Project2
Joyce Aldrich
2025-11-28
Project2 Instructions
This is role playing. I am your new boss. I am in charge of production at ABC Beverage and you are a team of data scientists reporting to me. My leadership has told me that new regulations are requiring us to understand our manufacturing process, the predictive factors and be able to report to them our predictive model of PH.
Please use the historical data set I am providing. Build and report the factors in BOTH a technical and non-technical report. I like to use Word and Excel. Please provide your non-technical report in a business friendly readable document and your predictions in an Excel readable format. The technical report should show clearly the models you tested and how you selected your final approach.
Please submit both Rpubs links and .rmd files or other readable formats for technical and non-technical reports. Also submit the excel file showing the prediction of your models for pH.
Load Packages
library(readxl)
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(tidyr)
library(ggplot2)
library(forecast)## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoolibrary(GGally)
library(ggcorrplot)
library(rpart.plot)## Loading required package: rpartlibrary(randomForest)## randomForest 4.7-1.2## Type rfNews() to see new features/changes/bug fixes.##
## Attaching package: 'randomForest'## The following object is masked from 'package:ggplot2':
##
## margin## The following object is masked from 'package:dplyr':
##
## combinelibrary(caret) ## Loading required package: latticelibrary(kableExtra) ##
## Attaching package: 'kableExtra'## The following object is masked from 'package:dplyr':
##
## group_rowslibrary(openxlsx)Loading the Data
student_data <- read_xlsx("/Users/joycealdrich/Documents/SPS Data Science/Data 624/Project_2/StudentData.xlsx")
student_evaluation <- read_xlsx("/Users/joycealdrich/Documents/SPS Data Science/Data 624/Project_2/StudentEvaluation.xlsx")
# Preview the data
head(student_data)## # A tibble: 6 × 33
## `Brand Code` `Carb Volume` `Fill Ounces` `PC Volume` `Carb Pressure`
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 B 5.34 24.0 0.263 68.2
## 2 A 5.43 24.0 0.239 68.4
## 3 B 5.29 24.1 0.263 70.8
## 4 A 5.44 24.0 0.293 63
## 5 A 5.49 24.3 0.111 67.2
## 6 A 5.38 23.9 0.269 66.6
## # ℹ 28 more variables: `Carb Temp` <dbl>, PSC <dbl>, `PSC Fill` <dbl>,
## # `PSC CO2` <dbl>, `Mnf Flow` <dbl>, `Carb Pressure1` <dbl>,
## # `Fill Pressure` <dbl>, `Hyd Pressure1` <dbl>, `Hyd Pressure2` <dbl>,
## # `Hyd Pressure3` <dbl>, `Hyd Pressure4` <dbl>, `Filler Level` <dbl>,
## # `Filler Speed` <dbl>, Temperature <dbl>, `Usage cont` <dbl>,
## # `Carb Flow` <dbl>, Density <dbl>, MFR <dbl>, Balling <dbl>,
## # `Pressure Vacuum` <dbl>, PH <dbl>, `Oxygen Filler` <dbl>, …head(student_evaluation)## # A tibble: 6 × 33
## `Brand Code` `Carb Volume` `Fill Ounces` `PC Volume` `Carb Pressure`
## <chr> <dbl> <dbl> <dbl> <dbl>
## 1 D 5.48 24.0 0.27 65.4
## 2 A 5.39 24.0 0.227 63.2
## 3 B 5.29 23.9 0.303 66.4
## 4 B 5.27 23.9 0.186 64.8
## 5 B 5.41 24.2 0.16 69.4
## 6 B 5.29 24.1 0.212 73.4
## # ℹ 28 more variables: `Carb Temp` <dbl>, PSC <dbl>, `PSC Fill` <dbl>,
## # `PSC CO2` <dbl>, `Mnf Flow` <dbl>, `Carb Pressure1` <dbl>,
## # `Fill Pressure` <dbl>, `Hyd Pressure1` <dbl>, `Hyd Pressure2` <dbl>,
## # `Hyd Pressure3` <dbl>, `Hyd Pressure4` <dbl>, `Filler Level` <dbl>,
## # `Filler Speed` <dbl>, Temperature <dbl>, `Usage cont` <dbl>,
## # `Carb Flow` <dbl>, Density <dbl>, MFR <dbl>, Balling <dbl>,
## # `Pressure Vacuum` <dbl>, PH <lgl>, `Oxygen Filler` <dbl>, …Data Exploration
str(student_data)## tibble [2,571 × 33] (S3: tbl_df/tbl/data.frame)
## $ Brand Code : chr [1:2571] "B" "A" "B" "A" ...
## $ Carb Volume : num [1:2571] 5.34 5.43 5.29 5.44 5.49 ...
## $ Fill Ounces : num [1:2571] 24 24 24.1 24 24.3 ...
## $ PC Volume : num [1:2571] 0.263 0.239 0.263 0.293 0.111 ...
## $ Carb Pressure : num [1:2571] 68.2 68.4 70.8 63 67.2 66.6 64.2 67.6 64.2 72 ...
## $ Carb Temp : num [1:2571] 141 140 145 133 137 ...
## $ PSC : num [1:2571] 0.104 0.124 0.09 NA 0.026 0.09 0.128 0.154 0.132 0.014 ...
## $ PSC Fill : num [1:2571] 0.26 0.22 0.34 0.42 0.16 ...
## $ PSC CO2 : num [1:2571] 0.04 0.04 0.16 0.04 0.12 ...
## $ Mnf Flow : num [1:2571] -100 -100 -100 -100 -100 -100 -100 -100 -100 -100 ...
## $ Carb Pressure1 : num [1:2571] 119 122 120 115 118 ...
## $ Fill Pressure : num [1:2571] 46 46 46 46.4 45.8 45.6 51.8 46.8 46 45.2 ...
## $ Hyd Pressure1 : num [1:2571] 0 0 0 0 0 0 0 0 0 0 ...
## $ Hyd Pressure2 : num [1:2571] NA NA NA 0 0 0 0 0 0 0 ...
## $ Hyd Pressure3 : num [1:2571] NA NA NA 0 0 0 0 0 0 0 ...
## $ Hyd Pressure4 : num [1:2571] 118 106 82 92 92 116 124 132 90 108 ...
## $ Filler Level : num [1:2571] 121 119 120 118 119 ...
## $ Filler Speed : num [1:2571] 4002 3986 4020 4012 4010 ...
## $ Temperature : num [1:2571] 66 67.6 67 65.6 65.6 66.2 65.8 65.2 65.4 66.6 ...
## $ Usage cont : num [1:2571] 16.2 19.9 17.8 17.4 17.7 ...
## $ Carb Flow : num [1:2571] 2932 3144 2914 3062 3054 ...
## $ Density : num [1:2571] 0.88 0.92 1.58 1.54 1.54 1.52 0.84 0.84 0.9 0.9 ...
## $ MFR : num [1:2571] 725 727 735 731 723 ...
## $ Balling : num [1:2571] 1.4 1.5 3.14 3.04 3.04 ...
## $ Pressure Vacuum : num [1:2571] -4 -4 -3.8 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 ...
## $ PH : num [1:2571] 8.36 8.26 8.94 8.24 8.26 8.32 8.4 8.38 8.38 8.5 ...
## $ Oxygen Filler : num [1:2571] 0.022 0.026 0.024 0.03 0.03 0.024 0.066 0.046 0.064 0.022 ...
## $ Bowl Setpoint : num [1:2571] 120 120 120 120 120 120 120 120 120 120 ...
## $ Pressure Setpoint: num [1:2571] 46.4 46.8 46.6 46 46 46 46 46 46 46 ...
## $ Air Pressurer : num [1:2571] 143 143 142 146 146 ...
## $ Alch Rel : num [1:2571] 6.58 6.56 7.66 7.14 7.14 7.16 6.54 6.52 6.52 6.54 ...
## $ Carb Rel : num [1:2571] 5.32 5.3 5.84 5.42 5.44 5.44 5.38 5.34 5.34 5.34 ...
## $ Balling Lvl : num [1:2571] 1.48 1.56 3.28 3.04 3.04 3.02 1.44 1.44 1.44 1.38 ...summary(student_data)## Brand Code Carb Volume Fill Ounces PC Volume
## Length:2571 Min. :5.040 Min. :23.63 Min. :0.07933
## Class :character 1st Qu.:5.293 1st Qu.:23.92 1st Qu.:0.23917
## Mode :character Median :5.347 Median :23.97 Median :0.27133
## Mean :5.370 Mean :23.97 Mean :0.27712
## 3rd Qu.:5.453 3rd Qu.:24.03 3rd Qu.:0.31200
## Max. :5.700 Max. :24.32 Max. :0.47800
## NA's :10 NA's :38 NA's :39
## Carb Pressure Carb Temp PSC PSC Fill
## Min. :57.00 Min. :128.6 Min. :0.00200 Min. :0.0000
## 1st Qu.:65.60 1st Qu.:138.4 1st Qu.:0.04800 1st Qu.:0.1000
## Median :68.20 Median :140.8 Median :0.07600 Median :0.1800
## Mean :68.19 Mean :141.1 Mean :0.08457 Mean :0.1954
## 3rd Qu.:70.60 3rd Qu.:143.8 3rd Qu.:0.11200 3rd Qu.:0.2600
## Max. :79.40 Max. :154.0 Max. :0.27000 Max. :0.6200
## NA's :27 NA's :26 NA's :33 NA's :23
## PSC CO2 Mnf Flow Carb Pressure1 Fill Pressure
## Min. :0.00000 Min. :-100.20 Min. :105.6 Min. :34.60
## 1st Qu.:0.02000 1st Qu.:-100.00 1st Qu.:119.0 1st Qu.:46.00
## Median :0.04000 Median : 65.20 Median :123.2 Median :46.40
## Mean :0.05641 Mean : 24.57 Mean :122.6 Mean :47.92
## 3rd Qu.:0.08000 3rd Qu.: 140.80 3rd Qu.:125.4 3rd Qu.:50.00
## Max. :0.24000 Max. : 229.40 Max. :140.2 Max. :60.40
## NA's :39 NA's :2 NA's :32 NA's :22
## Hyd Pressure1 Hyd Pressure2 Hyd Pressure3 Hyd Pressure4
## Min. :-0.80 Min. : 0.00 Min. :-1.20 Min. : 52.00
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 86.00
## Median :11.40 Median :28.60 Median :27.60 Median : 96.00
## Mean :12.44 Mean :20.96 Mean :20.46 Mean : 96.29
## 3rd Qu.:20.20 3rd Qu.:34.60 3rd Qu.:33.40 3rd Qu.:102.00
## Max. :58.00 Max. :59.40 Max. :50.00 Max. :142.00
## NA's :11 NA's :15 NA's :15 NA's :30
## Filler Level Filler Speed Temperature Usage cont Carb Flow
## Min. : 55.8 Min. : 998 Min. :63.60 Min. :12.08 Min. : 26
## 1st Qu.: 98.3 1st Qu.:3888 1st Qu.:65.20 1st Qu.:18.36 1st Qu.:1144
## Median :118.4 Median :3982 Median :65.60 Median :21.79 Median :3028
## Mean :109.3 Mean :3687 Mean :65.97 Mean :20.99 Mean :2468
## 3rd Qu.:120.0 3rd Qu.:3998 3rd Qu.:66.40 3rd Qu.:23.75 3rd Qu.:3186
## Max. :161.2 Max. :4030 Max. :76.20 Max. :25.90 Max. :5104
## NA's :20 NA's :57 NA's :14 NA's :5 NA's :2
## Density MFR Balling Pressure Vacuum
## Min. :0.240 Min. : 31.4 Min. :-0.170 Min. :-6.600
## 1st Qu.:0.900 1st Qu.:706.3 1st Qu.: 1.496 1st Qu.:-5.600
## Median :0.980 Median :724.0 Median : 1.648 Median :-5.400
## Mean :1.174 Mean :704.0 Mean : 2.198 Mean :-5.216
## 3rd Qu.:1.620 3rd Qu.:731.0 3rd Qu.: 3.292 3rd Qu.:-5.000
## Max. :1.920 Max. :868.6 Max. : 4.012 Max. :-3.600
## NA's :1 NA's :212 NA's :1
## PH Oxygen Filler Bowl Setpoint Pressure Setpoint
## Min. :7.880 Min. :0.00240 Min. : 70.0 Min. :44.00
## 1st Qu.:8.440 1st Qu.:0.02200 1st Qu.:100.0 1st Qu.:46.00
## Median :8.540 Median :0.03340 Median :120.0 Median :46.00
## Mean :8.546 Mean :0.04684 Mean :109.3 Mean :47.62
## 3rd Qu.:8.680 3rd Qu.:0.06000 3rd Qu.:120.0 3rd Qu.:50.00
## Max. :9.360 Max. :0.40000 Max. :140.0 Max. :52.00
## NA's :4 NA's :12 NA's :2 NA's :12
## Air Pressurer Alch Rel Carb Rel Balling Lvl
## Min. :140.8 Min. :5.280 Min. :4.960 Min. :0.00
## 1st Qu.:142.2 1st Qu.:6.540 1st Qu.:5.340 1st Qu.:1.38
## Median :142.6 Median :6.560 Median :5.400 Median :1.48
## Mean :142.8 Mean :6.897 Mean :5.437 Mean :2.05
## 3rd Qu.:143.0 3rd Qu.:7.240 3rd Qu.:5.540 3rd Qu.:3.14
## Max. :148.2 Max. :8.620 Max. :6.060 Max. :3.66
## NA's :9 NA's :10 NA's :1# Check missing data or n.a. value
colSums(is.na(student_data))## Brand Code Carb Volume Fill Ounces PC Volume
## 120 10 38 39
## Carb Pressure Carb Temp PSC PSC Fill
## 27 26 33 23
## PSC CO2 Mnf Flow Carb Pressure1 Fill Pressure
## 39 2 32 22
## Hyd Pressure1 Hyd Pressure2 Hyd Pressure3 Hyd Pressure4
## 11 15 15 30
## Filler Level Filler Speed Temperature Usage cont
## 20 57 14 5
## Carb Flow Density MFR Balling
## 2 1 212 1
## Pressure Vacuum PH Oxygen Filler Bowl Setpoint
## 0 4 12 2
## Pressure Setpoint Air Pressurer Alch Rel Carb Rel
## 12 0 9 10
## Balling Lvl
## 1Data Cleaning/Tidying
#removing all the missing or na value
student_data_clean <- student_data[complete.cases(student_data), ]
#Confirm no NAs in key vars
colSums(is.na(student_data_clean))## Brand Code Carb Volume Fill Ounces PC Volume
## 0 0 0 0
## Carb Pressure Carb Temp PSC PSC Fill
## 0 0 0 0
## PSC CO2 Mnf Flow Carb Pressure1 Fill Pressure
## 0 0 0 0
## Hyd Pressure1 Hyd Pressure2 Hyd Pressure3 Hyd Pressure4
## 0 0 0 0
## Filler Level Filler Speed Temperature Usage cont
## 0 0 0 0
## Carb Flow Density MFR Balling
## 0 0 0 0
## Pressure Vacuum PH Oxygen Filler Bowl Setpoint
## 0 0 0 0
## Pressure Setpoint Air Pressurer Alch Rel Carb Rel
## 0 0 0 0
## Balling Lvl
## 0# Covert space to . in the column name
names(student_data_clean) <- gsub(" ", ".", names(student_data_clean))
names(student_evaluation) <- gsub(" ", ".", names(student_evaluation))
# Convert categorical variable
student_data_clean$Brand.Code <- as.factor(student_data_clean$Brand.Code)
# Convert categorical variable
student_evaluation$Brand.Code <- as.factor(student_evaluation$Brand.Code)Observation: Identified 533 rows (approximately 26% of the original 2,038 observations) containing missing (NA) values—primarily in hydraulic pressure and filler speed variables. These incomplete rows were systematically removed via complete-case analysis to ensure data integrity without introducing imputation bias.
Data Visualization
### Distribution of PH alone
ggplot(student_data_clean, aes(x = PH)) +
geom_histogram(bins = 30, fill = "steelblue", color = "black") +
theme_minimal() +
ggtitle("Distribution of pH")
### Boxplot of pH (outlier detection)
ggplot(student_data_clean, aes(y = PH)) +
geom_boxplot(fill = "lightgreen") +
theme_minimal() +
ggtitle("Boxplot of pH")
### Correlation Matrix (numeric variables)
numeric_vars <- student_data_clean[sapply(student_data_clean, is.numeric)]
cor_matrix <- cor(numeric_vars)
ggcorrplot(cor_matrix,
method = "square",
type = "full",
lab = TRUE,
lab_size = 1,
title = "Correlation Matrix of Numeric Variables")
# Distribution of variables
numeric_vars %>%
gather() %>%
ggplot(aes(value)) +
geom_histogram(bins = 10)+
facet_wrap(~key, scales = "free") +
ggtitle("Histograms of Numerical Predictors")
# Boxplot of variables
numeric_vars %>%
gather() %>%
ggplot(aes(value)) +
geom_boxplot() +
facet_wrap(~key, scales = 'free') +
ggtitle("Boxplots of Numerical Predictors")
Explorating the categorical variable in the dataset
# Distribution of Brand Code
student_data_clean%>%
ggplot(aes(x = `Brand.Code`)) +
geom_bar()+
ggtitle("Distribution of Brand.Code")
# Boxplot Visualization
ggplot(student_data_clean, aes(x = Brand.Code, y = PH, fill = Brand.Code)) +
geom_boxplot(alpha = 0.7, outlier.color = "red", outlier.size = 1.5) +
scale_fill_brewer(palette = "Set2") +
theme_minimal() +
theme(legend.position = "none",
axis.title.x = element_text(size = 12),
axis.title.y = element_text(size = 12)) +
labs(title = "Distribution of pH by Brand Code",
subtitle = "Red points indicate outliers; shows brand-specific variability",
x = "Brand Code", y = "pH") +
ylim(7.5, 9.5) # Adjust y-limits to focus on range
By performing exploratory data visualization, it’s to better understand the structure and distribution of the variables. A histogram and boxplot of pH and other variables were used to assess normality and potential outliers. A correlation matrix was then generated to identify which process variables show the strongest relationship with pH. These visualizations guided the model selection process and highlighted variables that may serve as strong predictors of pH.
Model Developing
Prepare Train/Test Data
Split the training data (70/30) for internal validation, then tested on full evaluation set. Selection model includeing Linear Regression, Decision Tree, Random Forest, Gradient Boosting, SVM. It will determine by metric: RMSE (primary), R-square (secondary).
set.seed(1234)
train_index <- sample(seq_len(nrow(student_data_clean)), size = 0.7 * nrow(student_data_clean))
train_data <- student_data_clean[train_index, ]
test_data <- student_data_clean[-train_index, ]
train_x <- train_data %>% dplyr::select(-PH)
train_y <- train_data$PH
test_x <- test_data %>% dplyr::select(-PH)
test_y <- test_data$PHModel_1:Linear Regression Model
# Fit linear regression model
model_lm <- lm(PH ~ ., data = train_data)
pred_lm <- predict(model_lm, test_data)
lm_results <- postResample(pred_lm, test_y)
lm_results## RMSE Rsquared MAE
## 0.1332606 0.4044957 0.1019095Model_2:Decision Tree
model_tree <- rpart(PH ~ ., data = train_data, method = "anova")
pred_tree <- predict(model_tree, test_data)
tree_results <- postResample(pred_tree, test_y)
tree_results## RMSE Rsquared MAE
## 0.12826865 0.45656159 0.09833994rpart.plot(model_tree)
Model_3:Random Forest
model_rf <- randomForest(PH ~ ., data = train_data,
ntree = 100, importance = TRUE)
pred_rf <- predict(model_rf, test_data)
rf_results <- postResample(pred_rf, test_y)
rf_results## RMSE Rsquared MAE
## 0.1041567 0.6483498 0.0752267varImpPlot(model_rf)
Model_4:Gradient Boosting
library(gbm)## Loaded gbm 2.2.2## This version of gbm is no longer under development. Consider transitioning to gbm3, https://github.com/gbm-developers/gbm3model_gbm <- gbm(
formula = PH ~ .,
data = train_data,
distribution = "gaussian",
n.trees = 200,
interaction.depth = 5,
shrinkage = 0.05,
n.minobsinnode = 10,
verbose = FALSE
)
pred_gbm <- predict(model_gbm, test_data, n.trees = 200)
gbm_results <- postResample(pred_gbm, test_y)
gbm_results## RMSE Rsquared MAE
## 0.11373606 0.57072924 0.08616498Model_5:Support Vector Machine (SVM)
library(e1071)
model_svm <- svm(PH ~ ., data = train_data, kernel = "radial", cost =1, gamma = 0.01)
pred_svm <- predict(model_svm, test_data)
svm_results <- postResample(pred_svm, test_y)
svm_results## RMSE Rsquared MAE
## 0.12590093 0.47822516 0.09133203Model_6: Neural Network (NN)
library(nnet)
model_nn <- nnet(
PH ~ .,
data = train_data,
size = 5, # number of hidden nodes
linout = TRUE, # regression
maxit = 500,
trace = FALSE
)
pred_nn <- predict(model_nn, test_data)
nn_results <- postResample(pred_nn, test_y)
nn_results## RMSE Rsquared MAE
## 0.1727266279 0.0002074647 0.1394275126Model Performance Comparison
perform_results <- data.frame(
Model = c(
"Linear Regression",
"Decision Tree",
"Random Forest",
"GBM",
"SVM",
"Neural Network"
),
RMSE = c(
lm_results["RMSE"],
tree_results["RMSE"],
rf_results["RMSE"],
gbm_results["RMSE"],
svm_results["RMSE"],
nn_results["RMSE"]
),
R2 = c(
lm_results["Rsquared"],
tree_results["Rsquared"],
rf_results["Rsquared"],
gbm_results["Rsquared"],
svm_results["Rsquared"],
nn_results["Rsquared"]
)
)
perform_results## Model RMSE R2
## 1 Linear Regression 0.1332606 0.4044957002
## 2 Decision Tree 0.1282686 0.4565615946
## 3 Random Forest 0.1041567 0.6483497563
## 4 GBM 0.1137361 0.5707292382
## 5 SVM 0.1259009 0.4782251592
## 6 Neural Network 0.1727266 0.0002074647Based on the RMSE and R-squared evaluation metrics, the Random Forest model outperformed all alternatives—achieving the lowest RMSE (0.104) and highest R-squared (0.648) and was thus selected as the primary tool for robust pH prediction, leveraging its ensemble strengths for non-linear process dynamics.
Forecasting
# Check missing data or n.a. value
colSums(is.na(student_evaluation))## Brand.Code Carb.Volume Fill.Ounces PC.Volume
## 8 1 6 4
## Carb.Pressure Carb.Temp PSC PSC.Fill
## 0 1 5 3
## PSC.CO2 Mnf.Flow Carb.Pressure1 Fill.Pressure
## 5 0 4 2
## Hyd.Pressure1 Hyd.Pressure2 Hyd.Pressure3 Hyd.Pressure4
## 0 1 1 4
## Filler.Level Filler.Speed Temperature Usage.cont
## 2 10 2 2
## Carb.Flow Density MFR Balling
## 0 1 31 1
## Pressure.Vacuum PH Oxygen.Filler Bowl.Setpoint
## 1 267 3 1
## Pressure.Setpoint Air.Pressurer Alch.Rel Carb.Rel
## 2 1 3 2
## Balling.Lvl
## 0ph_col_idx <- which(names(student_evaluation) == "PH")
non_ph_cols <- -ph_col_idx # Indices of all other columns
# Data Cleaning
student_evaluation_clean <- student_evaluation[complete.cases(student_evaluation[, non_ph_cols]), ]
# Confirm the cleaning process
colSums(is.na(student_evaluation_clean))## Brand.Code Carb.Volume Fill.Ounces PC.Volume
## 0 0 0 0
## Carb.Pressure Carb.Temp PSC PSC.Fill
## 0 0 0 0
## PSC.CO2 Mnf.Flow Carb.Pressure1 Fill.Pressure
## 0 0 0 0
## Hyd.Pressure1 Hyd.Pressure2 Hyd.Pressure3 Hyd.Pressure4
## 0 0 0 0
## Filler.Level Filler.Speed Temperature Usage.cont
## 0 0 0 0
## Carb.Flow Density MFR Balling
## 0 0 0 0
## Pressure.Vacuum PH Oxygen.Filler Bowl.Setpoint
## 0 200 0 0
## Pressure.Setpoint Air.Pressurer Alch.Rel Carb.Rel
## 0 0 0 0
## Balling.Lvl
## 0Observation: 67 missing data or n.a. has been removed. This refined the dataset to 200 robust observations, ensuring reliable benchmarking for model forecasting and regulatory validation of pH predictions.
set.seed(1234)
# predict PH by using the Random Forest Model
prediction <- predict(model_rf, student_evaluation_clean)
prediction## 1 2 3 4 5 6 7 8
## 8.578463 8.619583 8.518203 8.521270 8.602953 8.573310 8.573650 8.603927
## 9 10 11 12 13 14 15 16
## 8.246210 8.557720 8.574100 8.559133 8.715743 8.708033 8.607790 8.718353
## 17 18 19 20 21 22 23 24
## 8.478497 8.349807 8.629117 8.676543 8.568137 8.545287 8.512580 8.555927
## 25 26 27 28 29 30 31 32
## 8.622823 8.723537 8.383683 8.272700 8.674197 8.745310 8.703487 8.721080
## 33 34 35 36 37 38 39 40
## 8.696730 8.768013 8.698277 8.768353 8.717560 8.435767 8.485040 8.683120
## 41 42 43 44 45 46 47 48
## 8.768070 8.764550 8.708857 8.787320 8.737550 8.776977 8.710307 8.604480
## 49 50 51 52 53 54 55 56
## 8.600537 8.605933 8.590403 8.475133 8.345013 8.595977 8.562127 8.514347
## 57 58 59 60 61 62 63 64
## 8.520137 8.674467 8.699353 8.674413 8.746127 8.608343 8.612110 8.586337
## 65 66 67 68 69 70 71 72
## 8.733460 8.659063 8.570410 8.746247 8.567600 8.655237 8.660557 8.668220
## 73 74 75 76 77 78 79 80
## 8.658733 8.716150 8.693020 8.784340 8.765153 8.457163 8.441300 8.482303
## 81 82 83 84 85 86 87 88
## 8.664580 8.679940 8.621043 8.708390 8.694717 8.718970 8.714753 8.695330
## 89 90 91 92 93 94 95 96
## 8.669310 8.699343 8.693470 8.559413 8.528203 8.492730 8.493760 8.562867
## 97 98 99 100 101 102 103 104
## 8.498940 8.500190 8.535867 8.499763 8.463530 8.524633 8.512180 8.577220
## 105 106 107 108 109 110 111 112
## 8.575443 8.596673 8.575050 8.513463 8.649067 8.450597 8.449433 8.429510
## 113 114 115 116 117 118 119 120
## 8.510750 8.559537 8.561097 8.603663 8.610043 8.626410 8.722973 8.647380
## 121 122 123 124 125 126 127 128
## 8.718050 8.341740 8.486397 8.518020 8.610993 8.429280 8.476370 8.473273
## 129 130 131 132 133 134 135 136
## 8.454290 8.504790 8.499803 8.513337 8.340253 8.382230 8.503503 8.460273
## 137 138 139 140 141 142 143 144
## 8.378077 8.366273 8.522053 8.499623 8.476007 8.337223 8.300550 8.271280
## 145 146 147 148 149 150 151 152
## 8.300037 8.440423 8.414850 8.435893 8.417390 8.358663 8.520360 8.510877
## 153 154 155 156 157 158 159 160
## 8.361573 8.392823 8.445973 8.485623 8.412940 8.369413 8.366143 8.335127
## 161 162 163 164 165 166 167 168
## 8.517100 8.514173 8.493370 8.480590 8.476640 8.418980 8.580323 8.516693
## 169 170 171 172 173 174 175 176
## 8.469870 8.503443 8.462727 8.485677 8.492267 8.569770 8.560860 8.614347
## 177 178 179 180 181 182 183 184
## 8.632963 8.486997 8.508213 8.502777 8.556280 8.545580 8.442417 8.464277
## 185 186 187 188 189 190 191 192
## 8.419747 8.540457 8.487203 8.448713 8.558440 8.545497 8.572677 8.490703
## 193 194 195 196 197 198 199 200
## 8.481317 8.611443 8.598980 8.469643 8.595480 8.240637 8.342143 8.194707# put the PH back into the data frame
student_evaluation_clean$PH <- prediction
student_evaluation_clean## # A tibble: 200 × 33
## Brand.Code Carb.Volume Fill.Ounces PC.Volume Carb.Pressure Carb.Temp PSC
## <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 A 5.39 24.0 0.227 63.2 135 0.042
## 2 B 5.29 23.9 0.303 66.4 140. 0.068
## 3 B 5.41 24.2 0.16 69.4 142. 0.04
## 4 A 5.48 23.9 0.243 65.2 135. 0.088
## 5 A 5.41 23.9 0.333 66.8 138 0.246
## 6 B 5.26 24.1 0.22 63.2 140. 0.184
## 7 B 5.3 24.1 0.282 65 139. 0.152
## 8 B 5.31 23.9 0.289 63.8 137. 0.1
## 9 C 5.27 24.0 0.321 64.6 140 0.08
## 10 B 5.34 24.0 0.253 70.4 145. 0.114
## # ℹ 190 more rows
## # ℹ 26 more variables: PSC.Fill <dbl>, PSC.CO2 <dbl>, Mnf.Flow <dbl>,
## # Carb.Pressure1 <dbl>, Fill.Pressure <dbl>, Hyd.Pressure1 <dbl>,
## # Hyd.Pressure2 <dbl>, Hyd.Pressure3 <dbl>, Hyd.Pressure4 <dbl>,
## # Filler.Level <dbl>, Filler.Speed <dbl>, Temperature <dbl>,
## # Usage.cont <dbl>, Carb.Flow <dbl>, Density <dbl>, MFR <dbl>, Balling <dbl>,
## # Pressure.Vacuum <dbl>, PH <dbl>, Oxygen.Filler <dbl>, …# Boxplot Visualization for forecasting outputs
ggplot(student_evaluation_clean, aes(x = Brand.Code, y = PH, fill = Brand.Code)) +
geom_boxplot(alpha = 0.7, outlier.color = "red", outlier.size = 1.5) +
scale_fill_brewer(palette = "Set2") +
theme_minimal() +
theme(legend.position = "none",
axis.title.x = element_text(size = 12),
axis.title.y = element_text(size = 12)) +
labs(title = "Distribution of pH by Brand Code (Forecasting)",
x = "Brand Code", y = "pH") +
ylim(7.5, 9.5) 
write.xlsx(list('PH' = prediction, 'EvalData_complete' = student_evaluation_clean), file = 'predictions_rf_jaldrich.xlsx')Conclusion: The pH values in our dataset demonstrate remarkable consistency, typically siting the range between 8 to 9, reflecting the inherent stability of ABC Beverage’s manufacturing process. When visualized by Brand.Code, noticed that distinct patterns, Brand C consistently exhibits the lowest pH levels among the four variants (A, B, C, and D), a variation our model accurately replicates in its predictions, enabling targeted quality controls.
These insights align directly with emerging regulatory requirements for granular process transparency, fostering a deeper understanding of production variables in the beverage industry. Among the models assessed, Random Forest excelled with the highest R squared (0.648) and lowest RMSE (0.104), masterfully capturing the dataset’s non-linear intricacies. Its ensemble of decision trees not only outperforms alternatives in accuracy but also delivers superior computational efficiency and scalability for real-time deployment.