(beverages_data_df$PSC.CO2, na.rm = TRUE)) + 1
PSC_Fill_shift <- abs(min(beverages_data_df$PSC.Fill, na.rm = TRUE)) + 1

trainX <- trainX %>%
  mutate(
    Hyd.Pressure1.Shifted = Hyd.Pressure1 + Hyd_Pressure1_shift,
    Hyd.Pressure2.Shifted = Hyd.Pressure2 + Hyd_Pressure2_shift,
    Hyd.Pressure3.Shifted = Hyd.Pressure3 + Hyd_Pressure3_shift,
    Mnf.Flow.Shifted = Mnf.Flow + Mnf_Flow_shift,
    Pressure.Vacuum.Shifted = Pressure.Vacuum + Pressure_Vacuum_shift,
    PSC.CO2.Shifted = PSC.CO2 + PSC_CO2_shift,
    PSC.Fill.Shifted = PSC.Fill + PSC_Fill_shift
  )

testX <- testX %>%
  mutate(
    Hyd.Pressure1.Shifted = Hyd.Pressure1 + Hyd_Pressure1_shift,
    Hyd.Pressure2.Shifted = Hyd.Pressure2 + Hyd_Pressure2_shift,
    Hyd.Pressure3.Shifted = Hyd.Pressure3 + Hyd_Pressure3_shift,
    Mnf.Flow.Shifted = Mnf.Flow + Mnf_Flow_shift,
    Pressure.Vacuum.Shifted = Pressure.Vacuum + Pressure_Vacuum_shift,
    PSC.CO2.Shifted = PSC.CO2 + PSC_CO2_shift,
    PSC.Fill.Shifted = PSC.Fill + PSC_Fill_shift
  )

evalX <- evalX %>%
  mutate(
    Hyd.Pressure1.Shifted = Hyd.Pressure1 + Hyd_Pressure1_shift,
    Hyd.Pressure2.Shifted = Hyd.Pressure2 + Hyd_Pressure2_shift,
    Hyd.Pressure3.Shifted = Hyd.Pressure3 + Hyd_Pressure3_shift,
    Mnf.Flow.Shifted = Mnf.Flow + Mnf_Flow_shift,
    Pressure.Vacuum.Shifted = Pressure.Vacuum + Pressure_Vacuum_shift,
    PSC.CO2.Shifted = PSC.CO2 + PSC_CO2_shift,
    PSC.Fill.Shifted = PSC.Fill + PSC_Fill_shift
  )

To avoid target leakage, I calculated optimal lambda values for Box-Cox transformations using the training dataset and then used the same values to transform the training, test, and holdout evaluation datasets.

# Only unimodal variables are transformed because Box-Cox transformation cannot normalize multimodal distributions
# As noted in the previous block, variables that are not positive definite have been replaced with their shifted version
boxcox_transform_vars <- 
  c('Alch.Rel', 'Carb.Pressure', 'Carb.Pressure1', 'Carb.Rel', 'Carb.Temp', 
    'Carb.Volume', 'Fill.Ounces', 'Filler.Level', 'Filler.Speed', 
    'Hyd.Pressure1.Shifted', 'Hyd.Pressure2.Shifted', 'Hyd.Pressure3.Shifted', 
    'Hyd.Pressure4', 'MFR', 'Mnf.Flow.Shifted', 'Oxygen.Filler', 'PC.Volume', 
    'Pressure.Vacuum.Shifted', 'PSC', 'PSC.CO2.Shifted', 'PSC.Fill.Shifted', 
    'Temperature', 'Usage.cont')

lambdas_vec <- trainX %>%
  select(all_of(boxcox_transform_vars)) %>%
  purrr::map_dbl(., ~ { caret::BoxCoxTrans(.x)$lambda })

# Comment out lines below to show lambda values
# ---------------------------------------------
# optimal_lambdas <- as.data.frame(lambdas_vec)
# optimal_lambdas$variable <- rownames(optimal_lambdas)
# rownames(optimal_lambdas) <- NULL
# optimal_lambdas %>%
#   select(variable, 'lambda' = 'lambdas_vec') %>%
#   arrange(desc(lambda)) %>%
#   kbl() %>%
#   kable_minimal()

# Box-Cox transformations for training dataset using optimal lambda values (previous block)
train_predictors_transformed <- purrr::map2_dfc(
  .x = select(trainX, all_of(boxcox_transform_vars)),
  .y = lambdas_vec,
  .f = ~forecast::BoxCox(.x, .y)
)

## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo

# Combine transformed variables with other variables
trainX <- bind_cols(train_predictors_transformed,
  select(trainX, -c(all_of(boxcox_transform_vars))))

# Box-Cox transformations for test dataset using same lambda values
test_predictors_transformed <- purrr::map2_dfc(
  .x = select(testX, all_of(boxcox_transform_vars)),
  .y = lambdas_vec,
  .f = ~forecast::BoxCox(.x, .y)
)

# Combine transformed variables with other variables
testX <- bind_cols(test_predictors_transformed,
  select(testX, -c(all_of(boxcox_transform_vars))))

# Box-Cox transformations for holdout evaluation dataset using same lambda values
eval_predictors_transformed <- purrr::map2_dfc(
  .x = select(evalX, all_of(boxcox_transform_vars)),
  .y = lambdas_vec,
  .f = ~forecast::BoxCox(.x, .y)
)

# Combine transformed variables with other variables
evalX <- bind_cols(eval_predictors_transformed,
  select(evalX, -c(all_of(boxcox_transform_vars))))

Feature engineering

Scaling multimodal variables

Because variables with a multimodal distribution suggest the presence of two or more distinct subgroups of values, I used a Gaussian mixture model (GMM)⁴ to identify the component normal distributions. Then, I created new features by scaling the original values by Z-scores weighted by the posterior probabilities of the component distributions. The goal of this scaling is to remove the “structure” of the multimodal distribution so that it collapses into a single normal (or near normal) distribution.

To avoid target leakage, I used the GMM fit to the training dataset to calculate the posterior probability matrix for the training, test, and holdout evaluation datasets, which were used to create new scaled variables in the respective datasets. I applied this process to five variables.

Air.Pressurer

The plot below shows that a two-component GMM separated the distribution of Air.Pressurer into two component Gaussian distributions (red and green density curves).⁵

set.seed(144)

# Fit 2-component GMM
air_pressurer_GMM <- normalmixEM(trainX$Air.Pressurer, k = 2)

## number of iterations= 18

# Overlay density curves on variable distribution
# ann=FALSE suppresses default plot title
plot(air_pressurer_GMM, which = 2, ann=FALSE)
# Use custom titles 
title(main = 'GMM Density Curves for Air.Pressurer in Training Dataset')
title(xlab = 'Value')
title(ylab = 'Density')

# Fit 2-component GMM on training data using variable variance model ('V' model)
air_pressurer_GMM_fit <- Mclust(trainX$Air.Pressurer, G = 2, modelNames = 'V', verbose = FALSE)

# Create new scaled variables
scaled_vars_list <- scale_multimodal_var(air_pressurer_GMM_fit, 
                                         trainX$Air.Pressurer, testX$Air.Pressurer, evalX$Air.Pressurer)
trainX$Air.Pressurer.Scaled <- scaled_vars_list$train_vec_scaled
testX$Air.Pressurer.Scaled <- scaled_vars_list$test_vec_scaled
evalX$Air.Pressurer.Scaled <- scaled_vars_list$eval_vec_scaled

The histogram below shows that the scaling collapses the bimodal distribution of Air.Pressurer into an approximately normal distribution.

ggplot(trainX, aes(x = Air.Pressurer.Scaled)) +
  geom_histogram(bins = 15, fill = 'steelblue') +
  ylim(0, 600) +
  guides(y = guide_axis(cap = 'upper')) +
  labs(x = 'Value', y = 'Count') +
  ggtitle('Distribution of Air.Pressurer.Scaled in Training Dataset') +
  theme_classic() +
  theme(
    axis.title = element_text(face = 'bold'),
    plot.title = element_text(face = 'bold')
  )

Balling

A two-component GMM separated the bimodal distribution of Balling into two component Gaussian distributions. New scaled variables were created in the training and test datasets as above.

set.seed(144)

balling_GMM <- normalmixEM(trainX$Balling, k = 2)

## number of iterations= 14

plot(air_pressurer_GMM, which = 2, ann=FALSE)
title(main = 'GMM Density Curves for Balling in Training Dataset')
title(xlab = 'Value')
title(ylab = 'Density')

# Fit 2-component GMM on training data
balling_GMM_fit <- Mclust(trainX$Balling, G = 2, modelNames = 'V', verbose = FALSE)

# Create new scaled variables
scaled_vars_list <- scale_multimodal_var(balling_GMM_fit, trainX$Balling, testX$Balling, evalX$Balling)
trainX$Balling.Scaled <- scaled_vars_list$train_vec_scaled
testX$Balling.Scaled <- scaled_vars_list$test_vec_scaled
evalX$Balling.Scaled <- scaled_vars_list$eval_vec_scaled

The histogram below confirms that the distribution of Balling.Scaled is approximately normal.

ggplot(trainX, aes(x = Balling.Scaled)) +
  geom_histogram(bins = 15, fill = 'steelblue') +
  ylim(0, 600) +
  guides(y = guide_axis(cap = 'upper')) +
  labs(x = 'Value', y = 'Count') +
  ggtitle('Distribution of Balling.Scaled in Training Dataset') +
  theme_classic() +
  theme(
    axis.title = element_text(face = 'bold'),
    plot.title = element_text(face = 'bold')
  )

Balling.Lvl

A two-component GMM separated the bimodal distribution of Balling into two component Gaussian distributions. New scaled variables were created in the training and test datasets as above.

set.seed(144)

balling_lvl_GMM <- normalmixEM(trainX$Balling.Lvl, k = 2)

## number of iterations= 12

plot(balling_lvl_GMM, which = 2, ann=FALSE)
title(main = 'GMM Density Curves for Balling.Lvl in Training Dataset')
title(xlab = 'Value')
title(ylab = 'Density')

# Fit 2-component GMM on training data
balling_lvl_GMM_fit <- Mclust(trainX$Balling.Lvl, G = 2, modelNames = 'V', verbose = FALSE)

# Create new scaled variables
scaled_vars_list <- scale_multimodal_var(balling_lvl_GMM_fit, 
                                         trainX$Balling.Lvl, testX$Balling.Lvl, evalX$Balling.Lvl)
trainX$Balling.Lvl.Scaled <- scaled_vars_list$train_vec_scaled
testX$Balling.Lvl.Scaled <- scaled_vars_list$test_vec_scaled
evalX$Balling.Lvl.Scaled <- scaled_vars_list$eval_vec_scaled

The histogram below confirms that the distribution of Balling.Lvl.Scaled is roughly normal (it appears skewed due to an outlier, but the distribution is centered at zero).

ggplot(trainX, aes(x = Balling.Lvl.Scaled)) +
  geom_histogram(bins = 15, fill = 'steelblue') +
  ylim(0, 1000) +
  guides(y = guide_axis(cap = 'upper')) +
  labs(x = 'Value', y = 'Count') +
  ggtitle('Distribution of Balling.Lvl.Scaled in Training Dataset') +
  theme_classic() +
  theme(
    axis.title = element_text(face = 'bold'),
    plot.title = element_text(face = 'bold')
  )

Density

A two-component GMM separated the distribution of Balling into two component Gaussian distributions; however, one density curve (green) does not have a distinct peak and overlaps with the other density curve (red). New scaled variables were created in the training and test datasets as above.

set.seed(144)

density_GMM <- normalmixEM(trainX$Density, k = 2)

## number of iterations= 17

plot(density_GMM, which = 2, ann=FALSE)
title(main = 'GMM Density Curves for Density in Training Dataset')
title(xlab = 'Value')
title(ylab = 'Density')

# Fit 2-component GMM on training data
density_GMM_fit <- Mclust(trainX$Density, G = 2, modelNames = 'V', verbose = FALSE)

# Create new scaled variables
scaled_vars_list <- scale_multimodal_var(density_GMM_fit, 
                                         trainX$Density, testX$Density, evalX$Density)
trainX$Density.Scaled <- scaled_vars_list$train_vec_scaled
testX$Density.Scaled <- scaled_vars_list$test_vec_scaled
evalX$Density.Scaled <- scaled_vars_list$eval_vec_scaled

The histogram below shows that the scaling Density was not as effective as other multimodal variables, which may reflect the overlapping GMM component density curves. However, the multi-modality of Density.Scaled is less pronounced.

ggplot(trainX, aes(x = Density.Scaled)) +
  geom_histogram(bins = 15, fill = 'steelblue') +
  ylim(0, 400) +
  guides(y = guide_axis(cap = 'upper')) +
  labs(x = 'Value', y = 'Count') +
  ggtitle('Distribution of Density.Scaled in Training Dataset') +
  theme_classic() +
  theme(
    axis.title = element_text(face = 'bold'),
    plot.title = element_text(face = 'bold')
  )

Carb.Flow

A two-component GMM separated the distribution of Carb.Flow into two component Gaussian distributions. New scaled variables were created in the training and test datasets as above.

set.seed(144)

carb_flow_GMM <- normalmixEM(trainX$Carb.Flow, k = 2)

## number of iterations= 19

plot(carb_flow_GMM, which = 2, ann=FALSE)
title(main = 'GMM Density Curves for Carb.Flow in Training Dataset')
title(xlab = 'Value')
title(ylab = 'Density')

# Fit 2-component GMM on training data
carb_flow_GMM_fit <- Mclust(trainX$Carb.Flow, G = 2, modelNames = 'V', verbose = FALSE)

# Create new scaled variables
scaled_vars_list <- scale_multimodal_var(carb_flow_GMM_fit, 
                                         trainX$Carb.Flow, testX$Carb.Flow, evalX$Carb.Flow)
trainX$Carb.Flow.Scaled <- scaled_vars_list$train_vec_scaled
testX$Carb.Flow.Scaled <- scaled_vars_list$test_vec_scaled
evalX$Carb.Flow.Scaled <- scaled_vars_list$eval_vec_scaled

The histogram below shows that the distribution of Carb.Flow.Scaled is somewhat skewed, but the scaling did collapse the bimodal distribution of Carb.Flow.

ggplot(trainX, aes(x = Carb.Flow.Scaled)) +
  geom_histogram(bins = 15, fill = 'steelblue') +
  ylim(0, 1000) +
  guides(y = guide_axis(cap = 'upper')) +
  labs(x = 'Value', y = 'Count') +
  ggtitle('Distribution of Carb.Flow.Scaled in Training Dataset') +
  theme_classic() +
  theme(
    axis.title = element_text(face = 'bold'),
    plot.title = element_text(face = 'bold')
  )

Target encoding

Because Brand.Code was significantly related to pH values, I encoded the category levels with the mean pH value in each category. One concern with mean encoding is that the subgroup mean for minority classes may be skewed by outliers, which can be mitigated by partial pooling. However, when there are few category levels, as is the case with four brand codes, partial pooled means are reported to be not much better than raw means.⁶ Here, I implement a modification of the latter, which introduces a small amount of noise to the encoded value in the training dataset to reduce the possibility of target leakage and overfitting.⁷

# Encode brand codes in training and test datasets
# Noise (sigma) is only added to training dataset
# Reference: https://www.r-bloggers.com/2020/02/a-guide-to-encoding-categorical-features-using-r/

# Due to dummy encoding, Brand.Code no longer exists in trainX/testX datasets
trainX$Brand.Code.Encoded <- encode_target(trainX_brand_code, trainY, sigma = 0.05)
testX$Brand.Code.Encoded <- encode_target(testX_brand_code, testY)

Since the holdout evaluation dataset does not have the target variable (PH), I manually assigned the group (brand) means from the training set.

# Encode brand codes in holdout evaluation datasets using group means from training dataset
trainY_group_means <- aggregate(x = trainY, by = list(trainX_brand_code), FUN = mean)
colnames(trainY_group_means) <- c('group', 'mean')
get_grouped_mean <- setNames(trainY_group_means$mean, trainY_group_means$group)

evalX <- evalX %>%
  mutate(Brand.Code.Encoded = case_when(Brand.Code.A == 1 ~ unname(get_grouped_mean['A']),
                                        Brand.Code.B == 1 ~ unname(get_grouped_mean['B']),
                                        Brand.Code.C == 1 ~ unname(get_grouped_mean['C']),
                                        Brand.Code.D == 1 ~ unname(get_grouped_mean['D']),
                                        TRUE ~ NA))

Clean up

Finally, I removed variables that are no longer needed (eg, un-transformed or intermediate variables).

trainX <- select(trainX, -c(ends_with('.Shifted')))
testX <- select(testX, -c(ends_with('.Shifted')))
evalX <- select(evalX, -c(ends_with('.Shifted')))

I also changed trainX and testX from tibbles to dataframes, which are needed for caret::train (next section).

trainX <- as.data.frame(trainX)
testX <- as.data.frame(testX)

Model development

I trained and tested 11 models, including four linear models (OLS, PLS, Ridge regression, and elastic net regression) and seven nonlinear models (MARS, GBM, RF, Cubist, SVM, kNN, and neural network). These models where chosen to explore a range of model types, including all-purpose models (e.g., RF, GBM), suitability to moderate-sized datasets (e.g., SVM, kNN), robustness to multicollinearity effects (e.g., ridge, elastic net), and model interpretability (e.g., MARS, Cubist).

Performance metrics are summarized at the end of this subsection.

Ordinary linear regression

set.seed(144)

# Omitting redundant variables or variables weakly correlated with target
# did not have much effect on model performance
lmTune <- train(
  x = trainX,
  y = trainY,
  method = 'lm',
  preProcess = c('center', 'scale'),
  trControl = trainControl(method = 'cv', number = 10)  
)

lmTune

## Linear Regression 
## 
## 1799 samples
##   40 predictor
## 
## Pre-processing: centered (40), scaled (40) 
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 1618, 1619, 1619, 1621, 1619, 1620, ... 
## Resampling results:
## 
##   RMSE       Rsquared   MAE      
##   0.1345182  0.4025294  0.1043644
## 
## Tuning parameter 'intercept' was held constant at a value of TRUE

# Make predictions using test data
lmPredict <- predict(lmTune, newdata = testX)
# Evaluate predictive performance (predicted vs actual)
ols_metrics <- caret::postResample(pred = lmPredict, obs = testY)

Partial least squares

set.seed(144)

# Omitting redundant variables or variables weakly correlated with target
# did not have much effect on model performance
plsTune <- train(
  x = trainX,
  y = trainY,
  method = 'pls',
  preProcess = c('center', 'scale'),
  tuneLength = 20,
  trControl = trainControl(method = 'cv', number = 10)
)

plsTune

## Partial Least Squares 
## 
## 1799 samples
##   40 predictor
## 
## Pre-processing: centered (40), scaled (40) 
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 1618, 1619, 1619, 1621, 1619, 1620, ... 
## Resampling results across tuning parameters:
## 
##   ncomp  RMSE       Rsquared   MAE      
##    1     0.1498860  0.2569405  0.1180558
##    2     0.1414371  0.3393281  0.1107326
##    3     0.1389493  0.3617449  0.1091943
##    4     0.1370334  0.3790935  0.1071519
##    5     0.1358903  0.3895904  0.1057718
##    6     0.1353421  0.3948513  0.1047799
##    7     0.1347303  0.4006810  0.1046211
##    8     0.1345705  0.4019173  0.1042495
##    9     0.1344392  0.4029938  0.1042481
##   10     0.1343063  0.4043043  0.1040303
##   11     0.1343114  0.4044054  0.1040986
##   12     0.1342106  0.4051434  0.1039893
##   13     0.1342037  0.4052048  0.1040472
##   14     0.1342701  0.4046726  0.1041018
##   15     0.1342721  0.4046455  0.1040942
##   16     0.1342904  0.4044881  0.1041087
##   17     0.1343352  0.4041204  0.1041611
##   18     0.1343841  0.4036435  0.1042126
##   19     0.1344330  0.4032322  0.1042614
##   20     0.1344405  0.4031741  0.1042582
## 
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was ncomp = 13.

# Make predictions using test data
plsPredict <- predict(plsTune, newdata = testX)
# Evaluate predictive performance (predicted vs actual)
pls_metrics <- caret::postResample(pred = plsPredict, obs = testY)

Ridge regression

set.seed(144)

ridgeGrid <- data.frame(.lambda = seq(0.01, 1, length = 20))

ridgeTune <- train(
  x = trainX,
  y = trainY,
  method = 'ridge',
  preProcess = c('center', 'scale'),
  tuneGrid = ridgeGrid,
  trControl = trainControl(method = 'cv', number = 10)
)

ridgeTune

## Ridge Regression 
## 
## 1799 samples
##   40 predictor
## 
## Pre-processing: centered (40), scaled (40) 
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 1618, 1619, 1619, 1621, 1619, 1620, ... 
## Resampling results across tuning parameters:
## 
##   lambda      RMSE       Rsquared   MAE      
##   0.01000000  0.1342602  0.4045538  0.1040879
##   0.06210526  0.1344406  0.4028590  0.1042667
##   0.11421053  0.1348945  0.3992895  0.1047287
##   0.16631579  0.1353782  0.3958934  0.1051876
##   0.21842105  0.1358838  0.3927484  0.1056458
##   0.27052632  0.1364147  0.3898223  0.1061155
##   0.32263158  0.1369735  0.3870806  0.1066137
##   0.37473684  0.1375615  0.3844960  0.1071295
##   0.42684211  0.1381788  0.3820478  0.1076650
##   0.47894737  0.1388248  0.3797200  0.1082160
##   0.53105263  0.1394985  0.3774998  0.1087781
##   0.58315789  0.1401986  0.3753769  0.1093583
##   0.63526316  0.1409236  0.3733427  0.1099602
##   0.68736842  0.1416718  0.3713901  0.1106018
##   0.73947368  0.1424418  0.3695129  0.1112645
##   0.79157895  0.1432319  0.3677056  0.1119481
##   0.84368421  0.1440405  0.3659635  0.1126472
##   0.89578947  0.1448661  0.3642825  0.1133554
##   0.94789474  0.1457074  0.3626587  0.1140775
##   1.00000000  0.1465628  0.3610887  0.1148150
## 
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was lambda = 0.01.

# Make predictions using test data
ridgePredict <- predict(ridgeTune, newdata = testX)
# Evaluate predictive performance (predicted vs actual)
ridge_metrics <- caret::postResample(pred = ridgePredict, obs = testY)

Elastic net regression

set.seed(144)

enetGrid <- expand.grid(.lambda = c(0.001, 0.01, 0.1), .fraction = seq(0.05, 1, length = 20))

enetTune <- train(
  x = trainX,
  y = trainY,
  method = 'enet',
  preProcess = c('center', 'scale'),
  tuneGrid = enetGrid,
  trControl = trainControl(method = 'cv', number = 10)
)

enetTune

## Elasticnet 
## 
## 1799 samples
##   40 predictor
## 
## Pre-processing: centered (40), scaled (40) 
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 1618, 1619, 1619, 1621, 1619, 1620, ... 
## Resampling results across tuning parameters:
## 
##   lambda  fraction  RMSE       Rsquared   MAE      
##   0.001   0.05      0.1615658  0.2516364  0.1291321
##   0.001   0.10      0.1531226  0.2951393  0.1217863
##   0.001   0.15      0.1474562  0.3231029  0.1168771
##   0.001   0.20      0.1433431  0.3413587  0.1133012
##   0.001   0.25      0.1407766  0.3559462  0.1111036
##   0.001   0.30      0.1389007  0.3706586  0.1092686
##   0.001   0.35      0.1374650  0.3816016  0.1077617
##   0.001   0.40      0.1364306  0.3891894  0.1066826
##   0.001   0.45      0.1355728  0.3954168  0.1057914
##   0.001   0.50      0.1348281  0.4007917  0.1049897
##   0.001   0.55      0.1343585  0.4039906  0.1043781
##   0.001   0.60      0.1341669  0.4052005  0.1040501
##   0.001   0.65      0.1341656  0.4050121  0.1039096
##   0.001   0.70      0.1341146  0.4054400  0.1038550
##   0.001   0.75      0.1340671  0.4058668  0.1038394
##   0.001   0.80      0.1340871  0.4057606  0.1038731
##   0.001   0.85      0.1341786  0.4050747  0.1039716
##   0.001   0.90      0.1342904  0.4042479  0.1040961
##   0.001   0.95      0.1343814  0.4035930  0.1042072
##   0.001   1.00      0.1344683  0.4029274  0.1043119
##   0.010   0.05      0.1624589  0.2426083  0.1298978
##   0.010   0.10      0.1543800  0.2903528  0.1229261
##   0.010   0.15      0.1488359  0.3156748  0.1180911
##   0.010   0.20      0.1444983  0.3369041  0.1142849
##   0.010   0.25      0.1417385  0.3493219  0.1119614
##   0.010   0.30      0.1398009  0.3629246  0.1101910
##   0.010   0.35      0.1382757  0.3751395  0.1086334
##   0.010   0.40      0.1370926  0.3840897  0.1073946
##   0.010   0.45      0.1362007  0.3906314  0.1064540
##   0.010   0.50      0.1354267  0.3963186  0.1056501
##   0.010   0.55      0.1347682  0.4010851  0.1049280
##   0.010   0.60      0.1343698  0.4037726  0.1043909
##   0.010   0.65      0.1342468  0.4044549  0.1041139
##   0.010   0.70      0.1342391  0.4043019  0.1040019
##   0.010   0.75      0.1341930  0.4046824  0.1039355
##   0.010   0.80      0.1341398  0.4051682  0.1039034
##   0.010   0.85      0.1341305  0.4053225  0.1039080
##   0.010   0.90      0.1341619  0.4051462  0.1039527
##   0.010   0.95      0.1342134  0.4048165  0.1040248
##   0.010   1.00      0.1342602  0.4045538  0.1040879
##   0.100   0.05      0.1646575  0.2126806  0.1317583
##   0.100   0.10      0.1577539  0.2761150  0.1259077
##   0.100   0.15      0.1523972  0.3016541  0.1212004
##   0.100   0.20      0.1484287  0.3187897  0.1177290
##   0.100   0.25      0.1450222  0.3349578  0.1147402
##   0.100   0.30      0.1426363  0.3436248  0.1127049
##   0.100   0.35      0.1409233  0.3521964  0.1112800
##   0.100   0.40      0.1396274  0.3613528  0.1100081
##   0.100   0.45      0.1385929  0.3689827  0.1089489
##   0.100   0.50      0.1376835  0.3762865  0.1079924
##   0.100   0.55      0.1369716  0.3818649  0.1072438
##   0.100   0.60      0.1363801  0.3865104  0.1066149
##   0.100   0.65      0.1358716  0.3904919  0.1060682
##   0.100   0.70      0.1354304  0.3940352  0.1055856
##   0.100   0.75      0.1351188  0.3965238  0.1052228
##   0.100   0.80      0.1349407  0.3980249  0.1049642
##   0.100   0.85      0.1348169  0.3991797  0.1047673
##   0.100   0.90      0.1347630  0.3998172  0.1046401
##   0.100   0.95      0.1347662  0.4000178  0.1046143
##   0.100   1.00      0.1347665  0.4002576  0.1045997
## 
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were fraction = 0.75 and lambda = 0.001.

# Make predictions using test data
enetPredict <- predict(enetTune, newdata = testX)
# Evaluate predictive performance (predicted vs actual)
enet_metrics <- caret::postResample(pred = enetPredict, obs = testY)

Multivariate adaptive regression spline (MARS)

# This block uses parallelization to reduce runtime
set.seed(144)

# Establish parallelization clusters and backend
cl <- makePSOCKcluster(n_cores)
registerDoParallel(cl)

# Define candidate models to test
marsGrid <- expand.grid(.degree = 1:2, .nprune = 2:38)

# Fit model using training data
# Note that in MARS, the selection of cut points does not depend on the 
# scale of the predictor variables; however, to ensure that all models
# are compared relative to the same training data, I included pre-processing
marsModel <- train(x = trainX, 
                   y = trainY, 
                   method = 'earth',
                   preProcess = c('center', 'scale'),
                   tuneGrid = marsGrid,
                   trControl = trainControl(method = 'cv', number = 10,
                                            allowParallel = TRUE))
# End parallel execution
stopCluster(cl)
registerDoSEQ()

marsModel

## Multivariate Adaptive Regression Spline 
## 
## 1799 samples
##   40 predictor
## 
## Pre-processing: centered (40), scaled (40) 
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 1618, 1619, 1619, 1621, 1619, 1620, ... 
## Resampling results across tuning parameters:
## 
##   degree  nprune  RMSE       Rsquared   MAE       
##   1        2      0.1538124  0.2189125  0.12022105
##   1        3      0.1440909  0.3155560  0.11272220
##   1        4      0.1423837  0.3305559  0.11131664
##   1        5      0.1393731  0.3581347  0.10910574
##   1        6      0.1374659  0.3752362  0.10572536
##   1        7      0.1364578  0.3847058  0.10487529
##   1        8      0.1368081  0.3817654  0.10526122
##   1        9      0.1349901  0.3976398  0.10337837
##   1       10      0.1344281  0.4033788  0.10314826
##   1       11      0.1336853  0.4100356  0.10218892
##   1       12      0.1329899  0.4158749  0.10188073
##   1       13      0.1329401  0.4166285  0.10171756
##   1       14      0.1324603  0.4204076  0.10110301
##   1       15      0.1322105  0.4228448  0.10090771
##   1       16      0.1322277  0.4228740  0.10084981
##   1       17      0.1321436  0.4236477  0.10074523
##   1       18      0.1321436  0.4236477  0.10074523
##   1       19      0.1321436  0.4236477  0.10074523
##   1       20      0.1321436  0.4236477  0.10074523
##   1       21      0.1321436  0.4236477  0.10074523
##   1       22      0.1321436  0.4236477  0.10074523
##   1       23      0.1321436  0.4236477  0.10074523
##   1       24      0.1321436  0.4236477  0.10074523
##   1       25      0.1321436  0.4236477  0.10074523
##   1       26      0.1321436  0.4236477  0.10074523
##   1       27      0.1321436  0.4236477  0.10074523
##   1       28      0.1321436  0.4236477  0.10074523
##   1       29      0.1321436  0.4236477  0.10074523
##   1       30      0.1321436  0.4236477  0.10074523
##   1       31      0.1321436  0.4236477  0.10074523
##   1       32      0.1321436  0.4236477  0.10074523
##   1       33      0.1321436  0.4236477  0.10074523
##   1       34      0.1321436  0.4236477  0.10074523
##   1       35      0.1321436  0.4236477  0.10074523
##   1       36      0.1321436  0.4236477  0.10074523
##   1       37      0.1321436  0.4236477  0.10074523
##   1       38      0.1321436  0.4236477  0.10074523
##   2        2      0.1538124  0.2189125  0.12022105
##   2        3      0.1452629  0.3037679  0.11411641
##   2        4      0.1425916  0.3287725  0.11085809
##   2        5      0.1405590  0.3474387  0.11032350
##   2        6      0.1380086  0.3713671  0.10755008
##   2        7      0.1356142  0.3948066  0.10498220
##   2        8      0.1333856  0.4148415  0.10307585
##   2        9      0.1326446  0.4196156  0.10275253
##   2       10      0.1314524  0.4302231  0.10121230
##   2       11      0.1302517  0.4405919  0.10006250
##   2       12      0.1289072  0.4520325  0.09875381
##   2       13      0.1284570  0.4561735  0.09828427
##   2       14      0.1283257  0.4580122  0.09793531
##   2       15      0.1277854  0.4631053  0.09733744
##   2       16      0.1276566  0.4641367  0.09720369
##   2       17      0.1272217  0.4678228  0.09645037
##   2       18      0.1268323  0.4705380  0.09590230
##   2       19      0.1266008  0.4723149  0.09563125
##   2       20      0.1260116  0.4773837  0.09517805
##   2       21      0.1256407  0.4807858  0.09464321
##   2       22      0.1255265  0.4824188  0.09451326
##   2       23      0.1252396  0.4846171  0.09436159
##   2       24      0.1249081  0.4872455  0.09396639
##   2       25      0.1247159  0.4889192  0.09370788
##   2       26      0.1247783  0.4882978  0.09374045
##   2       27      0.1246783  0.4890188  0.09369598
##   2       28      0.1244721  0.4906483  0.09362425
##   2       29      0.1243260  0.4917019  0.09353390
##   2       30      0.1243402  0.4915448  0.09356326
##   2       31      0.1244272  0.4909789  0.09364277
##   2       32      0.1242670  0.4921285  0.09345007
##   2       33      0.1242586  0.4922162  0.09341128
##   2       34      0.1242586  0.4922162  0.09341128
##   2       35      0.1242586  0.4922162  0.09341128
##   2       36      0.1242586  0.4922162  0.09341128
##   2       37      0.1242586  0.4922162  0.09341128
##   2       38      0.1242586  0.4922162  0.09341128
## 
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were nprune = 33 and degree = 2.

# Make predictions using test data
marsPred <- predict(marsModel, newdata = testX)
# Evaluate predictive performance (predicted vs actual)
mars_metrics <- postResample(pred = marsPred, obs = testY)

Gradient boosting machine (GBM)

set.seed(144)

# Fit model using training data
gbmModel <- train(x = trainX, 
                  y = trainY,
                  method = 'gbm',
                  verbose = FALSE,
                  trControl = trainControl(method = 'cv', number = 10))  
  
gbmModel

## Stochastic Gradient Boosting 
## 
## 1799 samples
##   40 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 1618, 1619, 1619, 1621, 1619, 1620, ... 
## Resampling results across tuning parameters:
## 
##   interaction.depth  n.trees  RMSE       Rsquared   MAE       
##   1                   50      0.1352382  0.4122648  0.10702058
##   1                  100      0.1311213  0.4414301  0.10319490
##   1                  150      0.1293977  0.4522903  0.10150570
##   2                   50      0.1282895  0.4699345  0.10092659
##   2                  100      0.1244326  0.4931310  0.09712057
##   2                  150      0.1231739  0.5002890  0.09538713
##   3                   50      0.1249120  0.4946593  0.09780628
##   3                  100      0.1213326  0.5160971  0.09394344
##   3                  150      0.1194779  0.5288061  0.09193928
## 
## Tuning parameter 'shrinkage' was held constant at a value of 0.1
## 
## Tuning parameter 'n.minobsinnode' was held constant at a value of 10
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were n.trees = 150, interaction.depth =
##  3, shrinkage = 0.1 and n.minobsinnode = 10.

# Make predictions using test data
gbmPred <- predict(gbmModel, newdata = testX)
# Evaluate predictive performance (predicted vs actual)
gbm_metrics <- postResample(pred = gbmPred, obs = testY)

Random forest

# This block uses parallelization to reduce runtime
set.seed(144)

# Establish parallelization clusters and backend
cl <- makePSOCKcluster(n_cores)
registerDoParallel(cl)

# Fit model using training data
rfModel <- train(x = trainX, 
                 y = trainY,
                 method = 'rf',
                 preProcess = c('center', 'scale'),
                 trControl = trainControl(method = 'cv', number = 10,
                                          allowParallel = TRUE))

# End parallel execution
stopCluster(cl)
registerDoSEQ()

rfModel

## Random Forest 
## 
## 1799 samples
##   40 predictor
## 
## Pre-processing: centered (40), scaled (40) 
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 1618, 1619, 1619, 1621, 1619, 1620, ... 
## Resampling results across tuning parameters:
## 
##   mtry  RMSE       Rsquared   MAE       
##    2    0.1153603  0.6078529  0.08734703
##   21    0.1016088  0.6711022  0.07430062
##   40    0.1005563  0.6713783  0.07250454
## 
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was mtry = 40.

# Make predictions using test data
rfPred <- predict(rfModel, newdata = testX)
# Evaluate predictive performance (predicted vs actual)
rf_metrics <- postResample(pred = rfPred, obs = testY)

Cubist

set.seed(144)

# Fit model using training data
cubistModel <- train(x = trainX, 
                     y = trainY,
                     method = 'cubist',
                     trControl = trainControl(method = 'cv', number = 10))  
  
cubistModel

## Cubist 
## 
## 1799 samples
##   40 predictor
## 
## No pre-processing
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 1618, 1619, 1619, 1621, 1619, 1620, ... 
## Resampling results across tuning parameters:
## 
##   committees  neighbors  RMSE       Rsquared   MAE       
##    1          0          0.1236472  0.5155824  0.08880599
##    1          5          0.1171326  0.5718857  0.08259007
##    1          9          0.1175477  0.5646168  0.08346279
##   10          0          0.1106959  0.5994353  0.08146406
##   10          5          0.1044209  0.6414464  0.07471649
##   10          9          0.1043529  0.6408618  0.07554967
##   20          0          0.1074805  0.6251504  0.07960715
##   20          5          0.1019229  0.6575562  0.07310063
##   20          9          0.1015850  0.6593064  0.07397149
## 
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were committees = 20 and neighbors = 9.

# Make predictions using test data
cubistPred <- predict(cubistModel, newdata = testX)
# Evaluate predictive performance (predicted vs actual)
cubist_metrics <- postResample(pred = cubistPred, obs = testY)

Support vector machine (SVM)

set.seed(144) 

# Fit model using training data
svmModel <- train(x = trainX, 
                  y = trainY, 
                  method = 'svmRadial',
                  preProcess = c('center', 'scale'),
                  tuneLength = 10,
                  trControl = trainControl(method = 'cv', number = 10))

svmModel

## Support Vector Machines with Radial Basis Function Kernel 
## 
## 1799 samples
##   40 predictor
## 
## Pre-processing: centered (40), scaled (40) 
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 1618, 1619, 1619, 1621, 1619, 1620, ... 
## Resampling results across tuning parameters:
## 
##   C       RMSE       Rsquared   MAE       
##     0.25  0.1270577  0.4785759  0.09366959
##     0.50  0.1233590  0.5036740  0.09038644
##     1.00  0.1196823  0.5307021  0.08762611
##     2.00  0.1169562  0.5497866  0.08573503
##     4.00  0.1158258  0.5578210  0.08562901
##     8.00  0.1160010  0.5586601  0.08657849
##    16.00  0.1168702  0.5565404  0.08724791
##    32.00  0.1205621  0.5383580  0.08964824
##    64.00  0.1261331  0.5112752  0.09336524
##   128.00  0.1318129  0.4850916  0.09740967
## 
## Tuning parameter 'sigma' was held constant at a value of 0.01627391
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were sigma = 0.01627391 and C = 4.

# Make predictions using test data
svmPred <- predict(svmModel, newdata = testX)
# Evaluate predictive performance (predicted vs actual)
svm_metrics <- postResample(pred = svmPred, obs = testY)

k-Nearest Neighbors (kNN)

set.seed(144)

# Fit model using training data
knnModel <- train(x = trainX, 
                  y = trainY, 
                  method = 'knn',
                  preProc = c('center', 'scale'),
                  tuneLength = 10,
                  trControl = trainControl(method = 'cv', number = 10))


knnModel

## k-Nearest Neighbors 
## 
## 1799 samples
##   40 predictor
## 
## Pre-processing: centered (40), scaled (40) 
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 1618, 1619, 1619, 1621, 1619, 1620, ... 
## Resampling results across tuning parameters:
## 
##   k   RMSE       Rsquared   MAE       
##    5  0.1216142  0.5166979  0.08845746
##    7  0.1216598  0.5129583  0.08971252
##    9  0.1222568  0.5071793  0.09080370
##   11  0.1225470  0.5046420  0.09146971
##   13  0.1241751  0.4915024  0.09295644
##   15  0.1252545  0.4829420  0.09417810
##   17  0.1262438  0.4751441  0.09512465
##   19  0.1269459  0.4696370  0.09626618
##   21  0.1275443  0.4654743  0.09691539
##   23  0.1280581  0.4615528  0.09773080
## 
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was k = 5.

# Make predictions using test data
knnPred <- predict(knnModel, newdata = testX)
# Evaluate predictive performance (predicted vs actual)
knn_metrics <- postResample(pred = knnPred, obs = testY)

Neural network

# This block uses parallelization to reduce runtime
set.seed(144)

# Establish parallelization clusters and backend
cl <- makePSOCKcluster(n_cores)
registerDoParallel(cl)

# Define candidate models to test
nnetGrid <- expand.grid(.decay = c(0, 0.01, .1), .size = c(1:5), .bag = FALSE)

# Fit model using training data
# 'avNNet' method is used to perform model averaging
nnetModel <- train(x = trainX, 
                   y = trainY, 
                  method = 'avNNet',
                  preProc = c('center', 'scale'),
                  tuneGrid = nnetGrid,
                  trControl = trainControl(method = 'cv', number = 10,
                                           allowParallel = TRUE),
                  # number of models to average
                  repeats = 5,
                  # maximum iterations
                  maxit = 500,
                  # maximum number of weights
                  MaxNWts = 5 * (ncol(trainX) + 1) + 5 + 1,
                  # linear output units
                  linout = TRUE,
                  # suppress tracing optimization
                  trace = FALSE)

# End parallel execution
stopCluster(cl)
registerDoSEQ()

nnetModel

## Model Averaged Neural Network 
## 
## 1799 samples
##   40 predictor
## 
## Pre-processing: centered (40), scaled (40) 
## Resampling: Cross-Validated (10 fold) 
## Summary of sample sizes: 1618, 1619, 1619, 1621, 1619, 1620, ... 
## Resampling results across tuning parameters:
## 
##   decay  size  RMSE       Rsquared   MAE       
##   0.00   1     0.1368041  0.3986876  0.10526936
##   0.00   2     0.1630957  0.3783512  0.10375383
##   0.00   3     0.1382453  0.3992475  0.09869750
##   0.00   4     0.2179239  0.3404007  0.10701371
##   0.00   5     0.3452087  0.4806614  0.12520030
##   0.01   1     0.1329777  0.4166199  0.10388025
##   0.01   2     0.1261798  0.4763050  0.09541247
##   0.01   3     0.1196972  0.5250155  0.09040403
##   0.01   4     0.1162798  0.5535528  0.08740031
##   0.01   5     0.1173828  0.5460097  0.08715184
##   0.10   1     0.1346126  0.4018510  0.10464239
##   0.10   2     0.1265836  0.4707341  0.09615291
##   0.10   3     0.1205893  0.5190120  0.09116213
##   0.10   4     0.1185110  0.5356727  0.08925677
##   0.10   5     0.1169355  0.5489536  0.08739199
## 
## Tuning parameter 'bag' was held constant at a value of FALSE
## RMSE was used to select the optimal model using the smallest value.
## The final values used for the model were size = 4, decay = 0.01 and bag = FALSE.

# Make predictions using test data
nnetPred <- predict(nnetModel, newdata = testX)
nnet_metrics <- postResample(pred = nnetPred, obs = testY)

Model comparison and selection

Of the 11 models, Cubist and random forest had the lowest RMSE (0.10) and MAE (0.07) and the highest \(R^2 = 0.64\), which indicates that they are the best fit for the data. Both models had nearly identical performance metrics; however, a key difference is that the Cubist model is highly interpretable (because it is rule-based) whereas the random forest model is a “black-box” model. Since management requested both non-technical and technical reports, the target audience probably includes non-technical individuals. Because of this, I selected the Cubist model as the final model for prediction.

The Cubist model rules are shown in Appendix 1.

# Combine performance metrics from all models into dataframe
model_performance_df <- as.data.frame(rbind(
  ols_metrics,
  pls_metrics,
  ridge_metrics,
  enet_metrics,
  mars_metrics,
  gbm_metrics,
  rf_metrics,
  cubist_metrics,
  svm_metrics,
  knn_metrics,
  nnet_metrics))

model_performance_df$model <- 
  c('OLS', 'PLS', 'Ridge', 'ElasticNet', 'MARS', 'GBM', 'RF', 'Cubist',
    'SVM', 'kNN', 'NeuralNet')
rownames(model_performance_df) <- NULL

model_performance_df %>%
  select(model, RMSE, Rsquared, MAE) %>%
  arrange(RMSE) %>%
  kbl() %>%
  kable_minimal()  

model	RMSE	Rsquared	MAE
Cubist	0.1024605	0.6364740	0.0730529
RF	0.1025437	0.6361065	0.0723338
SVM	0.1173731	0.5250713	0.0843024
NeuralNet	0.1206323	0.4978233	0.0867856
GBM	0.1212388	0.4900736	0.0907832
kNN	0.1238252	0.4813066	0.0882726
MARS	0.1272256	0.4447518	0.0933107
PLS	0.1348383	0.3704530	0.1050445
Ridge	0.1350254	0.3686562	0.1050955
OLS	0.1350335	0.3688165	0.1051041
ElasticNet	0.1350430	0.3673372	0.1052959

Key predictive factors in final model

In the Cubist model, the most important predictive factor is Mnf.Flow, followed by Balling.Lvl, Alch.Rel, Balling, and Oxygen.Filter. Previously, I showed in the EDA correlation analysis that Mnf.Flow had the strongest (albeit moderate) correlation with the target variable PH (r=0.45). This correlation is consistent with its importance in the Cubist model.

cubist_var_importance <- varImp(cubistModel, scale = FALSE)
print(cubist_var_importance)

## cubist variable importance
## 
##   only 20 most important variables shown (out of 40)
## 
##                    Overall
## Mnf.Flow              82.5
## Alch.Rel              45.5
## Balling.Lvl           45.0
## Balling               39.5
## Pressure.Vacuum       38.0
## Bowl.Setpoint         38.0
## Air.Pressurer         34.0
## Hyd.Pressure3         34.0
## Filler.Speed          33.0
## Oxygen.Filler         33.0
## Brand.Code.C          31.5
## Density.Scaled        29.5
## Carb.Pressure1        29.5
## Balling.Lvl.Scaled    27.0
## Usage.cont            26.0
## Carb.Flow             21.5
## Hyd.Pressure1         21.0
## MFR                   21.0
## Hyd.Pressure2         20.5
## Balling.Scaled        20.5

ubist_imp_df <- as.data.frame(cubist_var_importance$importance$Overall) %>%
  rownames_to_column(var = 'Variable')

ggplot(cubist_var_importance, aes(x = reorder(Variable, Overall), y = Overall)) +
  geom_col(fill = 'steelblue') +
  labs(
    x = 'Feature',
    y = 'Importance Score',
    title = 'Variable Importance in Cubist Model', 
    caption = 'Importance scores are raw scores (not scaled).'
  ) + 
  theme_bw() +
  theme(
    axis.title = element_text(face = 'bold'),
    plot.title = element_text(face = 'bold'),
    plot.caption = element_text(color = "darkgray", hjust = 0)
  )

Predictions using final model

Finally, I used the Cubist model to predict pH values in the holdout evaluation dataset and saved the results to an Excel file.

# Make predictions
evalY <- predict(cubistModel, newdata = evalX)
# Bind predictions to original holdout evaluation dataset
eval_predictions_df <- bind_cols(select(beverages_eval_df, -c(PH)), PH = evalY) %>%
  mutate(
    # Round pH values to 2 significant digits for consistency with format in StudentData dataset
    PH = round(PH, 2)
  )

write.xlsx(eval_predictions_df, file = 'project2_predictions.xlsx')

Conclusions

This project underscored the importance of detailed eploratory data analysis (EDA) and methodical model development to make accurate predictions. Key insights from EDA were the predictive importance of brand codes and the mechanism of missing data, which informed the selection of an appropriate data imputation method (random forest). In addition, consistent application of data processing techniques to all three datasets (training, test, and holdout evaluation) were critical to avoid target leakage and introducing artifacts in the data.

Training and testing a variety of linear and nonlinear models revealed that Cubist and random forest models had the best accuracy (lowest RMSE), and both explained approximately 64% of the variation in the target variable PH. The Cubist model was selected as the final model because it provided the best combination of predictive performance and interpretability, which is important for ABC Beverage stakeholders who may be specialists or non-specialists. The top 5 most important predictors in this model were Mnf.Flow, Balling.Lvl, Alch.Rel, Balling, and Oxygen.Filter. These factors will be important for management to understand the manufacturing process and comply with the new regulations.

Future work with this dataset could implement multiple imputation techniques, such as MICE, which is the gold standard for data imputation in many applications. In addition, if updated data are available, the models could be refit to counter the effects of data drift and leverage larger sample sizes.

Appendix 1

The Cubist model rules are shown below (click the ‘Show’ button on the right).

summary(cubistModel$finalModel)
## 
## Call:
## cubist.default(x = x, y = y, committees = param$committees)
## 
## 
## Cubist [Release 2.07 GPL Edition]
## ---------------------------------
## 
##     Target attribute `outcome'
## 
## Read 1799 cases (41 attributes) from undefined.data
## 
## Model 1:
## 
##   Rule 1/1: [31 cases, mean 8.252, range 8.08 to 8.78, est err 0.138]
## 
##     if
##  Alch.Rel > 0.48831
##  Oxygen.Filler <= -1.870865
##  PC.Volume > -0.8901629
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = 7.701 - 0.45 PC.Volume + 0.079 Oxygen.Filler
##            - 0.063 Pressure.Vacuum
## 
##   Rule 1/2: [32 cases, mean 8.303, range 8.06 to 8.64, est err 0.109]
## 
##     if
##  Alch.Rel <= 0.4902469
##  Filler.Speed > 6837602
##  Oxygen.Filler > -2.491261
##  Mnf.Flow > -100
##  Balling.Lvl > 1.5
##  Balling.Lvl.Scaled <= 0.6624301
##     then
##  outcome = 2.673 + 0.322 Balling.Lvl + 0.0021 Mnf.Flow
##            - 0.0086 Hyd.Pressure3 - 0.0012 Usage.cont
##            + 2.93e-08 Filler.Speed + 9 Alch.Rel
##            + 0.009 Balling.Lvl.Scaled - 5e-06 Carb.Flow
##            + 0.03 Carb.Pressure1 - 0.011 Density
## 
##   Rule 1/3: [31 cases, mean 8.314, range 7.88 to 8.8, est err 0.201]
## 
##     if
##  Alch.Rel <= 0.4902469
##  Mnf.Flow > -100
##  Balling.Lvl > 1.5
##  Density.Scaled <= -1.901343
##     then
##  outcome = -0.746 - 0.00042 Mnf.Flow + 0.0024 Hyd.Pressure3
##            - 0.09 Brand.Code.C + 18 Alch.Rel + 0.0015 Bowl.Setpoint
##            - 0.00032 Usage.cont + 0.11 Carb.Pressure1 - 0.018 Balling.Lvl
##            - 0.014 Density.Scaled + 0.012 Balling.Lvl.Scaled
##            + 4.9e-09 Filler.Speed + 0.022 Brand.Code.D - 1.5e-07 MFR
##            - 0.0005 Hyd.Pressure2 - 5e-06 Filler.Level + 7e-06 Carb.Flow
##            - 0.0035 Pressure.Setpoint - 0.006 Air.Pressurer
##            - 0.012 Oxygen.Filler - 0.06 PC.Volume
##            + 0.006 Air.Pressurer.Scaled - 0.005 Density
## 
##   Rule 1/4: [86 cases, mean 8.378, range 8.08 to 8.62, est err 0.072]
## 
##     if
##  Alch.Rel <= 0.4902469
##  Mnf.Flow > -100
##  Balling.Lvl > 1.5
##  Balling.Lvl.Scaled > 0.6624301
##  Density.Scaled > -1.901343
##     then
##  outcome = 4.235 + 0.051 Balling.Lvl.Scaled - 0.32 PC.Volume
##            + 0.058 Oxygen.Filler - 2.7e-05 Carb.Flow
##            + 0.021 Air.Pressurer + 2 Alch.Rel + 1.2e-09 Filler.Speed
##            - 4e-08 MFR - 4e-05 Usage.cont - 2e-05 Mnf.Flow
##            + 0.0001 Hyd.Pressure3
## 
##   Rule 1/5: [74 cases, mean 8.389, range 8.08 to 8.74, est err 0.083]
## 
##     if
##  Carb.Flow <= 1082
##  Bowl.Setpoint <= 100
##  Balling.Lvl <= 1.5
##     then
##  outcome = 3.29 + 0.33 Balling.Lvl - 0.042 Balling.Lvl.Scaled
##            - 0.00018 Mnf.Flow + 9.2e-09 Filler.Speed - 2.7e-07 MFR
##            + 0.001 Hyd.Pressure3 + 0.01 Air.Pressurer
##            - 0.012 Density.Scaled + 0.0007 Bowl.Setpoint - 0.011 Balling
##            - 0.0043 Pressure.Setpoint + 6 Alch.Rel + 0.04 Carb.Pressure1
##            + 6e-06 Carb.Flow - 6e-05 Usage.cont
##            + 0.002 Air.Pressurer.Scaled
## 
##   Rule 1/6: [144 cases, mean 8.402, range 8 to 8.7, est err 0.072]
## 
##     if
##  Mnf.Flow > -100
##  Hyd.Pressure3 <= 37.6
##  Carb.Flow > 1082
##  Bowl.Setpoint <= 100
##  Balling.Lvl <= 1.5
##  Balling.Lvl.Scaled > -0.9272727
##     then
##  outcome = 6.352 + 0.392 Balling.Lvl + 0.0096 Hyd.Pressure3
##            + 0.000139 Carb.Flow - 0.0069 Bowl.Setpoint
##            + 4.8e-05 Filler.Level - 0.047 Balling.Lvl.Scaled
##            - 0.046 Balling.Scaled + 0.021 Air.Pressurer.Scaled
##            + 0.008 Air.Pressurer - 0.005 Carb.Flow.Scaled
##            - 0.008 Pressure.Vacuum
## 
##   Rule 1/7: [36 cases, mean 8.429, range 8.16 to 8.66, est err 0.050]
## 
##     if
##  Alch.Rel > 0.4902469
##  Mnf.Flow > -100
##  Hyd.Pressure3 <= 32.4
##  Bowl.Setpoint > 96.34333
##  Balling.Lvl > 1.5
##  Balling.Lvl.Scaled <= 0.05682904
##     then
##  outcome = 6.996 + 0.0087 Bowl.Setpoint + 0.081 Balling.Lvl
##            - 0.057 Oxygen.Filler
## 
##   Rule 1/8: [41 cases, mean 8.444, range 8.02 to 8.68, est err 0.087]
## 
##     if
##  Alch.Rel <= 0.4902469
##  Filler.Speed <= 6837602
##  Mnf.Flow > -100
##  Balling.Lvl > 1.5
##     then
##  outcome = 8.321 + 0.063 Balling.Lvl + 0.00043 Mnf.Flow
##            - 0.0016 Hyd.Pressure3 - 0.00021 Usage.cont
## 
##   Rule 1/9: [65 cases, mean 8.484, range 8.26 to 8.7, est err 0.057]
## 
##     if
##  Alch.Rel > 0.4902469
##  Mnf.Flow > -100
##  Hyd.Pressure3 <= 32.4
##  Balling.Lvl.Scaled > 0.05682904
##     then
##  outcome = 7.644 + 0.00365 Mnf.Flow - 0.0133 Hyd.Pressure3
##            - 0.095 Pressure.Vacuum - 4.3e-05 Carb.Flow
##            - 0.038 Density.Scaled + 0.077 Density
##            + 0.009 Balling.Lvl.Scaled - 0.00015 Usage.cont
##            + 0.0003 Hyd.Pressure1 + 0.02 Carb.Pressure1
##            - 0.0002 Bowl.Setpoint - 0.03 PC.Volume
##            - 0.003 Carb.Flow.Scaled + 1e-06 Filler.Level
## 
##   Rule 1/10: [36 cases, mean 8.486, range 8.2 to 8.7, est err 0.100]
## 
##     if
##  Hyd.Pressure3 <= 32.4
##  Bowl.Setpoint <= 96.34333
##  Balling.Lvl > 1.5
##  Balling.Lvl.Scaled <= 0.05682904
##     then
##  outcome = -11.915 - 0.102 Density.Scaled + 0.0041 Hyd.Pressure3
##            + 0.166 Density - 0.00095 Usage.cont + 36 Alch.Rel
##            + 0.037 Balling.Lvl.Scaled + 0.15 Carb.Pressure1
##            - 0.0002 Mnf.Flow + 0.019 Balling.Lvl - 1.8e-07 MFR
##            - 0.11 PC.Volume + 4.9e-09 Filler.Speed
##            - 0.016 Pressure.Vacuum + 0.0007 Hyd.Pressure1
##            + 0.007 Air.Pressurer - 7e-06 Carb.Flow
##            - 0.006 Carb.Flow.Scaled + 3e-06 Filler.Level
##            - 0.0022 Pressure.Setpoint - 0.0002 Bowl.Setpoint
##            - 0.003 Balling
## 
##   Rule 1/11: [45 cases, mean 8.493, range 8.18 to 8.64, est err 0.068]
## 
##     if
##  Alch.Rel <= 0.4902469
##  Filler.Speed > 6837602
##  Oxygen.Filler <= -2.491261
##  Mnf.Flow > -100
##  Balling.Lvl > 1.5
##  Balling.Lvl.Scaled <= 0.6624301
##     then
##  outcome = -0.749 + 2.101e-07 Filler.Speed + 0.059 Balling.Lvl
##            - 0.00048 Usage.cont + 0.00018 Mnf.Flow + 14 Alch.Rel
##            + 0.016 Balling.Lvl.Scaled - 1.1e-05 Carb.Flow - 1.7e-07 MFR
##            + 0.04 Carb.Pressure1 - 0.013 Density + 0.002 Air.Pressurer
## 
##   Rule 1/12: [26 cases, mean 8.501, range 8.18 to 8.84, est err 0.099]
## 
##     if
##  Alch.Rel > 0.48831
##  PC.Volume <= -0.8901629
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = -12.808 - 0.1275 Mnf.Flow + 0.31 Carb.Pressure1
##            + 1.43 Carb.Pressure - 0.049 Balling - 0.08 Brand.Code.C
##            + 0.029 Balling.Lvl - 0.012 Air.Pressurer + 6 Alch.Rel
##            - 0.38 Hyd.Pressure4 - 0.016 Oxygen.Filler
##            + 0.017 Brand.Code.D - 0.007 Density.Scaled
##            + 0.005 Air.Pressurer.Scaled + 0.0004 Hyd.Pressure1
## 
##   Rule 1/13: [210 cases, mean 8.503, range 8.24 to 8.86, est err 0.071]
## 
##     if
##  Mnf.Flow > -100
##  Bowl.Setpoint > 100
##  Balling.Lvl <= 1.5
##     then
##  outcome = 4.994 + 0.276 Balling.Lvl - 0.061 Balling.Lvl.Scaled
##            - 0.0039 Bowl.Setpoint - 0.00046 Mnf.Flow
##            + 0.0034 Hyd.Pressure3 + 3.6e-05 Carb.Flow - 5e-07 MFR
##            + 1.7e-05 Filler.Level - 0.0133 Pressure.Setpoint
##            + 0.15 Carb.Pressure1 + 1.08e-08 Filler.Speed
##            - 0.014 Density.Scaled + 0.01 Air.Pressurer
##            + 0.004 Air.Pressurer.Scaled + 2 Alch.Rel
## 
##   Rule 1/14: [46 cases, mean 8.527, range 8.2 to 8.84, est err 0.122]
## 
##     if
##  Carb.Pressure1 <= 10.51956
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##     then
##  outcome = -119.779 - 1.28629 Mnf.Flow + 0.096 Pressure.Vacuum
##            - 0.078 Oxygen.Filler - 0.018 Balling + 0.02 Brand.Code.D
##            + 0.008 Balling.Lvl + 0.04 Carb.Pressure1
##            - 0.004 Air.Pressurer + 0.0002 Hyd.Pressure3
##            - 0.007 Brand.Code.C + 0.0001 Bowl.Setpoint
## 
##   Rule 1/15: [26 cases, mean 8.535, range 8.22 to 8.64, est err 0.050]
## 
##     if
##  Hyd.Pressure3 > 37.6
##  Carb.Flow > 1082
##  Bowl.Setpoint <= 100
##  Balling.Lvl <= 1.5
##  Balling.Lvl.Scaled > -0.9272727
##     then
##  outcome = 8.468 - 0.0334 Hyd.Pressure3 + 0.000301 Carb.Flow
##            + 0.276 Balling.Lvl - 0.0053 Bowl.Setpoint
##            - 0.033 Balling.Lvl.Scaled - 0.008 Balling.Scaled
##            + 4e-06 Filler.Level + 0.003 Air.Pressurer
##            - 0.006 Pressure.Vacuum - 0.003 Carb.Flow.Scaled
## 
##   Rule 1/16: [32 cases, mean 8.547, range 8.4 to 8.64, est err 0.045]
## 
##     if
##  Alch.Rel <= 0.48831
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = -3.623 - 0.11494 Mnf.Flow - 0.045 Balling - 0.072 Brand.Code.C
##            + 0.026 Balling.Lvl - 0.011 Air.Pressurer
##            + 0.06 Carb.Pressure1 - 0.34 Hyd.Pressure4 + 5 Alch.Rel
##            + 0.015 Brand.Code.D - 0.007 Density.Scaled
##            + 0.004 Air.Pressurer.Scaled + 0.0003 Hyd.Pressure1
##            + 0.007 Oxygen.Filler
## 
##   Rule 1/17: [51 cases, mean 8.551, range 8.4 to 8.74, est err 0.052]
## 
##     if
##  Carb.Flow > 1082
##  Bowl.Setpoint <= 100
##  Balling.Lvl <= 1.5
##  Balling.Lvl.Scaled <= -0.9272727
##     then
##  outcome = 0.774 + 3.625 Balling.Lvl - 0.43 Balling.Lvl.Scaled
##            + 0.0112 Bowl.Setpoint + 0.000139 Carb.Flow
##            - 8.2e-05 Filler.Level - 0.133 Oxygen.Filler
##            + 0.004 Hyd.Pressure1 - 0.036 Carb.Flow.Scaled
##            - 0.00015 Mnf.Flow + 0.0009 Hyd.Pressure3 + 6e-09 Filler.Speed
##            - 1.6e-07 MFR + 0.007 Air.Pressurer - 0.008 Density.Scaled
##            - 0.0028 Pressure.Setpoint - 0.005 Balling.Scaled
##            + 0.02 Carb.Pressure1 - 0.004 Pressure.Vacuum
##            + 0.002 Air.Pressurer.Scaled
## 
##   Rule 1/18: [43 cases, mean 8.568, range 8.26 to 8.84, est err 0.090]
## 
##     if
##  Oxygen.Filler > -1.870865
##  Brand.Code.C > 0
##     then
##  outcome = -1.363 - 0.06991 Mnf.Flow + 0.081 Pressure.Vacuum
##            + 0.0026 Hyd.Pressure3 - 0.084 Brand.Code.C - 0.027 Balling
##            - 0.016 Carb.Flow.Scaled + 0.08 Carb.Pressure1 + 9 Alch.Rel
##            - 0.01 Air.Pressurer + 0.0007 Bowl.Setpoint
##            - 0.01 Density.Scaled + 0.019 Brand.Code.D
##            - 0.014 Oxygen.Filler - 0.00011 Usage.cont + 0.006 Balling.Lvl
##            + 0.005 Air.Pressurer.Scaled + 2.2e-09 Filler.Speed
##            - 0.21 Hyd.Pressure4 - 7e-08 MFR + 4e-06 Carb.Flow
##            + 0.004 Balling.Lvl.Scaled - 0.0016 Pressure.Setpoint
##            - 0.0002 Hyd.Pressure2 - 2e-06 Filler.Level - 0.03 PC.Volume
##            + 0.0002 Hyd.Pressure1
## 
##   Rule 1/19: [44 cases, mean 8.576, range 8.24 to 8.76, est err 0.087]
## 
##     if
##  Alch.Rel > 0.4902469
##  Filler.Speed <= 7753922
##  Mnf.Flow > -100
##  Hyd.Pressure3 > 32.4
##     then
##  outcome = 3.947 + 0.256 Balling.Lvl - 0.094 Density.Scaled
##            - 0.068 Carb.Flow.Scaled + 0.157 Density - 0.00074 Usage.cont
##            - 0.032 Balling.Scaled + 8 Alch.Rel - 0.09 PC.Volume
##            - 0.36 Hyd.Pressure4 + 0.014 Oxygen.Filler
##            + 0.0004 Hyd.Pressure3 - 9e-08 MFR + 2.4e-09 Filler.Speed
##            + 0.003 Air.Pressurer + 0.02 PSC + 0.02 Carb.Pressure1
##            + 0.0002 Bowl.Setpoint - 0.0011 Pressure.Setpoint
## 
##   Rule 1/20: [32 cases, mean 8.600, range 8.18 to 8.86, est err 0.092]
## 
##     if
##  Alch.Rel <= 0.48831
##  Carb.Volume > 0.4826396
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##     then
##  outcome = -52.676 - 0.5797 Mnf.Flow - 0.114 Balling + 0.051 Balling.Lvl
##            + 0.1 Brand.Code.D + 0.23 Carb.Pressure1 - 0.026 Air.Pressurer
##            + 10 Alch.Rel - 0.014 Oxygen.Filler - 1.1e-07 MFR
##            + 3.1e-09 Filler.Speed - 0.14 Hyd.Pressure4
##            - 0.003 Balling.Scaled - 0.004 Pressure.Vacuum
##            + 0.002 Air.Pressurer.Scaled
## 
##   Rule 1/21: [71 cases, mean 8.628, range 8.26 to 8.92, est err 0.111]
## 
##     if
##  Alch.Rel > 0.48831
##  Carb.Pressure1 > 10.51956
##  Carb.Volume > 0.4826396
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##  Air.Pressurer > 142
##     then
##  outcome = -18.429 - 0.10679 Mnf.Flow - 4.77e-06 MFR
##            + 1.221e-07 Filler.Speed + 0.135 Balling
##            - 0.15 Pressure.Vacuum + 0.4 Carb.Pressure1 + 23 Alch.Rel
##            + 0.028 Carb.Flow.Scaled
## 
##   Rule 1/22: [97 cases, mean 8.629, range 8.42 to 8.86, est err 0.057]
## 
##     if
##  Alch.Rel > 0.4902469
##  Filler.Speed > 7753922
##  Mnf.Flow > -100
##  Hyd.Pressure3 > 32.4
##  Balling.Lvl > 1.5
##     then
##  outcome = 13.217 - 5.031e-07 Filler.Speed - 0.144 Density.Scaled
##            - 0.099 Carb.Flow.Scaled - 0.00059 Mnf.Flow + 0.14 Density
##            - 0.0026 Hyd.Pressure1 - 0.0002 Usage.cont - 0.06 PC.Volume
##            - 0.26 Hyd.Pressure4 + 0.011 Oxygen.Filler
##            + 0.0003 Hyd.Pressure3 + 0.02 PSC + 0.003 Balling.Lvl.Scaled
## 
##   Rule 1/23: [138 cases, mean 8.666, range 8.28 to 8.94, est err 0.095]
## 
##     if
##  Carb.Pressure1 > 10.51956
##  Carb.Volume <= 0.4826396
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##  Air.Pressurer > 142
##     then
##  outcome = -68.916 - 0.62672 Mnf.Flow + 38 Alch.Rel - 0.06 Balling.Lvl
##            - 0.033 Air.Pressurer + 0.11 Carb.Pressure1 - 0.016 Balling
##            + 0.016 Brand.Code.D - 0.004 Oxygen.Filler
## 
##   Rule 1/24: [369 cases, mean 8.680, range 8.3 to 8.92, est err 0.060]
## 
##     if
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum <= -5
##     then
##  outcome = -25.306 - 0.01304 Mnf.Flow - 0.106 Balling
##            + 0.156 Pressure.Vacuum + 59 Alch.Rel + 0.033 Air.Pressurer
##            - 0.035 Balling.Lvl.Scaled - 0.064 Oxygen.Filler
##            + 5.2e-09 Filler.Speed + 0.003 Balling.Lvl
## 
##   Rule 1/25: [60 cases, mean 8.701, range 8.24 to 8.94, est err 0.084]
## 
##     if
##  Carb.Pressure1 > 10.51956
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##  Air.Pressurer <= 142
##     then
##  outcome = -28.457 - 0.36372 Mnf.Flow - 0.1 Balling + 0.055 Balling.Lvl
##            - 0.124 Brand.Code.C - 0.028 Air.Pressurer
##            + 0.058 Brand.Code.D + 0.15 Carb.Pressure1
##            - 0.59 Hyd.Pressure4 - 0.025 Oxygen.Filler + 9 Alch.Rel
##            - 0.011 Density.Scaled + 0.008 Air.Pressurer.Scaled
##            + 0.0006 Hyd.Pressure1
## 
## Model 2:
## 
##   Rule 2/1: [32 cases, mean 8.339, range 8 to 8.66, est err 0.110]
## 
##     if
##  Alch.Rel <= 0.4906174
##  Filler.Speed <= 7920200
##  Temperature > 0.4998866
##  Mnf.Flow > 135.6
##  Bowl.Setpoint > 80
##     then
##  outcome = 7.077 + 0.00506 Mnf.Flow - 0.085 Density.Scaled
##            + 0.0041 Bowl.Setpoint - 7e-08 MFR + 0.004 Balling
## 
##   Rule 2/2: [54 cases, mean 8.356, range 8.02 to 8.58, est err 0.117]
## 
##     if
##  Alch.Rel <= 0.4906174
##  Filler.Speed > 7920200
##  Mnf.Flow > -100
##  Carb.Flow > 1084
##  Bowl.Setpoint > 80
##  Balling.Scaled > -0.3523095
##  Density.Scaled > -1.934118
##     then
##  outcome = -6.605 - 4.423e-07 Filler.Speed - 0.0035 Usage.cont
##            + 0.13 Air.Pressurer + 0.147 Balling.Scaled - 1.3 PSC.CO2
##            + 0.087 Brand.Code.Encoded - 0.036 Density.Scaled
##            + 1.5e-05 Carb.Flow - 0.028 Pressure.Vacuum
##            + 0.013 Balling.Lvl.Scaled
## 
##   Rule 2/3: [28 cases, mean 8.370, range 8.08 to 8.84, est err 0.135]
## 
##     if
##  Alch.Rel > 0.4885216
##  Filler.Speed > 6896898
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = -73.395 - 0.88134 Mnf.Flow - 4.725e-07 Filler.Speed
##            - 0.00216 Usage.cont - 0.017 Air.Pressurer
##            + 0.03 Oxygen.Filler - 0.15 PC.Volume
## 
##   Rule 2/4: [128 cases, mean 8.388, range 8 to 8.74, est err 0.102]
## 
##     if
##  Filler.Speed <= 7920200
##  Temperature > 0.4998866
##  Mnf.Flow > -100
##  Bowl.Setpoint > 80
##  Air.Pressurer <= 144.2
##     then
##  outcome = -16429.482 + 115.36 Air.Pressurer
##            - 57.962 Air.Pressurer.Scaled + 0.00059 Mnf.Flow
##            - 1.08e-06 MFR + 1.4e-08 Filler.Speed - 0.022 Density.Scaled
##            + 0.019 Balling + 0.001 Bowl.Setpoint
## 
##   Rule 2/5: [302 cases, mean 8.407, range 8 to 8.86, est err 0.101]
## 
##     if
##  Alch.Rel <= 0.4906174
##  Filler.Speed <= 7920200
##  Mnf.Flow > -100
##  Bowl.Setpoint > 80
##  Air.Pressurer <= 144.2
##     then
##  outcome = -0.203 + 0.00065 Mnf.Flow + 0.059 Air.Pressurer - 8.7e-07 MFR
##            + 0.0033 Bowl.Setpoint + 0.0008 Hyd.Pressure2
##            + 5.6e-09 Filler.Speed - 0.005 Density.Scaled
##            - 0.0016 Pressure.Setpoint - 0.003 Balling.Lvl.Scaled
##            + 0.0002 Hyd.Pressure1
## 
##   Rule 2/6: [75 cases, mean 8.421, range 7.88 to 8.8, est err 0.145]
## 
##     if
##  Alch.Rel <= 0.4906174
##  Mnf.Flow > -100
##  Density.Scaled <= -1.934118
##     then
##  outcome = 8.463 - 0.613 Balling.Lvl + 0.00219 Mnf.Flow
##            - 0.0176 Hyd.Pressure1 + 5.4e-09 Filler.Speed - 1.8e-07 MFR
##            + 0.0005 Hyd.Pressure2 + 0.0004 Bowl.Setpoint
##            - 0.017 Brand.Code.C + 0.0003 Hyd.Pressure3
##            + 0.004 Air.Pressurer - 0.005 Density.Scaled
##            - 0.011 Brand.Code.A + 0.02 Carb.Pressure1 - 5e-05 Usage.cont
##            - 0.001 Pressure.Setpoint
## 
##   Rule 2/7: [489 cases, mean 8.443, range 8 to 8.86, est err 0.092]
## 
##     if
##  Mnf.Flow > -100
##  Hyd.Pressure3 <= 32.6
##     then
##  outcome = 7.286 - 0.00042 Mnf.Flow - 0.088 Brand.Code.C
##            + 0.0019 Hyd.Pressure3 + 1.28e-08 Filler.Speed - 3.6e-07 MFR
##            + 0.024 Balling.Lvl - 0.06 Brand.Code.A + 0.0012 Bowl.Setpoint
##            + 0.1 Carb.Pressure1 - 0.00027 Usage.cont
##            - 0.016 Density.Scaled - 0.0002 Hyd.Pressure2
## 
##   Rule 2/8: [18 cases, mean 8.458, range 8.14 to 8.7, est err 0.166]
## 
##     if
##  Filler.Speed <= 6896898
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = 8.546 + 0.0107 Hyd.Pressure2 + 0.048 Oxygen.Filler
## 
##   Rule 2/9: [80 cases, mean 8.459, range 8.26 to 8.56, est err 0.058]
## 
##     if
##  Alch.Rel <= 0.4906174
##  Bowl.Setpoint <= 80
##  Air.Pressurer <= 144.2
##  Density.Scaled > -1.934118
##     then
##  outcome = 2.941 - 0.0039 Mnf.Flow + 0.114 Balling.Scaled
##            - 0.118 Density.Scaled + 0.0066 Hyd.Pressure1 + 1.15e-06 MFR
##            + 0.04 Air.Pressurer - 0.17 PSC.Fill + 0.0005 Hyd.Pressure2
##            + 3.1e-09 Filler.Speed - 0.0011 Pressure.Setpoint
##            + 0.0001 Bowl.Setpoint
## 
##   Rule 2/10: [40 cases, mean 8.469, range 8.26 to 8.78, est err 0.115]
## 
##     if
##  Alch.Rel <= 0.4906174
##  Temperature > 0.4998859
##  Air.Pressurer > 144.2
##     then
##  outcome = 8.307 + 0.00162 Mnf.Flow - 0.005 Hyd.Pressure2
##            + 2.9e-05 Filler.Level - 0.03 Carb.Flow.Scaled
## 
##   Rule 2/11: [19 cases, mean 8.489, range 8.18 to 8.82, est err 0.144]
## 
##     if
##  Filler.Speed > 7944098
##  Oxygen.Filler <= -1.858051
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##  Brand.Code.Encoded <= 8.028012
##     then
##  outcome = -241.595 - 2.463 Mnf.Flow + 1.108e-07 Filler.Speed
##            + 0.346 Pressure.Vacuum - 0.077 Balling + 0.069 Balling.Lvl
##            + 8 Alch.Rel - 0.019 Oxygen.Filler + 0.009 Balling.Scaled
##            - 0.005 Air.Pressurer.Scaled - 0.005 Balling.Lvl.Scaled
##            + 0.03 Carb.Pressure1 - 0.011 Brand.Code.A
## 
##   Rule 2/12: [68 cases, mean 8.502, range 8.1 to 8.78, est err 0.105]
## 
##     if
##  Alch.Rel <= 0.4885216
##  Filler.Speed > 6896898
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = 15.689 - 1.926e-07 Filler.Speed - 0.04 Air.Pressurer
##            + 0.071 Oxygen.Filler - 0.35 PC.Volume - 0.00048 Usage.cont
## 
##   Rule 2/13: [196 cases, mean 8.503, range 8.08 to 8.74, est err 0.075]
## 
##     if
##  Filler.Speed > 7920200
##  Carb.Flow <= 1084
##     then
##  outcome = -780.679 + 5.566 Air.Pressurer - 2.776 Air.Pressurer.Scaled
##            - 4.342e-07 Filler.Speed + 0.0095 Hyd.Pressure2
##            - 0.0075 Hyd.Pressure3 + 0.147 Oxygen.Filler
##            + 3.1e-05 Filler.Level - 0.00019 Mnf.Flow - 0.00037 Usage.cont
##            - 0.022 Density.Scaled - 1.7e-05 Carb.Flow - 2.1e-07 MFR
##            + 0.0003 Bowl.Setpoint - 0.0019 Pressure.Setpoint
##            + 0.0003 Hyd.Pressure1 - 0.003 Balling.Lvl.Scaled
## 
##   Rule 2/14: [18 cases, mean 8.523, range 8.34 to 8.88, est err 0.142]
## 
##     if
##  Filler.Speed > 7944098
##  Oxygen.Filler <= -1.858051
##  Brand.Code.C <= 0
##  PSC.Fill <= 0.06
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##  Brand.Code.Encoded > 8.028012
##     then
##  outcome = 128.003 + 1.29912 Mnf.Flow + 10.95 PSC.Fill
##            + 2.445e-07 Filler.Speed - 0.493 Oxygen.Filler
##            - 0.022 Balling.Lvl + 13 Alch.Rel - 0.018 Pressure.Vacuum
##            - 0.007 Air.Pressurer.Scaled + 0.04 Carb.Pressure1
## 
##   Rule 2/15: [95 cases, mean 8.542, range 8.22 to 8.74, est err 0.080]
## 
##     if
##  Filler.Speed > 7920200
##  Mnf.Flow > -100
##  Bowl.Setpoint > 80
##  Air.Pressurer <= 144.2
##  Balling.Scaled <= -0.3523095
##     then
##  outcome = -8.642 - 1.7389e-06 Filler.Speed + 0.263 Air.Pressurer
##            - 0.0141 Hyd.Pressure3 - 0.131 Air.Pressurer.Scaled
##            - 0.0078 Hyd.Pressure1 - 0.088 Density.Scaled
##            + 0.064 Balling.Scaled - 2.62 Hyd.Pressure4
##            - 0.0026 Bowl.Setpoint
## 
##   Rule 2/16: [50 cases, mean 8.547, range 8.2 to 8.82, est err 0.137]
## 
##     if
##  Filler.Speed > 7944098
##  Oxygen.Filler > -1.858051
##  Pressure.Vacuum > -5
##     then
##  outcome = -187.782 - 1.91809 Mnf.Flow + 1.413e-07 Filler.Speed
##            + 0.527 Pressure.Vacuum - 0.00188 Usage.cont - 0.78 PSC.Fill
##            + 12 Alch.Rel - 0.018 Balling - 0.011 Oxygen.Filler
##            - 0.004 Air.Pressurer.Scaled + 0.02 Carb.Pressure1
## 
##   Rule 2/17: [33 cases, mean 8.606, range 8.46 to 8.76, est err 0.040]
## 
##     if
##  Alch.Rel <= 0.4906174
##  Temperature <= 0.4998859
##  Mnf.Flow > -100
##  Air.Pressurer > 144.2
##     then
##  outcome = 7.446 + 3.6e-05 Filler.Level + 8.3e-09 Filler.Speed
##            - 2.6e-07 MFR - 0.037 Brand.Code.C + 0.0007 Hyd.Pressure3
##            + 0.0006 Bowl.Setpoint + 0.01 Balling.Lvl
##            - 0.009 Density.Scaled - 0.025 Brand.Code.A
##            + 0.04 Carb.Pressure1 - 0.0004 Hyd.Pressure2
##            - 0.0001 Usage.cont - 0.005 Carb.Flow.Scaled
##            + 0.004 Air.Pressurer + 2e-05 Mnf.Flow
##            - 0.001 Pressure.Setpoint + 0.0001 Hyd.Pressure1
## 
##   Rule 2/18: [125 cases, mean 8.620, range 8.24 to 8.86, est err 0.075]
## 
##     if
##  Alch.Rel > 0.4906174
##  Mnf.Flow > -100
##  Hyd.Pressure3 > 32.6
##     then
##  outcome = -3.64 - 0.078 Carb.Flow.Scaled + 21 Alch.Rel
##            - 0.027 Balling.Lvl + 1.06e-08 Filler.Speed - 3e-07 MFR
##            + 0.014 Air.Pressurer + 0.015 Balling - 0.012 Density.Scaled
##            + 0.0006 Hyd.Pressure3 - 0.0004 Hyd.Pressure2
##            - 4e-05 Usage.cont - 1e-06 Filler.Level
## 
##   Rule 2/19: [134 cases, mean 8.630, range 8.24 to 8.94, est err 0.106]
## 
##     if
##  Filler.Speed > 7944098
##  Oxygen.Filler <= -1.858051
##  Brand.Code.C <= 0
##  PSC.Fill > 0.06
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##  Brand.Code.Encoded > 8.028012
##     then
##  outcome = -63.337 + 1.8294e-06 Filler.Speed - 0.779 Balling
##            + 0.64 Balling.Lvl - 0.39 Oxygen.Filler + 108 Alch.Rel
##            + 0.104 Balling.Scaled - 0.141 Pressure.Vacuum
##            - 0.065 Air.Pressurer.Scaled + 0.3 Carb.Pressure1
##            + 0.15 PSC.Fill
## 
##   Rule 2/20: [336 cases, mean 8.638, range 8.18 to 8.94, est err 0.112]
## 
##     if
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##     then
##  outcome = -22.989 - 0.34623 Mnf.Flow + 0.086 Balling.Lvl - 0.076 Balling
##            - 0.138 Brand.Code.C - 0.132 Brand.Code.A
##            - 0.026 Air.Pressurer - 0.056 Oxygen.Filler
##            + 0.15 Carb.Pressure1 - 0.018 Balling.Scaled
##            - 0.01 Balling.Lvl.Scaled - 0.003 Air.Pressurer.Scaled
##            - 2 Alch.Rel + 1e-09 Filler.Speed - 3e-08 MFR
##            + 0.0001 Hyd.Pressure3
## 
##   Rule 2/21: [171 cases, mean 8.658, range 8.42 to 8.92, est err 0.064]
## 
##     if
##  Mnf.Flow <= -100
##  Pressure.Vacuum <= -5
##  Balling.Lvl > 1.54
##     then
##  outcome = -140.794 + 1.048 Air.Pressurer - 0.00856 Mnf.Flow
##            - 0.525 Air.Pressurer.Scaled + 0.254 Pressure.Vacuum
##            + 0.102 Balling.Lvl - 1.29e-06 MFR + 3.63e-08 Filler.Speed
##            - 0.0031 Hyd.Pressure1 + 0.0021 Hyd.Pressure3
##            - 1.48 Hyd.Pressure4 - 0.028 Balling.Scaled + 7 Alch.Rel
## 
##   Rule 2/22: [43 cases, mean 8.665, range 8.46 to 8.82, est err 0.072]
## 
##     if
##  Alch.Rel > 0.4906174
##  Hyd.Pressure3 > 32.6
##  Bowl.Setpoint <= 90
##     then
##  outcome = 8.094 + 0.0084 Bowl.Setpoint - 0.00038 Usage.cont
## 
##   Rule 2/23: [206 cases, mean 8.695, range 8.3 to 8.86, est err 0.062]
## 
##     if
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum <= -5
##  Balling.Lvl <= 1.54
##     then
##  outcome = -157.958 + 1.128 Air.Pressurer - 0.565 Air.Pressurer.Scaled
##            - 0.123 Oxygen.Filler + 0.18 Carb.Pressure1
##            + 0.025 Pressure.Vacuum - 0.014 Balling.Lvl + 8 Alch.Rel
## 
## Model 3:
## 
##   Rule 3/1: [24 cases, mean 8.247, range 7.88 to 8.66, est err 0.218]
## 
##     if
##  Carb.Rel <= 0.4819283
##  Brand.Code.C > 0
##  Mnf.Flow > -100.2
##     then
##  outcome = 10.188 - 0.0423 Hyd.Pressure2 + 0.00351 Mnf.Flow
##            + 0.0017 Hyd.Pressure3 + 0.055 Density - 0.08 Carb.Pressure1
##            + 0.018 Oxygen.Filler - 8e-06 Carb.Flow - 0.28 Hyd.Pressure4
## 
##   Rule 3/2: [102 cases, mean 8.389, range 8.08 to 8.8, est err 0.082]
## 
##     if
##  Carb.Rel > 0.4819283
##  Brand.Code.C > 0
##  Mnf.Flow > -100.2
##  Hyd.Pressure1 > 10.2
##     then
##  outcome = 5.46 + 0.0062 Hyd.Pressure3 - 0.00064 Mnf.Flow - 8.7e-07 MFR
##            - 3e-05 Carb.Flow + 0.06 Oxygen.Filler + 8 Alch.Rel
##            - 0.0006 Hyd.Pressure2 + 3.8e-09 Filler.Speed
##            - 0.021 Brand.Code.C - 0.03 Carb.Pressure1 - 8e-05 Usage.cont
##            + 0.0003 Bowl.Setpoint - 0.011 Density - 0.0003 Hyd.Pressure1
##            + 0.004 Balling - 0.0015 Pressure.Setpoint
##            - 0.12 Hyd.Pressure4
## 
##   Rule 3/3: [80 cases, mean 8.399, range 8.02 to 8.78, est err 0.150]
## 
##     if
##  PC.Volume > -0.9525701
##  Brand.Code.C > 0
##  Mnf.Flow <= 129.6
##  Hyd.Pressure1 <= 10.2
##     then
##  outcome = 8.493 - 1.96 PC.Volume - 0.33 PSC + 0.0025 Hyd.Pressure3
##            - 0.16 Carb.Pressure1 - 0.0012 Hyd.Pressure2 + 0.044 Density
##            + 0.031 Oxygen.Filler - 1.4e-05 Carb.Flow
##            - 0.0009 Hyd.Pressure1 - 0.22 Hyd.Pressure4
## 
##   Rule 3/4: [21 cases, mean 8.409, range 8.18 to 8.6, est err 0.121]
## 
##     if
##  PC.Volume <= -0.9525701
##  Brand.Code.C > 0
##  Mnf.Flow > -100.2
##  Hyd.Pressure1 <= 10.2
##     then
##  outcome = 5.864 - 0.25 PSC - 6e-05 Mnf.Flow - 0.016 Density + 4 Alch.Rel
##            - 0.016 Brand.Code.C + 0.0003 Hyd.Pressure3 + 0.005 Balling
##            + 0.02 Carb.Pressure1 + 0.0002 Bowl.Setpoint
##            - 0.003 Balling.Lvl + 2e-06 Carb.Flow - 3e-05 Usage.cont
##            - 0.002 Density.Scaled
## 
##   Rule 3/5: [118 cases, mean 8.453, range 8.08 to 8.74, est err 0.068]
## 
##     if
##  Brand.Code.C <= 0
##  Hyd.Pressure2 > 26
##  Carb.Flow <= 1084
##  Balling.Lvl <= 2.98
##     then
##  outcome = 7.161 - 0.499 Balling.Lvl + 5.9e-05 Filler.Level
##            - 0.086 Balling + 0.0043 Bowl.Setpoint
##            + 0.054 Carb.Flow.Scaled - 0.09 Pressure.Vacuum
##            + 0.0028 Hyd.Pressure2 - 0.0028 Hyd.Pressure3
##            - 0.0208 Pressure.Setpoint - 0.28 PC.Volume
##            + 1.9e-05 Carb.Flow + 0.0016 Hyd.Pressure1 - 0.13 PSC.Fill
##            - 0.016 Density + 3 Alch.Rel - 3e-05 Mnf.Flow
##            - 3e-05 Usage.cont + 8e-10 Filler.Speed + 0.01 Carb.Pressure1
## 
##   Rule 3/6: [99 cases, mean 8.462, range 8.06 to 8.74, est err 0.104]
## 
##     if
##  Alch.Rel <= 0.4916968
##  Oxygen.Filler > -2.523643
##  Mnf.Flow > -100.2
##  Pressure.Vacuum <= -5.4
##  Bowl.Setpoint > 80
##  Balling.Lvl > 2.98
##     then
##  outcome = 3.881 + 0.735 Balling.Lvl - 0.00075 Mnf.Flow + 9e-07 MFR
##            - 2.52e-08 Filler.Speed + 0.21 Carb.Pressure1
##            - 0.00055 Usage.cont - 0.033 Balling.Scaled
##            + 0.002 Hyd.Pressure1 + 0.0012 Hyd.Pressure2
## 
##   Rule 3/7: [373 cases, mean 8.475, range 7.88 to 8.86, est err 0.147]
## 
##     if
##  Carb.Rel <= 0.4824657
##  Mnf.Flow > -100.2
##  Bowl.Setpoint > 80
##     then
##  outcome = 3.901 - 2.137 Balling.Lvl + 1.816 Balling
##            - 0.363 Balling.Scaled + 0.214 Balling.Lvl.Scaled
##            + 0.077 Oxygen.Filler + 1.71e-08 Filler.Speed
##            + 0.0019 Bowl.Setpoint - 0.057 Density - 2.9e-07 MFR
##            - 1.5e-05 Carb.Flow - 0.00012 Mnf.Flow
##            + 0.013 Air.Pressurer.Scaled + 9 Alch.Rel
##            + 0.05 Carb.Pressure1 + 0.0005 Hyd.Pressure3
##            - 0.007 Pressure.Vacuum - 6e-05 Usage.cont
##            + 0.0002 Hyd.Pressure2 - 0.007 Brand.Code.C
## 
##   Rule 3/8: [114 cases, mean 8.481, range 8.02 to 8.86, est err 0.110]
## 
##     if
##  Brand.Code.C <= 0
##  Mnf.Flow > -100.2
##  Hyd.Pressure2 > 26
##  Carb.Flow > 1084
##  Bowl.Setpoint > 80
##  Balling.Lvl <= 2.98
##  Carb.Flow.Scaled <= 0.4856937
##     then
##  outcome = 6.379 + 0.0105 Bowl.Setpoint - 0.275 Density
##            + 8.1e-05 Carb.Flow + 4.8e-05 Filler.Level - 0.08 Balling
##            - 0.73 PC.Volume + 0.049 Carb.Flow.Scaled
##            - 0.082 Pressure.Vacuum + 0.0025 Hyd.Pressure2
##            + 0.0015 Hyd.Pressure1 - 0.007 Pressure.Setpoint
##            - 0.12 PSC.Fill
## 
##   Rule 3/9: [59 cases, mean 8.490, range 8.16 to 8.84, est err 0.149]
## 
##     if
##  Brand.Code.C <= 0
##  Mnf.Flow > -100.2
##  Hyd.Pressure2 <= 26
##  Bowl.Setpoint > 80
##  Balling.Lvl <= 2.98
##  Air.Pressurer.Scaled > 0.6150198
##  Carb.Flow.Scaled <= 0.4856937
##     then
##  outcome = -1.603 - 0.59 PSC + 4.4 Hyd.Pressure4 - 0.133 Oxygen.Filler
##            + 0.104 Pressure.Vacuum - 0.05 Balling.Lvl + 0.029 Balling
##            + 0.0012 Bowl.Setpoint + 0.013 Balling.Lvl.Scaled
##            - 0.012 Balling.Scaled - 7e-06 Carb.Flow + 1.2e-07 MFR
## 
##   Rule 3/10: [125 cases, mean 8.497, range 8.26 to 8.74, est err 0.072]
## 
##     if
##  Brand.Code.C <= 0
##  Bowl.Setpoint <= 80
##     then
##  outcome = 7.267 - 0.508 Oxygen.Filler - 0.00176 Mnf.Flow
##            + 0.0071 Hyd.Pressure3
## 
##   Rule 3/11: [166 cases, mean 8.513, range 8.16 to 8.82, est err 0.093]
## 
##     if
##  Brand.Code.C <= 0
##  Mnf.Flow > -100.2
##  Bowl.Setpoint > 80
##  Balling.Lvl <= 2.98
##  Carb.Flow.Scaled > 0.4856937
##     then
##  outcome = 9.021 - 4.484 Balling.Lvl + 3.732 Balling
##            - 0.739 Balling.Scaled + 0.436 Balling.Lvl.Scaled
##            + 3.58e-08 Filler.Speed + 0.06 Air.Pressurer.Scaled
##            - 0.00096 Usage.cont - 6e-07 MFR + 0.002 Bowl.Setpoint
## 
##   Rule 3/12: [17 cases, mean 8.518, range 8.26 to 8.86, est err 0.175]
## 
##     if
##  Brand.Code.C > 0
##  Mnf.Flow > 129.6
##  Hyd.Pressure1 <= 10.2
##     then
##  outcome = 4.544 + 0.03772 Mnf.Flow - 0.1287 Hyd.Pressure1
##            + 0.0003 Hyd.Pressure3 - 0.02 Carb.Pressure1
##            + 0.005 Oxygen.Filler - 2e-06 Carb.Flow
## 
##   Rule 3/13: [26 cases, mean 8.524, range 8.26 to 8.74, est err 0.096]
## 
##     if
##  Carb.Rel > 0.4835906
##  Bowl.Setpoint <= 80
##     then
##  outcome = 5.198 + 0.0457 Bowl.Setpoint + 0.285 Balling.Lvl.Scaled
##            - 0.015 Oxygen.Filler
## 
##   Rule 3/14: [41 cases, mean 8.542, range 8.42 to 8.72, est err 0.087]
## 
##     if
##  Oxygen.Filler <= -2.523643
##  Hyd.Pressure3 > 19.4
##  Carb.Flow <= 1066
##  Balling.Lvl > 2.98
##     then
##  outcome = 17.612 - 0.007743 Carb.Flow - 0.0224 Hyd.Pressure2
##            + 0.00217 Mnf.Flow - 0.108 Balling.Lvl + 0.0022 Hyd.Pressure3
##            + 0.016 Balling.Scaled + 0.0012 Hyd.Pressure1
##            - 0.0008 Bowl.Setpoint + 0.00016 Usage.cont
##            + 0.014 Oxygen.Filler + 0.03 PSC
## 
##   Rule 3/15: [165 cases, mean 8.567, range 8.4 to 8.8, est err 0.065]
## 
##     if
##  Oxygen.Filler <= -2.523643
##  Mnf.Flow > -100.2
##  Hyd.Pressure3 > 19.4
##  Bowl.Setpoint > 80
##  Balling.Lvl > 2.98
##     then
##  outcome = 6.296 - 0.344 Balling.Lvl + 0.0088 Hyd.Pressure3
##            - 0.00095 Mnf.Flow - 0.0036 Hyd.Pressure2
##            + 0.051 Balling.Scaled + 0.0038 Hyd.Pressure1
##            - 0.0024 Bowl.Setpoint + 0.00045 Usage.cont
##            + 0.046 Oxygen.Filler + 0.1 PSC - 0.028 Density + 7 Alch.Rel
##            + 0.03 Carb.Pressure1 + 9e-10 Filler.Speed + 0.002 Balling
## 
##   Rule 3/16: [111 cases, mean 8.574, range 8.2 to 8.88, est err 0.102]
## 
##     if
##  Oxygen.Filler > -2.523643
##  Mnf.Flow > -100.2
##  Pressure.Vacuum > -5.4
##  Bowl.Setpoint > 80
##  Balling.Lvl > 2.98
##     then
##  outcome = 2.87 + 0.355 Balling.Lvl - 0.00095 Mnf.Flow
##            + 0.006 Hyd.Pressure3 + 0.51 Carb.Pressure1
##            - 0.00079 Usage.cont + 6e-07 MFR - 1.71e-08 Filler.Speed
##            - 0.035 Balling.Scaled - 0.0017 Hyd.Pressure2
##            + 0.002 Hyd.Pressure1 - 0.025 Pressure.Vacuum
##            - 0.022 Oxygen.Filler - 0.5 Hyd.Pressure4
## 
##   Rule 3/17: [173 cases, mean 8.586, range 8.2 to 8.94, est err 0.117]
## 
##     if
##  Brand.Code.C <= 0
##  Mnf.Flow > -100.2
##  Hyd.Pressure2 <= 26
##  Bowl.Setpoint > 80
##  Balling.Lvl <= 2.98
##  Air.Pressurer.Scaled <= 0.6150198
##  Carb.Flow.Scaled <= 0.4856937
##     then
##  outcome = 4.006 - 0.636 Balling + 0.564 Balling.Lvl
##            + 0.0124 Bowl.Setpoint - 0.158 Pressure.Vacuum + 8.6e-07 MFR
##            + 0.045 Balling.Scaled + 0.21 Carb.Pressure1
##            + 0.024 Balling.Lvl.Scaled - 9e-05 Mnf.Flow
##            + 0.0005 Hyd.Pressure2 - 0.06 PC.Volume - 3e-06 Carb.Flow
## 
##   Rule 3/18: [130 cases, mean 8.586, range 8.2 to 8.94, est err 0.137]
## 
##     if
##  Mnf.Flow > -100.2
##  Hyd.Pressure3 <= 19.4
##  Bowl.Setpoint > 80
##  Balling.Lvl > 2.98
##     then
##  outcome = -0.006 + 0.585 Balling.Lvl - 0.00245 Mnf.Flow
##            + 0.0166 Hyd.Pressure3 - 0.135 Pressure.Vacuum
##            + 0.32 Carb.Pressure1 - 0.0015 Hyd.Pressure2
##            + 5.8e-09 Filler.Speed + 0.001 Hyd.Pressure1
##            - 0.00018 Usage.cont - 1.4e-07 MFR + 6 Alch.Rel
##            - 0.008 Balling.Scaled - 0.02 Density - 0.009 Oxygen.Filler
##            - 0.21 Hyd.Pressure4
## 
##   Rule 3/19: [402 cases, mean 8.681, range 8.12 to 8.92, est err 0.075]
## 
##     if
##  Mnf.Flow <= -100.2
##     then
##  outcome = -654.867 + 4.509 Air.Pressurer - 2.23 Air.Pressurer.Scaled
##            + 0.175 Pressure.Vacuum - 0.192 Brand.Code.C + 45 Alch.Rel
##            - 0.073 Balling.Lvl - 4e-05 Mnf.Flow - 0.01 Density
##            + 0.0002 Hyd.Pressure3 + 0.003 Balling + 0.01 Carb.Pressure1
##            + 0.0001 Bowl.Setpoint
## 
##   Rule 3/20: [20 cases, mean 8.701, range 8.4 to 8.82, est err 0.122]
## 
##     if
##  Alch.Rel > 0.4916968
##  Oxygen.Filler > -2.523643
##  Mnf.Flow > -100.2
##  Balling.Lvl > 2.98
##     then
##  outcome = 9.069 + 0.616 Oxygen.Filler - 1.18 PC.Volume
##            + 0.00093 Mnf.Flow - 0.006 Density
## 
## Model 4:
## 
##   Rule 4/1: [29 cases, mean 8.234, range 8.08 to 8.78, est err 0.300]
## 
##     if
##  Alch.Rel > 0.48831
##  Oxygen.Filler <= -1.884013
##  PC.Volume > -0.8901629
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = -76.556 - 0.84501 Mnf.Flow + 0.011 Oxygen.Filler
## 
##   Rule 4/2: [27 cases, mean 8.313, range 7.88 to 8.82, est err 0.209]
## 
##     if
##  Alch.Rel <= 0.4905657
##  Balling.Lvl > 1.54
##  Density.Scaled <= -1.934118
##     then
##  outcome = 60.549 - 0.371 Air.Pressurer - 1.79 PSC.Fill + 2 Alch.Rel
##            - 4e-08 MFR - 2e-05 Mnf.Flow + 1e-09 Filler.Speed
##            + 0.005 Density - 0.002 Density.Scaled + 0.0001 Hyd.Pressure2
## 
##   Rule 4/3: [111 cases, mean 8.375, range 8 to 8.74, est err 0.110]
## 
##     if
##  Alch.Rel <= 0.4905657
##  Filler.Speed <= 7920200
##  Temperature > 0.4998866
##  Mnf.Flow > -100
##  Bowl.Setpoint > 80
##     then
##  outcome = 3.686 + 0.00159 Mnf.Flow - 0.0074 Hyd.Pressure2
##            + 0.032 Air.Pressurer - 9.4e-09 Filler.Speed
##            + 0.0009 Bowl.Setpoint + 9e-06 Carb.Flow - 7e-08 MFR
##            - 0.004 Density.Scaled - 3e-05 Usage.cont
## 
##   Rule 4/4: [239 cases, mean 8.407, range 8 to 8.74, est err 0.107]
## 
##     if
##  Alch.Rel <= 0.4905657
##  Temperature > 0.4998859
##  Mnf.Flow > -100
##     then
##  outcome = 8.177 - 0.00151 Mnf.Flow + 0.0057 Hyd.Pressure3
##            + 2.3e-05 Filler.Level - 0.08 PSC
## 
##   Rule 4/5: [113 cases, mean 8.416, range 8.12 to 8.86, est err 0.103]
## 
##     if
##  Alch.Rel <= 0.4905657
##  Filler.Speed <= 7920200
##  Temperature <= 0.4998866
##  Mnf.Flow > -100
##  Bowl.Setpoint > 80
##  Air.Pressurer <= 145.8
##  Density.Scaled > -1.934118
##  Carb.Flow.Scaled <= 0.4983332
##     then
##  outcome = 7.121 + 0.0112 Hyd.Pressure2 - 6.59e-08 Filler.Speed
##            + 0.00106 Mnf.Flow - 0.103 Carb.Flow.Scaled
##            + 0.0063 Bowl.Setpoint - 0.098 Pressure.Vacuum
##            - 0.022 Balling.Lvl + 0.016 Balling + 6e-06 Carb.Flow
## 
##   Rule 4/6: [75 cases, mean 8.421, range 7.88 to 8.8, est err 0.148]
## 
##     if
##  Alch.Rel <= 0.4905657
##  Mnf.Flow > -100
##  Density.Scaled <= -1.934118
##     then
##  outcome = 17.931 - 0.085 Air.Pressurer - 0.00038 Mnf.Flow
##            + 0.0013 Hyd.Pressure3 - 0.053 Brand.Code.C
##            + 0.0009 Bowl.Setpoint - 0.015 Density.Scaled
##            + 0.07 Carb.Pressure1 - 0.018 Oxygen.Filler
##            - 0.00015 Usage.cont + 0.021 Brand.Code.D + 8e-06 Carb.Flow
##            - 5e-06 Filler.Level - 0.0035 Pressure.Setpoint + 4 Alch.Rel
##            + 0.0003 Hyd.Pressure2 - 7e-08 MFR + 1.8e-09 Filler.Speed
##            + 0.007 Density - 0.003 Balling.Lvl - 0.002 Balling
## 
##   Rule 4/7: [117 cases, mean 8.426, range 8.14 to 8.72, est err 0.092]
## 
##     if
##  Filler.Speed <= 7920200
##  Mnf.Flow > -100
##  Bowl.Setpoint > 80
##  Air.Pressurer <= 145.8
##  Carb.Flow.Scaled > 0.4983332
##     then
##  outcome = -1.712 - 0.00232 Mnf.Flow + 0.0072 Bowl.Setpoint
##            - 6.8e-05 Filler.Level + 0.071 Air.Pressurer
##            - 0.055 Balling.Lvl - 0.034 Density.Scaled + 0.24 PC.Volume
##            - 0.021 Carb.Flow.Scaled - 0.11 PSC + 0.0002 Hyd.Pressure3
##            - 0.009 Brand.Code.C + 2e-06 Carb.Flow + 0.01 Carb.Pressure1
##            - 0.0001 Hyd.Pressure2
## 
##   Rule 4/8: [272 cases, mean 8.464, range 8.02 to 8.74, est err 0.086]
## 
##     if
##  Alch.Rel <= 0.4905657
##  Filler.Speed > 7920200
##  Mnf.Flow > -100
##  Air.Pressurer <= 145.8
##  Density.Scaled > -1.934118
##     then
##  outcome = -14.25 - 0.142 Balling + 0.106 Air.Pressurer
##            + 0.136 Balling.Lvl + 1.57e-08 Filler.Speed - 5.3e-07 MFR
##            - 0.031 Density.Scaled - 0.00019 Mnf.Flow + 16 Alch.Rel
##            + 0.0013 Hyd.Pressure2 - 0.00027 Usage.cont
##            + 0.0007 Hyd.Pressure3 - 0.0027 Pressure.Setpoint
## 
##   Rule 4/9: [102 cases, mean 8.477, range 8.26 to 8.68, est err 0.100]
## 
##     if
##  Bowl.Setpoint <= 80
##  Air.Pressurer <= 145.8
##  Density.Scaled > -1.934118
##     then
##  outcome = 5.163 - 0.00384 Mnf.Flow - 8.8e-05 Filler.Level
##            + 4.54e-08 Filler.Speed - 0.095 Balling + 0.0066 Hyd.Pressure1
##            - 7.4e-07 MFR - 0.075 Pressure.Vacuum + 0.024 Air.Pressurer
##            + 0.00042 Usage.cont - 0.002 Density.Scaled
## 
##   Rule 4/10: [109 cases, mean 8.493, range 8.26 to 8.7, est err 0.090]
## 
##     if
##  Alch.Rel > 0.4905657
##  Mnf.Flow > -100
##  Hyd.Pressure3 <= 32.4
##     then
##  outcome = 7.87 + 0.08 Balling.Lvl - 0.091 Pressure.Vacuum
##            + 0.0022 Hyd.Pressure3 - 0.00034 Usage.cont
##            - 0.0011 Bowl.Setpoint
## 
##   Rule 4/11: [24 cases, mean 8.498, range 8.26 to 8.62, est err 0.087]
## 
##     if
##  Oxygen.Filler > -1.884013
##  Brand.Code.C > 0
##  Pressure.Vacuum <= -5.2
##     then
##  outcome = 5.866 - 0.558 Oxygen.Filler - 0.261 Pressure.Vacuum
##            - 8e-05 Mnf.Flow + 0.0003 Hyd.Pressure3 - 0.013 Brand.Code.C
##            + 0.02 Carb.Pressure1 + 0.0002 Bowl.Setpoint
##            - 0.003 Density.Scaled + 2e-06 Carb.Flow + 0.005 Brand.Code.D
##            - 3e-05 Usage.cont - 1e-06 Filler.Level
## 
##   Rule 4/12: [38 cases, mean 8.518, range 8.18 to 8.84, est err 0.113]
## 
##     if
##  PC.Volume <= -0.8901629
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = -18.621 - 0.11713 Mnf.Flow - 0.902 Density + 0.342 Balling
##            + 3.33 Carb.Pressure + 0.62 Carb.Pressure1
##            - 0.065 Brand.Code.C - 0.01 Air.Pressurer
##            - 0.023 Oxygen.Filler - 0.011 Balling.Scaled
##            + 0.022 Brand.Code.D - 0.42 Hyd.Pressure4
##            + 0.0004 Hyd.Pressure3
## 
##   Rule 4/13: [28 cases, mean 8.524, range 8.18 to 8.84, est err 0.194]
## 
##     if
##  Carb.Volume > 0.4825963
##  Carb.Volume <= 0.483228
##  Filler.Speed > 8016008
##  Pressure.Vacuum > -5
##  Brand.Code.Encoded <= 8.661835
##     then
##  outcome = -290.901 - 2.97256 Mnf.Flow + 0.614 Pressure.Vacuum
##            + 0.57 Brand.Code.Encoded + 0.181 Balling.Scaled
##            - 0.333 Oxygen.Filler - 0.123 Carb.Flow.Scaled
##            - 0.004 Air.Pressurer + 0.011 Brand.Code.D
## 
##   Rule 4/14: [32 cases, mean 8.547, range 8.4 to 8.64, est err 0.051]
## 
##     if
##  Alch.Rel <= 0.48831
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = -7.182 - 0.20867 Mnf.Flow - 2.285 Density + 0.867 Balling
##            - 0.165 Brand.Code.C - 0.025 Air.Pressurer
##            - 0.055 Oxygen.Filler - 0.028 Balling.Scaled
##            + 0.055 Brand.Code.D - 1.06 Hyd.Pressure4
##            + 0.14 Carb.Pressure1 + 0.0011 Hyd.Pressure3
## 
##   Rule 4/15: [36 cases, mean 8.599, range 8.34 to 8.82, est err 0.132]
## 
##     if
##  Carb.Volume > 0.4825963
##  Filler.Speed > 8016008
##  Pressure.Vacuum > -5
##  Brand.Code.Encoded > 8.661835
##     then
##  outcome = 77.528 + 0.65584 Mnf.Flow + 1.16 PC.Volume
##            - 0.016 Air.Pressurer + 0.044 Brand.Code.D
## 
##   Rule 4/16: [27 cases, mean 8.612, range 8.46 to 8.76, est err 0.072]
## 
##     if
##  Alch.Rel <= 0.4905657
##  Temperature <= 0.4998859
##  Mnf.Flow > -100
##  Air.Pressurer > 145.8
##     then
##  outcome = 8.087 - 0.00274 Mnf.Flow + 0.0103 Hyd.Pressure3
##            + 6.8e-05 Filler.Level - 0.14 PSC
## 
##   Rule 4/17: [127 cases, mean 8.619, range 8.24 to 8.86, est err 0.074]
## 
##     if
##  Alch.Rel > 0.4905657
##  Mnf.Flow > -100
##  Hyd.Pressure3 > 32.4
##     then
##  outcome = 2.242 - 0.0007 Usage.cont + 0.002 Hyd.Pressure3
##            - 0.032 Pressure.Vacuum + 11 Alch.Rel - 0.00013 Mnf.Flow
##            + 0.0009 Hyd.Pressure2 - 9e-06 Filler.Level
##            - 0.0008 Bowl.Setpoint + 0.008 Air.Pressurer - 1.4e-07 MFR
##            - 0.007 Density.Scaled - 0.006 Balling + 2.5e-09 Filler.Speed
##            - 0.0018 Pressure.Setpoint
## 
##   Rule 4/18: [799 cases, mean 8.630, range 8.08 to 8.94, est err 0.114]
## 
##     if
##  Oxygen.Filler > -2.921958
##  Mnf.Flow <= -100
##     then
##  outcome = -4.129 - 0.32757 Mnf.Flow - 3.417 Density + 0.963 Balling
##            + 0.376 Balling.Lvl - 0.145 Oxygen.Filler + 0.161 Brand.Code.D
##            - 0.06 Balling.Lvl.Scaled - 31 Alch.Rel - 0.033 Air.Pressurer
##            + 0.21 Carb.Pressure1 + 0.032 Balling.Scaled
##            + 0.0017 Hyd.Pressure3 - 0.72 Hyd.Pressure4
##            - 0.001 Hyd.Pressure1 - 0.008 Air.Pressurer.Scaled
## 
##   Rule 4/19: [21 cases, mean 8.644, range 8.5 to 8.84, est err 0.113]
## 
##     if
##  Oxygen.Filler > -1.884013
##  Brand.Code.C > 0
##  Pressure.Vacuum > -5.2
##     then
##  outcome = -38.322 + 96 Alch.Rel + 0.0049 Hyd.Pressure1
##            - 0.054 Balling.Scaled
## 
##   Rule 4/20: [171 cases, mean 8.658, range 8.42 to 8.92, est err 0.067]
## 
##     if
##  Mnf.Flow <= -100
##  Pressure.Vacuum <= -5
##  Balling.Lvl > 1.54
##     then
##  outcome = 9.087 + 0.03856 Mnf.Flow + 0.345 Pressure.Vacuum
##            + 0.0081 Hyd.Pressure2 - 0.0044 Hyd.Pressure3
##            - 0.0051 Hyd.Pressure1 - 0.043 Balling.Scaled
##            - 1.71 Hyd.Pressure4 - 0.033 Balling + 18 Alch.Rel
##            + 0.057 Brand.Code.D - 0.033 Oxygen.Filler
##            - 0.015 Balling.Lvl.Scaled + 3.3e-09 Filler.Speed
##            + 0.05 PC.Volume - 6e-08 MFR + 5e-05 Usage.cont
## 
##   Rule 4/21: [166 cases, mean 8.662, range 8.2 to 8.94, est err 0.122]
## 
##     if
##  Filler.Speed <= 8016008
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##     then
##  outcome = -102.41 - 1.16437 Mnf.Flow - 0.869 Density + 0.318 Balling.Lvl
##            - 3.53e-08 Filler.Speed + 0.129 Brand.Code.D
##            - 0.079 Oxygen.Filler + 0.034 Balling.Scaled
##            - 0.029 Balling.Lvl.Scaled + 4.2e-07 MFR - 0.012 Air.Pressurer
##            + 0.08 Carb.Pressure1 - 9 Alch.Rel
##            - 0.009 Air.Pressurer.Scaled + 0.002 Balling
## 
##   Rule 4/22: [190 cases, mean 8.691, range 8.3 to 8.86, est err 0.075]
## 
##     if
##  Oxygen.Filler > -2.921958
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum <= -5
##  Balling.Lvl <= 1.54
##     then
##  outcome = 33.012 + 0.35468 Mnf.Flow - 0.598 Balling.Lvl
##            - 0.251 Oxygen.Filler + 0.161 Pressure.Vacuum - 0.047 Balling
##            + 26 Alch.Rel + 0.29 PC.Volume - 0.022 Balling.Lvl.Scaled
##            - 0.0009 Hyd.Pressure1 + 4.8e-09 Filler.Speed
##            + 0.0006 Hyd.Pressure3 - 8e-08 MFR + 8e-05 Usage.cont
## 
##   Rule 4/23: [71 cases, mean 8.699, range 8.34 to 8.92, est err 0.109]
## 
##     if
##  Carb.Volume > 0.483228
##  Filler.Speed > 8016008
##  Mnf.Flow <= -100
##     then
##  outcome = 1.611 - 0.27203 Mnf.Flow - 3.238 Density + 1.052 Balling
##            + 0.209 Balling.Lvl - 0.135 Oxygen.Filler + 0.154 Brand.Code.D
##            - 0.047 Balling.Lvl.Scaled - 0.039 Air.Pressurer - 28 Alch.Rel
##            + 0.17 Carb.Pressure1 - 0.85 Hyd.Pressure4
##            + 0.0007 Hyd.Pressure3 - 0.0004 Hyd.Pressure1
##            - 2.1e-09 Filler.Speed + 0.004 Balling.Scaled + 6e-08 MFR
## 
##   Rule 4/24: [20 cases, mean 8.733, range 8.66 to 8.8, est err 0.047]
## 
##     if
##  Oxygen.Filler <= -2.921958
##  Mnf.Flow <= -100
##     then
##  outcome = 8.772
## 
## Model 5:
## 
##   Rule 5/1: [19 cases, mean 8.267, range 8.12 to 8.86, est err 0.211]
## 
##     if
##  Alch.Rel > 0.4883812
##  Carb.Rel > 0.4823337
##  Oxygen.Filler <= -2.543916
##  Brand.Code.C > 0
##     then
##  outcome = 10.919 + 0.757 Balling - 0.777 Balling.Lvl
##            - 0.123 Balling.Scaled + 0.106 Balling.Lvl.Scaled
##            - 1.62e-06 MFR + 4.6e-08 Filler.Speed + 0.152 Oxygen.Filler
##            + 0.00036 Mnf.Flow - 0.22 Carb.Pressure1 - 3.1e-05 Carb.Flow
##            - 0.0008 Hyd.Pressure1 + 0.003 Density.Scaled
## 
##   Rule 5/2: [23 cases, mean 8.327, range 8.08 to 8.84, est err 0.207]
## 
##     if
##  Filler.Speed > 8040050
##  Oxygen.Filler > -2.543916
##  Brand.Code.C > 0
##     then
##  outcome = 9.826 + 0.677 Oxygen.Filler + 0.093 Balling
##            - 0.099 Balling.Lvl - 0.015 Balling.Scaled
##            + 0.013 Balling.Lvl.Scaled - 2.1e-07 MFR + 6e-09 Filler.Speed
##            - 4e-06 Carb.Flow - 0.02 Carb.Pressure1
## 
##   Rule 5/3: [79 cases, mean 8.374, range 8.04 to 8.8, est err 0.135]
## 
##     if
##  Filler.Speed <= 7976018
##  Brand.Code.C <= 0
##  Mnf.Flow > -100.2
##  Bowl.Setpoint > 80
##  Bowl.Setpoint <= 100
##  Density.Scaled <= 0.577455
##  Carb.Flow.Scaled <= 0.5428292
##     then
##  outcome = -65.028 + 151 Alch.Rel + 0.0105 Hyd.Pressure2
##            - 0.193 Balling.Lvl - 0.0087 Bowl.Setpoint - 1.88e-06 MFR
##            + 0.055 Air.Pressurer.Scaled + 0.051 Balling
##            - 0.00015 Mnf.Flow + 0.017 Balling.Lvl.Scaled
##            - 0.0078 Pressure.Setpoint + 0.09 Carb.Pressure1
##            - 0.035 Density - 0.013 Density.Scaled - 0.018 Pressure.Vacuum
##            + 0.0008 Hyd.Pressure1 - 0.09 PC.Volume - 0.0004 Hyd.Pressure3
## 
##   Rule 5/4: [99 cases, mean 8.375, range 7.88 to 8.86, est err 0.155]
## 
##     if
##  Oxygen.Filler <= -2.543916
##  Brand.Code.C > 0
##     then
##  outcome = 8.338 + 0.571 Balling.Lvl - 0.0178 Hyd.Pressure1
##            + 0.00161 Mnf.Flow + 0.251 Oxygen.Filler
##            + 0.063 Density.Scaled
## 
##   Rule 5/5: [46 cases, mean 8.429, range 8.08 to 8.72, est err 0.108]
## 
##     if
##  Alch.Rel <= 0.4883812
##  Carb.Rel > 0.4823337
##  Oxygen.Filler <= -2.543916
##  Brand.Code.C > 0
##     then
##  outcome = 9.265 + 0.00276 Mnf.Flow + 0.38 Oxygen.Filler
##            + 0.000118 Filler.Level - 0.171 Carb.Flow.Scaled
##            + 0.168 Balling - 0.0113 Hyd.Pressure1 - 0.108 Balling.Lvl
##            - 0.027 Balling.Scaled + 0.024 Balling.Lvl.Scaled
##            - 3.6e-07 MFR + 1.02e-08 Filler.Speed - 0.05 Carb.Pressure1
##            - 7e-06 Carb.Flow + 0.008 Density.Scaled
## 
##   Rule 5/6: [162 cases, mean 8.432, range 8.02 to 8.84, est err 0.120]
## 
##     if
##  Oxygen.Filler > -2.543916
##  Brand.Code.C > 0
##     then
##  outcome = 10.259 + 4.99e-08 Filler.Speed - 1.39e-06 MFR
##            - 0.073 Balling.Lvl + 0.067 Balling + 0.106 Oxygen.Filler
##            - 3.5e-05 Carb.Flow - 0.0006 Usage.cont - 0.22 Carb.Pressure1
##            - 0.011 Balling.Scaled + 0.009 Balling.Lvl.Scaled
##            - 0.014 Brand.Code.C - 4e-05 Mnf.Flow + 0.0002 Hyd.Pressure3
##            + 0.0002 Bowl.Setpoint + 2 Alch.Rel
## 
##   Rule 5/7: [125 cases, mean 8.497, range 8.26 to 8.74, est err 0.068]
## 
##     if
##  Brand.Code.C <= 0
##  Bowl.Setpoint <= 80
##     then
##  outcome = 3.224 - 0.412 Oxygen.Filler + 0.0077 Bowl.Setpoint
##            + 0.024 Balling.Scaled + 7 Alch.Rel - 8e-05 Mnf.Flow
##            - 0.022 Density + 0.0004 Hyd.Pressure3 + 0.03 Carb.Pressure1
##            - 6e-05 Usage.cont + 0.003 Balling
## 
##   Rule 5/8: [168 cases, mean 8.521, range 8.16 to 8.86, est err 0.098]
## 
##     if
##  Mnf.Flow > -100.2
##  Mnf.Flow <= 135.4
##  Bowl.Setpoint > 80
##  Density.Scaled > 0.577455
##     then
##  outcome = 2.274 + 0.012 Bowl.Setpoint - 8.5e-05 Filler.Level
##            - 0.00093 Mnf.Flow - 0.074 Balling.Scaled
##            - 0.121 Oxygen.Filler - 0.05 Balling + 0.116 Density
##            + 0.0026 Hyd.Pressure1 + 10 Alch.Rel - 0.00016 Usage.cont
##            + 0.0006 Hyd.Pressure3 + 0.03 Carb.Pressure1
##            - 0.005 Balling.Lvl - 0.004 Density.Scaled - 3e-06 Carb.Flow
## 
##   Rule 5/9: [172 cases, mean 8.525, range 8.22 to 8.82, est err 0.082]
## 
##     if
##  Brand.Code.C <= 0
##  Mnf.Flow > 135.4
##  Bowl.Setpoint > 80
##  Density.Scaled > 0.577455
##     then
##  outcome = -27.447 - 1.371 Balling + 3.264 Density - 0.172 Balling.Scaled
##            + 71 Alch.Rel + 0.096 Balling.Lvl.Scaled - 0.00129 Usage.cont
##            - 0.13 Pressure.Vacuum + 0.0013 Bowl.Setpoint
##            - 1.1e-05 Filler.Level - 5e-05 Mnf.Flow - 5e-06 Carb.Flow
##            + 0.0003 Hyd.Pressure3 + 0.0003 Hyd.Pressure1
## 
##   Rule 5/10: [233 cases, mean 8.536, range 8.02 to 8.94, est err 0.126]
## 
##     if
##  Filler.Speed > 7976018
##  Brand.Code.C <= 0
##  Mnf.Flow > -100.2
##  Density.Scaled <= 0.577455
##  Carb.Flow.Scaled <= 0.5428292
##     then
##  outcome = -35.766 - 1.182 Balling + 1.134 Balling.Lvl
##            + 0.0141 Bowl.Setpoint + 0.172 Balling.Scaled + 85 Alch.Rel
##            - 0.149 Pressure.Vacuum - 0.083 Density.Scaled
##            + 0.025 Balling.Lvl.Scaled - 0.00015 Mnf.Flow
##            - 0.0071 Pressure.Setpoint + 0.08 Carb.Pressure1
##            + 0.0008 Hyd.Pressure1 - 0.08 PC.Volume + 0.0004 Hyd.Pressure2
## 
##   Rule 5/11: [199 cases, mean 8.543, range 8.14 to 8.92, est err 0.096]
## 
##     if
##  Brand.Code.C <= 0
##  Mnf.Flow > -100.2
##  Bowl.Setpoint > 80
##  Density.Scaled <= 0.577455
##  Carb.Flow.Scaled > 0.5428292
##     then
##  outcome = -46.792 - 0.00143 Mnf.Flow + 116 Alch.Rel - 0.156 Balling
##            - 0.000124 Carb.Flow - 0.00163 Usage.cont
##            - 4.7e-05 Filler.Level + 0.0043 Hyd.Pressure3 + 0.4 PC.Volume
##            + 0.029 Balling.Scaled - 0.008 Balling.Lvl
##            + 0.03 Carb.Pressure1 + 0.0003 Bowl.Setpoint
##            - 0.005 Density.Scaled + 0.003 Balling.Lvl.Scaled
## 
##   Rule 5/12: [17 cases, mean 8.599, range 8.46 to 8.74, est err 0.122]
## 
##     if
##  Carb.Rel > 0.4838259
##  Bowl.Setpoint <= 80
##     then
##  outcome = 7.392 - 0.00281 Mnf.Flow + 3 Alch.Rel - 0.011 Density
##            + 0.0002 Hyd.Pressure3 + 0.01 Carb.Pressure1
##            + 0.0001 Bowl.Setpoint
## 
##   Rule 5/13: [653 cases, mean 8.612, range 8.06 to 8.94, est err 0.108]
## 
##     if
##  Brand.Code.C <= 0
##  Bowl.Setpoint > 100
##  Density.Scaled <= 0.577455
##  Carb.Flow.Scaled <= 0.5428292
##     then
##  outcome = -1.938 + 0.154 Balling - 0.209 Density - 0.086 Balling.Lvl
##            + 0.004 Bowl.Setpoint - 0.00047 Mnf.Flow
##            + 0.0034 Hyd.Pressure2 + 0.2 Carb.Pressure1
##            - 0.0124 Pressure.Setpoint - 0.025 Carb.Flow.Scaled
##            + 17 Alch.Rel - 0.0015 Hyd.Pressure3
##            + 0.019 Balling.Lvl.Scaled - 0.018 Density.Scaled
##            + 0.0012 Hyd.Pressure1 - 0.13 PC.Volume + 4.5e-09 Filler.Speed
##            - 0.017 Pressure.Vacuum + 5e-06 Carb.Flow
## 
##   Rule 5/14: [402 cases, mean 8.681, range 8.12 to 8.92, est err 0.092]
## 
##     if
##  Mnf.Flow <= -100.2
##     then
##  outcome = -4.404 + 0.248 Pressure.Vacuum + 0.101 Air.Pressurer
##            + 0.098 Balling - 0.104 Balling.Lvl + 0.0022 Hyd.Pressure2
##            - 0.0024 Hyd.Pressure1
## 
## Model 6:
## 
##   Rule 6/1: [23 cases, mean 8.292, range 8.08 to 8.84, est err 0.162]
## 
##     if
##  Alch.Rel > 0.4885216
##  MFR > 245700
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = -160.524 - 1.5581 Mnf.Flow + 0.001535 Filler.Level
##            - 0.00226 Usage.cont - 0.247 Density + 0.088 Balling
##            + 6 Alch.Rel - 0.023 Brand.Code.C - 0.004 Air.Pressurer
##            - 0.009 Oxygen.Filler + 0.02 Carb.Pressure1
##            - 0.13 Hyd.Pressure4 - 0.003 Density.Scaled
## 
##   Rule 6/2: [19 cases, mean 8.318, range 7.9 to 8.62, est err 0.219]
## 
##     if
##  Carb.Rel <= 0.4816503
##  Mnf.Flow > -100
##     then
##  outcome = 7.397 - 1.8 PSC.Fill - 0.00013 Mnf.Flow - 0.015 Balling
##            + 0.01 Balling.Lvl + 0.0005 Hyd.Pressure3
##            + 3.1e-09 Filler.Speed - 0.013 Brand.Code.C
##            + 0.01 Brand.Code.D - 0.008 Oxygen.Filler - 6e-08 MFR
##            + 0.02 Carb.Pressure1 - 0.0002 Hyd.Pressure2
##            - 0.005 Pressure.Vacuum + 2 Alch.Rel - 0.003 Density.Scaled
##            - 4e-05 Usage.cont - 0.001 Pressure.Setpoint
## 
##   Rule 6/3: [25 cases, mean 8.322, range 8.18 to 8.48, est err 0.119]
## 
##     if
##  Alch.Rel <= 0.4902469
##  Carb.Rel > 0.4831045
##  Mnf.Flow > -100
##  Air.Pressurer <= 142
##     then
##  outcome = 8.19 + 0.0036 Hyd.Pressure3 + 0.0021 Hyd.Pressure1
##            - 1.2e-08 Filler.Speed - 0.013 Carb.Flow.Scaled
## 
##   Rule 6/4: [149 cases, mean 8.408, range 8.02 to 8.82, est err 0.135]
## 
##     if
##  Alch.Rel <= 0.4902469
##  Carb.Rel > 0.4824657
##  Mnf.Flow > -100
##  Pressure.Vacuum > -5.6
##  Air.Pressurer > 142
##  Density.Scaled > -1.901343
##     then
##  outcome = 7.13 - 0.00256 Mnf.Flow - 0.32 Balling + 0.337 Balling.Lvl
##            + 0.246 Pressure.Vacuum - 0.109 Density.Scaled
##            + 0.0058 Hyd.Pressure2 + 3.6e-08 Filler.Speed
##            - 0.0334 Pressure.Setpoint - 0.00074 Usage.cont
##            - 2.9e-05 Carb.Flow + 0.89 Carb.Pressure - 2e-07 MFR
##            + 0.009 Air.Pressurer + 0.007 Air.Pressurer.Scaled
## 
##   Rule 6/5: [39 cases, mean 8.415, range 7.88 to 8.8, est err 0.145]
## 
##     if
##  Carb.Rel > 0.4816503
##  Oxygen.Filler <= -2.632525
##  Air.Pressurer > 142
##  Density.Scaled <= -1.901343
##     then
##  outcome = 0.538 + 3.29e-08 Filler.Speed - 0.00053 Mnf.Flow - 8.4e-07 MFR
##            - 0.055 Balling + 0.037 Balling.Lvl + 0.0019 Hyd.Pressure3
##            + 0.025 Air.Pressurer - 0.022 Density.Scaled
##            - 0.009 Pressure.Setpoint - 0.049 Brand.Code.C
##            + 0.039 Brand.Code.D - 0.03 Oxygen.Filler
##            + 0.08 Carb.Pressure1 - 0.0008 Hyd.Pressure2 + 8 Alch.Rel
##            - 0.018 Pressure.Vacuum - 0.00016 Usage.cont - 0.12 PSC.CO2
##            - 0.12 Hyd.Pressure4
## 
##   Rule 6/6: [697 cases, mean 8.446, range 7.88 to 8.86, est err 0.101]
## 
##     if
##  Alch.Rel <= 0.4902469
##  Carb.Rel > 0.4816503
##  Mnf.Flow > -100
##     then
##  outcome = -3.208 + 0.0031 Hyd.Pressure3 - 7.1e-07 MFR
##            + 0.032 Air.Pressurer + 1.51e-08 Filler.Speed + 15 Alch.Rel
##            - 0.017 Balling - 0.017 Density.Scaled + 0.035 Brand.Code.D
##            + 0.0011 Hyd.Pressure1 - 0.0056 Pressure.Setpoint
##            - 0.007 Carb.Flow.Scaled
## 
##   Rule 6/7: [243 cases, mean 8.456, range 8.16 to 8.74, est err 0.083]
## 
##     if
##  Alch.Rel <= 0.4902469
##  Mnf.Flow > -100
##  Pressure.Vacuum <= -5.6
##  Air.Pressurer > 142
##  Density.Scaled > -1.901343
##     then
##  outcome = -1.295 + 0.00275 Mnf.Flow - 0.0095 Hyd.Pressure3
##            + 0.074 Air.Pressurer - 0.067 Density.Scaled
##            - 0.00083 Usage.cont - 0.15 Carb.Pressure1
##            + 1.3e-05 Filler.Level - 0.018 Balling.Lvl - 0.012 Balling
##            + 4.7e-09 Filler.Speed - 1.1e-07 MFR - 0.011 Brand.Code.C
##            + 0.009 Brand.Code.D - 0.007 Oxygen.Filler
##            - 0.0002 Hyd.Pressure2 + 2 Alch.Rel - 0.0013 Pressure.Setpoint
##            - 0.004 Pressure.Vacuum
## 
##   Rule 6/8: [119 cases, mean 8.481, range 8.16 to 8.7, est err 0.103]
## 
##     if
##  Alch.Rel > 0.4902469
##  Mnf.Flow > -100
##  Hyd.Pressure3 <= 32.2
##     then
##  outcome = 6.785 + 0.109 Balling + 0.0027 Hyd.Pressure3
##            - 0.0009 Bowl.Setpoint - 0.00011 Mnf.Flow + 8e-06 Filler.Level
##            - 0.12 PC.Volume + 0.06 PSC - 0.00016 Usage.cont
##            + 0.008 Balling.Lvl + 2.6e-09 Filler.Speed
##            - 0.011 Brand.Code.C + 0.009 Brand.Code.D
##            - 0.007 Oxygen.Filler + 0.02 Carb.Pressure1
##            - 0.0002 Hyd.Pressure2 - 5e-08 MFR + 2 Alch.Rel
##            - 0.004 Pressure.Vacuum - 0.002 Density.Scaled
## 
##   Rule 6/9: [79 cases, mean 8.492, range 8.1 to 8.78, est err 0.155]
## 
##     if
##  Alch.Rel <= 0.4885216
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = 55.089 + 0.47184 Mnf.Flow - 0.241 Density.Scaled
##            + 0.174 Balling.Scaled - 0.099 Density + 0.035 Balling
##            - 0.009 Brand.Code.C + 2 Alch.Rel - 0.002 Air.Pressurer
##            - 0.004 Oxygen.Filler
## 
##   Rule 6/10: [170 cases, mean 8.492, range 8 to 8.86, est err 0.078]
## 
##     if
##  Carb.Rel <= 0.4824657
##  Mnf.Flow > -100
##  Pressure.Vacuum > -5.6
##     then
##  outcome = 3.519 + 3.48e-08 Filler.Speed - 0.082 Density.Scaled
##            - 0.00056 Mnf.Flow + 0.04 Air.Pressurer
##            + 0.082 Pressure.Vacuum - 4.7e-07 MFR
##            - 0.008 Pressure.Setpoint + 0.009 Air.Pressurer.Scaled
## 
##   Rule 6/11: [24 cases, mean 8.498, range 8.02 to 8.8, est err 0.208]
## 
##     if
##  Carb.Rel > 0.4816503
##  Oxygen.Filler > -2.632525
##  Mnf.Flow > -100
##  Air.Pressurer > 142
##  Density.Scaled <= -1.901343
##     then
##  outcome = 14.202 - 2.083 Oxygen.Filler - 0.00232 Mnf.Flow - 3.47 PSC.CO2
##            - 4.88 Hyd.Pressure4
## 
##   Rule 6/12: [39 cases, mean 8.504, range 8.2 to 8.84, est err 0.133]
## 
##     if
##  Carb.Pressure1 <= 10.51956
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##     then
##  outcome = -160.268 - 1.53263 Mnf.Flow - 0.698 Density + 0.212 Balling
##            + 0.171 Pressure.Vacuum + 36 Alch.Rel - 0.043 Oxygen.Filler
##            - 0.018 Air.Pressurer + 0.13 Carb.Pressure1
## 
##   Rule 6/13: [291 cases, mean 8.504, range 8.02 to 8.82, est err 0.118]
## 
##     if
##  Mnf.Flow > -100
##  Hyd.Pressure3 > 32.2
##  Balling.Lvl.Scaled <= -0.09457123
##     then
##  outcome = 4.326 + 0.00144 Mnf.Flow + 0.179 Brand.Code.D
##            + 0.131 Pressure.Vacuum - 2.1e-07 MFR + 5.8e-09 Filler.Speed
##            + 0.01 Air.Pressurer + 0.0007 Hyd.Pressure3 + 7 Alch.Rel
##            - 0.008 Balling - 0.005 Density.Scaled
##            - 0.002 Pressure.Setpoint - 0.002 Carb.Flow.Scaled
## 
##   Rule 6/14: [30 cases, mean 8.539, range 8.14 to 8.8, est err 0.145]
## 
##     if
##  MFR <= 245700
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = 2.396 - 0.03958 Mnf.Flow - 0.268 Density
##            + 4.69e-08 Filler.Speed + 0.095 Balling - 0.025 Brand.Code.C
##            + 6 Alch.Rel - 0.005 Air.Pressurer - 0.01 Oxygen.Filler
##            - 0.004 Density.Scaled + 0.02 Carb.Pressure1
##            - 0.14 Hyd.Pressure4
## 
##   Rule 6/15: [97 cases, mean 8.585, range 8.24 to 8.86, est err 0.068]
## 
##     if
##  Alch.Rel > 0.4902469
##  Mnf.Flow > -100
##  Hyd.Pressure3 > 32.2
##  Balling.Lvl.Scaled > -0.09457123
##     then
##  outcome = 7.639 - 0.00523 Mnf.Flow + 2.847e-07 Filler.Speed
##            - 3.4e-06 MFR + 0.0115 Hyd.Pressure2 - 0.202 Density.Scaled
##            - 0.157 Carb.Flow.Scaled + 2.9e-05 Filler.Level
##            + 0.0006 Hyd.Pressure3 + 0.02 PSC - 0.0002 Bowl.Setpoint
##            - 0.03 PC.Volume - 3e-05 Usage.cont
## 
##   Rule 6/16: [140 cases, mean 8.607, range 8.18 to 8.92, est err 0.106]
## 
##     if
##  Filler.Speed > 8024018
##  Brand.Code.C <= 0
##  Pressure.Vacuum > -5
##  Air.Pressurer > 142
##     then
##  outcome = -29.947 - 0.23933 Mnf.Flow - 0.789 Density + 0.26 Balling
##            - 0.06 Air.Pressurer + 46 Alch.Rel - 0.03 Balling.Lvl
##            + 0.11 Carb.Pressure1 - 0.033 Oxygen.Filler
## 
##   Rule 6/17: [120 cases, mean 8.656, range 8.2 to 8.94, est err 0.109]
## 
##     if
##  Filler.Speed <= 8024018
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##  Air.Pressurer > 142
##     then
##  outcome = -144.33 - 1.00161 Mnf.Flow - 3.475 Density + 1.164 Balling
##            + 111 Alch.Rel - 0.142 Pressure.Vacuum + 1.07 PSC.CO2
##            - 0.028 Balling.Lvl - 0.009 Air.Pressurer
##            + 0.06 Carb.Pressure1
## 
##   Rule 6/18: [705 cases, mean 8.660, range 8.18 to 8.94, est err 0.101]
## 
##     if
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##     then
##  outcome = -11.714 - 0.10664 Mnf.Flow - 0.571 Density + 0.186 Balling
##            + 22 Alch.Rel - 0.037 Oxygen.Filler - 0.011 Air.Pressurer
##            + 0.07 Carb.Pressure1 - 0.005 Brand.Code.C
## 
##   Rule 6/19: [346 cases, mean 8.678, range 8.3 to 8.92, est err 0.075]
## 
##     if
##  Oxygen.Filler > -2.652763
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum <= -5
##     then
##  outcome = -50.726 - 0.208 Balling + 124 Alch.Rel + 0.176 Pressure.Vacuum
##            - 0.183 Oxygen.Filler + 3.11e-08 Filler.Speed
##            - 0.064 Balling.Lvl.Scaled - 8.5e-07 MFR
##            - 0.0025 Hyd.Pressure1 + 0.26 PC.Volume
## 
##   Rule 6/20: [60 cases, mean 8.701, range 8.24 to 8.94, est err 0.106]
## 
##     if
##  Carb.Pressure1 > 10.51956
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##  Air.Pressurer <= 142
##     then
##  outcome = -57.135 - 0.39568 Mnf.Flow - 1.495 Density + 0.483 Balling
##            + 61 Alch.Rel - 0.099 Oxygen.Filler - 0.035 Air.Pressurer
##            + 0.18 Carb.Pressure1
## 
## Model 7:
## 
##   Rule 7/1: [24 cases, mean 8.247, range 7.88 to 8.66, est err 0.221]
## 
##     if
##  Carb.Rel <= 0.4819283
##  Brand.Code.C > 0
##  Mnf.Flow > -100.2
##     then
##  outcome = 8.702 - 0.00128 Mnf.Flow + 0.036 Density
##            + 0.0008 Hyd.Pressure3 - 2e-07 MFR + 3.9e-09 Filler.Speed
##            - 0.04 Carb.Pressure1
## 
##   Rule 7/2: [118 cases, mean 8.362, range 7.88 to 8.8, est err 0.105]
## 
##     if
##  Brand.Code.C > 0
##  Mnf.Flow > -100.2
##  Hyd.Pressure1 > 10.2
##     then
##  outcome = 9.441 - 2.84e-06 MFR + 7.36e-08 Filler.Speed
##            - 0.00106 Mnf.Flow - 3e-05 Carb.Flow + 0.066 Density
##            + 0.0015 Hyd.Pressure3 - 0.08 Carb.Pressure1
## 
##   Rule 7/3: [59 cases, mean 8.387, range 8.02 to 8.64, est err 0.178]
## 
##     if
##  PC.Volume > -0.9525701
##  Brand.Code.C > 0
##  Mnf.Flow > -100.2
##  Mnf.Flow <= 129.6
##  Hyd.Pressure1 <= 10.2
##     then
##  outcome = 5.496 + 1.216 Density - 0.378 Balling.Lvl - 2.99 PC.Volume
##            - 8e-08 MFR + 0.0003 Hyd.Pressure3 - 4e-05 Mnf.Flow
##            - 0.02 Carb.Pressure1 + 1.5e-09 Filler.Speed
## 
##   Rule 7/4: [41 cases, mean 8.406, range 8.06 to 8.74, est err 0.203]
## 
##     if
##  Alch.Rel > 0.490137
##  Alch.Rel <= 0.4902469
##  Mnf.Flow > -100.2
##     then
##  outcome = 10.482 - 0.605 Balling + 0.00225 Mnf.Flow
##            - 0.0143 Hyd.Pressure2 - 0.00295 Usage.cont
##            + 0.161 Balling.Scaled - 0.046 Density.Scaled + 0.072 Density
##            + 0.01 Balling.Lvl.Scaled + 0.06 Carb.Pressure1
## 
##   Rule 7/5: [236 cases, mean 8.426, range 8.02 to 8.86, est err 0.135]
## 
##     if
##  Carb.Rel > 0.4819283
##  Brand.Code.C > 0
##     then
##  outcome = 1.886 + 13 Alch.Rel - 0.046 Brand.Code.C - 0.00013 Mnf.Flow
##            - 0.039 Density + 0.0009 Bowl.Setpoint + 0.0008 Hyd.Pressure3
##            + 0.06 Carb.Pressure1 - 0.00015 Usage.cont - 1e-07 MFR
##            + 2.6e-09 Filler.Speed - 0.0019 Pressure.Setpoint
##            - 0.003 Air.Pressurer + 3e-06 Carb.Flow - 2e-06 Filler.Level
##            - 0.03 PC.Volume + 0.003 Air.Pressurer.Scaled
## 
##   Rule 7/6: [22 cases, mean 8.433, range 8.06 to 8.68, est err 0.192]
## 
##     if
##  Alch.Rel <= 0.490137
##  Carb.Volume > 0.4824219
##  Mnf.Flow > -100.2
##  Carb.Flow > 1084
##  Bowl.Setpoint > 80
##  Air.Pressurer.Scaled > 0.3366049
##  Balling.Lvl.Scaled <= 0.5110298
##  Density.Scaled <= 0.2717527
##  Carb.Flow.Scaled <= 0.4983332
##     then
##  outcome = 8.914 + 0.302 Pressure.Vacuum + 0.0067 Bowl.Setpoint
##            + 0.083 Balling.Lvl.Scaled + 0.00025 Mnf.Flow
## 
##   Rule 7/7: [365 cases, mean 8.480, range 8.02 to 8.88, est err 0.120]
## 
##     if
##  Mnf.Flow > -100.2
##  Carb.Flow <= 1084
##  Bowl.Setpoint > 80
##     then
##  outcome = 6.561 + 0.374 Balling.Lvl - 0.204 Balling
##            + 0.0088 Hyd.Pressure2 + 0.0071 Bowl.Setpoint
##            - 0.0066 Hyd.Pressure3 - 0.228 Density - 0.134 Pressure.Vacuum
##            + 4.1e-05 Filler.Level + 0.005 Hyd.Pressure1 - 4.9e-07 MFR
##            + 0.039 Oxygen.Filler + 0.018 Balling.Scaled
##            - 0.006 Density.Scaled + 0.03 Carb.Pressure1 - 3e-05 Mnf.Flow
##            - 0.0017 Pressure.Setpoint - 0.03 PC.Volume
##            + 0.003 Air.Pressurer.Scaled
## 
##   Rule 7/8: [20 cases, mean 8.482, range 8.18 to 8.86, est err 0.165]
## 
##     if
##  Alch.Rel <= 0.490137
##  Carb.Volume > 0.4824219
##  Brand.Code.C <= 0
##  Mnf.Flow > -100.2
##  Carb.Flow > 1084
##  Balling.Lvl.Scaled > 0.5110298
##  Carb.Flow.Scaled <= 0.4983332
##     then
##  outcome = 7.42 + 0.0082 Bowl.Setpoint + 0.112 Balling.Lvl.Scaled
## 
##   Rule 7/9: [91 cases, mean 8.484, range 8.02 to 8.84, est err 0.180]
## 
##     if
##  Carb.Volume > 0.4824219
##  Brand.Code.C <= 0
##  Mnf.Flow > -100.2
##  Carb.Flow > 1084
##  Bowl.Setpoint > 80
##  Balling.Lvl.Scaled <= 0.5110298
##  Density.Scaled <= 0.2717527
##  Carb.Flow.Scaled <= 0.4983332
##     then
##  outcome = 2.416 + 0.0288 Bowl.Setpoint + 0.239 Balling.Lvl.Scaled
##            + 0.00076 Mnf.Flow + 6.6e-05 Carb.Flow + 0.34 Carb.Pressure1
##            - 0.115 Brand.Code.Encoded + 0.0002 Hyd.Pressure2
##            - 0.003 Density.Scaled - 0.005 Oxygen.Filler
##            - 0.004 Pressure.Vacuum - 1e-06 Filler.Level
## 
##   Rule 7/10: [137 cases, mean 8.490, range 8.26 to 8.74, est err 0.096]
## 
##     if
##  Bowl.Setpoint <= 80
##     then
##  outcome = 5.998 - 0.285 Oxygen.Filler + 0.0082 Bowl.Setpoint
##            - 0.0075 Hyd.Pressure2 - 0.096 Balling + 3.91e-08 Filler.Speed
##            - 1.1e-06 MFR - 3.8e-05 Filler.Level + 0.061 Density.Scaled
##            + 0.00061 Usage.cont - 0.059 Pressure.Vacuum + 3 Alch.Rel
##            - 0.03 PSC.Fill - 0.03 PC.Volume - 0.13 Hyd.Pressure4
## 
##   Rule 7/11: [167 cases, mean 8.493, range 8.06 to 8.84, est err 0.104]
## 
##     if
##  Usage.cont > 201.9072
##  Brand.Code.C <= 0
##  Mnf.Flow > -100.2
##  Bowl.Setpoint > 80
##  Density.Scaled > -2.275767
##  Carb.Flow.Scaled > 0.4983332
##     then
##  outcome = 9.299 + 1.099 Balling.Lvl - 1.013 Balling
##            + 0.259 Balling.Scaled - 0.00344 Usage.cont
##            - 0.198 Balling.Lvl.Scaled - 0.113 Density.Scaled
##            + 0.066 Air.Pressurer.Scaled - 3.4e-05 Filler.Level
##            + 0.0025 Bowl.Setpoint + 0.35 PC.Volume - 0.47 PSC.CO2
##            - 7e-05 Mnf.Flow + 0.0004 Hyd.Pressure3 + 0.03 Carb.Pressure1
## 
##   Rule 7/12: [61 cases, mean 8.506, range 8.2 to 8.86, est err 0.137]
## 
##     if
##  Alch.Rel <= 0.490137
##  Brand.Code.C <= 0
##  Mnf.Flow > -100.2
##  Carb.Flow > 1084
##  Bowl.Setpoint > 80
##  Balling.Lvl.Scaled <= 0.5110298
##  Density.Scaled > 0.2717527
##  Carb.Flow.Scaled <= 0.4983332
##     then
##  outcome = 7.338 + 0.327 Balling.Lvl.Scaled + 0.217 Density.Scaled
##            + 0.0068 Bowl.Setpoint - 0.00082 Mnf.Flow - 0.064 Balling
##            + 0.068 Balling.Lvl - 2.3e-05 Filler.Level + 2.1e-05 Carb.Flow
##            + 0.0012 Hyd.Pressure2 - 0.028 Pressure.Vacuum
##            - 0.026 Oxygen.Filler + 0.011 Balling.Scaled
##            - 0.0006 Hyd.Pressure3 + 0.01 Carb.Pressure1
## 
##   Rule 7/13: [17 cases, mean 8.518, range 8.26 to 8.86, est err 0.184]
## 
##     if
##  Brand.Code.C > 0
##  Mnf.Flow > 129.6
##  Hyd.Pressure1 <= 10.2
##     then
##  outcome = 3.721 + 0.02884 Mnf.Flow - 0.0624 Hyd.Pressure1
##            + 0.763 Balling.Lvl
## 
##   Rule 7/14: [31 cases, mean 8.518, range 8.4 to 8.66, est err 0.105]
## 
##     if
##  Usage.cont > 201.9072
##  Brand.Code.C <= 0
##  Density.Scaled <= -2.275767
##     then
##  outcome = 239.269 - 56.108 Balling + 56.542 Density.Scaled
## 
##   Rule 7/15: [19 cases, mean 8.532, range 8.2 to 8.68, est err 0.094]
## 
##     if
##  Alch.Rel > 0.490137
##  Filler.Speed <= 6480000
##  Hyd.Pressure3 > 25.4
##     then
##  outcome = 7.056 - 0.373 Balling.Lvl + 5.13e-08 Filler.Speed
##            - 6e-05 Carb.Flow - 0.00092 Usage.cont - 0.075 Pressure.Vacuum
##            + 0.0031 Hyd.Pressure1 - 1.4 Hyd.Pressure4
##            - 0.0019 Bowl.Setpoint + 10 Alch.Rel + 0.0005 Hyd.Pressure2
##            - 0.009 Density.Scaled + 0.008 Balling.Lvl.Scaled
##            - 6e-05 Mnf.Flow + 0.04 Carb.Pressure1
## 
##   Rule 7/16: [45 cases, mean 8.533, range 8.22 to 8.86, est err 0.079]
## 
##     if
##  Alch.Rel > 0.490137
##  Filler.Speed > 6480000
##  Hyd.Pressure1 <= 8.6
##  Hyd.Pressure3 > 25.4
##  Bowl.Setpoint > 80
##     then
##  outcome = 6.348 + 1.438e-07 Filler.Speed - 0.0161 Hyd.Pressure1
##            + 0.0101 Hyd.Pressure3 - 0.136 Density.Scaled
##            - 0.193 Pressure.Vacuum - 0.086 Oxygen.Filler
##            - 0.029 Balling.Lvl - 0.00032 Usage.cont - 1e-05 Carb.Flow
##            - 0.0007 Bowl.Setpoint - 0.11 Hyd.Pressure4
## 
##   Rule 7/17: [99 cases, mean 8.535, range 8.24 to 8.82, est err 0.114]
## 
##     if
##  Alch.Rel > 0.490137
##  Carb.Pressure1 <= 10.68296
##  Mnf.Flow > -100.2
##  Bowl.Setpoint > 80
##     then
##  outcome = -23.135 - 0.214 Balling + 59 Alch.Rel + 0.057 Balling.Scaled
##            + 0.0037 Bowl.Setpoint - 0.057 Density.Scaled
##            + 0.048 Balling.Lvl.Scaled - 0.055 Balling.Lvl
##            + 0.29 Carb.Pressure1 - 0.00079 Usage.cont - 0.00038 Mnf.Flow
##            + 0.0026 Hyd.Pressure2 - 0.048 Pressure.Vacuum - 1.3e-07 MFR
##            + 0.0005 Hyd.Pressure3 + 3.6e-09 Filler.Speed - 0.01 Density
##            - 0.01 Brand.Code.C
## 
##   Rule 7/18: [35 cases, mean 8.546, range 8.22 to 8.84, est err 0.200]
## 
##     if
##  Alch.Rel <= 0.490137
##  Mnf.Flow > -100.2
##  Bowl.Setpoint > 80
##  Air.Pressurer.Scaled > 1.494793
##  Carb.Flow.Scaled <= 0.4983332
##     then
##  outcome = -10.102 - 0.412 Balling + 0.421 Balling.Lvl
##            + 0.0081 Bowl.Setpoint + 0.076 Balling.Scaled
##            + 0.0038 Hyd.Pressure2 - 0.102 Pressure.Vacuum
##            - 0.056 Density.Scaled + 31 Alch.Rel - 0.0026 Hyd.Pressure3
##            + 0.24 Carb.Pressure1 - 0.0003 Mnf.Flow
##            + 0.025 Balling.Lvl.Scaled + 0.0019 Hyd.Pressure1
##            - 0.00035 Usage.cont - 0.0084 Pressure.Setpoint
##            - 0.17 PC.Volume
## 
##   Rule 7/19: [305 cases, mean 8.547, range 8.02 to 8.94, est err 0.118]
## 
##     if
##  Alch.Rel <= 0.490137
##  Brand.Code.C <= 0
##  Mnf.Flow > -100.2
##  Carb.Flow > 1084
##  Bowl.Setpoint > 80
##  Carb.Flow.Scaled <= 0.4983332
##     then
##  outcome = 5.871 + 0.354 Balling.Lvl - 0.328 Balling
##            + 0.0102 Bowl.Setpoint + 0.0044 Hyd.Pressure2
##            - 0.00056 Mnf.Flow + 0.057 Balling.Scaled
##            - 0.101 Oxygen.Filler - 0.071 Pressure.Vacuum
##            - 0.038 Density.Scaled + 2.9e-05 Carb.Flow
##            - 0.0018 Hyd.Pressure3 + 0.015 Balling.Lvl.Scaled
##            + 0.08 Carb.Pressure1 + 0.0007 Hyd.Pressure1 - 0.07 PC.Volume
##            - 0.0034 Pressure.Setpoint
## 
##   Rule 7/20: [19 cases, mean 8.565, range 8.12 to 8.8, est err 0.251]
## 
##     if
##  Oxygen.Filler <= -2.57927
##  Temperature > 0.4998845
##  Mnf.Flow <= -100.2
##  Hyd.Pressure3 <= 16.2
##  Pressure.Vacuum <= -4.8
##     then
##  outcome = 24.738 + 10.994 Oxygen.Filler - 0.221 Carb.Flow.Scaled
##            - 0.97 PSC.Fill + 0.09 Air.Pressurer
##            - 0.045 Air.Pressurer.Scaled + 0.003 Pressure.Vacuum
## 
##   Rule 7/21: [439 cases, mean 8.571, range 8.18 to 8.94, est err 0.124]
## 
##     if
##  Brand.Code.C <= 0
##  Mnf.Flow > -100.2
##  Hyd.Pressure3 <= 25.4
##     then
##  outcome = -12.959 + 41 Alch.Rel - 0.00047 Mnf.Flow - 0.129 Density
##            + 0.0031 Bowl.Setpoint + 0.0028 Hyd.Pressure3
##            - 0.126 Brand.Code.C + 0.23 Carb.Pressure1
##            - 0.00046 Usage.cont - 0.012 Air.Pressurer + 1.2e-05 Carb.Flow
##            - 0.12 PC.Volume + 0.012 Air.Pressurer.Scaled
##            - 7e-06 Filler.Level - 0.0052 Pressure.Setpoint
##            + 0.23 Carb.Pressure - 0.005 Oxygen.Filler
##            + 0.002 Balling.Lvl.Scaled - 0.002 Density.Scaled
##            - 0.002 Balling.Lvl
## 
##   Rule 7/22: [161 cases, mean 8.574, range 8.16 to 8.82, est err 0.073]
## 
##     if
##  Alch.Rel > 0.4902469
##  Filler.Speed > 6480000
##  Mnf.Flow > -100.2
##  Hyd.Pressure1 > 8.6
##  Hyd.Pressure3 > 25.4
##  Bowl.Setpoint > 80
##     then
##  outcome = 3.196 + 1.553e-07 Filler.Speed - 0.166 Balling
##            - 0.00144 Usage.cont + 0.044 Balling.Scaled
##            - 0.061 Pressure.Vacuum - 0.0021 Bowl.Setpoint
##            - 2.7e-05 Carb.Flow + 0.0017 Hyd.Pressure1 + 9 Alch.Rel
##            - 0.013 Density.Scaled + 0.06 Carb.Pressure1
##            + 0.0005 Hyd.Pressure3 - 6e-05 Mnf.Flow - 0.01 Density
##            + 0.003 Balling.Lvl.Scaled - 0.0014 Pressure.Setpoint
## 
##   Rule 7/23: [118 cases, mean 8.596, range 8.06 to 8.82, est err 0.073]
## 
##     if
##  Alch.Rel > 0.490137
##  Filler.Speed > 7644050
##  Mnf.Flow > -100.2
##  Hyd.Pressure1 > 8.6
##  Hyd.Pressure3 > 25.4
##  Bowl.Setpoint > 80
##     then
##  outcome = 9.055 - 0.175 Pressure.Vacuum - 0.00122 Usage.cont
##            - 0.072 Balling.Lvl - 0.0036 Bowl.Setpoint
##            + 2.13e-08 Filler.Speed - 1.4e-05 Carb.Flow
##            + 0.0008 Hyd.Pressure1 - 0.28 Hyd.Pressure4
## 
##   Rule 7/24: [17 cases, mean 8.599, range 8.46 to 8.74, est err 0.127]
## 
##     if
##  Carb.Rel > 0.4838259
##  Bowl.Setpoint <= 80
##     then
##  outcome = 6.871 - 0.00318 Mnf.Flow + 0.053 Carb.Flow.Scaled
##            - 0.048 Oxygen.Filler + 0.0012 Bowl.Setpoint
##            - 0.0011 Hyd.Pressure2 - 0.013 Balling - 1.7e-07 MFR
##            + 0.011 Density.Scaled + 4.4e-09 Filler.Speed + 5 Alch.Rel
##            - 0.06 PC.Volume - 0.05 PSC.Fill - 0.25 Hyd.Pressure4
## 
##   Rule 7/25: [75 cases, mean 8.612, range 8.4 to 8.92, est err 0.096]
## 
##     if
##  Usage.cont <= 201.9072
##  Mnf.Flow > -100.2
##  Bowl.Setpoint > 80
##  Carb.Flow.Scaled > 0.4983332
##     then
##  outcome = 3.444 + 0.772 Balling.Lvl - 0.717 Balling
##            + 0.009 Bowl.Setpoint + 0.137 Balling.Scaled
##            - 8.4e-05 Filler.Level - 0.09 Balling.Lvl.Scaled
##            + 0.46 Carb.Pressure1 - 0.00058 Mnf.Flow - 0.00043 Usage.cont
##            + 0.0015 Hyd.Pressure3 - 0.024 Density.Scaled + 0.18 PC.Volume
##            + 0.015 Air.Pressurer.Scaled - 0.28 PSC.CO2
## 
##   Rule 7/26: [66 cases, mean 8.617, range 8.22 to 8.88, est err 0.102]
## 
##     if
##  Oxygen.Filler > -2.57927
##  Temperature > 0.4998845
##  Mnf.Flow <= -100.2
##  Hyd.Pressure3 <= 16.2
##  Pressure.Vacuum <= -4.8
##     then
##  outcome = -12.399 + 0.35 Pressure.Vacuum + 0.122 Air.Pressurer
##            + 0.41 Carb.Pressure1 - 0.06 Air.Pressurer.Scaled
##            + 0.0002 Bowl.Setpoint + 2 Alch.Rel - 0.007 Density
##            - 0.007 Brand.Code.C - 2e-05 Mnf.Flow + 0.0001 Hyd.Pressure3
## 
##   Rule 7/27: [51 cases, mean 8.626, range 8.4 to 8.8, est err 0.083]
## 
##     if
##  Temperature > 0.4998845
##  Mnf.Flow <= -100.2
##  Hyd.Pressure3 > 16.2
##  Pressure.Vacuum <= -4.8
##     then
##  outcome = 10.052 - 0.013 Hyd.Pressure3 - 0.062 Balling.Lvl
##            + 0.075 Pressure.Vacuum - 0.21 Carb.Pressure1
##            + 0.0157 Pressure.Setpoint - 0.25 PSC.Fill - 3e-05 Mnf.Flow
##            - 0.009 Brand.Code.C + 0.0002 Bowl.Setpoint - 0.008 Density
##            + 2 Alch.Rel
## 
##   Rule 7/28: [160 cases, mean 8.664, range 8.22 to 8.92, est err 0.071]
## 
##     if
##  Mnf.Flow <= -100.2
##  Pressure.Vacuum <= -4.8
##  Balling.Lvl > 1.48
##     then
##  outcome = -256.463 + 1.644 Air.Pressurer - 0.8 Air.Pressurer.Scaled
##            - 0.236 Balling.Lvl + 0.179 Balling + 0.288 Pressure.Vacuum
##            + 67 Alch.Rel - 0.0038 Hyd.Pressure1 + 0.0021 Hyd.Pressure2
##            - 0.028 Balling.Scaled - 0.0071 Pressure.Setpoint
## 
##   Rule 7/29: [227 cases, mean 8.686, range 8.12 to 8.92, est err 0.082]
## 
##     if
##  Mnf.Flow <= -100.2
##  Balling.Lvl <= 1.48
##     then
##  outcome = -316.85 + 2.197 Air.Pressurer - 1.083 Air.Pressurer.Scaled
##            - 0.355 Balling.Lvl + 0.162 Pressure.Vacuum + 0.094 Balling
##            + 25 Alch.Rel - 0.063 Oxygen.Filler + 0.14 Carb.Pressure1
##            + 0.0008 Hyd.Pressure2 - 0.013 Balling.Scaled
##            - 0.001 Hyd.Pressure1 - 0.031 Brand.Code.C - 9e-05 Mnf.Flow
##            + 0.0007 Bowl.Setpoint - 0.028 Density
##            - 0.0044 Pressure.Setpoint + 0.0005 Hyd.Pressure3
##            - 0.0001 Usage.cont + 3e-06 Carb.Flow - 2e-06 Filler.Level
##            - 0.03 PC.Volume
## 
##   Rule 7/30: [44 cases, mean 8.791, range 8.52 to 8.92, est err 0.074]
## 
##     if
##  Mnf.Flow <= -100.2
##  Pressure.Vacuum > -4.8
##     then
##  outcome = -36.309 + 0.305 Air.Pressurer - 0.382 Pressure.Vacuum
##            - 0.078 Air.Pressurer.Scaled + 0.034 Balling.Scaled
## 
## Model 8:
## 
##   Rule 8/1: [19 cases, mean 8.318, range 7.9 to 8.62, est err 0.193]
## 
##     if
##  Carb.Rel <= 0.4816503
##  Mnf.Flow > -100
##     then
##  outcome = -6.627 - 0.078 Balling.Scaled - 0.054 Balling.Lvl
##            + 29 Alch.Rel - 0.00033 Mnf.Flow + 0.0019 Hyd.Pressure3
##            - 0.056 Brand.Code.C + 0.015 Balling + 0.0009 Bowl.Setpoint
##            + 0.013 Balling.Lvl.Scaled - 0.013 Density.Scaled
##            + 5.3e-09 Filler.Speed - 0.0006 Hyd.Pressure2
##            + 0.05 Carb.Pressure1 - 5e-06 Filler.Level
##            - 0.012 Pressure.Vacuum - 0.0027 Pressure.Setpoint - 4e-08 MFR
##            + 0.002 Air.Pressurer
## 
##   Rule 8/2: [75 cases, mean 8.385, range 8.12 to 8.58, est err 0.091]
## 
##     if
##  Alch.Rel <= 0.4902469
##  Carb.Rel > 0.4824657
##  Mnf.Flow > -100
##  Air.Pressurer.Scaled <= -0.8215829
##     then
##  outcome = 4.755 + 0.422 Balling.Lvl - 0.388 Balling
##            + 0.088 Balling.Scaled - 0.057 Balling.Lvl.Scaled
##            + 1.58e-08 Filler.Speed - 3.7e-07 MFR + 0.0018 Hyd.Pressure1
##            + 0.018 Air.Pressurer - 0.022 Density.Scaled
##            + 0.01 Air.Pressurer.Scaled + 2 Alch.Rel
## 
##   Rule 8/3: [59 cases, mean 8.389, range 8.08 to 8.84, est err 0.304]
## 
##     if
##  Alch.Rel > 0.48831
##  MFR > 242207.5
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = -148.215 - 1.52812 Mnf.Flow + 1.173e-05 MFR
##            - 0.00246 Usage.cont + 0.095 Oxygen.Filler - 0.006 Balling.Lvl
##            + 0.0002 Hyd.Pressure3 + 2 Alch.Rel + 0.002 Balling
##            - 0.005 Brand.Code.C
## 
##   Rule 8/4: [17 cases, mean 8.392, range 8.02 to 8.74, est err 0.088]
## 
##     if
##  Alch.Rel <= 0.4902469
##  Carb.Rel > 0.4824657
##  Filler.Speed > 7904288
##  Bowl.Setpoint <= 110
##  Air.Pressurer.Scaled > -0.8215829
##  Balling.Lvl.Scaled <= -0.7758724
##     then
##  outcome = 8.252 - 0.01049 Mnf.Flow + 0.000161 Filler.Level
##            + 0.0097 Bowl.Setpoint + 0.101 Air.Pressurer.Scaled
##            - 2.02e-08 Filler.Speed
## 
##   Rule 8/5: [138 cases, mean 8.398, range 8.02 to 8.82, est err 0.123]
## 
##     if
##  Alch.Rel <= 0.4902469
##  Carb.Rel > 0.4824657
##  Filler.Speed <= 7904288
##  Mnf.Flow > -100
##  Air.Pressurer.Scaled > -0.8215829
##     then
##  outcome = 0.688 + 0.00102 Mnf.Flow - 0.0045 Hyd.Pressure2
##            + 0.049 Air.Pressurer - 0.06 Balling + 0.123 Density
##            + 1.62e-08 Filler.Speed - 0.048 Pressure.Vacuum - 4e-07 MFR
##            + 0.0015 Bowl.Setpoint - 0.025 Density.Scaled - 0.17 PC.Volume
##            + 0.018 Balling.Lvl - 0.008 Balling.Lvl.Scaled
##            - 0.002 Balling.Scaled
## 
##   Rule 8/6: [22 cases, mean 8.418, range 8.1 to 8.58, est err 0.107]
## 
##     if
##  Filler.Speed > 7944098
##  Oxygen.Filler > -2.445618
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##  Air.Pressurer.Scaled > 0.3366049
##     then
##  outcome = -37.494 - 0.21421 Mnf.Flow + 0.398 Pressure.Vacuum
##            + 4.14e-08 Filler.Speed + 51 Alch.Rel - 0.083 Balling.Lvl
##            - 0.029 Balling.Scaled + 0.29 Carb.Pressure
##            - 0.009 Air.Pressurer.Scaled + 0.003 Balling.Lvl.Scaled
## 
##   Rule 8/7: [18 cases, mean 8.427, range 8.06 to 8.62, est err 0.219]
## 
##     if
##  Alch.Rel <= 0.4902469
##  Carb.Rel > 0.4824657
##  Filler.Speed > 7904288
##  Mnf.Flow > -100
##  Bowl.Setpoint > 110
##  Air.Pressurer.Scaled > -0.8215829
##     then
##  outcome = 10.094 - 2.11e-07 Filler.Speed - 0.0281 Hyd.Pressure3
##            + 0.000216 Filler.Level - 0.000314 Carb.Flow
##            - 0.0006 Bowl.Setpoint + 0.009 Air.Pressurer.Scaled
##            - 0.006 Density.Scaled + 0.014 Density - 0.11 PSC.CO2
##            + 0.008 Oxygen.Filler
## 
##   Rule 8/8: [697 cases, mean 8.446, range 7.88 to 8.86, est err 0.095]
## 
##     if
##  Alch.Rel <= 0.4902469
##  Carb.Rel > 0.4816503
##  Mnf.Flow > -100
##     then
##  outcome = 2.747 - 0.829 Balling + 0.869 Balling.Lvl
##            + 0.154 Balling.Scaled - 0.106 Balling.Lvl.Scaled
##            + 3.72e-08 Filler.Speed - 8.7e-07 MFR + 0.033 Air.Pressurer
##            - 0.03 Density.Scaled + 2 Alch.Rel - 2e-05 Mnf.Flow
##            + 0.0001 Hyd.Pressure3
## 
##   Rule 8/9: [193 cases, mean 8.457, range 7.88 to 8.8, est err 0.089]
## 
##     if
##  Alch.Rel <= 0.4902469
##  Carb.Rel > 0.4816503
##  Filler.Speed > 7904288
##  Bowl.Setpoint <= 110
##  Air.Pressurer.Scaled > -0.8215829
##  Balling.Lvl.Scaled > -0.7758724
##     then
##  outcome = 11.936 - 5.759e-07 Filler.Speed + 0.058 Air.Pressurer.Scaled
##            + 2e-05 Filler.Level + 0.061 Oxygen.Filler + 0.072 Density
##            - 0.57 PSC.CO2 - 0.022 Density.Scaled - 0.014 Balling.Scaled
##            - 0.012 Balling.Lvl + 0.007 Air.Pressurer
##            + 0.0005 Bowl.Setpoint - 0.013 Pressure.Vacuum - 9e-08 MFR
##            - 0.05 PC.Volume
## 
##   Rule 8/10: [43 cases, mean 8.473, range 8.16 to 8.68, est err 0.138]
## 
##     if
##  Alch.Rel > 0.4902469
##  Mnf.Flow > -100
##  Hyd.Pressure3 > 13.4
##  Hyd.Pressure3 <= 32.6
##  Balling.Scaled <= 0.2335605
##     then
##  outcome = -1.915 + 0.0138 Hyd.Pressure3 + 0.069 Balling.Lvl.Scaled
##            + 4.1e-05 Carb.Flow - 0.037 Balling.Lvl + 19 Alch.Rel
##            - 0.023 Carb.Flow.Scaled - 0.00015 Mnf.Flow + 0.014 Balling
##            - 0.024 Brand.Code.C + 3.5e-09 Filler.Speed
##            - 0.008 Density.Scaled - 0.0004 Hyd.Pressure2
##            + 0.0003 Bowl.Setpoint - 0.004 Balling.Scaled - 6e-08 MFR
##            + 0.003 Air.Pressurer + 0.02 Carb.Pressure1
##            - 2e-06 Filler.Level - 0.005 Pressure.Vacuum
##            - 0.0012 Pressure.Setpoint
## 
##   Rule 8/11: [62 cases, mean 8.491, range 8.1 to 8.78, est err 0.126]
## 
##     if
##  Alch.Rel <= 0.4885216
##  MFR > 242207.5
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = -1.936 - 0.11824 Mnf.Flow - 6.61e-08 Filler.Speed
##            + 0.216 Oxygen.Filler + 9.6e-07 MFR - 0.00079 Usage.cont
##            - 0.008 Balling - 0.016 Brand.Code.C + 0.006 Balling.Lvl
##            - 0.003 Air.Pressurer - 0.11 Hyd.Pressure4
##            - 0.002 Density.Scaled + 0.01 Carb.Pressure1
## 
##   Rule 8/12: [52 cases, mean 8.502, range 8.2 to 8.94, est err 0.194]
## 
##     if
##  Filler.Speed > 7944098
##  Filler.Speed <= 8024018
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##     then
##  outcome = -255.268 - 2.36544 Mnf.Flow + 3.304e-07 Filler.Speed
##            - 0.205 Oxygen.Filler - 0.079 Balling.Lvl + 46 Alch.Rel
##            - 0.035 Balling.Scaled + 0.023 Balling.Lvl.Scaled
##            + 0.3 Carb.Pressure + 0.05 Carb.Pressure1
## 
##   Rule 8/13: [23 cases, mean 8.534, range 8.14 to 8.8, est err 0.166]
## 
##     if
##  Alch.Rel > 0.48831
##  MFR <= 242207.5
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = 8.103 - 0.00247 Mnf.Flow + 0.37 Oxygen.Filler + 2.7e-06 MFR
##            - 0.003 Balling.Lvl + 1 Alch.Rel
## 
##   Rule 8/14: [32 cases, mean 8.547, range 8.4 to 8.64, est err 0.095]
## 
##     if
##  Alch.Rel <= 0.48831
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = 64.215 + 0.54029 Mnf.Flow - 0.022 Balling - 0.047 Brand.Code.C
##            + 0.017 Balling.Lvl - 0.008 Air.Pressurer - 0.32 Hyd.Pressure4
##            - 0.006 Density.Scaled - 0.01 Oxygen.Filler
##            + 0.03 Carb.Pressure1 + 0.0003 Hyd.Pressure3
## 
##   Rule 8/15: [265 cases, mean 8.552, range 8.16 to 8.86, est err 0.092]
## 
##     if
##  Alch.Rel > 0.4902469
##  Mnf.Flow > -100
##     then
##  outcome = 8.74 + 0.0085 Hyd.Pressure3 - 0.0036 Hyd.Pressure2
##            - 0.096 Density - 0.0015 Bowl.Setpoint
## 
##   Rule 8/16: [151 cases, mean 8.557, range 8.28 to 8.8, est err 0.070]
## 
##     if
##  Alch.Rel > 0.4902469
##  Mnf.Flow > -100
##  Hyd.Pressure3 > 13.4
##  Balling.Scaled > 0.2335605
##     then
##  outcome = 8.697 + 0.0119 Hyd.Pressure3 - 0.192 Density
##            - 5.9e-05 Carb.Flow - 0.0039 Bowl.Setpoint
##            + 0.104 Oxygen.Filler - 0.078 Pressure.Vacuum
##            + 2.7e-05 Filler.Level - 0.0002 Hyd.Pressure2
## 
##   Rule 8/17: [72 cases, mean 8.594, range 8.36 to 8.82, est err 0.090]
## 
##     if
##  Filler.Speed > 8024018
##  Oxygen.Filler > -2.445618
##  Brand.Code.C <= 0
##  Pressure.Vacuum > -5
##  Air.Pressurer.Scaled <= 0.3366049
##     then
##  outcome = -66.495 - 0.32586 Mnf.Flow + 7.33e-08 Filler.Speed
##            - 0.156 Balling.Lvl + 85 Alch.Rel - 0.042 Balling.Scaled
##            + 0.0022 Hyd.Pressure3 - 0.078 Brand.Code.C
##            + 0.022 Balling.Lvl.Scaled + 0.12 Carb.Pressure1
##            + 0.0011 Bowl.Setpoint + 0.016 Balling - 0.015 Density.Scaled
##            - 0.012 Air.Pressurer.Scaled - 0.0007 Hyd.Pressure2
##            + 0.29 Carb.Pressure - 6e-06 Filler.Level
##            - 0.008 Air.Pressurer - 0.014 Pressure.Vacuum
##            - 0.0033 Pressure.Setpoint - 0.27 Hyd.Pressure4
##            - 0.011 Oxygen.Filler
## 
##   Rule 8/18: [819 cases, mean 8.633, range 8.08 to 8.94, est err 0.114]
## 
##     if
##  Mnf.Flow <= -100
##     then
##  outcome = -6.096 - 0.12336 Mnf.Flow - 0.032 Balling
##            - 0.012 Air.Pressurer - 0.025 Oxygen.Filler + 8 Alch.Rel
##            - 0.032 Brand.Code.C + 0.012 Balling.Lvl + 0.06 Carb.Pressure1
##            - 0.21 Hyd.Pressure4 - 0.004 Density.Scaled
##            + 0.0002 Hyd.Pressure3
## 
##   Rule 8/19: [58 cases, mean 8.639, range 8.24 to 8.86, est err 0.097]
## 
##     if
##  Alch.Rel > 0.4902469
##  Hyd.Pressure3 > 32.6
##  Balling.Scaled <= 0.2335605
##     then
##  outcome = -0.385 - 0.0081 Hyd.Pressure3 + 0.116 Balling.Lvl.Scaled
##            - 0.095 Carb.Flow.Scaled + 5.9e-05 Carb.Flow
##            - 1.07 Carb.Pressure + 24 Alch.Rel - 0.031 Balling.Lvl
##            + 0.009 Air.Pressurer + 4.8e-09 Filler.Speed - 1.6e-07 MFR
##            + 0.01 Balling - 0.01 Density.Scaled - 0.007 Density
##            - 0.0001 Hyd.Pressure2
## 
##   Rule 8/20: [108 cases, mean 8.657, range 8.18 to 8.94, est err 0.128]
## 
##     if
##  Filler.Speed > 7944098
##  Oxygen.Filler <= -2.445618
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##     then
##  outcome = -74.063 - 0.05306 Mnf.Flow + 1.1993e-06 Filler.Speed
##            - 0.233 Balling.Lvl + 134 Alch.Rel - 0.08 Air.Pressurer.Scaled
##            + 0.079 Balling.Lvl.Scaled + 0.48 Carb.Pressure1
##            - 0.052 Balling.Scaled - 0.069 Oxygen.Filler
##            - 0.016 Air.Pressurer - 0.18 Hyd.Pressure4
## 
##   Rule 8/21: [346 cases, mean 8.678, range 8.3 to 8.92, est err 0.065]
## 
##     if
##  Oxygen.Filler > -2.652763
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum <= -5
##     then
##  outcome = -17.962 - 0.107 Balling + 0.164 Pressure.Vacuum + 56 Alch.Rel
##            - 0.144 Oxygen.Filler - 0.042 Balling.Lvl.Scaled
##            + 0.00035 Usage.cont
## 
##   Rule 8/22: [117 cases, mean 8.728, range 8.38 to 8.92, est err 0.088]
## 
##     if
##  Filler.Speed <= 7944098
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##     then
##  outcome = -38.683 - 0.54885 Mnf.Flow - 0.05 Air.Pressurer
##            - 0.045 Balling.Lvl - 1.63e-08 Filler.Speed
##            + 0.06 Carb.Pressure1 - 0.41 Hyd.Pressure4
##            - 0.007 Air.Pressurer.Scaled
## 
## Model 9:
## 
##   Rule 9/1: [24 cases, mean 8.247, range 7.88 to 8.66, est err 0.187]
## 
##     if
##  Carb.Rel <= 0.4819283
##  Brand.Code.C > 0
##  Mnf.Flow > -100.2
##     then
##  outcome = 8.664 - 0.00228 Usage.cont + 0.038 Density
##            + 0.0008 Hyd.Pressure3 - 0.0001 Mnf.Flow
##            + 0.0004 Bowl.Setpoint
## 
##   Rule 9/2: [44 cases, mean 8.335, range 8.08 to 8.62, est err 0.150]
## 
##     if
##  Carb.Rel > 0.4819283
##  Temperature > 0.4998866
##  Brand.Code.C > 0
##  Mnf.Flow > -100.2
##  Mnf.Flow <= 129.6
##  Hyd.Pressure1 <= 10.2
##     then
##  outcome = 19.867 - 0.55 Carb.Pressure1 - 0.43 PSC - 2.91 Hyd.Pressure4
##            - 2.69e-08 Filler.Speed
## 
##   Rule 9/3: [75 cases, mean 8.341, range 7.88 to 8.8, est err 0.113]
## 
##     if
##  Brand.Code.C > 0
##  Mnf.Flow > -100.2
##  Hyd.Pressure1 > 10.2
##  Carb.Flow > 1144
##     then
##  outcome = 8.4 - 0.0013 Mnf.Flow + 3.4e-05 Carb.Flow
##            + 0.0017 Hyd.Pressure3 + 0.034 Density + 5e-06 Filler.Level
##            + 0.0004 Bowl.Setpoint - 0.06 Carb.Pressure
## 
##   Rule 9/4: [18 cases, mean 8.397, range 8.24 to 8.52, est err 0.096]
## 
##     if
##  Oxygen.Filler > -2.636518
##  Brand.Code.C > 0
##  Mnf.Flow > -100.2
##  Hyd.Pressure1 > 10.2
##  Carb.Flow <= 1144
##     then
##  outcome = 3.637 - 1.45 Oxygen.Filler - 0.218 Pressure.Vacuum
##            + 0.016 Density - 5e-05 Mnf.Flow + 0.0003 Hyd.Pressure3
##            + 0.0002 Bowl.Setpoint
## 
##   Rule 9/5: [24 cases, mean 8.402, range 8.06 to 8.68, est err 0.138]
## 
##     if
##  Alch.Rel <= 0.4916538
##  Carb.Pressure1 <= 10.82152
##  Filler.Speed > 7753922
##  Filler.Speed <= 8016008
##  Oxygen.Filler > -2.523643
##  Mnf.Flow > -100.2
##  Balling.Lvl > 2.98
##     then
##  outcome = 9.154 + 0.0049 Hyd.Pressure2 - 0.00065 Mnf.Flow
##            + 0.36 Carb.Pressure1 - 0.00092 Usage.cont
##            - 2.17 Hyd.Pressure4
## 
##   Rule 9/6: [24 cases, mean 8.417, range 8.08 to 8.6, est err 0.083]
## 
##     if
##  Carb.Rel > 0.4819283
##  Oxygen.Filler <= -2.636518
##  Brand.Code.C > 0
##  Hyd.Pressure1 > 10.2
##  Carb.Flow <= 1144
##     then
##  outcome = 8.014 + 0.347 Oxygen.Filler + 0.0007 Hyd.Pressure3
##            - 9e-05 Mnf.Flow - 0.013 Brand.Code.C + 3 Alch.Rel
##            - 0.004 Balling.Lvl + 2e-06 Filler.Level
##            + 0.0002 Bowl.Setpoint - 4e-05 Usage.cont
##            + 0.01 Carb.Pressure1
## 
##   Rule 9/7: [72 cases, mean 8.436, range 8.14 to 8.7, est err 0.131]
## 
##     if
##  Filler.Speed <= 7753922
##  Oxygen.Filler > -2.523643
##  Oxygen.Filler <= -2.301372
##  Brand.Code.C <= 0
##  Mnf.Flow > -100.2
##  Bowl.Setpoint > 80
##  Balling.Lvl > 2.98
##     then
##  outcome = 3.933 - 1.123 Oxygen.Filler - 0.00212 Usage.cont
##            - 3.02e-08 Filler.Speed - 3.5e-05 Filler.Level
##            + 0.0033 Bowl.Setpoint + 0.039 Balling.Scaled + 1.9e-07 MFR
##            + 0.07 Carb.Pressure1 - 6e-05 Mnf.Flow + 3 Alch.Rel
##            + 0.003 Balling.Lvl.Scaled - 0.003 Density.Scaled
##            + 0.0001 Hyd.Pressure2
## 
##   Rule 9/8: [119 cases, mean 8.453, range 8.08 to 8.74, est err 0.075]
## 
##     if
##  Brand.Code.C <= 0
##  Hyd.Pressure2 > 23
##  Carb.Flow <= 1084
##  Balling.Lvl <= 2.98
##     then
##  outcome = 10.846 - 0.001228 Carb.Flow - 0.535 Balling.Lvl
##            + 7.9e-05 Filler.Level + 0.0062 Bowl.Setpoint
##            + 0.0031 Hyd.Pressure2 + 0.025 Carb.Flow.Scaled
##            + 0.002 Hyd.Pressure1 - 0.0117 Pressure.Setpoint
##            - 0.22 PC.Volume - 0.00016 Mnf.Flow - 0.0011 Hyd.Pressure3
##            + 0.017 Balling.Scaled - 0.018 Pressure.Vacuum
##            + 0.01 Air.Pressurer.Scaled - 0.008 Air.Pressurer
##            + 0.00012 Usage.cont - 0.016 Brand.Code.Encoded
##            - 0.006 Brand.Code.C - 3e-08 MFR
## 
##   Rule 9/9: [134 cases, mean 8.459, range 8.16 to 8.74, est err 0.086]
## 
##     if
##  Usage.cont > 237.12
##  Brand.Code.C <= 0
##  Mnf.Flow > -100.2
##  Balling.Lvl <= 2.98
##  Carb.Flow.Scaled > 0.4856937
##     then
##  outcome = 2.267 - 0.00264 Usage.cont - 0.311 Density - 0.076 Balling.Lvl
##            + 0.048 Air.Pressurer + 0.48 PC.Volume - 0.00039 Mnf.Flow
##            - 0.073 Pressure.Vacuum + 0.06 Oxygen.Filler
##            + 0.002 Bowl.Setpoint - 0.028 Balling.Scaled
##            + 0.021 Air.Pressurer.Scaled + 3.1e-07 MFR
##            - 0.019 Density.Scaled + 0.015 Balling.Lvl.Scaled
##            - 9e-06 Filler.Level + 1.2e-05 Carb.Flow + 0.04 Carb.Pressure1
##            + 0.0004 Hyd.Pressure3 + 0.0003 Hyd.Pressure2
## 
##   Rule 9/10: [33 cases, mean 8.484, range 8.18 to 8.84, est err 0.176]
## 
##     if
##  Mnf.Flow > -100.2
##  Pressure.Vacuum > -5
##  Balling.Lvl <= 2.98
##  Air.Pressurer.Scaled > 0.6150198
##  Carb.Flow.Scaled <= 0.4856937
##     then
##  outcome = 2.451 + 0.000887 Filler.Level - 0.0829 Bowl.Setpoint
##            + 0.566 Pressure.Vacuum + 5.73 Hyd.Pressure4
##            + 0.001 Hyd.Pressure2 - 0.0007 Hyd.Pressure3
##            + 0.002 Balling.Scaled - 0.002 Density.Scaled
## 
##   Rule 9/11: [42 cases, mean 8.485, range 8.02 to 8.8, est err 0.137]
## 
##     if
##  Temperature <= 0.4998866
##  Brand.Code.C > 0
##  Mnf.Flow > -100.2
##  Mnf.Flow <= 129.6
##     then
##  outcome = 9.59 + 0.228 Density + 0.0059 Hyd.Pressure1 - 0.00061 Mnf.Flow
##            + 0.0045 Hyd.Pressure3 + 0.0025 Bowl.Setpoint
##            + 1.1e-05 Filler.Level - 0.61 Hyd.Pressure4
##            - 0.04 Carb.Pressure1 - 0.03 PSC - 1.8e-09 Filler.Speed
## 
##   Rule 9/12: [120 cases, mean 8.485, range 8.02 to 8.86, est err 0.106]
## 
##     if
##  Brand.Code.C <= 0
##  Mnf.Flow > -100.2
##  Hyd.Pressure2 > 23
##  Carb.Flow > 1084
##  Bowl.Setpoint > 80
##  Balling.Lvl <= 2.98
##  Carb.Flow.Scaled <= 0.4856937
##     then
##  outcome = 6.708 - 0.545 Balling + 0.483 Balling.Lvl
##            + 0.011 Bowl.Setpoint + 6.8e-05 Filler.Level
##            + 0.099 Balling.Scaled + 6.5e-05 Carb.Flow - 0.61 PC.Volume
##            + 0.0023 Hyd.Pressure2 + 0.026 Carb.Flow.Scaled
##            + 0.0013 Hyd.Pressure1 - 0.0073 Pressure.Setpoint
##            - 0.016 Brand.Code.Encoded + 0.017 Density
##            + 0.003 Balling.Lvl.Scaled - 0.003 Density.Scaled
##            - 2e-05 Mnf.Flow - 0.004 Pressure.Vacuum
## 
##   Rule 9/13: [60 cases, mean 8.487, range 8.16 to 8.84, est err 0.145]
## 
##     if
##  Brand.Code.C <= 0
##  Mnf.Flow > -100.2
##  Hyd.Pressure2 <= 23
##  Balling.Lvl <= 2.98
##  Air.Pressurer.Scaled > 0.6150198
##  Carb.Flow.Scaled <= 0.4856937
##     then
##  outcome = 5.421 - 0.206 Balling.Lvl + 0.276 Density
##            + 0.0064 Bowl.Setpoint + 0.0043 Hyd.Pressure2
##            - 0.06 Density.Scaled + 0.042 Balling.Lvl.Scaled
##            - 0.064 Pressure.Vacuum + 3.2e-05 Carb.Flow
##            + 1.39 Hyd.Pressure4 - 0.00025 Mnf.Flow - 0.0017 Hyd.Pressure3
##            + 0.12 Carb.Pressure1 - 0.016 Air.Pressurer
##            + 0.019 Air.Pressurer.Scaled - 0.016 Balling.Scaled
##            - 0.14 PC.Volume
## 
##   Rule 9/14: [137 cases, mean 8.490, range 8.26 to 8.74, est err 0.072]
## 
##     if
##  Bowl.Setpoint <= 80
##     then
##  outcome = -7.159 + 0.0134 Bowl.Setpoint - 0.247 Oxygen.Filler
##            - 0.062 Balling + 28 Alch.Rel - 0.38 PC.Volume - 0.24 PSC.Fill
##            - 3e-05 Mnf.Flow + 0.02 Carb.Pressure1 + 0.0002 Hyd.Pressure3
##            - 0.007 Brand.Code.C - 4e-05 Usage.cont + 9e-10 Filler.Speed
##            - 3e-08 MFR
## 
##   Rule 9/15: [114 cases, mean 8.513, range 8.08 to 8.84, est err 0.129]
## 
##     if
##  Oxygen.Filler > -2.337689
##  Mnf.Flow > -100.2
##  Hyd.Pressure2 <= 23
##  Bowl.Setpoint > 80
##  Balling.Lvl <= 2.98
##  Air.Pressurer.Scaled <= 0.6150198
##  Carb.Flow.Scaled <= 0.4856937
##     then
##  outcome = 12.946 - 0.82 Balling + 0.669 Balling.Lvl
##            + 0.0162 Bowl.Setpoint - 0.197 Pressure.Vacuum
##            - 4.61 Hyd.Pressure4 + 0.06 Density - 0.016 Density.Scaled
##            + 0.014 Balling.Lvl.Scaled - 9e-05 Mnf.Flow + 8e-06 Carb.Flow
##            + 0.05 Carb.Pressure1 + 5 Alch.Rel + 0.0004 Hyd.Pressure2
##            - 0.005 Balling.Scaled + 0.004 Air.Pressurer.Scaled
##            - 6e-05 Usage.cont - 0.003 Air.Pressurer
##            + 0.0002 Hyd.Pressure3 - 0.03 PC.Volume
## 
##   Rule 9/16: [17 cases, mean 8.518, range 8.26 to 8.86, est err 0.274]
## 
##     if
##  Brand.Code.C > 0
##  Mnf.Flow > 129.6
##  Hyd.Pressure1 <= 10.2
##     then
##  outcome = 2.35 + 0.03305 Mnf.Flow - 0.0877 Hyd.Pressure1
##            + 2.538e-07 Filler.Speed + 9.9e-05 Filler.Level
##            - 0.121 Balling.Scaled
## 
##   Rule 9/17: [1498 cases, mean 8.535, range 7.88 to 8.92, est err 0.102]
## 
##     if
##  Pressure.Vacuum <= -4.8
##     then
##  outcome = -12.381 - 0.00058 Mnf.Flow - 0.193 Brand.Code.C + 41 Alch.Rel
##            - 0.064 Balling.Lvl + 0.0028 Bowl.Setpoint
##            + 0.0024 Hyd.Pressure3 + 0.21 Carb.Pressure1
##            - 0.00055 Usage.cont - 0.025 Density.Scaled
##            + 1.9e-05 Carb.Flow + 0.019 Balling.Lvl.Scaled
##            - 0.15 PC.Volume + 0.015 Air.Pressurer.Scaled
##            - 0.028 Oxygen.Filler - 0.011 Air.Pressurer
##            + 0.022 Pressure.Vacuum + 0.006 Balling + 0.0002 Hyd.Pressure2
##            - 0.0002 Hyd.Pressure1
## 
##   Rule 9/18: [91 cases, mean 8.568, range 8.2 to 8.88, est err 0.118]
## 
##     if
##  Oxygen.Filler > -2.301372
##  Mnf.Flow > -100.2
##  Bowl.Setpoint > 80
##  Balling.Lvl > 2.98
##     then
##  outcome = 4.83 + 0.093 Balling.Lvl - 0.00052 Mnf.Flow
##            - 0.00064 Usage.cont + 0.18 Carb.Pressure1
##            - 1.02e-08 Filler.Speed + 0.0011 Bowl.Setpoint
##            - 0.029 Oxygen.Filler + 0.0008 Hyd.Pressure3 + 7e-08 MFR
##            + 3 Alch.Rel + 0.003 Balling.Lvl.Scaled - 0.003 Density.Scaled
##            + 0.0001 Hyd.Pressure2
## 
##   Rule 9/19: [207 cases, mean 8.577, range 8.32 to 8.94, est err 0.079]
## 
##     if
##  Oxygen.Filler <= -2.523643
##  Mnf.Flow > -100.2
##  Bowl.Setpoint > 80
##  Balling.Lvl > 2.98
##     then
##  outcome = 5.531 - 0.00052 Mnf.Flow + 0.06 Balling.Lvl
##            - 0.087 Pressure.Vacuum + 0.049 Oxygen.Filler
##            - 0.0004 Usage.cont + 0.11 Carb.Pressure1
##            + 0.0006 Hyd.Pressure3 + 0.0003 Bowl.Setpoint + 3 Alch.Rel
##            + 0.004 Balling.Lvl.Scaled + 0.0002 Hyd.Pressure2
##            - 0.003 Density.Scaled - 0.002 Balling
## 
##   Rule 9/20: [117 cases, mean 8.595, range 8.16 to 8.94, est err 0.148]
## 
##     if
##  Oxygen.Filler <= -2.337689
##  Brand.Code.C <= 0
##  Mnf.Flow > -100.2
##  Hyd.Pressure2 <= 23
##  Bowl.Setpoint > 80
##  Balling.Lvl <= 2.98
##  Carb.Flow.Scaled <= 0.4856937
##     then
##  outcome = 8.417 + 0.0158 Hyd.Pressure2 - 0.012 Hyd.Pressure3
##            + 0.0103 Bowl.Setpoint - 0.061 Balling.Lvl - 0.35 PC.Volume
##            - 0.00028 Mnf.Flow + 0.081 Density - 0.052 Pressure.Vacuum
##            + 0.00043 Usage.cont + 1.3e-05 Filler.Level
##            + 0.019 Air.Pressurer.Scaled - 0.014 Air.Pressurer
##            - 0.016 Density.Scaled + 0.0011 Hyd.Pressure1
##            - 0.006 Pressure.Setpoint + 0.012 Balling.Lvl.Scaled
##            + 9e-06 Carb.Flow + 1.3e-07 MFR - 0.007 Balling.Scaled
##            - 0.013 Oxygen.Filler + 0.03 Carb.Pressure1
## 
##   Rule 9/21: [64 cases, mean 8.615, range 8.4 to 8.82, est err 0.111]
## 
##     if
##  Usage.cont <= 237.12
##  Brand.Code.C <= 0
##  Mnf.Flow > -100.2
##  Bowl.Setpoint > 80
##  Balling.Lvl <= 2.98
##  Carb.Flow.Scaled > 0.4856937
##     then
##  outcome = 8.941 + 8.26e-08 Filler.Speed - 1.61e-06 MFR
##            - 0.00076 Mnf.Flow - 0.191 Density - 0.00067 Usage.cont
##            - 0.057 Pressure.Vacuum + 0.29 PC.Volume
##            - 0.021 Balling.Scaled - 1.1e-05 Filler.Level
##            + 0.016 Air.Pressurer.Scaled - 0.001 Bowl.Setpoint
## 
##   Rule 9/22: [68 cases, mean 8.637, range 8.24 to 8.94, est err 0.096]
## 
##     if
##  Alch.Rel <= 0.4916538
##  Carb.Pressure1 <= 10.82152
##  Filler.Speed > 8016008
##  Balling.Lvl > 2.98
##     then
##  outcome = 1.607 + 2.735e-07 Filler.Speed - 0.00139 Mnf.Flow
##            + 3.58 Carb.Pressure - 0.056 Air.Pressurer
##            - 4.1e-05 Filler.Level + 0.0043 Bowl.Setpoint + 4e-08 MFR
##            - 4e-05 Usage.cont + 0.01 Carb.Pressure1
## 
##   Rule 9/23: [36 cases, mean 8.662, range 8.36 to 8.84, est err 0.104]
## 
##     if
##  Alch.Rel <= 0.4916538
##  Carb.Pressure1 > 10.82152
##  Filler.Speed > 7753922
##  Oxygen.Filler > -2.523643
##  Bowl.Setpoint > 80
##  Balling.Lvl > 2.98
##     then
##  outcome = 8.398 - 0.00451 Mnf.Flow + 0.023 Hyd.Pressure2
## 
##   Rule 9/24: [173 cases, mean 8.664, range 8.28 to 8.94, est err 0.103]
## 
##     if
##  Temperature <= 0.4998852
##  Brand.Code.C <= 0
##  Hyd.Pressure2 <= 23
##  Bowl.Setpoint > 80
##  Balling.Lvl <= 2.98
##  Air.Pressurer.Scaled <= 0.6150198
##  Carb.Flow.Scaled <= 0.4856937
##     then
##  outcome = 9.469 + 0.0174 Hyd.Pressure2 - 0.0126 Hyd.Pressure3
##            + 0.0107 Bowl.Setpoint - 0.065 Balling.Lvl - 0.34 PC.Volume
##            + 0.087 Density - 0.00027 Mnf.Flow - 0.045 Pressure.Vacuum
##            + 0.00041 Usage.cont - 0.027 Density.Scaled
##            - 0.02 Air.Pressurer + 0.019 Air.Pressurer.Scaled
##            + 0.013 Balling.Lvl.Scaled + 0.001 Hyd.Pressure1
##            - 0.0057 Pressure.Setpoint + 1e-05 Carb.Flow + 1.2e-07 MFR
##            + 0.04 Carb.Pressure1 + 0.004 Balling.Scaled
## 
##   Rule 9/25: [180 cases, mean 8.676, range 8.42 to 8.92, est err 0.077]
## 
##     if
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100.2
##  Pressure.Vacuum <= -4.8
##  Balling.Lvl > 1.44
##     then
##  outcome = -4.974 + 0.429 Pressure.Vacuum + 0.212 Balling
##            - 0.211 Balling.Lvl + 0.0073 Hyd.Pressure2
##            + 0.097 Air.Pressurer - 1.27e-06 MFR - 0.0056 Hyd.Pressure1
##            - 0.0036 Hyd.Pressure3 + 2.39e-08 Filler.Speed
##            - 1.07 Hyd.Pressure4 - 0.015 Balling.Lvl.Scaled + 9 Alch.Rel
## 
##   Rule 9/26: [352 cases, mean 8.705, range 8.42 to 8.92, est err 0.069]
## 
##     if
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100.2
##     then
##  outcome = -3.802 - 0.093 Oxygen.Filler + 0.084 Pressure.Vacuum
##            - 0.055 Balling.Lvl - 0.038 Balling.Scaled + 19 Alch.Rel
##            + 0.021 Air.Pressurer + 0.025 Balling - 0.06 Brand.Code.C
##            - 0.00011 Mnf.Flow + 0.0008 Hyd.Pressure2
##            - 0.0008 Hyd.Pressure1 + 0.0005 Hyd.Pressure3
##            + 0.0005 Bowl.Setpoint - 0.00011 Usage.cont
##            + 0.04 Carb.Pressure1 - 0.005 Density.Scaled + 4e-06 Carb.Flow
##            - 0.004 Balling.Lvl.Scaled - 0.03 PC.Volume
##            + 0.003 Air.Pressurer.Scaled
## 
##   Rule 9/27: [26 cases, mean 8.725, range 8.56 to 8.82, est err 0.085]
## 
##     if
##  Alch.Rel > 0.4916538
##  Filler.Speed > 7753922
##  Oxygen.Filler > -2.523643
##  Balling.Lvl > 2.98
##     then
##  outcome = 2.538 - 2.625e-07 Filler.Speed - 0.00033 Mnf.Flow
##            - 0.00061 Usage.cont + 0.22 Carb.Pressure1
##            + 0.0019 Hyd.Pressure2 + 15 Alch.Rel + 0.0013 Bowl.Setpoint
##            - 0.71 Hyd.Pressure4 + 0.011 Balling.Lvl.Scaled
##            - 0.012 Density.Scaled - 0.009 Balling + 0.0005 Hyd.Pressure3
##            - 0.009 Balling.Lvl - 0.01 Pressure.Vacuum
##            - 0.014 Brand.Code.C + 3e-06 Carb.Flow + 0.002 Balling.Scaled
##            + 3e-08 MFR
## 
##   Rule 9/28: [44 cases, mean 8.791, range 8.52 to 8.92, est err 0.079]
## 
##     if
##  Mnf.Flow <= -100.2
##  Pressure.Vacuum > -4.8
##     then
##  outcome = 3.487 - 0.272 Pressure.Vacuum - 1.32 Carb.Pressure
##            + 0.023 Air.Pressurer - 0.019 Balling.Lvl + 11 Alch.Rel
##            - 0.036 Brand.Code.C + 0.0007 Hyd.Pressure2
##            - 0.021 Oxygen.Filler - 0.0008 Hyd.Pressure1
## 
## Model 10:
## 
##   Rule 10/1: [18 cases, mean 8.301, range 7.9 to 8.62, est err 0.179]
## 
##     if
##  Alch.Rel <= 0.4906686
##  Carb.Rel <= 0.4816503
##  Mnf.Flow > -100
##     then
##  outcome = 4.644 - 0.103 Balling.Lvl.Scaled - 0.00015 Mnf.Flow
##            + 0.0007 Hyd.Pressure3 + 7 Alch.Rel + 0.0006 Bowl.Setpoint
##            + 3.6e-09 Filler.Speed - 0.021 Brand.Code.C
##            - 4e-06 Filler.Level - 9e-08 MFR - 0.006 Balling.Lvl
##            + 0.03 Carb.Pressure1 - 0.0003 Hyd.Pressure2
##            - 0.002 Pressure.Setpoint - 0.004 Density.Scaled
## 
##   Rule 10/2: [46 cases, mean 8.353, range 8.08 to 8.78, est err 0.205]
## 
##     if
##  Oxygen.Filler <= -2.1146
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = 4.396 - 0.02371 Mnf.Flow - 0.98 PC.Volume - 0.197 Density
##            + 0.068 Balling + 0.006 Balling.Lvl - 0.013 Brand.Code.C
##            + 2 Alch.Rel - 0.002 Air.Pressurer - 0.08 Hyd.Pressure4
##            + 0.01 Carb.Pressure1
## 
##   Rule 10/3: [124 cases, mean 8.368, range 8.12 to 8.74, est err 0.115]
## 
##     if
##  Alch.Rel <= 0.4906686
##  Carb.Rel > 0.4827255
##  Mnf.Flow > -100
##  Bowl.Setpoint <= 100
##  Air.Pressurer <= 145.8
##     then
##  outcome = 7.074 - 0.206 Balling + 0.15 Balling.Lvl + 0.306 Density
##            - 0.00161 Usage.cont + 0.065 Balling.Lvl.Scaled
##            - 0.0009 Bowl.Setpoint + 0.01 Air.Pressurer
##            + 0.012 Balling.Scaled + 1e-05 Carb.Flow
##            - 0.005 Density.Scaled - 0.007 Pressure.Vacuum
##            + 1.8e-09 Filler.Speed - 0.003 Carb.Flow.Scaled
## 
##   Rule 10/4: [351 cases, mean 8.405, range 8.02 to 8.74, est err 0.104]
## 
##     if
##  Alch.Rel <= 0.4906686
##  Carb.Rel > 0.4816503
##  Bowl.Setpoint <= 100
##  Balling.Lvl > 1.32
##     then
##  outcome = 2.928 - 0.094 Balling + 0.231 Density + 0.00071 Mnf.Flow
##            + 0.038 Air.Pressurer - 7.3e-07 MFR + 1.16e-08 Filler.Speed
##            - 0.0004 Bowl.Setpoint
## 
##   Rule 10/5: [139 cases, mean 8.409, range 8 to 8.64, est err 0.083]
## 
##     if
##  Carb.Rel <= 0.4827255
##  Mnf.Flow > -100
##  Carb.Flow > 1084
##  Bowl.Setpoint <= 100
##  Air.Pressurer <= 145.8
##  Balling.Lvl > 1.32
##     then
##  outcome = -0.829 - 0.537 Balling + 0.000222 Carb.Flow + 0.00185 Mnf.Flow
##            - 0.0142 Bowl.Setpoint + 0.0085 Hyd.Pressure3
##            + 7.7e-05 Filler.Level + 0.132 Balling.Lvl
##            + 0.062 Air.Pressurer - 0.115 Pressure.Vacuum + 0.119 Density
##            + 0.018 Balling.Scaled - 0.008 Balling.Lvl.Scaled
##            - 0.007 Density.Scaled + 2.7e-09 Filler.Speed
##            - 9e-05 Usage.cont - 0.005 Carb.Flow.Scaled
## 
##   Rule 10/6: [78 cases, mean 8.445, range 8.02 to 8.66, est err 0.117]
## 
##     if
##  Alch.Rel <= 0.4906686
##  Filler.Speed <= 7326792
##  Mnf.Flow > -100
##  Bowl.Setpoint > 100
##  Balling.Lvl > 1.32
##     then
##  outcome = 7.962 - 2.94e-06 MFR + 6.11e-08 Filler.Speed
##            + 0.162 Oxygen.Filler + 0.0044 Hyd.Pressure2
##            + 0.0003 Usage.cont + 1.1e-05 Filler.Level + 0.019 Balling.Lvl
##            - 0.015 Density.Scaled + 0.006 Air.Pressurer
## 
##   Rule 10/7: [54 cases, mean 8.448, range 7.88 to 8.8, est err 0.172]
## 
##     if
##  Alch.Rel <= 0.4906686
##  Carb.Rel > 0.4816503
##  Oxygen.Filler > -2.648659
##  Mnf.Flow > -100
##  Bowl.Setpoint > 100
##  Air.Pressurer <= 145.8
##  Balling.Lvl > 1.32
##     then
##  outcome = 7.363 + 0.00459 Mnf.Flow - 0.0136 Hyd.Pressure2 - 2.32 PSC.CO2
##            - 1.6e-07 MFR + 0.007 Air.Pressurer + 2.5e-09 Filler.Speed
## 
##   Rule 10/8: [165 cases, mean 8.471, range 7.98 to 8.86, est err 0.082]
## 
##     if
##  Alch.Rel <= 0.4906686
##  Carb.Rel > 0.4816503
##  Filler.Speed > 7326792
##  Oxygen.Filler <= -2.648659
##  Mnf.Flow > -100
##  Bowl.Setpoint > 100
##  Balling.Lvl > 1.32
##     then
##  outcome = 12.765 - 4.964e-07 Filler.Speed + 0.0112 Hyd.Pressure2
##            + 0.209 Oxygen.Filler - 9.2e-07 MFR + 0.00025 Usage.cont
##            + 9e-06 Filler.Level + 0.016 Balling.Lvl
##            - 0.009 Density.Scaled
## 
##   Rule 10/9: [46 cases, mean 8.527, range 8.2 to 8.84, est err 0.161]
## 
##     if
##  Carb.Pressure1 <= 10.51956
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##     then
##  outcome = -182.262 - 1.91218 Mnf.Flow + 0.203 Pressure.Vacuum
##            - 0.13 Oxygen.Filler
## 
##   Rule 10/10: [101 cases, mean 8.528, range 8.36 to 8.74, est err 0.081]
## 
##     if
##  Carb.Rel > 0.4816503
##  Mnf.Flow > -100
##  Air.Pressurer <= 145.8
##  Balling.Lvl <= 1.32
##     then
##  outcome = 5.959 + 1.37e-07 Filler.Speed - 0.00179 Mnf.Flow
##            - 2.28e-06 MFR - 0.0074 Hyd.Pressure3 - 0.34 PC.Volume
##            + 0.016 Air.Pressurer - 0.011 Density.Scaled
## 
##   Rule 10/11: [68 cases, mean 8.536, range 8.08 to 8.84, est err 0.118]
## 
##     if
##  Oxygen.Filler > -2.1146
##  Brand.Code.C > 0
##     then
##  outcome = -6.531 - 0.00068 Mnf.Flow + 0.0034 Hyd.Pressure3 + 29 Alch.Rel
##            + 0.0025 Bowl.Setpoint + 1.6e-08 Filler.Speed
##            - 0.097 Brand.Code.C - 1.8e-05 Filler.Level - 4e-07 MFR
##            - 0.028 Balling.Lvl + 0.12 Carb.Pressure1
##            - 0.0012 Hyd.Pressure2 - 0.009 Pressure.Setpoint
##            - 0.019 Density.Scaled + 0.013 Oxygen.Filler
## 
##   Rule 10/12: [49 cases, mean 8.560, range 8.36 to 8.76, est err 0.067]
## 
##     if
##  Mnf.Flow > -100
##  Air.Pressurer > 145.8
##     then
##  outcome = -3.028 - 0.00043 Mnf.Flow + 0.0021 Hyd.Pressure3 + 21 Alch.Rel
##            + 1.36e-08 Filler.Speed + 0.0016 Bowl.Setpoint
##            + 1.5e-05 Filler.Level - 3.5e-07 MFR - 0.061 Brand.Code.C
##            - 0.022 Balling.Lvl - 0.015 Density.Scaled
##            + 0.08 Carb.Pressure1 - 0.0008 Hyd.Pressure2
##            - 0.0057 Pressure.Setpoint + 0.004 Air.Pressurer
##            + 0.009 Density
## 
##   Rule 10/13: [234 cases, mean 8.562, range 8.24 to 8.86, est err 0.100]
## 
##     if
##  Alch.Rel > 0.4906686
##  Mnf.Flow > -100
##     then
##  outcome = 8.857 + 0.006 Hyd.Pressure3 - 0.068 Density.Scaled
##            - 0.00042 Mnf.Flow - 0.0026 Bowl.Setpoint - 3.6e-05 Carb.Flow
##            - 0.034 Balling.Lvl.Scaled - 0.00045 Usage.cont
## 
##   Rule 10/14: [21 cases, mean 8.588, range 8.4 to 8.8, est err 0.192]
## 
##     if
##  Oxygen.Filler > -2.1146
##  Brand.Code.C > 0
##  Hyd.Pressure2 > 27
##     then
##  outcome = -53.527 - 0.64864 Mnf.Flow - 0.038 Hyd.Pressure2
##            + 0.439 Oxygen.Filler + 0.148 Pressure.Vacuum
##            - 0.075 Balling.Lvl.Scaled - 0.02 Density + 0.007 Balling
## 
##   Rule 10/15: [83 cases, mean 8.596, range 8.24 to 8.86, est err 0.074]
## 
##     if
##  Alch.Rel > 0.4906686
##  Mnf.Flow > -100
##  Hyd.Pressure3 > 32.4
##  Bowl.Setpoint > 90
##     then
##  outcome = 8.903 - 0.197 Carb.Flow.Scaled - 0.169 Density.Scaled
##            - 0.00031 Mnf.Flow - 0.0008 Bowl.Setpoint
## 
##   Rule 10/16: [379 cases, mean 8.616, range 8.08 to 8.94, est err 0.120]
## 
##     if
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##     then
##  outcome = -44.087 - 0.46249 Mnf.Flow - 1.784 Density + 0.623 Balling
##            - 0.032 Air.Pressurer + 0.043 Balling.Lvl + 22 Alch.Rel
##            + 0.16 Carb.Pressure1 - 0.048 Oxygen.Filler
##            - 0.064 Brand.Code.C - 0.39 Hyd.Pressure4
##            - 2.9e-09 Filler.Speed
## 
##   Rule 10/17: [44 cases, mean 8.662, range 8.46 to 8.82, est err 0.093]
## 
##     if
##  Alch.Rel > 0.4906686
##  Hyd.Pressure3 > 32.4
##  Bowl.Setpoint <= 90
##     then
##  outcome = 12.546 + 0.0114 Bowl.Setpoint - 0.0076 Hyd.Pressure2
##            - 1.29 Carb.Pressure - 0.027 Density.Scaled - 0.0002 Mnf.Flow
##            - 0.02 Carb.Flow.Scaled + 0.0007 Hyd.Pressure3
##            - 4e-06 Carb.Flow - 0.004 Balling.Lvl.Scaled
##            - 5e-05 Usage.cont
## 
##   Rule 10/18: [369 cases, mean 8.680, range 8.3 to 8.92, est err 0.069]
## 
##     if
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum <= -5
##     then
##  outcome = -1206.871 + 8.244 Air.Pressurer - 4.129 Air.Pressurer.Scaled
##            - 4.046 Balling + 9.785 Density + 0.213 Pressure.Vacuum
##            + 80 Alch.Rel - 0.112 Oxygen.Filler + 0.00053 Usage.cont
##            + 0.3 PC.Volume - 0.032 Balling.Lvl - 0.0016 Hyd.Pressure1
## 
## Model 11:
## 
##   Rule 11/1: [68 cases, mean 8.318, range 8 to 8.64, est err 0.162]
## 
##     if
##  Alch.Rel <= 0.4902469
##  Filler.Level <= 4939.68
##  Mnf.Flow > 141.6
##  Balling.Lvl.Scaled <= -0.1702714
##     then
##  outcome = 8.162 - 0.437 Balling.Lvl + 0.363 Balling
##            - 0.026 Pressure.Vacuum - 0.012 Density.Scaled
##            - 0.00017 Usage.cont + 0.006 Carb.Flow.Scaled
##            + 3e-06 Filler.Level
## 
##   Rule 11/2: [43 cases, mean 8.328, range 8.08 to 8.86, est err 0.156]
## 
##     if
##  Alch.Rel > 0.4883812
##  Brand.Code.C > 0
##  Mnf.Flow > -100.2
##  Hyd.Pressure1 <= 9.6
##     then
##  outcome = 22.385 + 0.348 Balling - 0.125 Balling.Scaled
##            + 0.009 Hyd.Pressure1 - 0.6 Carb.Pressure1
##            - 0.167 Pressure.Vacuum - 4.29 Hyd.Pressure4
## 
##   Rule 11/3: [142 cases, mean 8.397, range 7.88 to 8.8, est err 0.141]
## 
##     if
##  Brand.Code.C > 0
##  Hyd.Pressure1 > 9.6
##     then
##  outcome = 9.268 - 0.00193 Mnf.Flow + 0.022 Balling
##            - 0.008 Balling.Scaled - 0.009 Pressure.Vacuum
##            - 0.23 Hyd.Pressure4 - 0.03 Carb.Pressure1
## 
##   Rule 11/4: [151 cases, mean 8.401, range 8 to 8.84, est err 0.118]
## 
##     if
##  Brand.Code.C > 0
##  Density > 0.92
##     then
##  outcome = 8.059 + 0.0037 Hyd.Pressure3 - 0.00046 Mnf.Flow
##            - 4.3e-05 Carb.Flow - 0.039 Pressure.Vacuum
##            + 0.001 Bowl.Setpoint
## 
##   Rule 11/5: [18 cases, mean 8.434, range 8.18 to 8.62, est err 0.128]
## 
##     if
##  Brand.Code.C > 0
##  Mnf.Flow > -100.2
##  Density > 0.92
##  Pressure.Vacuum <= -6
##     then
##  outcome = 11.424 + 0.565 Pressure.Vacuum + 0.0057 Bowl.Setpoint
## 
##   Rule 11/6: [30 cases, mean 8.444, range 8.06 to 8.64, est err 0.113]
## 
##     if
##  Alch.Rel <= 0.4902469
##  Carb.Volume > 0.4824219
##  Filler.Level > 4939.68
##  Brand.Code.C <= 0
##  Mnf.Flow > 141.6
##  Air.Pressurer <= 143.2
##  Balling.Lvl.Scaled <= -0.1702714
##     then
##  outcome = 9.221 + 0.00466 Mnf.Flow - 0.00028 Filler.Level
##            + 0.084 Balling + 0.009 Balling.Lvl - 0.006 Pressure.Vacuum
##            - 0.003 Density.Scaled - 4e-05 Usage.cont
## 
##   Rule 11/7: [129 cases, mean 8.477, range 8.14 to 8.74, est err 0.131]
## 
##     if
##  Alch.Rel <= 0.4902469
##  Carb.Volume > 0.4824219
##  Mnf.Flow > -100.2
##  Mnf.Flow <= 141.6
##  Balling.Lvl.Scaled <= -0.1702714
##     then
##  outcome = 9.53 - 1.76e-06 MFR + 4.76e-08 Filler.Speed
##            + 0.0458 Pressure.Setpoint - 0.39 Carb.Pressure1
##            - 0.009 Balling + 0.007 Balling.Lvl - 6e-05 Usage.cont
##            - 0.004 Density.Scaled - 0.006 Pressure.Vacuum
##            + 2e-06 Filler.Level + 0.0002 Hyd.Pressure3 + 2 Alch.Rel
##            - 2e-05 Mnf.Flow + 0.002 Carb.Flow.Scaled
## 
##   Rule 11/8: [304 cases, mean 8.477, range 8.02 to 8.92, est err 0.119]
## 
##     if
##  Carb.Volume > 0.4824219
##  Filler.Speed <= 7984008
##  Mnf.Flow > -100.2
##  Hyd.Pressure3 <= 32.2
##     then
##  outcome = -4.257 - 0.00086 Usage.cont - 0.00038 Mnf.Flow
##            - 0.41 PC.Volume - 6.1e-07 MFR + 0.23 Carb.Pressure1
##            + 1.68e-08 Filler.Speed - 0.053 Pressure.Vacuum + 18 Alch.Rel
##            + 0.022 Balling.Lvl.Scaled - 0.019 Air.Pressurer.Scaled
##            - 0.017 Density.Scaled + 0.0007 Hyd.Pressure3
##            + 0.5 Hyd.Pressure4 - 0.012 Balling.Lvl + 1e-06 Filler.Level
## 
##   Rule 11/9: [624 cases, mean 8.503, range 7.9 to 8.94, est err 0.119]
## 
##     if
##  Carb.Volume <= 0.4824219
##  Mnf.Flow > -100.2
##     then
##  outcome = 1.138 - 0.44 Balling + 0.411 Balling.Lvl - 0.00082 Mnf.Flow
##            + 0.096 Balling.Scaled + 0.0059 Hyd.Pressure3 + 0.242 Density
##            - 0.062 Density.Scaled - 0.046 Balling.Lvl.Scaled
##            + 0.23 Carb.Pressure1 - 0.066 Oxygen.Filler
##            - 0.00052 Usage.cont + 1.7e-05 Filler.Level
##            + 2.5e-05 Carb.Flow - 0.022 Carb.Flow.Scaled + 9 Alch.Rel
##            - 0.035 Brand.Code.C + 0.0006 Bowl.Setpoint
##            - 0.006 Pressure.Vacuum - 0.03 PC.Volume
## 
##   Rule 11/10: [205 cases, mean 8.532, range 8.2 to 8.88, est err 0.136]
## 
##     if
##  Carb.Volume > 0.4824219
##  Oxygen.Filler > -2.51375
##  Brand.Code.C <= 0
##  Mnf.Flow > -100.2
##  Balling.Lvl.Scaled > -0.1702714
##     then
##  outcome = 16.007 + 0.0161 Hyd.Pressure1 - 0.0068 Hyd.Pressure2
##            - 0.101 Density.Scaled - 0.052 Air.Pressurer
##            - 0.0019 Hyd.Pressure3 + 0.01 Balling.Lvl
##            + 0.006 Balling.Lvl.Scaled - 4e-05 Mnf.Flow
##            - 0.008 Pressure.Vacuum - 0.0018 Pressure.Setpoint
##            - 0.003 Balling
## 
##   Rule 11/11: [37 cases, mean 8.538, range 8.24 to 8.74, est err 0.117]
## 
##     if
##  Alch.Rel <= 0.4902469
##  Carb.Volume > 0.4824219
##  Air.Pressurer > 143.2
##  Balling.Lvl.Scaled <= -0.1702714
##     then
##  outcome = 8.263 + 0.338 Oxygen.Filler - 0.00011 Carb.Flow
##            - 0.074 Balling - 0.111 Pressure.Vacuum - 3e-05 Mnf.Flow
##            + 0.0002 Hyd.Pressure3 + 2 Alch.Rel
## 
##   Rule 11/12: [23 cases, mean 8.558, range 8.02 to 8.8, est err 0.187]
## 
##     if
##  Alch.Rel <= 0.4883812
##  Brand.Code.C > 0
##  Mnf.Flow > -100.2
##  Hyd.Pressure1 <= 9.6
##  Density <= 0.92
##     then
##  outcome = 7.391 + 3.039 Density + 0.0509 Hyd.Pressure1 + 0.003 Mnf.Flow
##            + 1.34 PSC.CO2 - 0.06 Carb.Pressure1 - 0.012 Pressure.Vacuum
##            - 0.31 Hyd.Pressure4
## 
##   Rule 11/13: [287 cases, mean 8.579, range 8.18 to 8.94, est err 0.093]
## 
##     if
##  Oxygen.Filler <= -2.51375
##  Brand.Code.C <= 0
##  Mnf.Flow > -100.2
##  Balling.Lvl.Scaled > -0.1702714
##     then
##  outcome = 11.002 - 0.005 Hyd.Pressure3 + 0.134 Oxygen.Filler
##            + 0.003 Hyd.Pressure2 + 0.0024 Hyd.Pressure1
##            - 0.029 Density.Scaled - 0.013 Air.Pressurer
##            - 0.0046 Pressure.Setpoint + 0.01 Balling.Lvl
##            + 0.006 Balling.Lvl.Scaled + 0.006 Balling - 4e-05 Mnf.Flow
##            - 0.008 Pressure.Vacuum
## 
##   Rule 11/14: [53 cases, mean 8.593, range 8.3 to 8.86, est err 0.126]
## 
##     if
##  Alch.Rel > 0.4902469
##  Carb.Volume > 0.4824219
##  Filler.Speed > 7984008
##  Mnf.Flow > -100.2
##  Hyd.Pressure3 <= 32.2
##  Carb.Flow.Scaled <= 0.01879859
##     then
##  outcome = -45.53 + 5.9109e-06 Filler.Speed - 0.0116 Hyd.Pressure3
##            - 0.178 Pressure.Vacuum + 1.67 Carb.Pressure
##            - 0.00084 Usage.cont - 6e-08 MFR + 0.02 Carb.Pressure1
##            - 2e-05 Mnf.Flow - 0.02 PC.Volume - 0.002 Air.Pressurer.Scaled
## 
##   Rule 11/15: [209 cases, mean 8.597, range 8.24 to 8.92, est err 0.088]
## 
##     if
##  Alch.Rel > 0.4902469
##  Carb.Volume > 0.4824219
##  Brand.Code.C <= 0
##  Carb.Flow.Scaled > 0.01879859
##     then
##  outcome = 4.413 - 0.005 Hyd.Pressure3 + 2.06e-08 Filler.Speed
##            - 6.3e-07 MFR + 0.23 Carb.Pressure1 + 0.003 Hyd.Pressure1
##            - 0.00049 Usage.cont - 0.00023 Mnf.Flow + 4 Alch.Rel
##            + 2e-06 Filler.Level - 0.003 Balling.Lvl
##            - 0.002 Density.Scaled
## 
##   Rule 11/16: [150 cases, mean 8.607, range 8.24 to 8.82, est err 0.091]
## 
##     if
##  Alch.Rel > 0.4902469
##  Carb.Volume > 0.4824219
##  Brand.Code.C <= 0
##  Mnf.Flow > -100.2
##  Hyd.Pressure3 > 32.2
##     then
##  outcome = 6.939 + 7.42e-08 Filler.Speed - 0.00124 Usage.cont
##            + 0.0005 Hyd.Pressure3 + 0.04 Carb.Pressure1 - 5e-05 Mnf.Flow
##            + 2e-06 Filler.Level - 0.03 PC.Volume + 2 Alch.Rel
## 
##   Rule 11/17: [402 cases, mean 8.681, range 8.12 to 8.92, est err 0.079]
## 
##     if
##  Mnf.Flow <= -100.2
##     then
##  outcome = 6.63 + 0.156 Pressure.Vacuum - 0.215 Brand.Code.C
##            + 0.076 Balling - 0.079 Balling.Lvl + 0.0023 Hyd.Pressure2
##            + 0.026 Air.Pressurer.Scaled - 0.025 Balling.Lvl.Scaled
##            - 0.0018 Hyd.Pressure1 - 9e-05 Mnf.Flow + 0.0005 Hyd.Pressure3
##            + 0.0005 Bowl.Setpoint + 5 Alch.Rel + 0.03 Carb.Pressure1
##            - 8e-05 Usage.cont - 0.005 Density.Scaled - 0.04 PC.Volume
##            + 3e-06 Carb.Flow
## 
## Model 12:
## 
##   Rule 12/1: [18 cases, mean 8.301, range 7.9 to 8.62, est err 0.211]
## 
##     if
##  Alch.Rel <= 0.4906174
##  Carb.Rel <= 0.4816503
##  Mnf.Flow > -100
##     then
##  outcome = 2.43 - 0.176 Balling.Scaled + 11 Alch.Rel - 0.0001 Mnf.Flow
##            + 4.6e-09 Filler.Speed - 0.024 Density - 1.3e-07 MFR
##            + 0.0005 Bowl.Setpoint - 0.02 Brand.Code.C
##            - 4e-06 Filler.Level + 0.03 Carb.Pressure1
##            + 0.0002 Hyd.Pressure2 + 0.0002 Hyd.Pressure3
##            - 0.0013 Pressure.Setpoint - 0.003 Balling.Lvl
##            - 4e-05 Usage.cont + 0.002 Air.Pressurer
## 
##   Rule 12/2: [217 cases, mean 8.368, range 8.02 to 8.68, est err 0.166]
## 
##     if
##  Alch.Rel <= 0.4906174
##  Carb.Rel > 0.4816503
##  Usage.cont > 246.8088
##  Mnf.Flow > -100
##  Bowl.Setpoint <= 100
##  Air.Pressurer <= 144.2
##  Density.Scaled > -0.3396519
##     then
##  outcome = -28793.564 + 202.13 Air.Pressurer
##            - 101.581 Air.Pressurer.Scaled + 0.263 Balling
##            + 0.0019 Mnf.Flow - 0.2 Balling.Lvl + 0.0079 Hyd.Pressure2
##            - 0.0058 Hyd.Pressure3 + 0.053 Balling.Lvl.Scaled
##            - 2.34e-08 Filler.Speed - 0.00069 Usage.cont
## 
##   Rule 12/3: [42 cases, mean 8.416, range 8.02 to 8.7, est err 0.202]
## 
##     if
##  Alch.Rel <= 0.4906174
##  Oxygen.Filler > -2.543916
##  Mnf.Flow > -100
##  Bowl.Setpoint > 100
##  Air.Pressurer <= 144.2
##     then
##  outcome = -741.603 + 5.269 Air.Pressurer - 2.5 Air.Pressurer.Scaled
##            - 9.2e-05 Filler.Level - 2.68 PSC.CO2 - 9e-08 MFR
##            + 2.4e-09 Filler.Speed
## 
##   Rule 12/4: [82 cases, mean 8.430, range 8.08 to 8.84, est err 0.163]
## 
##     if
##  Alch.Rel > 0.48831
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = -76.426 - 0.83568 Mnf.Flow + 0.407 Oxygen.Filler
##            - 0.168 Density + 0.054 Balling + 0.007 Balling.Lvl
##            + 4 Alch.Rel - 0.015 Brand.Code.C + 0.01 Carb.Pressure1
## 
##   Rule 12/5: [692 cases, mean 8.436, range 7.88 to 8.86, est err 0.128]
## 
##     if
##  Alch.Rel <= 0.4906174
##  Mnf.Flow > -100
##  Air.Pressurer <= 144.2
##     then
##  outcome = 6.224 + 0.138 Oxygen.Filler + 2.95e-08 Filler.Speed
##            - 6.5e-07 MFR - 7e-05 Mnf.Flow + 5 Alch.Rel
##            + 0.0004 Bowl.Setpoint - 0.016 Density - 0.013 Brand.Code.C
##            + 0.02 Carb.Pressure1 - 2e-06 Filler.Level
##            - 0.0009 Pressure.Setpoint + 0.0001 Hyd.Pressure3
## 
##   Rule 12/6: [101 cases, mean 8.438, range 8 to 8.56, est err 0.080]
## 
##     if
##  Carb.Rel <= 0.4823337
##  Mnf.Flow > -100
##  Bowl.Setpoint <= 100
##  Air.Pressurer <= 144.2
##  Density.Scaled > -0.3396519
##     then
##  outcome = -4541.987 + 31.885 Air.Pressurer - 15.992 Air.Pressurer.Scaled
##            + 1.525e-07 Filler.Speed - 4.18e-06 MFR + 3.33 Hyd.Pressure4
##            + 0.00047 Mnf.Flow - 2.7e-05 Filler.Level
##            - 0.0026 Bowl.Setpoint + 0.031 Balling + 0.03 Density.Scaled
##            - 0.028 Balling.Lvl + 0.00033 Usage.cont
##            - 0.025 Pressure.Vacuum
## 
##   Rule 12/7: [34 cases, mean 8.440, range 8.16 to 8.62, est err 0.155]
## 
##     if
##  Alch.Rel <= 0.4906174
##  Carb.Rel > 0.4823337
##  Usage.cont <= 246.8088
##  Bowl.Setpoint <= 100
##  Air.Pressurer <= 144.2
##  Density.Scaled > -0.3396519
##     then
##  outcome = -7431.799 + 52.228 Air.Pressurer - 26.25 Air.Pressurer.Scaled
##            - 0.0143 Bowl.Setpoint + 0.191 Balling.Lvl
##            + 0.114 Balling.Scaled + 0.197 Pressure.Vacuum + 0.04 Balling
##            + 0.002 Hyd.Pressure2 + 0.014 Balling.Lvl.Scaled
##            - 6e-09 Filler.Speed - 0.00018 Usage.cont
## 
##   Rule 12/8: [109 cases, mean 8.455, range 8.02 to 8.82, est err 0.093]
## 
##     if
##  Alch.Rel <= 0.4906174
##  Carb.Rel > 0.4824657
##  Mnf.Flow > -100
##  Air.Pressurer <= 144.2
##  Density.Scaled <= -0.3396519
##     then
##  outcome = -2366.896 + 16.588 Air.Pressurer - 8.324 Air.Pressurer.Scaled
##            + 23 Alch.Rel + 1.5e-08 Filler.Speed - 0.00025 Mnf.Flow
##            - 4e-07 MFR - 0.059 Density + 0.0013 Bowl.Setpoint
##            - 0.048 Brand.Code.C - 9e-06 Filler.Level - 0.24 PSC.CO2
##            + 0.011 Density.Scaled + 0.06 Carb.Pressure1
##            + 0.0005 Hyd.Pressure3 - 0.0033 Pressure.Setpoint
##            - 9e-05 Usage.cont + 0.0003 Hyd.Pressure2 - 0.004 Balling.Lvl
##            + 0.005 Oxygen.Filler
## 
##   Rule 12/9: [38 cases, mean 8.470, range 8.02 to 8.82, est err 0.145]
## 
##     if
##  Alch.Rel <= 0.4906174
##  Carb.Rel > 0.4824657
##  Mnf.Flow > -100
##  Hyd.Pressure1 <= 14
##  Air.Pressurer <= 144.2
##  Density.Scaled <= -0.3396519
##     then
##  outcome = -22.397 + 0.0226 Hyd.Pressure1 + 0.217 Air.Pressurer
##            + 0.124 Density.Scaled - 0.11 PSC.CO2
## 
##   Rule 12/10: [155 cases, mean 8.476, range 8.08 to 8.8, est err 0.086]
## 
##     if
##  Alch.Rel <= 0.4906174
##  Oxygen.Filler <= -2.543916
##  Mnf.Flow > -100
##  Bowl.Setpoint > 100
##  Density.Scaled > -0.3396519
##     then
##  outcome = -6.944 + 6.66e-08 Filler.Speed - 2.25e-06 MFR
##            + 0.093 Air.Pressurer - 0.0152 Pressure.Setpoint
##            + 0.053 Oxygen.Filler + 0.0012 Hyd.Pressure3
##            + 0.001 Hyd.Pressure1 - 8e-05 Mnf.Flow + 6 Alch.Rel
##            - 0.02 Density + 0.00012 Usage.cont - 0.016 Brand.Code.Encoded
##            + 0.0004 Bowl.Setpoint - 0.016 Brand.Code.C
##            - 3e-06 Filler.Level + 0.02 Carb.Pressure1
## 
##   Rule 12/11: [46 cases, mean 8.527, range 8.2 to 8.84, est err 0.126]
## 
##     if
##  Carb.Pressure1 <= 10.51956
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##     then
##  outcome = -164.554 - 1.74661 Mnf.Flow - 0.234 Balling
##            + 0.235 Balling.Lvl + 0.242 Pressure.Vacuum
##            - 0.135 Oxygen.Filler - 0.00071 Usage.cont
##            + 0.04 Balling.Scaled - 0.026 Balling.Lvl.Scaled
##            - 0.4 Hyd.Pressure4 + 0.05 Carb.Pressure1
##            - 2.5e-09 Filler.Speed - 0.003 Air.Pressurer
## 
##   Rule 12/12: [58 cases, mean 8.561, range 8.36 to 8.76, est err 0.070]
## 
##     if
##  Mnf.Flow > -100
##  Air.Pressurer > 144.2
##     then
##  outcome = 7.318 + 0.937 Density - 0.399 Balling.Lvl
##            + 5.2e-05 Filler.Level + 6.4e-09 Filler.Speed - 1.8e-07 MFR
##            + 0.005 Air.Pressurer - 0.006 Density.Scaled
## 
##   Rule 12/13: [235 cases, mean 8.562, range 8.24 to 8.86, est err 0.089]
## 
##     if
##  Alch.Rel > 0.4906174
##  Mnf.Flow > -100
##     then
##  outcome = 6.838 + 0.0089 Hyd.Pressure3 - 0.0048 Hyd.Pressure2
##            + 1.12e-06 MFR - 5.4e-05 Carb.Flow - 0.057 Balling.Lvl.Scaled
##            - 2.43e-08 Filler.Speed - 0.00075 Usage.cont
##            - 0.0027 Bowl.Setpoint - 6e-05 Mnf.Flow + 4 Alch.Rel
##            - 0.013 Density - 0.011 Brand.Code.C - 2e-06 Filler.Level
##            + 0.01 Carb.Pressure1
## 
##   Rule 12/14: [61 cases, mean 8.601, range 8.24 to 8.86, est err 0.117]
## 
##     if
##  Alch.Rel > 0.4906174
##  Mnf.Flow > -100
##  Carb.Flow.Scaled > 0.4205449
##     then
##  outcome = 9.386 - 0.00686 Mnf.Flow - 0.000165 Carb.Flow
##            - 0.136 Carb.Flow.Scaled - 0.78 PC.Volume
## 
##   Rule 12/15: [79 cases, mean 8.615, range 8.42 to 8.82, est err 0.075]
## 
##     if
##  Alch.Rel > 0.4906174
##  Mnf.Flow > -100
##  Hyd.Pressure3 > 32.6
##  Carb.Flow.Scaled <= 0.4205449
##     then
##  outcome = 12.178 + 0.0161 Hyd.Pressure2 - 0.185 Carb.Flow.Scaled
##            - 0.48 Carb.Pressure1 + 0.132 Oxygen.Filler
##            - 3e-06 Filler.Level - 4e-05 Mnf.Flow + 3 Alch.Rel
##            - 0.009 Density + 0.0002 Bowl.Setpoint - 0.007 Brand.Code.C
##            + 1.1e-09 Filler.Speed + 0.0001 Hyd.Pressure3
## 
##   Rule 12/16: [819 cases, mean 8.633, range 8.08 to 8.94, est err 0.108]
## 
##     if
##  Mnf.Flow <= -100
##     then
##  outcome = -16.078 - 0.1521 Mnf.Flow - 1.735 Density + 0.568 Balling
##            + 0.075 Balling.Lvl - 0.129 Brand.Code.C + 26 Alch.Rel
##            + 0.11 Carb.Pressure1 - 0.015 Air.Pressurer
##            - 0.77 Hyd.Pressure4 - 0.012 Oxygen.Filler
## 
##   Rule 12/17: [155 cases, mean 8.645, range 8.18 to 8.84, est err 0.082]
## 
##     if
##  Oxygen.Filler > -2.363049
##  Mnf.Flow <= -100
##  Pressure.Vacuum <= -5
##  Balling.Lvl <= 1.44
##     then
##  outcome = -135.498 + 0.05018 Mnf.Flow - 10.181 Density + 3.852 Balling
##            + 1.005 Air.Pressurer - 0.504 Air.Pressurer.Scaled
##            - 0.288 Oxygen.Filler + 19 Alch.Rel + 0.035 Pressure.Vacuum
##            - 0.015 Balling.Lvl - 0.008 Balling.Lvl.Scaled
##            + 0.04 PC.Volume - 0.0003 Hyd.Pressure1 + 6e-05 Usage.cont
## 
##   Rule 12/18: [210 cases, mean 8.661, range 8.42 to 8.92, est err 0.078]
## 
##     if
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum <= -5
##  Balling.Lvl > 1.44
##     then
##  outcome = -409.578 + 0.49547 Mnf.Flow + 2.856 Air.Pressurer
##            - 1.556 Balling - 1.433 Air.Pressurer.Scaled + 3.752 Density
##            + 0.392 Pressure.Vacuum + 127 Alch.Rel - 0.15 Balling.Lvl
##            - 0.005 Hyd.Pressure1 + 0.0028 Hyd.Pressure2
##            - 0.066 Oxygen.Filler - 0.024 Balling.Lvl.Scaled
##            + 0.11 PC.Volume + 0.00017 Usage.cont
## 
##   Rule 12/19: [623 cases, mean 8.669, range 8.18 to 8.94, est err 0.105]
## 
##     if
##  Carb.Pressure1 > 10.51956
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##     then
##  outcome = -32.713 - 0.45009 Mnf.Flow + 1.041 Balling.Lvl - 0.946 Balling
##            + 0.175 Balling.Scaled - 0.114 Balling.Lvl.Scaled
##            - 0.239 Density - 1.84 Hyd.Pressure4 + 0.24 Carb.Pressure1
##            - 0.071 Oxygen.Filler - 0.029 Air.Pressurer
##            - 1.11e-08 Filler.Speed - 0.018 Brand.Code.C + 4 Alch.Rel
## 
##   Rule 12/20: [107 cases, mean 8.729, range 8.48 to 8.92, est err 0.067]
## 
##     if
##  Oxygen.Filler <= -2.363049
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum <= -5
##     then
##  outcome = -48.391 + 0.01795 Mnf.Flow - 0.866 Balling + 0.577 Balling.Lvl
##            + 0.394 Air.Pressurer + 0.536 Density
##            - 0.197 Air.Pressurer.Scaled + 0.151 Density.Scaled
##            - 0.0015 Hyd.Pressure1 + 0.016 Pressure.Vacuum + 6 Alch.Rel
##            - 0.004 Balling.Lvl.Scaled - 0.007 Oxygen.Filler
## 
## Model 13:
## 
##   Rule 13/1: [24 cases, mean 8.247, range 7.88 to 8.66, est err 0.204]
## 
##     if
##  Carb.Rel <= 0.4819283
##  Brand.Code.C > 0
##  Mnf.Flow > -100.2
##     then
##  outcome = 9.053 - 0.00359 Usage.cont
## 
##   Rule 13/2: [24 cases, mean 8.385, range 8.02 to 8.62, est err 0.138]
## 
##     if
##  Brand.Code.C > 0
##  Mnf.Flow > -100.2
##  Hyd.Pressure1 <= 10.2
##  Carb.Flow <= 1176
##     then
##  outcome = 7.455 + 0.533 Balling.Lvl + 0.0285 Hyd.Pressure1
##            - 5e-05 Mnf.Flow + 0.0002 Hyd.Pressure2
## 
##   Rule 13/3: [124 cases, mean 8.422, range 8.08 to 8.8, est err 0.106]
## 
##     if
##  Carb.Rel > 0.4819283
##  Brand.Code.C > 0
##  Hyd.Pressure1 > 10.2
##     then
##  outcome = 6.187 - 0.0015 Mnf.Flow - 4.1e-05 Carb.Flow
##            + 0.0014 Hyd.Pressure3 - 0.039 Brand.Code.C - 2e-07 MFR
##            + 5.5e-09 Filler.Speed - 0.00015 Usage.cont
##            + 0.02 Brand.Code.D + 0.05 Carb.Pressure1
##            + 0.0005 Bowl.Setpoint - 0.008 Balling - 0.014 Oxygen.Filler
##            + 4 Alch.Rel - 0.006 Density.Scaled - 0.0025 Pressure.Setpoint
##            + 0.0002 Hyd.Pressure2
## 
##   Rule 13/4: [62 cases, mean 8.423, range 8.06 to 8.74, est err 0.170]
## 
##     if
##  Alch.Rel > 0.4900813
##  Alch.Rel <= 0.4902469
##  Mnf.Flow > -100.2
##     then
##  outcome = 7.437 + 0.256 Balling.Lvl.Scaled + 0.00143 Mnf.Flow
##            - 0.0087 Hyd.Pressure2 - 0.219 Oxygen.Filler
##            - 0.00173 Usage.cont + 2 Alch.Rel
## 
##   Rule 13/5: [69 cases, mean 8.424, range 8.08 to 8.86, est err 0.180]
## 
##     if
##  Brand.Code.C > 0
##  Mnf.Flow > -100.2
##  Hyd.Pressure1 <= 10.2
##  Carb.Flow > 1176
##     then
##  outcome = 17.735 - 2.12 Density - 3.8 Hyd.Pressure4 - 0.45 PSC
## 
##   Rule 13/6: [363 cases, mean 8.465, range 8 to 8.92, est err 0.140]
## 
##     if
##  Alch.Rel <= 0.4900813
##  Temperature > 0.4998859
##  Bowl.Setpoint > 80
##     then
##  outcome = -3.552 - 0.632 Density + 0.254 Balling.Lvl - 0.00076 Mnf.Flow
##            + 0.0055 Bowl.Setpoint + 3.7 Hyd.Pressure4
##            + 0.0045 Hyd.Pressure3 + 0.0041 Hyd.Pressure2 - 0.023 Balling
##            + 7 Alch.Rel - 0.006 Density.Scaled + 0.005 Balling.Scaled
##            + 0.03 Carb.Pressure1 - 8e-05 Usage.cont - 0.009 Oxygen.Filler
##            - 0.0014 Pressure.Setpoint - 0.005 Pressure.Vacuum
##            + 2e-06 Carb.Flow
## 
##   Rule 13/7: [137 cases, mean 8.490, range 8.26 to 8.74, est err 0.063]
## 
##     if
##  Bowl.Setpoint <= 80
##     then
##  outcome = 5.886 - 0.392 Oxygen.Filler + 0.0104 Bowl.Setpoint
##            + 0.185 Brand.Code.D - 0.063 Balling.Lvl
##            + 0.022 Air.Pressurer.Scaled - 0.006 Balling - 3e-05 Mnf.Flow
##            + 2 Alch.Rel + 0.0001 Hyd.Pressure3
## 
##   Rule 13/8: [148 cases, mean 8.508, range 8.16 to 8.92, est err 0.097]
## 
##     if
##  Alch.Rel > 0.4900813
##  Filler.Speed <= 7984008
##  Brand.Code.C <= 0
##  Mnf.Flow > -100.2
##  Hyd.Pressure3 <= 32.2
##  Bowl.Setpoint > 80
##     then
##  outcome = -5.751 - 0.00057 Mnf.Flow + 2.66e-08 Filler.Speed
##            - 8.7e-07 MFR + 0.3 Carb.Pressure1 + 0.003 Bowl.Setpoint
##            - 0.045 Balling - 0.071 Pressure.Vacuum - 0.00064 Usage.cont
##            - 0.32 PC.Volume + 21 Alch.Rel + 0.002 Hyd.Pressure1
##            + 0.02 Balling.Lvl.Scaled + 0.001 Hyd.Pressure2
##            - 0.018 Density.Scaled + 0.005 Balling.Scaled
##            - 4e-06 Carb.Flow
## 
##   Rule 13/9: [392 cases, mean 8.529, range 8.02 to 8.94, est err 0.106]
## 
##     if
##  Alch.Rel <= 0.4900813
##  Temperature <= 0.4998859
##  Mnf.Flow > -100.2
##  Bowl.Setpoint > 80
##  Carb.Flow.Scaled <= 0.431403
##     then
##  outcome = 9.061 - 0.261 Balling + 0.275 Balling.Lvl
##            + 0.0097 Bowl.Setpoint - 0.067 Carb.Flow.Scaled
##            - 0.1 Pressure.Vacuum - 0.00036 Mnf.Flow - 0.38 PC.Volume
##            + 2.3e-05 Filler.Level + 0.032 Balling.Scaled
##            - 0.024 Air.Pressurer + 0.0017 Hyd.Pressure2
##            - 0.02 Balling.Lvl.Scaled + 0.001 Hyd.Pressure3
##            + 1.4e-05 Carb.Flow + 0.07 Carb.Pressure1
## 
##   Rule 13/10: [885 cases, mean 8.530, range 7.88 to 8.94, est err 0.118]
## 
##     if
##  Temperature <= 0.4998859
##  Mnf.Flow > -100.2
##  Bowl.Setpoint > 80
##     then
##  outcome = 6.045 - 0.406 Balling + 0.426 Balling.Lvl - 0.00096 Usage.cont
##            + 0.049 Balling.Scaled + 0.0024 Bowl.Setpoint
##            - 0.03 Balling.Lvl.Scaled - 0.033 Density.Scaled
##            + 0.0016 Hyd.Pressure3 + 2.2e-05 Carb.Flow + 3.7e-07 MFR
##            - 0.019 Carb.Flow.Scaled - 0.033 Pressure.Vacuum
##            + 0.11 Carb.Pressure1 - 0.00012 Mnf.Flow + 2 Alch.Rel
## 
##   Rule 13/11: [69 cases, mean 8.567, range 8.22 to 8.94, est err 0.138]
## 
##     if
##  Alch.Rel > 0.4900813
##  Filler.Speed > 7984008
##  Mnf.Flow > -100.2
##  Hyd.Pressure3 <= 32.2
##  Carb.Flow.Scaled <= 0.01879859
##     then
##  outcome = -43.154 + 6.2327e-06 Filler.Speed - 6.59e-06 MFR
##            - 0.0074 Hyd.Pressure1 - 0.148 Pressure.Vacuum
##            - 0.00084 Usage.cont - 0.012 Balling - 7e-05 Mnf.Flow
##            + 5 Alch.Rel + 0.04 Carb.Pressure1 + 0.0003 Bowl.Setpoint
##            + 0.005 Balling.Lvl + 0.0002 Hyd.Pressure3
##            + 0.003 Balling.Scaled - 0.003 Density.Scaled
##            - 0.004 Oxygen.Filler
## 
##   Rule 13/12: [81 cases, mean 8.596, range 8.36 to 8.92, est err 0.102]
## 
##     if
##  Alch.Rel > 0.4902469
##  Hyd.Pressure3 <= 32.2
##  Bowl.Setpoint > 80
##  Carb.Flow.Scaled > 0.01879859
##     then
##  outcome = 3.674 - 0.00142 Usage.cont + 0.0049 Bowl.Setpoint
##            + 0.45 Carb.Pressure1 - 0.052 Balling + 1.39e-08 Filler.Speed
##            - 3.9e-07 MFR - 0.0001 Mnf.Flow + 0.012 Balling.Scaled
##            - 0.015 Pressure.Vacuum - 0.006 Density.Scaled
##            + 0.004 Balling.Lvl.Scaled
## 
##   Rule 13/13: [136 cases, mean 8.614, range 8.24 to 8.86, est err 0.081]
## 
##     if
##  Alch.Rel > 0.4902469
##  Mnf.Flow > -100.2
##  Hyd.Pressure3 > 32.2
##  Bowl.Setpoint > 80
##     then
##  outcome = 6.466 + 6.6e-08 Filler.Speed - 0.097 Balling
##            + 0.00051 Mnf.Flow - 0.00082 Usage.cont + 3e-05 Carb.Flow
##            - 0.0015 Bowl.Setpoint + 0.022 Balling.Scaled
##            - 0.013 Density.Scaled + 0.07 Carb.Pressure1
##            + 0.009 Balling.Lvl.Scaled - 1.3e-07 MFR
##            - 0.01 Pressure.Vacuum + 3 Alch.Rel + 0.0001 Hyd.Pressure2
## 
##   Rule 13/14: [402 cases, mean 8.681, range 8.12 to 8.92, est err 0.083]
## 
##     if
##  Mnf.Flow <= -100.2
##     then
##  outcome = -753.111 + 5.355 Air.Pressurer - 2.65 Air.Pressurer.Scaled
##            + 0.294 Balling - 0.285 Balling.Lvl + 0.248 Pressure.Vacuum
##            - 0.233 Brand.Code.C - 0.055 Density.Scaled
##            + 0.0012 Hyd.Pressure2 - 2e-05 Mnf.Flow
## 
## Model 14:
## 
##   Rule 14/1: [66 cases, mean 8.366, range 8.16 to 8.7, est err 0.102]
## 
##     if
##  Carb.Rel > 0.4823337
##  Filler.Level > 3215.52
##  Mnf.Flow > -100
##  Carb.Flow > 1084
##  Balling > 1.616
##  Balling <= 2.956
##  Density.Scaled > -2.122159
##     then
##  outcome = 0.903 - 0.277 Balling + 0.244 Balling.Lvl + 6.4e-05 Carb.Flow
##            + 0.048 Air.Pressurer + 0.052 Balling.Scaled
##            - 0.00041 Mnf.Flow - 0.077 Pressure.Vacuum
##            + 0.0024 Hyd.Pressure2 - 0.038 Density.Scaled
##            - 0.031 Balling.Lvl.Scaled + 9.5e-09 Filler.Speed
##            - 3.3e-07 MFR + 9e-06 Filler.Level + 0.005 Oxygen.Filler
## 
##   Rule 14/2: [55 cases, mean 8.422, range 7.88 to 8.86, est err 0.197]
## 
##     if
##  Mnf.Flow > -100
##  Carb.Flow > 1084
##  Density.Scaled <= -2.122159
##     then
##  outcome = 18.958 - 1.949 Density.Scaled + 0.904 Balling
##            + 0.000416 Carb.Flow - 8.43 Hyd.Pressure4 - 2.01 PSC.CO2
##            + 0.132 Oxygen.Filler - 0.011 Balling.Lvl - 5e-05 Mnf.Flow
##            + 2.3e-09 Filler.Speed - 8e-08 MFR + 0.0003 Hyd.Pressure3
##            - 0.012 Brand.Code.C + 0.0002 Bowl.Setpoint
##            + 0.003 Balling.Lvl.Scaled + 2 Alch.Rel + 0.01 Carb.Pressure1
##            - 0.0001 Hyd.Pressure2 - 1e-06 Filler.Level
## 
##   Rule 14/3: [631 cases, mean 8.442, range 7.88 to 8.86, est err 0.110]
## 
##     if
##  Mnf.Flow > -100
##  Balling <= 2.956
##     then
##  outcome = 3.782 - 0.103 Balling.Lvl + 3.84e-08 Filler.Speed
##            - 1.29e-06 MFR - 0.016 Balling.Scaled + 0.00012 Mnf.Flow
##            + 0.01 Air.Pressurer + 0.01 Balling.Lvl.Scaled + 7 Alch.Rel
##            + 0.0004 Hyd.Pressure3 + 0.0003 Hyd.Pressure2
##            + 0.005 Oxygen.Filler - 0.0012 Pressure.Setpoint
##            - 0.002 Balling
## 
##   Rule 14/4: [116 cases, mean 8.451, range 8.02 to 8.86, est err 0.159]
## 
##     if
##  Carb.Rel > 0.4823337
##  Filler.Level > 3215.52
##  Mnf.Flow > -100
##  Carb.Flow > 1084
##  Balling <= 1.616
##  Density.Scaled > -2.122159
##     then
##  outcome = -9.871 - 0.00251 Mnf.Flow + 0.0128 Hyd.Pressure2
##            + 0.000152 Carb.Flow + 0.123 Air.Pressurer
##            - 0.099 Density.Scaled + 5.5e-05 Filler.Level - 0.093 Balling
## 
##   Rule 14/5: [114 cases, mean 8.463, range 8.08 to 8.84, est err 0.143]
## 
##     if
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = -0.088 - 0.06358 Mnf.Flow - 0.736 Density + 0.256 Balling
##            + 0.316 Oxygen.Filler - 0.051 Brand.Code.C + 0.018 Balling.Lvl
##            + 9 Alch.Rel - 0.007 Air.Pressurer - 0.31 Hyd.Pressure4
##            + 0.04 Carb.Pressure1
## 
##   Rule 14/6: [93 cases, mean 8.471, range 8.12 to 8.76, est err 0.129]
## 
##     if
##  Alch.Rel <= 0.4914786
##  Filler.Speed <= 7753922
##  Balling > 2.956
##     then
##  outcome = 10.844 - 0.361 Balling + 0.253 Balling.Lvl.Scaled
##            - 0.00212 Usage.cont + 0.64 PC.Volume + 0.00021 Mnf.Flow
##            - 0.0011 Hyd.Pressure2 - 4.7e-09 Filler.Speed
##            + 0.0005 Hyd.Pressure3 - 4e-06 Filler.Level
##            - 0.004 Carb.Flow.Scaled + 6e-08 MFR
## 
##   Rule 14/7: [63 cases, mean 8.473, range 8.28 to 8.56, est err 0.041]
## 
##     if
##  Filler.Level <= 3215.52
##  Balling <= 2.956
##  Air.Pressurer <= 143.4
##     then
##  outcome = 4.833 - 0.000303 Carb.Flow - 0.07 Balling + 0.053 Balling.Lvl
##            - 0.05 Density.Scaled + 0.013 Balling.Scaled
##            + 0.01 Air.Pressurer + 0.0007 Hyd.Pressure3 + 7 Alch.Rel
##            - 8e-05 Mnf.Flow - 1.2e-07 MFR - 0.019 Brand.Code.C
##            + 2.4e-09 Filler.Speed - 0.005 Balling.Lvl.Scaled
##            + 0.0003 Bowl.Setpoint - 0.0016 Pressure.Setpoint
##            + 0.02 Carb.Pressure1 - 2e-06 Filler.Level
##            - 0.14 Hyd.Pressure4 - 3e-05 Usage.cont - 0.0001 Hyd.Pressure2
## 
##   Rule 14/8: [198 cases, mean 8.484, range 8 to 8.8, est err 0.098]
## 
##     if
##  Carb.Rel <= 0.4823337
##  Carb.Flow > 1084
##  Air.Pressurer <= 143.4
##  Density.Scaled > -2.122159
##     then
##  outcome = -1.218 - 0.259 Balling + 0.235 Balling.Lvl + 9.7e-05 Carb.Flow
##            + 0.046 Air.Pressurer - 0.06 Density.Scaled
##            + 0.048 Balling.Scaled - 0.028 Balling.Lvl.Scaled
##            - 3.5e-07 MFR + 9.9e-09 Filler.Speed + 6 Alch.Rel
##            + 0.0005 Hyd.Pressure3 - 4e-05 Mnf.Flow - 0.009 Brand.Code.C
##            - 0.0012 Pressure.Setpoint + 0.0001 Bowl.Setpoint
## 
##   Rule 14/9: [29 cases, mean 8.499, range 8.22 to 8.68, est err 0.147]
## 
##     if
##  Alch.Rel <= 0.4914786
##  Filler.Speed <= 7753922
##  Mnf.Flow > -100
##  Balling > 2.956
##  Balling.Lvl.Scaled > -0.1702714
##     then
##  outcome = 8.558 + 0.268 Balling.Lvl.Scaled + 0.00187 Mnf.Flow
##            - 9.7e-05 Carb.Flow - 3.9e-07 MFR + 0.17 PC.Volume
## 
##   Rule 14/10: [39 cases, mean 8.504, range 8.2 to 8.84, est err 0.130]
## 
##     if
##  Carb.Pressure1 <= 10.51956
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##     then
##  outcome = -30.874 - 0.21716 Mnf.Flow - 1.537 Density + 0.454 Balling
##            + 46 Alch.Rel + 0.067 Balling.Lvl - 0.145 Brand.Code.C
##            - 0.032 Air.Pressurer + 0.22 Carb.Pressure1
##            - 0.056 Oxygen.Filler - 0.95 Hyd.Pressure4
##            + 0.0009 Hyd.Pressure3 + 0.0006 Bowl.Setpoint - 1.3e-07 MFR
##            - 0.0004 Hyd.Pressure2 - 4e-06 Filler.Level
##            + 2.2e-09 Filler.Speed - 0.0019 Pressure.Setpoint
##            - 6e-05 Usage.cont - 0.03 PC.Volume + 0.003 Balling.Lvl.Scaled
##            + 0.003 Balling.Scaled + 0.002 Air.Pressurer.Scaled
## 
##   Rule 14/11: [90 cases, mean 8.511, range 8.24 to 8.76, est err 0.089]
## 
##     if
##  Alch.Rel > 0.4914786
##  Filler.Speed <= 7753922
##  Mnf.Flow > -100
##  Balling > 2.956
##     then
##  outcome = 8.422 + 0.00381 Mnf.Flow - 0.0199 Hyd.Pressure2
##            + 0.0072 Hyd.Pressure3 - 0.079 Balling.Lvl.Scaled
##            - 0.00127 Usage.cont - 0.6 PC.Volume - 0.055 Carb.Flow.Scaled
##            - 0.0031 Bowl.Setpoint + 0.015 Balling - 2.7e-09 Filler.Speed
##            - 2e-06 Filler.Level + 4e-08 MFR
## 
##   Rule 14/12: [69 cases, mean 8.541, range 8.22 to 8.76, est err 0.111]
## 
##     if
##  Mnf.Flow > -100
##  Balling <= 2.956
##  Air.Pressurer > 143.4
##     then
##  outcome = 6.208 - 0.524 Balling.Lvl + 0.057 Balling + 0.00068 Usage.cont
##            + 0.0023 Bowl.Setpoint - 0.014 Balling.Scaled - 2.1e-07 MFR
##            + 5.3e-09 Filler.Speed + 0.011 Balling.Lvl.Scaled
##            - 6e-05 Mnf.Flow + 0.0004 Hyd.Pressure3 + 0.005 Air.Pressurer
##            + 4 Alch.Rel - 0.014 Brand.Code.C + 0.004 Oxygen.Filler
##            - 0.0009 Pressure.Setpoint + 0.01 Carb.Pressure1
##            - 1e-06 Filler.Level
## 
##   Rule 14/13: [189 cases, mean 8.565, range 8.06 to 8.82, est err 0.075]
## 
##     if
##  Filler.Speed > 7753922
##  Mnf.Flow > -100
##  Balling > 2.956
##     then
##  outcome = 13.57 - 7.047e-07 Filler.Speed + 0.175 Balling
##            + 0.007 Hyd.Pressure3 - 0.077 Carb.Flow.Scaled
##            - 0.076 Pressure.Vacuum + 0.08 Oxygen.Filler
##            - 0.002 Bowl.Setpoint - 0.00034 Usage.cont - 1.3e-05 Carb.Flow
##            - 0.0007 Hyd.Pressure2 - 6e-06 Filler.Level
## 
##   Rule 14/14: [705 cases, mean 8.660, range 8.18 to 8.94, est err 0.096]
## 
##     if
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##     then
##  outcome = -9.852 - 0.13358 Mnf.Flow - 0.97 Density + 0.263 Balling.Lvl
##            + 0.071 Balling - 0.043 Air.Pressurer + 0.27 Carb.Pressure1
##            + 0.044 Balling.Scaled + 23 Alch.Rel
##            - 0.026 Balling.Lvl.Scaled - 1.13 Hyd.Pressure4
##            - 0.067 Brand.Code.C - 1.03e-08 Filler.Speed
##            - 0.034 Oxygen.Filler
## 
##   Rule 14/15: [369 cases, mean 8.680, range 8.3 to 8.92, est err 0.073]
## 
##     if
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum <= -5
##     then
##  outcome = -42.52 - 0.196 Balling + 107 Alch.Rel + 0.18 Pressure.Vacuum
##            - 0.06 Balling.Lvl.Scaled - 0.095 Oxygen.Filler
##            + 2.01e-08 Filler.Speed - 5.3e-07 MFR - 0.0025 Hyd.Pressure1
##            + 0.00037 Usage.cont - 3e-05 Mnf.Flow
## 
## Model 15:
## 
##   Rule 15/1: [17 cases, mean 8.221, range 7.88 to 8.8, est err 0.376]
## 
##     if
##  Carb.Rel <= 0.4819672
##  Brand.Code.C > 0
##  Mnf.Flow > -100
##     then
##  outcome = 8.711 - 0.03497 Mnf.Flow + 0.1185 Hyd.Pressure3
##            - 4.53 PSC.Fill + 0.000254 Filler.Level - 5e-08 MFR
##            + 0.008 Density
## 
##   Rule 15/2: [28 cases, mean 8.279, range 8.02 to 8.54, est err 0.177]
## 
##     if
##  Oxygen.Filler <= -2.57927
##  Usage.cont > 273.28
##  Brand.Code.C <= 0
##  Pressure.Vacuum > -5.6
##  Bowl.Setpoint <= 100
##     then
##  outcome = 4.064 - 4.611 Carb.Flow.Scaled + 0.01695 Mnf.Flow
##            + 1.784e-05 MFR - 0.0337 Hyd.Pressure2
##            + 0.335 Balling.Lvl.Scaled
## 
##   Rule 15/3: [43 cases, mean 8.389, range 8.08 to 8.82, est err 0.265]
## 
##     if
##  Alch.Rel > 0.4883812
##  Temperature > 0.4998845
##  Usage.cont > 148.7992
##  Mnf.Flow <= -100
##  Hyd.Pressure3 <= 16.2
##  Pressure.Vacuum > -5.4
##  Air.Pressurer <= 142.8
##  Balling.Scaled > -1.128191
##     then
##  outcome = 142.893 - 1.17357 Mnf.Flow - 473 Alch.Rel + 0.551 Balling
##            - 13.86 Hyd.Pressure4 - 1.309e-07 Filler.Speed
##            + 0.41 Oxygen.Filler - 1.97 PC.Volume - 0.185 Balling.Scaled
##            + 2.17 Carb.Pressure + 0.053 Brand.Code.B - 0.015 Balling.Lvl
##            - 7e-05 Usage.cont + 0.003 Air.Pressurer.Scaled
## 
##   Rule 15/4: [235 cases, mean 8.425, range 8.02 to 8.86, est err 0.199]
## 
##     if
##  Carb.Rel > 0.4819672
##  Brand.Code.C > 0
##     then
##  outcome = 3.944 + 0.0111 Hyd.Pressure3 - 1.3e-06 MFR
##            + 3.3e-05 Filler.Level + 0.035 Balling.Lvl.Scaled
##            - 1.4e-05 Carb.Flow - 0.0001 Mnf.Flow + 8 Alch.Rel
##            + 0.0006 Bowl.Setpoint - 0.009 Balling - 0.009 Density.Scaled
##            + 2.8e-09 Filler.Speed - 0.0001 Usage.cont
##            + 0.011 Brand.Code.B - 0.015 Brand.Code.C
##            + 0.03 Carb.Pressure1 + 0.01 Density + 0.003 Balling.Scaled
##            - 0.0011 Pressure.Setpoint - 0.02 PC.Volume
## 
##   Rule 15/5: [111 cases, mean 8.425, range 8.12 to 8.68, est err 0.083]
## 
##     if
##  Oxygen.Filler > -2.57927
##  Usage.cont > 273.28
##  Brand.Code.C <= 0
##  Mnf.Flow > -100
##  Pressure.Vacuum > -5.6
##  Bowl.Setpoint <= 100
##     then
##  outcome = -15.931 - 0.478 Oxygen.Filler + 0.165 Air.Pressurer
##            + 0.343 Pressure.Vacuum - 0.16 Density.Scaled
##            + 0.114 Balling.Scaled + 2.72e-08 Filler.Speed - 4.7e-07 MFR
##            - 0.0007 Bowl.Setpoint - 6e-05 Mnf.Flow + 3 Alch.Rel
##            - 0.002 Balling + 0.0001 Hyd.Pressure3
## 
##   Rule 15/6: [38 cases, mean 8.454, range 8.06 to 8.7, est err 0.114]
## 
##     if
##  Filler.Level > 7080
##  Usage.cont > 273.28
##  Brand.Code.C <= 0
##  Mnf.Flow > -100
##  Bowl.Setpoint > 100
##     then
##  outcome = -0.882 - 0.288 Density + 0.12 Balling.Lvl - 0.103 Balling
##            - 0.09 Oxygen.Filler - 0.042 Balling.Lvl.Scaled
##            + 0.035 Balling.Scaled - 2.3e-05 Carb.Flow + 17 Alch.Rel
##            - 0.00017 Mnf.Flow + 0.0016 Hyd.Pressure1
##            - 0.0059 Pressure.Setpoint + 0.008 Air.Pressurer
##            + 2.6e-09 Filler.Speed + 0.0003 Bowl.Setpoint
##            + 0.005 Density.Scaled + 0.12 Hyd.Pressure4
## 
##   Rule 15/7: [377 cases, mean 8.460, range 7.88 to 8.86, est err 0.141]
## 
##     if
##  Usage.cont > 273.28
##  Mnf.Flow > -100
##  Pressure.Vacuum <= -5.6
##     then
##  outcome = -52.207 - 0.00385 Mnf.Flow - 0.375 Balling + 0.287 Balling.Lvl
##            + 0.0128 Hyd.Pressure2 + 119 Alch.Rel + 0.0126 Hyd.Pressure1
##            - 0.225 Pressure.Vacuum - 0.016 Density.Scaled
##            + 0.011 Balling.Scaled + 0.009 Air.Pressurer
## 
##   Rule 15/8: [288 cases, mean 8.517, range 8.06 to 8.76, est err 0.075]
## 
##     if
##  Usage.cont > 273.28
##  Brand.Code.C <= 0
##  Mnf.Flow > -100
##  Bowl.Setpoint > 100
##     then
##  outcome = -27.216 - 0.121 Balling + 0.123 Balling.Lvl + 74 Alch.Rel
##            - 0.258 Density - 0.0043 Hyd.Pressure3 + 0.00053 Mnf.Flow
##            - 0.044 Balling.Lvl.Scaled - 3.2e-05 Carb.Flow
##            + 1.23e-08 Filler.Speed - 0.045 Pressure.Vacuum
##            + 0.023 Balling.Scaled + 0.033 Oxygen.Filler
##            - 0.0066 Pressure.Setpoint + 0.0008 Hyd.Pressure1
## 
##   Rule 15/9: [20 cases, mean 8.521, range 8.4 to 8.72, est err 0.113]
## 
##     if
##  Filler.Level <= 7080
##  Usage.cont > 273.28
##  Brand.Code.C <= 0
##  Pressure.Vacuum <= -6
##  Bowl.Setpoint > 100
##     then
##  outcome = -0.59 - 1.487 Pressure.Vacuum + 0.00122 Mnf.Flow
##            + 0.006 Balling.Lvl - 0.004 Balling - 0.0002 Hyd.Pressure3
##            - 0.006 Density - 0.002 Balling.Lvl.Scaled
##            + 0.0001 Hyd.Pressure2
## 
##   Rule 15/10: [298 cases, mean 8.527, range 8.16 to 8.86, est err 0.089]
## 
##     if
##  Usage.cont <= 273.28
##  Mnf.Flow > -100
##     then
##  outcome = -28.165 + 75 Alch.Rel - 0.116 Balling.Lvl
##            - 0.098 Pressure.Vacuum + 2.4e-05 Filler.Level
##            - 0.04 Density.Scaled + 0.032 Carb.Flow.Scaled
##            + 0.18 Carb.Pressure1 - 0.28 PC.Volume + 0.00045 Usage.cont
##            + 1.18e-08 Filler.Speed - 0.025 Balling.Scaled
##            + 0.016 Balling.Lvl.Scaled - 0.42 Carb.Pressure
##            - 0.61 Hyd.Pressure4 - 0.0008 Bowl.Setpoint
##            - 0.0004 Hyd.Pressure1
## 
##   Rule 15/11: [124 cases, mean 8.535, range 8.06 to 8.74, est err 0.115]
## 
##     if
##  Oxygen.Filler > -3.009464
##  Usage.cont > 273.28
##  Brand.Code.C <= 0
##  Mnf.Flow > -100
##  Pressure.Vacuum > -6
##  Bowl.Setpoint > 100
##     then
##  outcome = 8.092 - 0.124 Balling.Lvl.Scaled - 9.5e-05 Carb.Flow
##            - 0.146 Pressure.Vacuum - 0.0051 Hyd.Pressure2
##            + 0.0046 Hyd.Pressure1 + 2.58e-08 Filler.Speed
##            - 0.022 Pressure.Setpoint - 0.24 PSC.Fill
##            - 0.045 Brand.Code.Encoded + 0.009 Balling.Lvl - 0.008 Balling
##            - 4e-05 Mnf.Flow - 0.009 Density - 0.0002 Hyd.Pressure3
##            + 0.003 Balling.Scaled + 2 Alch.Rel + 0.002 Air.Pressurer
## 
##   Rule 15/12: [81 cases, mean 8.536, range 8.14 to 8.88, est err 0.156]
## 
##     if
##  Alch.Rel <= 0.4883812
##  Hyd.Pressure4 <= 2.103777
##  Temperature > 0.4998845
##  Hyd.Pressure3 <= 16.2
##     then
##  outcome = 7.346 - 1.29 PC.Volume - 0.115 Carb.Flow.Scaled
##            - 0.44 PSC.Fill
## 
##   Rule 15/13: [18 cases, mean 8.547, range 8.26 to 8.86, est err 0.203]
## 
##     if
##  Alch.Rel > 0.4883812
##  Temperature > 0.4998845
##  Mnf.Flow <= -100
##  Hyd.Pressure3 <= 16.2
##  Pressure.Vacuum > -5.4
##  Air.Pressurer > 142.8
##  Balling.Scaled > -1.128191
##     then
##  outcome = -704.516 + 1464 Alch.Rel - 2.143 Balling.Lvl
##            + 0.27 Balling.Scaled - 0.369 Oxygen.Filler
##            + 0.089 Air.Pressurer.Scaled - 0.00058 Usage.cont
## 
##   Rule 15/14: [205 cases, mean 8.577, range 8.28 to 8.86, est err 0.098]
## 
##     if
##  Temperature <= 0.4998873
##  Usage.cont <= 273.28
##  Brand.Code.C <= 0
##  Mnf.Flow > -100
##     then
##  outcome = -28.784 - 0.00189 Mnf.Flow + 80 Alch.Rel - 0.121 Balling.Lvl
##            + 0.0054 Hyd.Pressure2 - 0.055 Density.Scaled
##            + 2.3e-05 Filler.Level - 0.065 Pressure.Vacuum
##            - 0.33 PC.Volume + 0.0024 Hyd.Pressure1 - 1.33 Hyd.Pressure4
##            + 0.13 Carb.Pressure1 + 9.1e-09 Filler.Speed
##            + 0.018 Carb.Flow.Scaled - 0.014 Balling.Scaled
##            + 0.00018 Usage.cont + 0.009 Balling.Lvl.Scaled
##            - 0.24 Carb.Pressure + 0.0004 Hyd.Pressure3 - 0.006 Balling
##            - 0.011 Density - 0.0015 Pressure.Setpoint
##            - 0.0002 Bowl.Setpoint + 2e-06 Carb.Flow
## 
##   Rule 15/15: [33 cases, mean 8.579, range 8.42 to 8.76, est err 0.178]
## 
##     if
##  Alch.Rel > 0.4883812
##  Temperature > 0.4998845
##  Mnf.Flow <= -100
##  Pressure.Vacuum <= -5.4
##  Balling.Scaled > -1.128191
##     then
##  outcome = -0.203 - 0.294 Oxygen.Filler + 0.053 Balling
##            - 0.047 Balling.Lvl + 0.062 Brand.Code.B + 16 Alch.Rel
##            - 0.12 PC.Volume
## 
##   Rule 15/16: [174 cases, mean 8.598, range 8.14 to 8.88, est err 0.134]
## 
##     if
##  Alch.Rel <= 0.4883812
##  Temperature > 0.4998845
##  Mnf.Flow <= -100
##     then
##  outcome = -5.308 - 0.01098 Mnf.Flow + 5.94 Hyd.Pressure4
##            - 0.128 Oxygen.Filler + 0.002 Balling
## 
##   Rule 15/17: [39 cases, mean 8.601, range 8.14 to 8.94, est err 0.161]
## 
##     if
##  Alch.Rel > 0.4883812
##  Temperature > 0.4998845
##  Mnf.Flow <= -100
##  Hyd.Pressure3 <= 16.2
##  Balling.Scaled <= -1.128191
##     then
##  outcome = -31.291 + 0.0275 Hyd.Pressure3 + 0.229 Balling + 77 Alch.Rel
##            - 0.122 Balling.Lvl - 0.00118 Usage.cont + 6.5e-05 Carb.Flow
##            + 0.156 Brand.Code.Encoded - 0.3 PSC + 0.073 Brand.Code.B
##            - 5.9e-07 MFR - 0.018 Balling.Scaled - 0.16 PC.Volume
##            - 0.024 Pressure.Vacuum
## 
##   Rule 15/18: [379 cases, mean 8.616, range 8.08 to 8.94, est err 0.139]
## 
##     if
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##     then
##  outcome = -172.262 - 0.67265 Mnf.Flow - 0.394 Balling.Lvl + 240 Alch.Rel
##            + 0.28 Carb.Pressure1 - 0.036 Air.Pressurer - 0.046 Balling
##            - 0.35 Hyd.Pressure4 - 0.012 Oxygen.Filler
##            + 0.006 Air.Pressurer.Scaled + 0.03 PC.Volume + 0.02 PSC.Fill
## 
##   Rule 15/19: [82 cases, mean 8.639, range 8.4 to 8.92, est err 0.094]
## 
##     if
##  Temperature > 0.4998845
##  Mnf.Flow <= -100
##  Hyd.Pressure3 > 16.2
##     then
##  outcome = 0.173 - 0.03498 Mnf.Flow - 1.544e-07 Filler.Speed
##            + 4.61e-06 MFR - 0.0125 Hyd.Pressure3
##            + 0.0426 Pressure.Setpoint - 0.072 Carb.Flow.Scaled
##            - 0.134 Oxygen.Filler - 0.075 Density.Scaled
##            + 1.43 Hyd.Pressure4 - 0.23 PSC.Fill + 0.011 Balling
##            + 0.0007 Hyd.Pressure1 + 0.0005 Hyd.Pressure2 - 0.06 PC.Volume
##            + 0.012 Brand.Code.B - 0.005 Balling.Lvl
##            - 0.004 Balling.Scaled
## 
##   Rule 15/20: [195 cases, mean 8.646, range 8.22 to 8.92, est err 0.068]
## 
##     if
##  Mnf.Flow <= -100
##  Pressure.Vacuum <= -5
##  Balling.Lvl > 1.48
##     then
##  outcome = -531.545 + 3.747 Air.Pressurer - 1.866 Air.Pressurer.Scaled
##            + 0.312 Pressure.Vacuum + 0.162 Balling - 0.116 Balling.Lvl
##            - 0.0037 Hyd.Pressure1 + 0.0027 Hyd.Pressure2 + 16 Alch.Rel
##            - 0.022 Balling.Lvl.Scaled - 0.028 Oxygen.Filler
##            + 0.13 PC.Volume
## 
##   Rule 15/21: [440 cases, mean 8.647, range 8.1 to 8.92, est err 0.094]
## 
##     if
##  Mnf.Flow <= -100
##  Pressure.Vacuum <= -5
##     then
##  outcome = -128.584 - 0.07165 Mnf.Flow + 0.871 Air.Pressurer
##            - 0.41 Air.Pressurer.Scaled + 6.4e-05 Carb.Flow
##            - 0.087 Oxygen.Filler - 1.77e-08 Filler.Speed + 0.03 Balling
##            + 0.051 Brand.Code.B - 0.027 Balling.Lvl + 12 Alch.Rel
##            + 0.025 Pressure.Vacuum - 0.012 Density.Scaled
##            + 0.0005 Hyd.Pressure3 + 0.0005 Bowl.Setpoint
##            + 0.04 Carb.Pressure1 - 0.25 Hyd.Pressure4
##            - 0.005 Balling.Lvl.Scaled - 0.004 Balling.Scaled
##            + 0.01 Density - 5e-05 Usage.cont + 0.0002 Hyd.Pressure1
## 
##   Rule 15/22: [112 cases, mean 8.677, range 8.28 to 8.92, est err 0.107]
## 
##     if
##  Usage.cont <= 148.7992
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5.4
##  Air.Pressurer <= 142.8
##  Balling.Scaled > -1.128191
##     then
##  outcome = -41.098 - 0.49767 Mnf.Flow + 0.14 Brand.Code.B
##            + 0.109 Oxygen.Filler + 0.059 Balling
## 
## Model 16:
## 
##   Rule 16/1: [19 cases, mean 8.238, range 8.08 to 8.6, est err 0.173]
## 
##     if
##  Alch.Rel > 0.48831
##  Filler.Speed > 8040050
##  Oxygen.Filler <= -1.870865
##  Brand.Code.C > 0
##     then
##  outcome = 12.46 + 0.257 Oxygen.Filler - 0.00126 Usage.cont
##            - 1.86 Hyd.Pressure4 - 0.4 PC.Volume
## 
##   Rule 16/2: [18 cases, mean 8.280, range 8.02 to 8.58, est err 0.144]
## 
##     if
##  Carb.Rel > 0.4823337
##  Filler.Speed > 7904288
##  Carb.Flow <= 3198
##  Bowl.Setpoint <= 100
##  Air.Pressurer <= 145.8
##  Balling.Lvl <= 2.98
##     then
##  outcome = 17.88 - 0.00886 Carb.Flow
## 
##   Rule 16/3: [19 cases, mean 8.281, range 8.16 to 8.6, est err 0.147]
## 
##     if
##  Alch.Rel > 0.4883812
##  Carb.Rel > 0.4823337
##  Filler.Speed <= 7904288
##  Carb.Flow <= 3198
##  Bowl.Setpoint <= 100
##  Balling.Lvl <= 2.98
##     then
##  outcome = 2.321 - 0.249 Balling.Lvl + 0.152 Balling + 0.00112 Mnf.Flow
##            - 0.0051 Hyd.Pressure3 + 2.57e-08 Filler.Speed
##            + 0.042 Air.Pressurer - 7.7e-07 MFR - 0.034 Balling.Scaled
##            - 0.022 Density.Scaled - 1.6e-05 Carb.Flow
##            + 0.017 Balling.Lvl.Scaled
## 
##   Rule 16/4: [56 cases, mean 8.329, range 8.12 to 8.74, est err 0.103]
## 
##     if
##  Carb.Rel > 0.4823337
##  Filler.Speed <= 7904288
##  Mnf.Flow > -100
##  Carb.Flow <= 3198
##  Bowl.Setpoint <= 100
##  Balling.Lvl <= 2.98
##  Density.Scaled > -1.934118
##     then
##  outcome = 5.053 + 0.00257 Mnf.Flow - 0.0117 Hyd.Pressure3
##            - 0.069 Balling.Lvl - 3.8e-05 Carb.Flow + 0.043 Balling
##            + 0.024 Air.Pressurer - 0.025 Density.Scaled
##            + 4.4e-09 Filler.Speed - 1.5e-07 MFR + 0.0003 Bowl.Setpoint
## 
##   Rule 16/5: [56 cases, mean 8.393, range 7.88 to 8.66, est err 0.134]
## 
##     if
##  Mnf.Flow > -100
##  Hyd.Pressure1 > 10.8
##  Density.Scaled <= -1.934118
##     then
##  outcome = -48.57 + 44.718 Density - 16.495 Density.Scaled
##            - 0.004075 Carb.Flow - 1.888 Balling.Lvl
##            + 0.677 Carb.Flow.Scaled + 0.0193 Hyd.Pressure3 - 2.44e-06 MFR
##            + 3 Alch.Rel - 3e-05 Mnf.Flow + 0.0002 Bowl.Setpoint
##            + 1.4e-09 Filler.Speed - 0.007 Brand.Code.C
##            - 1e-06 Filler.Level
## 
##   Rule 16/6: [92 cases, mean 8.414, range 8.12 to 8.74, est err 0.097]
## 
##     if
##  Carb.Rel > 0.4823337
##  Carb.Flow > 3198
##  Bowl.Setpoint <= 100
##  Air.Pressurer <= 145.8
##  Balling.Lvl <= 2.98
##  Density.Scaled > -1.934118
##     then
##  outcome = -1.101 + 9.5e-05 Filler.Level - 0.0094 Bowl.Setpoint
##            - 0.094 Density.Scaled + 0.07 Air.Pressurer
##            - 0.065 Balling.Lvl + 0.043 Balling
## 
##   Rule 16/7: [48 cases, mean 8.448, range 8.12 to 8.78, est err 0.141]
## 
##     if
##  Filler.Speed <= 8040050
##  Oxygen.Filler <= -1.870865
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = 9.678 + 0.491 Oxygen.Filler - 1.38 PC.Volume
##            - 0.63 Hyd.Pressure4 - 0.00018 Usage.cont
## 
##   Rule 16/8: [202 cases, mean 8.468, range 8 to 8.7, est err 0.069]
## 
##     if
##  Carb.Rel <= 0.4823337
##  Mnf.Flow > -100
##  Density.Scaled > -1.934118
##     then
##  outcome = 6.475 + 9.38e-08 Filler.Speed - 0.00157 Mnf.Flow
##            - 2.81e-06 MFR - 0.102 Balling.Scaled - 4.4e-05 Filler.Level
##            + 0.0043 Bowl.Setpoint + 0.0045 Hyd.Pressure1
##            + 4.1e-05 Carb.Flow - 0.077 Pressure.Vacuum
##            + 0.045 Density.Scaled - 0.064 Oxygen.Filler
##            + 0.00048 Usage.cont - 0.026 Balling.Lvl + 0.008 Air.Pressurer
##            + 0.01 Balling
## 
##   Rule 16/9: [208 cases, mean 8.472, range 8.02 to 8.86, est err 0.100]
## 
##     if
##  Carb.Rel > 0.4823337
##  Mnf.Flow > -100
##  Bowl.Setpoint > 100
##  Balling.Lvl <= 2.98
##     then
##  outcome = 1.788 - 0.17 Balling + 0.0043 Hyd.Pressure3
##            + 0.048 Air.Pressurer + 0.061 Balling.Lvl - 8.2e-07 MFR
##            + 0.04 Balling.Scaled - 0.028 Balling.Lvl.Scaled
##            + 4.1e-09 Filler.Speed - 0.002 Density.Scaled
## 
##   Rule 16/10: [92 cases, mean 8.472, range 8.08 to 8.86, est err 0.083]
## 
##     if
##  Carb.Rel > 0.4823337
##  Filler.Speed > 7605000
##  Mnf.Flow > -100
##  Hyd.Pressure3 <= 34
##  Bowl.Setpoint > 100
##  Balling.Lvl <= 2.98
##  Density.Scaled > -1.934118
##     then
##  outcome = 4.504 - 7.978e-07 Filler.Speed - 0.0078 Bowl.Setpoint
##            - 0.007 Hyd.Pressure3 - 0.117 Balling + 6.2e-05 Filler.Level
##            + 0.078 Air.Pressurer + 0.062 Balling.Lvl
##            - 0.0027 Hyd.Pressure1 - 4.1e-07 MFR - 0.023 Density.Scaled
##            + 0.017 Balling.Scaled - 0.13 PC.Volume
##            - 0.012 Balling.Lvl.Scaled
## 
##   Rule 16/11: [31 cases, mean 8.478, range 8.1 to 8.82, est err 0.149]
## 
##     if
##  Filler.Speed > 7952072
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##  Balling.Scaled <= 0.03563147
##  Brand.Code.Encoded <= 8.030843
##     then
##  outcome = -254.443 - 2.63851 Mnf.Flow + 0.52 Pressure.Vacuum
##            + 1.084e-07 Filler.Speed + 4e-06 Filler.Level
##            - 0.007 Oxygen.Filler - 0.003 Air.Pressurer.Scaled
##            + 0.06 Carb.Pressure + 0.01 Carb.Pressure1
## 
##   Rule 16/12: [20 cases, mean 8.522, range 8.02 to 8.86, est err 0.199]
## 
##     if
##  Mnf.Flow > -100
##  Hyd.Pressure1 <= 10.8
##  Density.Scaled <= -1.934118
##     then
##  outcome = 6.663 - 0.55 Density.Scaled + 0.00398 Mnf.Flow + 0.85 Density
##            - 0.0105 Hyd.Pressure1
## 
##   Rule 16/13: [31 cases, mean 8.526, range 8.32 to 8.74, est err 0.140]
## 
##     if
##  Carb.Rel > 0.4823337
##  Filler.Speed > 7605000
##  Mnf.Flow > -100
##  Hyd.Pressure3 > 34
##  Bowl.Setpoint > 100
##  Air.Pressurer <= 145.8
##  Balling.Lvl <= 2.98
##  Density.Scaled > -1.934118
##     then
##  outcome = 5.582 - 3.1363e-06 Filler.Speed - 1.515e-05 MFR
##            - 0.00591 Mnf.Flow - 0.733 Balling.Lvl + 0.027 Bowl.Setpoint
##            + 0.209 Air.Pressurer - 0.345 Oxygen.Filler
##            + 1.1e-05 Filler.Level - 0.009 Balling - 0.0005 Hyd.Pressure1
##            - 0.004 Density.Scaled - 0.02 PC.Volume
## 
##   Rule 16/14: [333 cases, mean 8.530, range 8.06 to 8.82, est err 0.092]
## 
##     if
##  Mnf.Flow > -100
##  Balling.Lvl > 2.98
##     then
##  outcome = 4.847 + 0.0083 Hyd.Pressure3 - 7.7e-05 Carb.Flow
##            - 0.00124 Usage.cont - 6.6e-07 MFR - 1.9e-05 Filler.Level
##            - 0.0007 Hyd.Pressure2 + 7 Alch.Rel + 4e-09 Filler.Speed
##            + 0.008 Balling - 0.019 Density + 0.005 Air.Pressurer
##            - 0.013 Brand.Code.C - 0.004 Balling.Lvl
## 
##   Rule 16/15: [45 cases, mean 8.545, range 8.2 to 8.76, est err 0.123]
## 
##     if
##  Filler.Speed > 7952072
##  Oxygen.Filler > -1.858051
##  Brand.Code.C <= 0
##  Pressure.Vacuum > -5
##  Balling.Scaled <= 0.03563147
##     then
##  outcome = -25.712 + 3.6574e-06 Filler.Speed - 0.0496 Mnf.Flow
##            + 0.263 Pressure.Vacuum - 0.00098 Usage.cont
##            + 1.4e-05 Filler.Level - 0.019 Oxygen.Filler
##            + 0.21 Carb.Pressure - 0.007 Air.Pressurer.Scaled
##            - 0.005 Balling.Scaled + 0.03 Carb.Pressure1
##            + 0.003 Balling.Lvl.Scaled
## 
##   Rule 16/16: [32 cases, mean 8.547, range 8.4 to 8.64, est err 0.152]
## 
##     if
##  Alch.Rel <= 0.48831
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = 67.307 + 0.58142 Mnf.Flow - 0.279 Balling
##            + 0.106 Oxygen.Filler + 0.42 PSC.Fill - 0.09 PC.Volume
## 
##   Rule 16/17: [43 cases, mean 8.548, range 8.36 to 8.76, est err 0.087]
## 
##     if
##  Mnf.Flow > -100
##  Air.Pressurer > 145.8
##  Balling.Lvl <= 2.98
##     then
##  outcome = -3.893 - 0.01492 Mnf.Flow + 0.025 Hyd.Pressure3
##            + 0.0202 Hyd.Pressure1 + 0.0137 Hyd.Pressure2
##            + 0.068 Air.Pressurer - 0.142 Brand.Code.C
##            + 3.7e-09 Filler.Speed + 5 Alch.Rel - 1e-07 MFR
##            + 0.0004 Bowl.Setpoint - 0.016 Density + 0.02 Carb.Pressure1
##            - 2e-06 Filler.Level - 0.003 Balling.Lvl - 3e-05 Usage.cont
## 
##   Rule 16/18: [156 cases, mean 8.554, range 8.06 to 8.76, est err 0.098]
## 
##     if
##  Alch.Rel <= 0.4916968
##  Mnf.Flow > -100
##  Hyd.Pressure3 > 32.6
##  Balling.Lvl > 2.98
##     then
##  outcome = 0.545 + 0.503 Balling.Lvl - 0.0131 Hyd.Pressure3
##            - 0.331 Density - 0.00141 Usage.cont + 0.053 Balling
##            + 13 Alch.Rel - 2.9e-07 MFR + 7.7e-09 Filler.Speed
##            + 0.009 Air.Pressurer - 0.025 Brand.Code.C - 6e-06 Carb.Flow
## 
##   Rule 16/19: [43 cases, mean 8.568, range 8.26 to 8.84, est err 0.123]
## 
##     if
##  Oxygen.Filler > -1.870865
##  Brand.Code.C > 0
##     then
##  outcome = -16.864 - 0.0212 Mnf.Flow + 46 Alch.Rel - 0.143 Density
##            + 0.0033 Hyd.Pressure3 + 0.0032 Bowl.Setpoint
##            + 2.06e-08 Filler.Speed - 0.121 Brand.Code.C - 5.2e-07 MFR
##            + 0.19 Carb.Pressure1 - 1.8e-05 Filler.Level
##            - 0.0014 Hyd.Pressure2 - 0.00031 Usage.cont
##            - 0.007 Pressure.Setpoint - 0.012 Balling
##            + 0.017 Oxygen.Filler + 0.01 Balling.Lvl - 0.23 Hyd.Pressure4
##            - 0.002 Air.Pressurer - 0.02 PC.Volume
## 
##   Rule 16/20: [113 cases, mean 8.587, range 8.24 to 8.94, est err 0.108]
## 
##     if
##  Filler.Speed > 7952072
##  Oxygen.Filler <= -1.858051
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##  Balling.Scaled <= 0.03563147
##  Brand.Code.Encoded > 8.030843
##     then
##  outcome = -20.987 - 0.07775 Mnf.Flow + 2.2673e-06 Filler.Speed
##            - 0.355 Oxygen.Filler + 2.8e-05 Filler.Level
##            - 0.018 Air.Pressurer.Scaled + 0.44 Carb.Pressure
##            + 0.09 Carb.Pressure1 - 0.004 Balling.Scaled - 0.004 Balling
##            + 0.003 Balling.Lvl.Scaled + 0.003 Balling.Lvl
## 
##   Rule 16/21: [69 cases, mean 8.673, range 8.14 to 8.92, est err 0.143]
## 
##     if
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##  Balling.Scaled > 0.03563147
##     then
##  outcome = 7.814 - 0.04193 Mnf.Flow + 0.000161 Carb.Flow
##            - 7.56e-08 Filler.Speed + 0.37 Carb.Pressure1
##            - 0.05 Air.Pressurer - 0.004 Oxygen.Filler
##            - 0.002 Air.Pressurer.Scaled
## 
##   Rule 16/22: [369 cases, mean 8.680, range 8.3 to 8.92, est err 0.064]
## 
##     if
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum <= -5
##     then
##  outcome = -17.327 + 0.12207 Mnf.Flow - 0.175 Balling + 82 Alch.Rel
##            + 0.175 Pressure.Vacuum - 0.054 Balling.Lvl.Scaled
##            - 0.0019 Hyd.Pressure1 + 0.027 Balling.Lvl
##            + 9.2e-09 Filler.Speed - 0.014 Oxygen.Filler
##            + 0.04 Carb.Pressure1 - 0.005 Air.Pressurer
##            - 0.19 Hyd.Pressure4
## 
##   Rule 16/23: [23 cases, mean 8.724, range 8.5 to 8.82, est err 0.136]
## 
##     if
##  Alch.Rel > 0.4916968
##  Mnf.Flow > -100
##  Hyd.Pressure3 > 32.6
##  Balling.Lvl > 2.98
##     then
##  outcome = 10.318 + 0.00723 Mnf.Flow - 0.979 Balling.Lvl + 2.1e-06 MFR
##            - 0.5 PSC.Fill + 0.031 Balling - 0.00015 Usage.cont
## 
##   Rule 16/24: [119 cases, mean 8.725, range 8.38 to 8.92, est err 0.105]
## 
##     if
##  Filler.Speed <= 7952072
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##     then
##  outcome = 6.867 - 0.06734 Mnf.Flow - 0.167 Pressure.Vacuum
##            - 0.04 Air.Pressurer + 1.11 PSC.CO2 - 0.047 Balling.Scaled
##            - 0.012 Balling + 0.011 Balling.Lvl + 4e-06 Filler.Level
##            - 0.006 Oxygen.Filler + 0.003 Balling.Lvl.Scaled
##            - 0.006 Brand.Code.C - 0.09 Hyd.Pressure4
##            + 0.01 Carb.Pressure1
## 
## Model 17:
## 
##   Rule 17/1: [37 cases, mean 8.252, range 8 to 8.5, est err 0.144]
## 
##     if
##  Alch.Rel <= 0.4903011
##  Usage.cont > 275.625
##  Mnf.Flow > -100
##  Carb.Flow > 1084
##  Pressure.Vacuum > -5.6
##  Bowl.Setpoint > 80
##  Density.Scaled > -0.1868007
##     then
##  outcome = 6.223 + 0.0173 Bowl.Setpoint - 0.000149 Filler.Level
##            + 0.16 Balling.Lvl - 0.136 Balling + 0.109 Balling.Lvl.Scaled
##            + 0.11 Brand.Code.Encoded - 0.0018 Hyd.Pressure2
##            + 0.024 Balling.Scaled + 0.044 Brand.Code.B
##            + 1.8e-05 Carb.Flow + 0.0007 Hyd.Pressure3
##            + 0.008 Air.Pressurer.Scaled - 0.008 Density.Scaled
##            - 0.00011 Usage.cont - 3e-05 Mnf.Flow
## 
##   Rule 17/2: [22 cases, mean 8.281, range 7.88 to 8.8, est err 0.228]
## 
##     if
##  Carb.Flow > 1084
##  Balling.Scaled > 1.74656
##  Density.Scaled <= -0.1868007
##     then
##  outcome = 13.048 + 1.771 Density.Scaled - 0.001128 Carb.Flow
##            + 0.00085 Mnf.Flow - 0.0037 Hyd.Pressure1
##            + 0.0028 Bowl.Setpoint - 0.021 Carb.Flow.Scaled
##            - 0.017 Balling.Scaled - 0.13 PSC.Fill
## 
##   Rule 17/3: [23 cases, mean 8.292, range 8.08 to 8.84, est err 0.159]
## 
##     if
##  Alch.Rel > 0.4885216
##  Filler.Speed > 7068800
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = -172.115 - 1.68251 Mnf.Flow + 2.2416e-06 Filler.Speed
##            - 4.77 Hyd.Pressure4 - 0.018 Balling.Lvl + 9 Alch.Rel
##            - 0.032 Brand.Code.C - 0.009 Density.Scaled
##            - 0.005 Air.Pressurer - 0.011 Oxygen.Filler
##            + 0.01 Brand.Code.B + 0.005 Air.Pressurer.Scaled
##            + 0.03 Carb.Pressure1 + 0.005 Balling + 0.011 Density
##            + 3e-06 Carb.Flow + 0.0002 Hyd.Pressure3
##            + 0.0002 Bowl.Setpoint + 0.003 Balling.Lvl.Scaled
##            + 0.0002 Hyd.Pressure1 + 0.004 Pressure.Vacuum
## 
##   Rule 17/4: [25 cases, mean 8.391, range 8.02 to 8.74, est err 0.203]
## 
##     if
##  Alch.Rel <= 0.4903011
##  Oxygen.Filler > -2.347717
##  Mnf.Flow > -100
##  Carb.Flow <= 1084
##     then
##  outcome = 9.154 + 0.00338 Mnf.Flow - 5.53e-06 MFR + 0.184 Density.Scaled
##            - 1.29 PSC.Fill + 0.052 Balling.Lvl - 0.045 Balling
##            + 0.008 Balling.Scaled + 0.012 Brand.Code.B
##            + 0.0003 Hyd.Pressure3 + 0.0001 Bowl.Setpoint
## 
##   Rule 17/5: [324 cases, mean 8.401, range 8 to 8.7, est err 0.103]
## 
##     if
##  Alch.Rel <= 0.4903011
##  Mnf.Flow > -100
##  Bowl.Setpoint > 80
##  Balling.Lvl > 1.32
##  Density.Scaled > -0.1868007
##     then
##  outcome = 8.04 - 0.00184 Mnf.Flow + 0.209 Balling.Lvl - 0.178 Balling
##            + 0.0079 Hyd.Pressure1 + 0.0047 Hyd.Pressure3
##            + 0.068 Density.Scaled + 0.0028 Bowl.Setpoint
##            + 0.032 Balling.Scaled + 0.031 Air.Pressurer.Scaled
##            + 0.056 Brand.Code.B - 1.6e-05 Filler.Level
##            + 2.3e-05 Carb.Flow - 0.00014 Usage.cont
## 
##   Rule 17/6: [255 cases, mean 8.445, range 8.02 to 8.74, est err 0.093]
## 
##     if
##  Alch.Rel <= 0.4903011
##  Mnf.Flow > -100
##  Carb.Flow <= 1084
##  Bowl.Setpoint > 80
##     then
##  outcome = 2.454 - 0.575 Balling + 0.598 Balling.Lvl + 0.00197 Mnf.Flow
##            - 0.00013 Carb.Flow + 0.0064 Bowl.Setpoint
##            + 0.065 Balling.Scaled - 0.113 Pressure.Vacuum
##            + 3.8e-05 Filler.Level + 1.69 Hyd.Pressure4
##            - 0.036 Balling.Lvl.Scaled - 0.27 PC.Volume
##            + 0.02 Brand.Code.B + 0.004 Air.Pressurer
##            + 0.0002 Hyd.Pressure1 - 3e-05 Usage.cont
##            + 0.0001 Hyd.Pressure2
## 
##   Rule 17/7: [114 cases, mean 8.478, range 8.26 to 8.7, est err 0.053]
## 
##     if
##  Alch.Rel <= 0.4903011
##  Bowl.Setpoint <= 80
##     then
##  outcome = 3.089 - 0.219 Oxygen.Filler - 0.086 Balling - 0.00028 Mnf.Flow
##            + 0.041 Brand.Code.B + 0.001 Hyd.Pressure3 + 10 Alch.Rel
##            + 0.014 Balling.Scaled + 0.0006 Bowl.Setpoint
##            - 0.01 Density.Scaled + 0.01 Balling.Lvl + 0.023 Density
##            + 8e-06 Carb.Flow + 0.03 Carb.Pressure1 - 8e-05 Usage.cont
##            - 0.012 Brand.Code.C + 0.004 Air.Pressurer.Scaled
##            + 2e-06 Filler.Level + 0.0002 Hyd.Pressure1
##            - 0.002 Air.Pressurer - 0.0011 Pressure.Setpoint
##            - 0.002 Carb.Flow.Scaled + 0.0001 Hyd.Pressure2
## 
##   Rule 17/8: [67 cases, mean 8.498, range 8.1 to 8.78, est err 0.128]
## 
##     if
##  Alch.Rel <= 0.4885216
##  Filler.Speed > 7068800
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = -19.797 - 0.19967 Mnf.Flow - 0.061 Balling.Lvl
##            - 0.143 Brand.Code.C + 24 Alch.Rel - 0.03 Density.Scaled
##            - 0.022 Air.Pressurer - 0.041 Oxygen.Filler
##            + 0.017 Air.Pressurer.Scaled + 0.1 Carb.Pressure1
##            + 0.017 Balling + 0.023 Pressure.Vacuum - 0.55 Hyd.Pressure4
##            + 0.0009 Hyd.Pressure1
## 
##   Rule 17/9: [47 cases, mean 8.501, range 8.16 to 8.8, est err 0.101]
## 
##     if
##  Alch.Rel > 0.4903011
##  Usage.cont <= 273.28
##  Mnf.Flow > -100
##  Bowl.Setpoint > 90
##     then
##  outcome = 5.005 + 0.0116 Bowl.Setpoint - 0.72 PC.Volume
##            + 0.0012 Usage.cont + 0.09 Carb.Pressure1
##            + 4.5e-09 Filler.Speed + 5e-06 Filler.Level
##            - 0.008 Density.Scaled + 0.013 Density + 0.002 Air.Pressurer
##            - 0.003 Pressure.Vacuum
## 
##   Rule 17/10: [107 cases, mean 8.502, range 8.04 to 8.86, est err 0.121]
## 
##     if
##  Alch.Rel <= 0.4903011
##  PC.Volume <= -0.8498141
##  Mnf.Flow > -100
##  Carb.Flow > 1084
##  Bowl.Setpoint > 80
##  Balling.Scaled <= 1.74656
##  Density.Scaled <= -0.1868007
##     then
##  outcome = 7.948 - 0.00404 Mnf.Flow + 0.016 Hyd.Pressure2
##            + 0.0148 Bowl.Setpoint + 0.000204 Carb.Flow
##            + 0.167 Balling.Scaled + 0.291 Pressure.Vacuum
##            + 0.18 Balling.Lvl - 0.171 Density.Scaled
##            + 0.091 Oxygen.Filler - 0.032 Balling - 0.08 PC.Volume
##            + 0.01 Brand.Code.B + 0.0002 Hyd.Pressure3
##            + 0.002 Air.Pressurer.Scaled
## 
##   Rule 17/11: [54 cases, mean 8.510, range 8.02 to 8.8, est err 0.239]
## 
##     if
##  Alch.Rel <= 0.4903011
##  PC.Volume > -0.8498141
##  Mnf.Flow > -100
##  Carb.Flow > 1084
##  Bowl.Setpoint > 80
##  Density.Scaled <= -0.1868007
##     then
##  outcome = 8.519 - 0.679 Balling.Lvl - 0.00269 Mnf.Flow
##            - 0.0115 Hyd.Pressure1 - 0.149 Density.Scaled - 0.103 Balling
##            - 0.86 PC.Volume + 0.021 Balling.Scaled + 0.0008 Bowl.Setpoint
##            + 0.021 Brand.Code.B + 0.0005 Hyd.Pressure2 + 6e-06 Carb.Flow
##            - 0.006 Balling.Lvl.Scaled + 0.005 Air.Pressurer
## 
##   Rule 17/12: [184 cases, mean 8.513, range 8.16 to 8.82, est err 0.098]
## 
##     if
##  Usage.cont <= 275.625
##  Mnf.Flow > -100
##  Carb.Flow > 1084
##  Balling.Lvl > 1.32
##  Density.Scaled > -0.1868007
##     then
##  outcome = 8.656 + 0.529 Balling - 0.407 Balling.Lvl
##            - 4.21e-08 Filler.Speed - 0.0027 Bowl.Setpoint
##            - 0.00019 Mnf.Flow + 0.0012 Hyd.Pressure3 + 0.037 Brand.Code.B
##            + 0.018 Balling.Scaled - 0.0004 Hyd.Pressure2
##            + 5e-06 Carb.Flow + 3e-06 Filler.Level - 0.003 Density.Scaled
##            + 0.002 Air.Pressurer.Scaled - 3e-05 Usage.cont
## 
##   Rule 17/13: [46 cases, mean 8.527, range 8.2 to 8.84, est err 0.138]
## 
##     if
##  Carb.Pressure1 <= 10.51956
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##     then
##  outcome = -57.009 - 0.36797 Mnf.Flow - 0.084 Balling + 52 Alch.Rel
##            + 6.5e-07 MFR - 0.044 Balling.Lvl + 1.1 Carb.Pressure
##            - 1.54e-08 Filler.Speed + 0.2 Carb.Pressure1
##            - 0.026 Density.Scaled + 0.022 Balling.Scaled
##            - 0.017 Air.Pressurer - 0.008 Oxygen.Filler
##            + 0.002 Air.Pressurer.Scaled
## 
##   Rule 17/14: [24 cases, mean 8.528, range 8.14 to 8.8, est err 0.136]
## 
##     if
##  Filler.Speed <= 7068800
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = 5.69 - 0.02022 Mnf.Flow + 0.017 Hyd.Pressure3
##            - 0.015 Brand.Code.C - 0.006 Balling.Lvl + 2 Alch.Rel
##            - 0.003 Density.Scaled - 0.002 Air.Pressurer
##            - 0.004 Oxygen.Filler
## 
##   Rule 17/15: [107 cases, mean 8.532, range 8.36 to 8.74, est err 0.101]
## 
##     if
##  Alch.Rel <= 0.4903011
##  Mnf.Flow > -100
##  Balling.Lvl <= 1.32
##     then
##  outcome = -1.663 - 0.14 Balling + 0.14 Balling.Lvl
##            + 2.8e-08 Filler.Speed + 2.7e-05 Filler.Level
##            + 0.083 Oxygen.Filler - 0.032 Balling.Scaled
##            + 0.059 Brand.Code.B - 0.00024 Mnf.Flow - 0.0023 Hyd.Pressure1
##            + 18 Alch.Rel + 0.0011 Bowl.Setpoint - 0.00027 Usage.cont
##            - 0.017 Density.Scaled + 1.1e-05 Carb.Flow
##            - 0.011 Balling.Lvl.Scaled + 0.029 Density - 0.09 PC.Volume
##            + 0.006 Air.Pressurer + 0.04 Carb.Pressure1
##            + 0.0004 Hyd.Pressure2 - 0.0027 Pressure.Setpoint
##            + 0.004 Air.Pressurer.Scaled
## 
##   Rule 17/16: [62 cases, mean 8.537, range 8.18 to 8.86, est err 0.110]
## 
##     if
##  Carb.Volume > 0.4826396
##  Carb.Volume <= 0.483228
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##     then
##  outcome = -92.644 - 0.88767 Mnf.Flow - 0.053 Balling + 25 Alch.Rel
##            - 0.039 Balling.Lvl + 0.15 Carb.Pressure1 + 2.9e-07 MFR
##            - 7.6e-09 Filler.Speed - 0.009 Air.Pressurer
##            - 0.006 Density.Scaled - 0.005 Oxygen.Filler
##            + 0.005 Brand.Code.B + 0.005 Density + 0.0001 Hyd.Pressure3
## 
##   Rule 17/17: [169 cases, mean 8.537, range 8.24 to 8.86, est err 0.074]
## 
##     if
##  Alch.Rel > 0.4903011
##  Usage.cont > 273.28
##  Mnf.Flow > -100
##     then
##  outcome = 0.631 - 0.166 Density.Scaled + 0.204 Density
##            + 0.036 Air.Pressurer + 0.21 Carb.Pressure1
##            - 0.055 Pressure.Vacuum - 0.00047 Usage.cont
##            - 0.025 Air.Pressurer.Scaled + 3.1e-07 MFR
## 
##   Rule 17/18: [257 cases, mean 8.621, range 8.18 to 8.86, est err 0.086]
## 
##     if
##  Oxygen.Filler > -2.166961
##  Mnf.Flow <= -100
##  Pressure.Vacuum <= -5
##     then
##  outcome = -1092.915 + 7.564 Air.Pressurer - 3.789 Air.Pressurer.Scaled
##            - 0.134 Balling.Lvl + 0.073 Balling + 0.115 Pressure.Vacuum
##            + 46 Alch.Rel - 0.124 Oxygen.Filler - 0.035 Balling.Scaled
##            + 0.0019 Hyd.Pressure2 + 0.029 Carb.Flow.Scaled
##            + 0.16 Carb.Pressure1
## 
##   Rule 17/19: [180 cases, mean 8.673, range 8.28 to 8.94, est err 0.100]
## 
##     if
##  Carb.Pressure1 > 10.51956
##  Carb.Volume <= 0.4826396
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##     then
##  outcome = -55.576 - 0.38628 Mnf.Flow - 0.125 Balling.Lvl + 61 Alch.Rel
##            - 0.037 Air.Pressurer + 6.1e-07 MFR - 1.68e-08 Filler.Speed
##            + 0.18 Carb.Pressure1 - 0.032 Oxygen.Filler
##            - 0.016 Density.Scaled + 0.01 Air.Pressurer.Scaled
##            - 0.027 Brand.Code.C + 0.012 Pressure.Vacuum
##            - 0.31 Hyd.Pressure4 + 0.0005 Hyd.Pressure1 + 0.003 Balling
## 
##   Rule 17/20: [42 cases, mean 8.679, range 8.46 to 8.82, est err 0.095]
## 
##     if
##  Alch.Rel > 0.4903011
##  Usage.cont <= 273.28
##  Bowl.Setpoint <= 90
##     then
##  outcome = -5.014 - 0.047 Density.Scaled + 0.22 Carb.Pressure1
##            + 0.086 Density - 0.26 PC.Volume + 1.19e-08 Filler.Speed
##            + 18 Alch.Rel - 0.024 Balling.Lvl + 0.041 Brand.Code.B
##            - 0.00032 Usage.cont + 0.016 Air.Pressurer
##            + 8e-06 Filler.Level + 0.019 Pressure.Vacuum
##            + 0.0007 Bowl.Setpoint + 0.01 Balling + 7e-06 Carb.Flow
##            - 0.007 Air.Pressurer.Scaled + 0.006 Balling.Lvl.Scaled
##            - 0.0028 Pressure.Setpoint + 9e-08 MFR
## 
##   Rule 17/21: [69 cases, mean 8.687, range 8.3 to 8.92, est err 0.098]
## 
##     if
##  Carb.Volume > 0.483228
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##     then
##  outcome = -24.871 - 0.23366 Mnf.Flow - 0.209 Pressure.Vacuum
##            - 0.038 Balling.Lvl + 19 Alch.Rel + 0.13 Carb.Pressure1
##            + 1.9e-07 MFR - 5.2e-09 Filler.Speed - 0.008 Air.Pressurer
##            - 0.011 Oxygen.Filler - 0.005 Density.Scaled
##            + 0.003 Air.Pressurer.Scaled - 0.09 Hyd.Pressure4
## 
##   Rule 17/22: [165 cases, mean 8.724, range 8.46 to 8.92, est err 0.057]
## 
##     if
##  Oxygen.Filler <= -2.166961
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum <= -5
##     then
##  outcome = -199.184 + 1.445 Air.Pressurer - 0.689 Air.Pressurer.Scaled
##            - 0.000105 Filler.Level - 0.0026 Hyd.Pressure3 - 0.031 Balling
##            + 0.0016 Hyd.Pressure1 + 0.017 Pressure.Vacuum
##            - 0.011 Balling.Lvl + 6 Alch.Rel - 0.015 Oxygen.Filler
## 
## Model 18:
## 
##   Rule 18/1: [18 cases, mean 8.260, range 8.1 to 8.78, est err 0.198]
## 
##     if
##  Alch.Rel > 0.48831
##  Oxygen.Filler <= -2.363049
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = 8.083
## 
##   Rule 18/2: [20 cases, mean 8.312, range 8.14 to 8.66, est err 0.136]
## 
##     if
##  Alch.Rel <= 0.4914786
##  Filler.Speed <= 7753922
##  Hyd.Pressure4 <= 2.106903
##  Oxygen.Filler > -2.540491
##  Mnf.Flow > -100
##  Balling.Lvl > 2.94
##     then
##  outcome = -0.93 + 0.212 Density.Scaled - 0.181 Balling
##            - 0.0056 Hyd.Pressure2 + 0.00074 Mnf.Flow
##            + 0.0043 Hyd.Pressure3 - 4.5e-05 Carb.Flow
##            - 0.066 Oxygen.Filler + 22 Alch.Rel - 4.7e-07 MFR
##            - 1.16 Hyd.Pressure4 + 1.11e-08 Filler.Speed
##            - 0.00039 Usage.cont - 8e-06 Filler.Level + 0.01 Air.Pressurer
##            - 0.0007 Bowl.Setpoint + 0.005 Balling.Scaled
##            + 0.0001 Hyd.Pressure1
## 
##   Rule 18/3: [19 cases, mean 8.319, range 8.08 to 8.58, est err 0.150]
## 
##     if
##  Alch.Rel > 0.48831
##  MFR > 266741.6
##  Oxygen.Filler > -2.363049
##  Brand.Code.C > 0
##     then
##  outcome = -132.12 - 1.20394 Mnf.Flow + 0.002176 Filler.Level
##            + 1.575e-05 MFR + 0.01 Oxygen.Filler - 0.02 PC.Volume
## 
##   Rule 18/4: [27 cases, mean 8.322, range 7.88 to 8.86, est err 0.211]
## 
##     if
##  Filler.Speed > 7753922
##  Balling.Lvl > 1.5
##  Density.Scaled <= -1.596914
##     then
##  outcome = 29.47 - 1.801e-07 Filler.Speed - 0.256 Air.Pressurer
##            - 0.0197 Hyd.Pressure1 - 0.097 Balling.Lvl + 0.088 Balling
##            + 36 Alch.Rel - 6.7e-07 MFR - 3.8e-05 Carb.Flow
##            + 0.0025 Hyd.Pressure2 - 0.00047 Usage.cont
##            - 0.047 Brand.Code.D + 0.036 Oxygen.Filler
##            - 0.0012 Bowl.Setpoint - 0.07 PSC.Fill
## 
##   Rule 18/5: [61 cases, mean 8.349, range 8.02 to 8.6, est err 0.101]
## 
##     if
##  Filler.Speed <= 7753922
##  Mnf.Flow > -100
##  Air.Pressurer > 141.8
##  Balling.Lvl > 1.5
##  Balling.Lvl <= 2.94
##     then
##  outcome = 39.124 - 76 Alch.Rel + 0.097 Balling - 7.5e-05 Carb.Flow
##            + 0.044 Air.Pressurer - 0.0027 Hyd.Pressure2
##            + 0.00032 Mnf.Flow + 0.0012 Hyd.Pressure3
##            - 0.026 Oxygen.Filler - 0.0005 Bowl.Setpoint
##            + 0.004 Balling.Scaled
## 
##   Rule 18/6: [223 cases, mean 8.440, range 8.02 to 8.76, est err 0.104]
## 
##     if
##  Filler.Speed <= 7753922
##  Mnf.Flow > -100
##  Balling.Lvl > 1.5
##     then
##  outcome = -8.851 + 0.00079 Mnf.Flow - 0.183 Oxygen.Filler
##            - 0.004 Hyd.Pressure2 + 27 Alch.Rel + 0.0019 Hyd.Pressure3
##            + 0.025 Air.Pressurer - 2.7e-05 Carb.Flow
## 
##   Rule 18/7: [294 cases, mean 8.452, range 8.02 to 8.86, est err 0.097]
## 
##     if
##  Carb.Rel > 0.4823337
##  Mnf.Flow > -100
##  Balling.Lvl <= 1.5
##     then
##  outcome = -0.801 + 0.634 Balling.Lvl - 0.295 Balling
##            - 0.08 Balling.Lvl.Scaled + 0.00045 Mnf.Flow
##            - 0.082 Pressure.Vacuum + 0.035 Air.Pressurer
##            + 1.5e-05 Filler.Level + 0.001 Bowl.Setpoint
##            + 5.6e-09 Filler.Speed + 6 Alch.Rel - 0.009 Density.Scaled
##            - 0.021 Brand.Code.C - 0.017 Density - 9e-08 MFR
##            + 0.0003 Hyd.Pressure3 + 0.02 Carb.Pressure1
##            - 4e-05 Usage.cont - 0.0011 Pressure.Setpoint
## 
##   Rule 18/8: [504 cases, mean 8.464, range 8 to 8.86, est err 0.091]
## 
##     if
##  Mnf.Flow > -100
##  Balling.Lvl <= 1.5
##     then
##  outcome = 3.509 + 1.028 Balling.Lvl - 0.128 Balling.Lvl.Scaled
##            + 0.12 Balling + 4.77e-08 Filler.Speed - 0.0033 Hyd.Pressure2
##            - 8.3e-07 MFR - 0.09 Density + 0.023 Air.Pressurer
##            - 0.025 Balling.Scaled + 0.0009 Bowl.Setpoint
##            - 0.014 Density.Scaled
## 
##   Rule 18/9: [41 cases, mean 8.464, range 8.24 to 8.74, est err 0.104]
## 
##     if
##  Alch.Rel > 0.4914786
##  Filler.Speed <= 7753922
##  Hyd.Pressure4 <= 2.106903
##  Oxygen.Filler > -2.46047
##  Mnf.Flow > -100
##     then
##  outcome = 17.634 - 0.902 Balling + 0.842 Density.Scaled
##            - 0.843 Balling.Lvl + 0.597 Oxygen.Filler
##            - 7.4e-05 Filler.Level - 1.06 Hyd.Pressure4
## 
##   Rule 18/10: [33 cases, mean 8.478, range 8.1 to 8.82, est err 0.184]
## 
##     if
##  Filler.Speed > 7944098
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##  Brand.Code.Encoded <= 8.028012
##     then
##  outcome = -307.425 - 3.17529 Mnf.Flow + 0.483 Pressure.Vacuum
##            + 2.59e-08 Filler.Speed + 2.9e-05 Carb.Flow
##            - 0.006 Carb.Flow.Scaled
## 
##   Rule 18/11: [152 cases, mean 8.483, range 8.14 to 8.76, est err 0.134]
## 
##     if
##  Filler.Speed <= 7753922
##  Mnf.Flow > -100
##  Balling.Lvl > 2.94
##     then
##  outcome = -2.516 + 0.29 Balling.Lvl + 0.0012 Mnf.Flow
##            - 0.0021 Hyd.Pressure2 + 16 Alch.Rel + 0.0013 Hyd.Pressure3
##            - 0.037 Oxygen.Filler + 0.015 Air.Pressurer
##            - 1.5e-05 Carb.Flow + 4.2e-09 Filler.Speed - 1.3e-07 MFR
##            + 0.0004 Hyd.Pressure1 - 0.004 Balling.Lvl.Scaled
##            - 0.004 Density.Scaled - 2e-06 Filler.Level
## 
##   Rule 18/12: [66 cases, mean 8.487, range 8.2 to 8.7, est err 0.099]
## 
##     if
##  Hyd.Pressure4 > 2.106903
##  Mnf.Flow > -100
##  Balling.Lvl > 2.94
##     then
##  outcome = 8.59 + 0.00094 Mnf.Flow - 1.64 PSC.CO2 - 3.04e-08 Filler.Speed
##            - 0.0024 Hyd.Pressure2 + 0.0023 Hyd.Pressure3
##            - 0.047 Oxygen.Filler + 0.0014 Hyd.Pressure1
##            - 9e-06 Filler.Level - 3e-06 Carb.Flow - 5e-08 MFR
##            - 5e-05 Usage.cont + 0.002 Balling
## 
##   Rule 18/13: [23 cases, mean 8.494, range 8.08 to 8.78, est err 0.132]
## 
##     if
##  Alch.Rel > 0.48831
##  MFR <= 266741.6
##  Oxygen.Filler > -2.363049
##  Usage.cont > 162.9432
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = -1.511 - 0.08244 Mnf.Flow + 0.00312 Usage.cont - 0.251 Density
##            + 0.091 Balling + 0.034 Oxygen.Filler - 0.07 PC.Volume
##            - 0.014 Brand.Code.C + 0.005 Balling.Lvl + 3 Alch.Rel
##            - 0.002 Air.Pressurer
## 
##   Rule 18/14: [408 cases, mean 8.499, range 8.02 to 8.82, est err 0.102]
## 
##     if
##  Filler.Speed > 7753922
##  Mnf.Flow > -100
##  Density.Scaled > -1.596914
##     then
##  outcome = -14.615 - 6.723e-07 Filler.Speed - 0.000116 Carb.Flow
##            - 0.00088 Mnf.Flow + 0.106 Balling.Lvl + 60 Alch.Rel
##            - 0.00126 Usage.cont - 0.0043 Bowl.Setpoint - 0.063 Balling
##            - 0.1 Pressure.Vacuum - 0.057 Density.Scaled
##            + 0.099 Oxygen.Filler - 0.05 Carb.Flow.Scaled
##            + 0.029 Air.Pressurer.Scaled - 3.8e-07 MFR
##            + 0.0011 Hyd.Pressure2 - 0.021 Brand.Code.D
##            - 0.0004 Hyd.Pressure1 + 0.0003 Hyd.Pressure3 - 0.03 PSC.Fill
##            - 0.007 Brand.Code.C - 0.005 Density - 1e-06 Filler.Level
## 
##   Rule 18/15: [26 cases, mean 8.543, range 8.22 to 8.74, est err 0.246]
## 
##     if
##  Carb.Rel > 0.4823337
##  Mnf.Flow > -100
##  Carb.Flow <= 3208
##  Air.Pressurer > 143.2
##  Balling.Lvl <= 1.5
##     then
##  outcome = 9.988 - 2.015 Balling.Lvl - 0.000279 Filler.Level
##            + 0.0275 Bowl.Setpoint - 0.000201 Carb.Flow - 0.019 Balling
##            + 0.0001 Mnf.Flow + 0.003 Air.Pressurer
##            - 0.006 Pressure.Vacuum - 1.1e-09 Filler.Speed
## 
##   Rule 18/16: [48 cases, mean 8.546, range 8.2 to 8.82, est err 0.146]
## 
##     if
##  Filler.Speed > 7944098
##  Oxygen.Filler > -1.858051
##  Brand.Code.C <= 0
##  Pressure.Vacuum > -5
##     then
##  outcome = -25.076 + 3.847e-06 Filler.Speed - 0.02444 Mnf.Flow
##            + 0.26 Pressure.Vacuum - 0.251 Density - 0.00155 Usage.cont
##            - 2.17 PSC.CO2 + 0.071 Balling + 0.024 Balling.Lvl
##            + 4 Alch.Rel + 2e-06 Filler.Level - 0.004 Oxygen.Filler
##            + 0.002 Balling.Scaled - 0.001 Air.Pressurer
## 
##   Rule 18/17: [32 cases, mean 8.547, range 8.4 to 8.64, est err 0.075]
## 
##     if
##  Alch.Rel <= 0.48831
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = 62.527 + 0.54297 Mnf.Flow - 0.207 Density + 0.075 Balling
##            + 0.015 Oxygen.Filler - 0.012 Brand.Code.C + 0.004 Balling.Lvl
##            - 0.03 PC.Volume + 2 Alch.Rel - 4e-05 Usage.cont
##            - 0.002 Air.Pressurer - 0.09 Hyd.Pressure4
## 
##   Rule 18/18: [35 cases, mean 8.569, range 8.38 to 8.76, est err 0.064]
## 
##     if
##  Carb.Rel > 0.4823337
##  Mnf.Flow > -100
##  Carb.Flow > 3208
##  Air.Pressurer > 143.2
##  Balling.Lvl <= 1.5
##     then
##  outcome = 9.394 - 1.69 Balling.Lvl + 0.339 Balling
##            - 7.55e-08 Filler.Speed + 0.00039 Mnf.Flow
##            + 2.6e-05 Filler.Level - 1.2e-05 Carb.Flow
##            + 0.0008 Bowl.Setpoint + 0.009 Air.Pressurer
##            - 0.007 Pressure.Vacuum
## 
##   Rule 18/19: [27 cases, mean 8.588, range 8.28 to 8.84, est err 0.137]
## 
##     if
##  MFR <= 266741.6
##  Oxygen.Filler > -2.363049
##  Usage.cont <= 162.9432
##  Brand.Code.C > 0
##  Mnf.Flow <= -100
##     then
##  outcome = -97.255 - 0.47696 Mnf.Flow - 0.98 Density + 0.354 Balling
##            + 0.00357 Usage.cont + 130 Alch.Rel - 0.39 Carb.Pressure1
##            - 0.054 Brand.Code.C + 0.021 Balling.Lvl - 0.009 Air.Pressurer
## 
##   Rule 18/20: [219 cases, mean 8.591, range 8.18 to 8.94, est err 0.143]
## 
##     if
##  Filler.Speed > 7944098
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##     then
##  outcome = -34.078 + 2.4669e-06 Filler.Speed + 0.002453 Carb.Flow
##            - 0.48 Carb.Flow.Scaled - 0.313 Oxygen.Filler - 0.15 Balling
##            + 0.107 Balling.Lvl + 0.09 Balling.Lvl.Scaled + 32 Alch.Rel
##            - 0.023 Air.Pressurer + 0.16 PSC.Fill + 0.08 Carb.Pressure1
##            - 0.013 Air.Pressurer.Scaled + 0.35 Carb.Pressure
## 
##   Rule 18/21: [50 cases, mean 8.604, range 8.4 to 8.82, est err 0.114]
## 
##     if
##  Alch.Rel > 0.4914786
##  Oxygen.Filler > -2.540491
##  Oxygen.Filler <= -2.46047
##  Mnf.Flow > -100
##  Balling.Lvl > 2.94
##     then
##  outcome = 10.145 - 0.859 Balling - 4e-05 Mnf.Flow + 3 Alch.Rel
##            - 0.011 Brand.Code.C + 0.0002 Hyd.Pressure3
##            + 0.0002 Bowl.Setpoint - 0.008 Density + 1.4e-09 Filler.Speed
##            - 4e-08 MFR
## 
##   Rule 18/22: [61 cases, mean 8.624, range 8.48 to 8.78, est err 0.062]
## 
##     if
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Hyd.Pressure1 > 18
##  Pressure.Vacuum <= -5
##  Balling.Lvl.Scaled > -0.01887109
##     then
##  outcome = 8.598 - 0.201 Balling.Lvl.Scaled + 0.223 Pressure.Vacuum
##            - 0.006 Hyd.Pressure1 - 0.005 Balling + 3 Alch.Rel
## 
##   Rule 18/23: [320 cases, mean 8.671, range 8.2 to 8.92, est err 0.106]
## 
##     if
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Balling.Lvl.Scaled <= -0.01887109
##     then
##  outcome = -81.052 - 0.324 Balling + 185 Alch.Rel + 0.011 Pressure.Vacuum
##            - 0.006 Balling.Lvl.Scaled - 0.0003 Hyd.Pressure1
## 
##   Rule 18/24: [369 cases, mean 8.680, range 8.3 to 8.92, est err 0.071]
## 
##     if
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum <= -5
##     then
##  outcome = -2.893 + 0.284 Pressure.Vacuum - 0.049 Balling + 27 Alch.Rel
##            - 0.02 Balling.Lvl.Scaled - 0.0007 Hyd.Pressure1
## 
##   Rule 18/25: [117 cases, mean 8.728, range 8.38 to 8.92, est err 0.087]
## 
##     if
##  Filler.Speed <= 7944098
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##     then
##  outcome = -50.796 - 0.61808 Mnf.Flow - 2.791 Density + 1.01 Balling.Lvl
##            + 0.159 Balling.Scaled + 0.142 Balling
##            - 0.092 Balling.Lvl.Scaled - 0.062 Oxygen.Filler
##            - 0.011 Air.Pressurer
## 
## Model 19:
## 
##   Rule 19/1: [35 cases, mean 8.265, range 8 to 8.58, est err 0.262]
## 
##     if
##  Carb.Pressure1 > 10.7951
##  Usage.cont > 269.5488
##  Mnf.Flow > -100
##  Hyd.Pressure1 > 7
##  Carb.Flow > 1084
##  Pressure.Vacuum > -5.6
##  Pressure.Vacuum <= -5.2
##  Bowl.Setpoint > 80
##  Balling.Lvl <= 3.2
##     then
##  outcome = 28.999 - 0.0168 Mnf.Flow + 0.0384 Hyd.Pressure1
##            - 1.84 Carb.Pressure1 + 0.000132 Carb.Flow
##            + 0.0056 Bowl.Setpoint + 0.065 Balling - 0.058 Balling.Lvl
##            - 0.061 Density - 0.012 Balling.Scaled - 0.015 Pressure.Vacuum
##            + 0.007 Balling.Lvl.Scaled + 0.004 Air.Pressurer.Scaled
## 
##   Rule 19/2: [25 cases, mean 8.283, range 7.88 to 8.8, est err 0.206]
## 
##     if
##  Carb.Flow > 1084
##  Pressure.Vacuum <= -5.2
##  Balling.Lvl <= 3.2
##  Balling.Scaled > 1.74656
##     then
##  outcome = 6.457 + 0.183 Balling - 0.139 Balling.Lvl + 8.1e-05 Carb.Flow
##            - 0.221 Density + 0.0036 Bowl.Setpoint - 0.00038 Mnf.Flow
##            + 0.0017 Hyd.Pressure3 + 0.12 Carb.Pressure1
##            + 0.045 Brand.Code.D - 0.015 Density.Scaled
##            - 0.018 Oxygen.Filler - 0.00013 Usage.cont
##            - 0.007 Carb.Flow.Scaled
## 
##   Rule 19/3: [22 cases, mean 8.324, range 8.04 to 8.64, est err 0.128]
## 
##     if
##  Carb.Pressure1 <= 10.7951
##  Usage.cont > 269.5488
##  Mnf.Flow > -100
##  Hyd.Pressure1 > 7
##  Carb.Flow > 1084
##  Pressure.Vacuum > -5.6
##  Bowl.Setpoint > 80
##  Balling.Lvl <= 3.2
##     then
##  outcome = 8.045 - 0.00869 Mnf.Flow + 0.0216 Hyd.Pressure1
##            + 0.000118 Carb.Flow - 0.094 Pressure.Vacuum
##            + 0.0027 Bowl.Setpoint - 0.076 Density - 0.17 PSC.CO2
## 
##   Rule 19/4: [18 cases, mean 8.342, range 8.08 to 8.84, est err 0.137]
## 
##     if
##  Alch.Rel > 0.4883812
##  Filler.Speed > 8016008
##  Temperature > 0.4998845
##  Balling.Lvl.Scaled > 0.5110298
##     then
##  outcome = -50.109 + 1.179e-05 MFR + 0.225 Carb.Flow.Scaled
##            + 109 Alch.Rel + 0.43 Carb.Pressure - 0.017 Pressure.Vacuum
##            + 0.008 Balling + 0.04 Carb.Pressure1
## 
##   Rule 19/5: [22 cases, mean 8.352, range 8.02 to 8.74, est err 0.203]
## 
##     if
##  Oxygen.Filler > -2.347717
##  Mnf.Flow > -100
##  Carb.Flow <= 1084
##  Bowl.Setpoint > 80
##  Balling.Lvl <= 3.2
##     then
##  outcome = 0.897 + 0.0034 Bowl.Setpoint - 0.045 Balling.Lvl
##            - 0.064 Density + 0.025 Balling + 15 Alch.Rel
##            + 0.018 Air.Pressurer.Scaled - 0.0065 Pressure.Setpoint
##            + 0.0009 Hyd.Pressure1
## 
##   Rule 19/6: [160 cases, mean 8.378, range 8 to 8.66, est err 0.105]
## 
##     if
##  Usage.cont > 269.5488
##  Mnf.Flow > -100
##  Hyd.Pressure1 > 7
##  Carb.Flow > 1084
##  Pressure.Vacuum <= -5.2
##  Bowl.Setpoint > 80
##  Balling.Lvl <= 3.2
##  Balling.Scaled <= 1.74656
##     then
##  outcome = 8.483 + 0.00374 Mnf.Flow - 0.0104 Hyd.Pressure3
##            - 0.217 Pressure.Vacuum + 0.0047 Bowl.Setpoint
##            + 0.078 Oxygen.Filler - 0.79 Carb.Pressure - 0.028 Density
##            + 8e-06 Carb.Flow - 0.005 Balling.Lvl + 0.004 Balling
##            + 2 Alch.Rel - 0.05 PSC.CO2 - 0.0009 Pressure.Setpoint
## 
##   Rule 19/7: [255 cases, mean 8.430, range 8.02 to 8.86, est err 0.114]
## 
##     if
##  Usage.cont > 269.5488
##  Mnf.Flow > -100
##  Mnf.Flow <= 140.6
##  Bowl.Setpoint > 80
##     then
##  outcome = 0.737 + 0.00304 Mnf.Flow - 0.0141 Hyd.Pressure3
##            - 0.079 Density + 0.026 Balling - 0.04 Pressure.Vacuum
##            + 16 Alch.Rel - 0.021 Balling.Lvl - 0.0066 Pressure.Setpoint
##            + 0.001 Hyd.Pressure1 + 0.0002 Bowl.Setpoint
## 
##   Rule 19/8: [24 cases, mean 8.432, range 8.18 to 8.86, est err 0.124]
## 
##     if
##  Usage.cont > 269.5488
##  Mnf.Flow > -100
##  Hyd.Pressure1 <= 7
##  Carb.Flow > 1084
##  Pressure.Vacuum <= -5.2
##  Bowl.Setpoint > 80
##  Balling.Lvl <= 3.2
##     then
##  outcome = 8.215 + 0.057 Hyd.Pressure1 - 0.00018 Carb.Flow
##            + 0.0087 Bowl.Setpoint - 5.5e-05 Filler.Level + 0.003 Balling
##            - 0.003 Balling.Lvl
## 
##   Rule 19/9: [223 cases, mean 8.438, range 8.02 to 8.74, est err 0.095]
## 
##     if
##  Usage.cont > 269.5488
##  Carb.Flow <= 1084
##  Bowl.Setpoint > 80
##  Balling.Lvl <= 3.2
##     then
##  outcome = 2.549 + 0.01001 Mnf.Flow - 0.0231 Hyd.Pressure3
##            - 0.00028 Carb.Flow + 0.0104 Bowl.Setpoint
##            - 0.0098 Hyd.Pressure1 - 0.12 Balling.Lvl + 0.087 Balling
##            - 8.3e-07 MFR + 2.21 Hyd.Pressure4 + 0.082 Oxygen.Filler
##            - 0.32 PC.Volume + 1.47e-08 Filler.Speed
##            - 0.019 Density.Scaled
## 
##   Rule 19/10: [27 cases, mean 8.461, range 8.24 to 8.74, est err 0.112]
## 
##     if
##  Temperature <= 0.4998845
##  Mnf.Flow <= -100
##  Air.Pressurer > 146
##     then
##  outcome = -1.164 - 0.02881 Mnf.Flow + 0.494 Pressure.Vacuum
##            - 0.102 Carb.Flow.Scaled - 0.037 Balling.Lvl + 20 Alch.Rel
##            - 0.01 Air.Pressurer - 0.009 Density.Scaled + 0.008 Balling
##            + 0.04 Carb.Pressure1 + 0.006 Air.Pressurer.Scaled
##            - 0.009 Oxygen.Filler + 7e-08 MFR - 0.0002 Hyd.Pressure1
##            + 0.02 PC.Volume + 3e-05 Usage.cont
## 
##   Rule 19/11: [27 cases, mean 8.481, range 8.22 to 8.74, est err 0.180]
## 
##     if
##  Carb.Pressure1 > 11.0236
##  Oxygen.Filler <= -2.347717
##  Usage.cont > 269.5488
##  Carb.Flow <= 1084
##  Bowl.Setpoint > 80
##  Balling.Lvl <= 3.2
##     then
##  outcome = 29.382 - 0.01656 Usage.cont - 0.000726 Carb.Flow
##            + 0.00292 Mnf.Flow + 0.0148 Hyd.Pressure3
##            - 1.21 Carb.Pressure1 - 0.0628 Pressure.Setpoint
##            - 0.104 Balling.Lvl - 1.15e-06 MFR + 0.0007 Bowl.Setpoint
##            - 0.0008 Hyd.Pressure1 + 0.008 Balling + 0.19 Hyd.Pressure4
##            - 0.03 PC.Volume + 1.3e-09 Filler.Speed + 0.005 Oxygen.Filler
## 
##   Rule 19/12: [137 cases, mean 8.490, range 8.26 to 8.74, est err 0.068]
## 
##     if
##  Bowl.Setpoint <= 80
##     then
##  outcome = -18.427 - 0.11 Balling + 54 Alch.Rel - 4.1e-05 Filler.Level
##            - 0.088 Pressure.Vacuum - 0.034 Carb.Flow.Scaled
##            - 0.00011 Mnf.Flow + 0.0005 Hyd.Pressure3
##            + 0.04 Carb.Pressure1 + 6e-06 Carb.Flow + 0.014 Brand.Code.D
##            - 0.015 Density + 0.0003 Bowl.Setpoint - 0.005 Density.Scaled
##            - 0.005 Balling.Lvl - 0.006 Oxygen.Filler
##            - 0.0015 Pressure.Setpoint + 0.0002 Hyd.Pressure1
##            - 4e-05 Usage.cont
## 
##   Rule 19/13: [19 cases, mean 8.491, range 8.18 to 8.8, est err 0.129]
## 
##     if
##  Alch.Rel <= 0.4883812
##  Filler.Speed > 8016008
##  Temperature > 0.4998845
##  Balling.Lvl.Scaled > 0.5110298
##     then
##  outcome = 0.038 - 0.15838 Mnf.Flow + 0.28 Carb.Pressure1
##            + 0.0035 Hyd.Pressure1 + 0.038 Balling.Lvl - 23 Alch.Rel
##            + 0.92 Carb.Pressure + 0.059 Brand.Code.D - 0.25 PC.Volume
##            - 3.9e-07 MFR - 0.022 Balling + 8.4e-09 Filler.Speed
##            - 0.034 Oxygen.Filler + 0.0009 Hyd.Pressure2
##            - 0.64 Hyd.Pressure4 - 0.013 Balling.Scaled
##            - 0.009 Air.Pressurer - 0.011 Pressure.Vacuum
## 
##   Rule 19/14: [24 cases, mean 8.528, range 8.12 to 8.68, est err 0.132]
## 
##     if
##  Usage.cont > 269.5488
##  Mnf.Flow > -100
##  Carb.Flow > 1084
##  Pressure.Vacuum > -5.2
##  Bowl.Setpoint > 80
##     then
##  outcome = -6.196 + 0.406 Balling - 0.388 Balling.Lvl - 0.307 Density
##            + 8.9e-05 Carb.Flow - 0.073 Balling.Scaled
##            + 0.0045 Bowl.Setpoint + 0.045 Balling.Lvl.Scaled
##            + 25 Alch.Rel + 0.027 Air.Pressurer.Scaled
##            + 0.0012 Hyd.Pressure3 - 0.00029 Usage.cont
##            + 0.011 Air.Pressurer - 0.014 Density.Scaled
##            + 0.07 Carb.Pressure1 - 0.1 PC.Volume
##            - 0.0043 Pressure.Setpoint - 3e-05 Mnf.Flow
##            + 0.004 Brand.Code.D
## 
##   Rule 19/15: [287 cases, mean 8.529, range 8.16 to 8.86, est err 0.096]
## 
##     if
##  Usage.cont <= 269.5488
##  Mnf.Flow > -100
##     then
##  outcome = -41.495 - 1.638 Balling + 2.619 Density + 0.513 Balling.Lvl
##            + 95 Alch.Rel + 0.00091 Mnf.Flow + 0.071 Balling.Scaled
##            - 0.061 Balling.Lvl.Scaled - 9.8e-07 MFR
##            + 2.51e-08 Filler.Speed + 0.0029 Hyd.Pressure3
##            - 0.0032 Hyd.Pressure1 + 0.22 Carb.Pressure1
##            + 0.00048 Usage.cont - 0.25 PC.Volume + 1.4e-05 Filler.Level
##            - 0.49 Carb.Pressure + 0.012 Air.Pressurer
## 
##   Rule 19/16: [29 cases, mean 8.555, range 8.1 to 8.84, est err 0.175]
## 
##     if
##  Filler.Speed > 8016008
##  PC.Volume > -0.8846295
##  Temperature > 0.4998845
##  Mnf.Flow <= -100
##  Balling.Lvl.Scaled <= 0.5110298
##     then
##  outcome = -258.618 - 2.65065 Mnf.Flow - 3.47 PC.Volume
##            + 0.265 Pressure.Vacuum + 0.08 Carb.Pressure
## 
##   Rule 19/17: [207 cases, mean 8.573, range 8.28 to 8.86, est err 0.082]
## 
##     if
##  Temperature <= 0.4998873
##  Usage.cont <= 269.5488
##  Mnf.Flow > -100
##     then
##  outcome = -53.958 - 0.49 Balling + 0.515 Density + 125 Alch.Rel
##            - 0.00094 Mnf.Flow + 0.097 Balling.Lvl + 0.0036 Hyd.Pressure2
##            - 0.5 PC.Volume + 0.0022 Bowl.Setpoint - 1.2 Hyd.Pressure4
##            + 0.15 Carb.Pressure1 + 0.00039 Usage.cont
##            + 0.018 Air.Pressurer.Scaled + 0.015 Air.Pressurer
##            + 0.0009 Hyd.Pressure3 + 0.014 Balling.Scaled
##            - 0.012 Balling.Lvl.Scaled - 1.9e-07 MFR
##            + 4.9e-09 Filler.Speed - 0.0006 Hyd.Pressure1
##            + 3e-06 Filler.Level - 0.1 Carb.Pressure + 3e-06 Carb.Flow
##            - 0.003 Density.Scaled
## 
##   Rule 19/18: [56 cases, mean 8.575, range 8.14 to 8.88, est err 0.149]
## 
##     if
##  Filler.Speed <= 6896898
##  Temperature > 0.4998845
##  Temperature <= 0.4998919
##  Mnf.Flow <= -100
##     then
##  outcome = 4.9 + 0.0103 Hyd.Pressure3 - 2.1e-06 MFR
##            + 2.88e-08 Filler.Speed - 0.059 Carb.Flow.Scaled
##            + 0.27 Carb.Pressure1 + 3.9e-05 Carb.Flow - 0.33 PC.Volume
##            - 0.16 PSC + 0.0003 Hyd.Pressure1 + 0.06 Carb.Pressure
## 
##   Rule 19/19: [111 cases, mean 8.577, range 8.4 to 8.76, est err 0.073]
## 
##     if
##  Mnf.Flow > 140.6
##  Bowl.Setpoint > 80
##  Balling.Lvl > 3.2
##     then
##  outcome = 8.446 - 0.00333 Mnf.Flow - 2.52e-06 MFR - 0.357 Density
##            + 0.19 PSC - 0.26 PC.Volume + 0.007 Balling + 4 Alch.Rel
##            - 0.005 Balling.Lvl - 0.0017 Pressure.Setpoint
##            + 0.0002 Hyd.Pressure1
## 
##   Rule 19/20: [146 cases, mean 8.584, range 8.12 to 8.92, est err 0.118]
## 
##     if
##  Filler.Speed > 6896898
##  Filler.Speed <= 8016008
##  Temperature > 0.4998845
##  Mnf.Flow <= -100
##     then
##  outcome = 65.078 - 0.01418 Mnf.Flow - 4.131e-07 Filler.Speed + 3e-06 MFR
##            - 117 Alch.Rel + 0.16 Balling.Lvl - 0.07 Density.Scaled
##            + 0.048 Balling.Lvl.Scaled - 0.069 Pressure.Vacuum
##            - 0.37 PC.Volume - 0.062 Oxygen.Filler + 0.0012 Hyd.Pressure3
##            + 0.0006 Hyd.Pressure1 - 0.007 Balling + 0.03 Carb.Pressure1
##            + 0.09 Carb.Pressure + 0.005 Brand.Code.D
## 
##   Rule 19/21: [84 cases, mean 8.587, range 8.1 to 8.94, est err 0.130]
## 
##     if
##  Filler.Speed > 8016008
##  Temperature > 0.4998845
##  Mnf.Flow <= -100
##  Balling.Lvl.Scaled <= 0.5110298
##     then
##  outcome = 1.768 - 0.03703 Mnf.Flow + 0.051 Balling.Lvl.Scaled
##            + 0.0037 Hyd.Pressure1 + 1.06 Carb.Pressure
##            + 0.2 Carb.Pressure1 - 0.27 PC.Volume - 4.1e-07 MFR
##            + 9e-09 Filler.Speed - 0.015 Pressure.Vacuum
##            + 0.009 Balling.Lvl - 5 Alch.Rel + 0.014 Brand.Code.D
##            - 0.008 Oxygen.Filler - 0.15 Hyd.Pressure4
##            + 0.0002 Hyd.Pressure2 - 0.003 Balling.Scaled
##            - 0.002 Air.Pressurer
## 
##   Rule 19/22: [82 cases, mean 8.618, range 8.14 to 8.92, est err 0.150]
## 
##     if
##  Filler.Speed <= 6896898
##  Temperature > 0.4998845
##  Mnf.Flow <= -100
##     then
##  outcome = 4.419 - 0.13414 Mnf.Flow + 4e-05 Carb.Flow
##            + 0.0021 Hyd.Pressure3 + 0.2 Carb.Pressure1
##            + 0.071 Brand.Code.D + 0.032 Balling.Lvl - 19 Alch.Rel
##            - 0.023 Balling - 3.3e-07 MFR - 0.038 Oxygen.Filler
##            - 0.54 Hyd.Pressure4 + 0.0007 Hyd.Pressure2
##            - 0.011 Balling.Scaled - 0.01 Carb.Flow.Scaled
##            - 0.008 Air.Pressurer + 4.4e-09 Filler.Speed
##            - 0.007 Density.Scaled + 0.0004 Bowl.Setpoint - 0.05 PC.Volume
##            - 6e-05 Usage.cont - 0.02 PSC
## 
##   Rule 19/23: [444 cases, mean 8.688, range 8.18 to 8.94, est err 0.085]
## 
##     if
##  Temperature <= 0.4998845
##  Mnf.Flow <= -100
##  Air.Pressurer <= 146
##     then
##  outcome = -42.235 - 0.21788 Mnf.Flow + 66 Alch.Rel - 0.062 Balling
##            - 0.054 Balling.Lvl - 0.083 Oxygen.Filler
##            - 0.045 Density.Scaled - 1.04 Hyd.Pressure4
##            + 0.022 Air.Pressurer.Scaled - 0.015 Air.Pressurer
##            + 0.1 Carb.Pressure1 - 0.026 Pressure.Vacuum + 1.4e-07 MFR
##            + 0.05 PC.Volume - 0.0004 Hyd.Pressure1 + 7e-05 Usage.cont
##            + 0.009 Brand.Code.D - 0.002 Balling.Scaled
##            + 0.0001 Hyd.Pressure2
## 
##   Rule 19/24: [51 cases, mean 8.758, range 8.56 to 8.92, est err 0.071]
## 
##     if
##  Carb.Pressure1 > 10.82836
##  Temperature <= 0.4998845
##  Mnf.Flow <= -100
##  Pressure.Vacuum <= -4.8
##     then
##  outcome = 0.518 - 0.03732 Mnf.Flow - 0.002 Hyd.Pressure2
##            + 0.032 Carb.Flow.Scaled + 0.17 Carb.Pressure1
##            - 0.015 Balling.Lvl + 7 Alch.Rel - 0.005 Air.Pressurer
##            - 0.01 Oxygen.Filler - 0.004 Density.Scaled + 5e-08 MFR
##            + 0.003 Air.Pressurer.Scaled + 0.006 Brand.Code.D
##            + 0.002 Balling
## 
##   Rule 19/25: [26 cases, mean 8.772, range 8.46 to 8.92, est err 0.137]
## 
##     if
##  Carb.Pressure1 > 10.82836
##  Temperature <= 0.4998845
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -4.8
##     then
##  outcome = -18.14 - 0.08296 Mnf.Flow - 0.301 Pressure.Vacuum
##            - 0.077 Balling.Lvl + 38 Alch.Rel - 0.018 Air.Pressurer
##            + 0.13 Carb.Pressure1 + 0.022 Balling - 0.018 Density.Scaled
##            - 0.026 Oxygen.Filler + 0.012 Air.Pressurer.Scaled
##            + 1.9e-07 MFR - 0.0005 Hyd.Pressure1 + 0.06 PC.Volume
##            + 9e-05 Usage.cont + 0.005 Carb.Flow.Scaled
##            - 0.0003 Hyd.Pressure2
## 
## Model 20:
## 
##   Rule 20/1: [18 cases, mean 8.182, range 7.88 to 8.38, est err 0.215]
## 
##     if
##  MFR > 266157.6
##  Oxygen.Filler <= -2.543916
##  Brand.Code.C > 0
##  Hyd.Pressure1 > 10.8
##     then
##  outcome = 6.163 + 0.025 Hyd.Pressure1 - 0.437 Oxygen.Filler
##            + 0.026 Density
## 
##   Rule 20/2: [66 cases, mean 8.391, range 8 to 8.86, est err 0.146]
## 
##     if
##  MFR <= 266157.6
##  Oxygen.Filler <= -2.543916
##  Brand.Code.C > 0
##     then
##  outcome = 8.611 - 0.0078 Hyd.Pressure1 + 1.83e-08 Filler.Speed
##            - 5.8e-07 MFR + 0.0002 Mnf.Flow + 0.061 Density
##            + 0.032 Oxygen.Filler + 0.019 Pressure.Vacuum
## 
##   Rule 20/3: [254 cases, mean 8.405, range 8.02 to 8.86, est err 0.113]
## 
##     if
##  Carb.Rel > 0.4824657
##  Mnf.Flow > -100
##  Balling <= 2.956
##  Bowl.Setpoint > 80
##  Air.Pressurer <= 145.6
##     then
##  outcome = -7.724 - 1.682 Balling.Lvl + 1.205 Balling
##            - 0.331 Balling.Scaled + 0.171 Balling.Lvl.Scaled
##            + 0.111 Air.Pressurer + 0.0055 Bowl.Setpoint
##            - 0.124 Pressure.Vacuum + 0.0037 Hyd.Pressure3
##            - 0.00036 Mnf.Flow - 0.11 Density - 0.0071 Pressure.Setpoint
##            + 9e-06 Carb.Flow
## 
##   Rule 20/4: [162 cases, mean 8.432, range 8.02 to 8.84, est err 0.118]
## 
##     if
##  Oxygen.Filler > -2.543916
##  Brand.Code.C > 0
##     then
##  outcome = 8.694 + 0.192 Oxygen.Filler + 1.16e-08 Filler.Speed
##            - 3.6e-07 MFR - 0.016 Brand.Code.C - 4e-05 Mnf.Flow
##            + 0.0002 Hyd.Pressure3 + 0.0002 Bowl.Setpoint
##            + 0.006 Brand.Code.D - 3e-05 Usage.cont + 0.01 Carb.Pressure1
## 
##   Rule 20/5: [45 cases, mean 8.448, range 8.1 to 8.86, est err 0.227]
## 
##     if
##  Oxygen.Filler <= -2.543916
##  Brand.Code.C > 0
##  Hyd.Pressure1 <= 10.8
##     then
##  outcome = 12.328 - 0.1231 Hyd.Pressure1 + 0.00909 Mnf.Flow
##            + 0.551 Oxygen.Filler + 0.445 Pressure.Vacuum
##            + 4.81e-08 Filler.Speed
## 
##   Rule 20/6: [74 cases, mean 8.474, range 8.28 to 8.6, est err 0.048]
## 
##     if
##  Balling <= 2.956
##  Bowl.Setpoint <= 80
##  Air.Pressurer <= 145.6
##     then
##  outcome = 3.162 - 0.00299 Mnf.Flow - 0.223 Balling
##            - 5.4e-05 Filler.Level + 0.084 Balling.Lvl
##            + 2.68e-08 Filler.Speed + 0.041 Air.Pressurer
##            + 0.0039 Hyd.Pressure1 - 0.038 Density
##            - 0.011 Balling.Lvl.Scaled + 0.0006 Hyd.Pressure3
##            + 0.009 Balling.Scaled + 0.0005 Bowl.Setpoint
##            - 0.01 Pressure.Vacuum - 0.0023 Pressure.Setpoint
##            + 2e-06 Carb.Flow - 0.0001 Hyd.Pressure2
## 
##   Rule 20/7: [369 cases, mean 8.475, range 7.88 to 8.86, est err 0.118]
## 
##     if
##  Carb.Rel <= 0.4824657
##  Balling <= 2.956
##  Bowl.Setpoint > 80
##  Air.Pressurer <= 145.6
##     then
##  outcome = 3.207 - 1.217 Balling.Lvl + 0.403 Balling
##            - 0.145 Balling.Scaled + 0.076 Balling.Lvl.Scaled
##            + 0.042 Air.Pressurer + 0.002 Hyd.Pressure3
##            + 0.0019 Bowl.Setpoint + 1.6e-05 Filler.Level
##            - 0.043 Pressure.Vacuum - 0.0002 Mnf.Flow
##            + 1.05e-08 Filler.Speed - 0.049 Density
##            - 0.0035 Pressure.Setpoint - 0.007 Density.Scaled
##            + 4e-06 Carb.Flow + 0.008 Brand.Code.D - 5e-05 Usage.cont
## 
##   Rule 20/8: [160 cases, mean 8.479, range 8.12 to 8.76, est err 0.101]
## 
##     if
##  Filler.Speed <= 7753922
##  Mnf.Flow > -100
##  Balling > 2.956
##     then
##  outcome = 0.912 - 0.0081 Hyd.Pressure2 + 0.0052 Hyd.Pressure3
##            - 0.146 Oxygen.Filler + 0.171 Brand.Code.D
##            + 0.0051 Hyd.Pressure1 + 0.032 Air.Pressurer
##            - 0.0025 Bowl.Setpoint - 0.065 Pressure.Vacuum
##            - 0.00057 Usage.cont - 0.025 Carb.Flow.Scaled
##            + 1.13 Hyd.Pressure4 - 6e-06 Carb.Flow + 1.7e-09 Filler.Speed
##            + 0.02 Carb.Pressure1 - 1e-06 Filler.Level
## 
##   Rule 20/9: [27 cases, mean 8.516, range 8.24 to 8.62, est err 0.107]
## 
##     if
##  Carb.Rel <= 0.4817901
##  Brand.Code.C <= 0
##  Bowl.Setpoint > 80
##     then
##  outcome = 7.783 + 0.0058 Hyd.Pressure3 - 0.007 Density.Scaled
##            + 0.004 Air.Pressurer + 0.008 Brand.Code.D + 0.008 Density
##            - 5e-05 Usage.cont + 0.003 Balling.Scaled
## 
##   Rule 20/10: [62 cases, mean 8.537, range 8.18 to 8.86, est err 0.119]
## 
##     if
##  Carb.Volume > 0.4826396
##  Carb.Volume <= 0.483228
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##     then
##  outcome = -143.233 - 1.53429 Mnf.Flow + 0.186 Pressure.Vacuum
##            - 0.055 Balling - 0.29 PSC - 0.0198 Pressure.Setpoint
##            - 4.3e-07 MFR - 0.66 Hyd.Pressure4 + 6.1e-09 Filler.Speed
##            + 0.07 Carb.Pressure1 + 6e-06 Filler.Level
##            - 0.008 Oxygen.Filler - 0.004 Air.Pressurer.Scaled
##            + 0.09 Carb.Pressure + 0.003 Balling.Lvl
## 
##   Rule 20/11: [54 cases, mean 8.563, range 8.36 to 8.76, est err 0.115]
## 
##     if
##  Mnf.Flow > -100
##  Air.Pressurer > 145.6
##     then
##  outcome = -7.472 + 0.11 Air.Pressurer
## 
##   Rule 20/12: [189 cases, mean 8.565, range 8.06 to 8.82, est err 0.085]
## 
##     if
##  Filler.Speed > 7753922
##  Mnf.Flow > -100
##  Balling > 2.956
##     then
##  outcome = 16.933 - 6.323e-07 Filler.Speed - 0.00231 Mnf.Flow
##            + 0.007 Hyd.Pressure2 - 0.099 Density.Scaled
##            - 0.085 Carb.Flow.Scaled - 6.8e-05 Carb.Flow
##            - 0.091 Pressure.Vacuum - 1.71 Hyd.Pressure4
##            - 0.0022 Bowl.Setpoint + 0.057 Oxygen.Filler
##            - 0.00042 Usage.cont + 0.0014 Hyd.Pressure3
##            + 0.03 Brand.Code.D + 0.05 Carb.Pressure1 - 4e-06 Filler.Level
## 
##   Rule 20/13: [440 cases, mean 8.647, range 8.1 to 8.92, est err 0.117]
## 
##     if
##  Mnf.Flow <= -100
##  Pressure.Vacuum <= -5
##     then
##  outcome = 8.061 + 0.07047 Mnf.Flow + 0.183 Pressure.Vacuum
##            - 0.084 Balling.Lvl.Scaled - 0.082 Oxygen.Filler
##            - 0.038 Balling.Lvl + 17 Alch.Rel + 0.0005 Hyd.Pressure3
##            + 0.008 Balling - 0.0004 Hyd.Pressure2 - 0.0005 Hyd.Pressure1
##            + 0.0003 Bowl.Setpoint - 0.005 Density.Scaled
##            + 0.01 Brand.Code.D + 0.04 PC.Volume - 6e-05 Usage.cont
##            + 0.02 Carb.Pressure1 - 0.0013 Pressure.Setpoint
##            + 1.2e-09 Filler.Speed - 0.006 Density
##            + 0.002 Air.Pressurer.Scaled - 1e-06 Filler.Level
## 
##   Rule 20/14: [705 cases, mean 8.660, range 8.18 to 8.94, est err 0.123]
## 
##     if
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##     then
##  outcome = -88.079 - 0.94431 Mnf.Flow - 0.096 Oxygen.Filler
##            - 0.047 Balling + 2.5e-05 Filler.Level - 1.17 Hyd.Pressure4
##            + 0.14 Carb.Pressure1 - 3.3e-07 MFR - 0.03 Pressure.Vacuum
##            - 0.015 Air.Pressurer.Scaled + 0.015 Balling.Lvl
##            + 0.34 Carb.Pressure + 4 Alch.Rel - 0.002 Air.Pressurer
## 
##   Rule 20/15: [319 cases, mean 8.684, range 8.3 to 8.92, est err 0.075]
## 
##     if
##  Carb.Rel > 0.4826334
##  Brand.Code.C <= 0
##  Mnf.Flow <= -100
##  Pressure.Vacuum <= -5
##     then
##  outcome = 8.769 + 0.33643 Mnf.Flow + 0.318 Pressure.Vacuum
##            - 0.169 Balling.Lvl + 73 Alch.Rel - 0.0025 Hyd.Pressure1
##            - 0.024 Balling.Lvl.Scaled + 0.2 PC.Volume
##            - 0.018 Balling.Scaled + 8.3e-09 Filler.Speed + 0.018 Balling
##            + 0.00017 Usage.cont + 0.008 Air.Pressurer.Scaled
##            - 0.015 Oxygen.Filler
## 
##   Rule 20/16: [69 cases, mean 8.687, range 8.3 to 8.92, est err 0.103]
## 
##     if
##  Carb.Volume > 0.483228
##  Mnf.Flow <= -100
##  Pressure.Vacuum > -5
##     then
##  outcome = -41.985 - 0.45998 Mnf.Flow - 1.45e-06 MFR
##            - 0.122 Pressure.Vacuum + 1.98e-08 Filler.Speed
##            - 0.041 Balling - 1.63 Hyd.Pressure4 + 0.2 Carb.Pressure1
##            + 12 Alch.Rel + 9e-06 Filler.Level - 0.025 Oxygen.Filler
##            + 0.011 Balling.Lvl - 0.005 Air.Pressurer
##            - 0.005 Air.Pressurer.Scaled + 0.12 Carb.Pressure
## 
## 
## Evaluation on training data (1799 cases):
## 
##     Average  |error|              0.070
##     Relative |error|               0.50
##     Correlation coefficient        0.82
## 
## 
##  Attribute usage:
##    Conds  Model
## 
##     83%    82%    Mnf.Flow
##     34%    29%    Brand.Code.C
##     27%    49%    Bowl.Setpoint
##     25%    66%    Alch.Rel
##     24%    52%    Pressure.Vacuum
##     18%    72%    Balling.Lvl
##     14%    52%    Filler.Speed
##     13%           Carb.Rel
##     12%    54%    Oxygen.Filler
##     11%    57%    Air.Pressurer
##     10%    49%    Density.Scaled
##      9%    59%    Hyd.Pressure3
##      8%           Temperature
##      8%    16%    Carb.Flow.Scaled
##      7%    36%    Carb.Flow
##      7%    45%    Usage.cont
##      5%           Carb.Volume
##      5%    49%    Balling.Lvl.Scaled
##      4%    75%    Balling
##      3%    39%    Hyd.Pressure1
##      3%    56%    Carb.Pressure1
##      2%    39%    Balling.Scaled
##      2%    32%    Air.Pressurer.Scaled
##      2%    39%    Hyd.Pressure2
##            29%    PC.Volume
##             1%    Brand.Code.Encoded
##            31%    Filler.Level
##            42%    MFR
##            23%    Hyd.Pressure4
##            39%    Density
##             4%    PSC.Fill
##            24%    Pressure.Setpoint
##            11%    Brand.Code.D
##             7%    Carb.Pressure
##             4%    Brand.Code.B
##             3%    PSC
##             2%    PSC.CO2
##             2%    Brand.Code.A

Session Details

pander::pander(sessionInfo())

R version 4.5.2 (2025-10-31)

Platform: aarch64-apple-darwin20

locale: en_US.UTF-8||en_US.UTF-8||en_US.UTF-8||C||en_US.UTF-8||en_US.UTF-8

attached base packages: parallel, stats, graphics, grDevices, utils, datasets, methods and base

other attached packages: pander(v.0.6.6), conflicted(v.1.2.0), kableExtra(v.1.4.0), doParallel(v.1.0.17), iterators(v.1.0.14), foreach(v.1.5.2), earth(v.5.3.5), plotmo(v.3.7.0), plotrix(v.3.8-14), Formula(v.1.2-5), mclust(v.6.1.2), mixtools(v.2.0.0.1), missForestPredict(v.1.0.1), missForest(v.1.6.1), caret(v.7.0-1), lattice(v.0.22-7), car(v.3.1-3), carData(v.3.0-5), e1071(v.1.7-17), FSA(v.0.10.1), rstatix(v.0.7.3), naniar(v.1.1.0), corrplot(v.0.95), openxlsx(v.4.2.8.1), lubridate(v.1.9.5), forcats(v.1.0.1), stringr(v.1.6.0), dplyr(v.1.2.0), purrr(v.1.2.1), readr(v.2.1.6), tidyr(v.1.3.2), tibble(v.3.3.1), ggplot2(v.4.0.2) and tidyverse(v.2.0.0)

loaded via a namespace (and not attached): RColorBrewer(v.1.1-3), rstudioapi(v.0.18.0), jsonlite(v.2.0.0), magrittr(v.2.0.4), dunn.test(v.1.3.7), elasticnet(v.1.3), farver(v.2.1.2), rmarkdown(v.2.30), lars(v.1.3), vctrs(v.0.7.2), memoise(v.2.0.1), htmltools(v.0.5.9), itertools(v.0.1-3), curl(v.7.0.0), broom(v.1.0.12), pROC(v.1.19.0.1), TTR(v.0.24.4), sass(v.0.4.10), parallelly(v.1.46.1), bslib(v.0.10.0), htmlwidgets(v.1.6.4), plyr(v.1.8.9), zoo(v.1.8-15), plotly(v.4.12.0), cachem(v.1.1.0), lifecycle(v.1.0.5), pkgconfig(v.2.0.3), Matrix(v.1.7-4), R6(v.2.6.1), fastmap(v.1.2.0), rbibutils(v.2.4.1), future(v.1.69.0), digest(v.0.6.39), colorspace(v.2.1-2), textshaping(v.1.0.4), labeling(v.0.4.3), randomForest(v.4.7-1.2), gbm(v.2.2.3), timechange(v.0.4.0), httr(v.1.4.7), abind(v.1.4-8), compiler(v.4.5.2), rngtools(v.1.5.2), proxy(v.0.4-29), withr(v.3.0.2), tseries(v.0.10-60), S7(v.0.2.1), backports(v.1.5.0), MASS(v.7.3-65), lava(v.1.8.2), ModelMetrics(v.1.2.2.2), tools(v.4.5.2), lmtest(v.0.9-40), ranger(v.0.18.0), otel(v.0.2.0), quantmod(v.0.4.28), zip(v.2.3.3), visdat(v.0.6.0), future.apply(v.1.20.1), nnet(v.7.3-20), quadprog(v.1.5-8), glue(v.1.8.0), nlme(v.3.1-168), grid(v.4.5.2), Cubist(v.0.6.0), reshape2(v.1.4.5), generics(v.0.1.4), recipes(v.1.3.1), gtable(v.0.3.6), tzdb(v.0.5.0), class(v.7.3-23), data.table(v.1.18.4), hms(v.1.1.4), xml2(v.1.5.2), pillar(v.1.11.1), splines(v.4.5.2), survival(v.3.8-6), tidyselect(v.1.2.1), knitr(v.1.51), urca(v.1.3-4), svglite(v.2.2.2), forecast(v.9.0.0), stats4(v.4.5.2), xfun(v.0.56), pls(v.2.9-0), hardhat(v.1.4.2), timeDate(v.4052.112), stringi(v.1.8.7), lazyeval(v.0.2.2), yaml(v.2.3.12), evaluate(v.1.0.5), codetools(v.0.2-20), kernlab(v.0.9-33), cli(v.3.6.5), rpart(v.4.1.24), systemfonts(v.1.3.1), Rdpack(v.2.6.5), segmented(v.2.2-1), jquerylib(v.0.1.4), Rcpp(v.1.1.1), globals(v.0.18.0), norm(v.1.0-11.1), fracdiff(v.1.5-3), gower(v.1.0.2), doRNG(v.1.8.6.3), listenv(v.0.10.0), viridisLite(v.0.4.3), ipred(v.0.9-15), xts(v.0.14.1), scales(v.1.4.0), prodlim(v.2025.04.28) and rlang(v.1.1.7)

---

1. What is the pH of foods? https://www.food-info.net/uk/qa/qa-fp65.htm↩︎

2. Tuzen MjF. (2025). Handling Misssing Data in R: A Comprehensive Guide. https://www.r-bloggers.com/2025/08/handling-missing-data-in-r-a-comprehensive-guide/↩︎

3. Aleksic D. (2023). A novel test of missing completely at random. https://arxiv.org/abs/2310.19189↩︎

4. Gaussian mixture models fit data to a mixture of univariate Gaussian (normal) distributions. The normalmixEM() function in the mixtools R package uses expectation maximization (EM) to estimate the mixing proportions of each component distribution.

   Benaglia T, Chauveau D, Hunter DR, and Young DS. mixtools: An R Package for Analyzing Finite Mixture Models. https://cran.r-project.org/web/packages/mixtools/vignettes/mixtools.pdf↩︎

5. From a data visualization perspective, red and green are not an ideal color combination because individuals with red-green color blindness cannot differentiate these colors. However, the data object for the GMM model that is produced by the normalmixEM() function is not compatible with ggplot and needs to be plotted using the base R plot() function, which is not straightforward to change plot colors.↩︎

6. Zumel N. (2017). Partial pooling for lower variance variable encoding. https://winvector.github.io/PartialPooling_R/PartialPooling_R.html↩︎

7. Mozumdar A. (2020). A guide to encoding categorical features using R. https://www.r-bloggers.com/2020/02/a-guide-to-encoding-categorical-features-using-r/↩︎