UofRStudentApplicant.Rmd

---
title: "Study Of Applicants Applying for Masters and PhD programs at UofR"
author: "Anik De, Babli Dey, Sharon Gilbert, Veronica Mata"
date: "2023-12-14"
output: pdf_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

<!-- importing student application data from the csv file "application_data_2015_2022.csv" -->

```{r importing student dataset, echo=FALSE}
applicantData<-read.csv("application_data_2015_2022.csv")
```

<!-- importing all the library here -->
```{r import require library, echo=FALSE, message=FALSE}
library(ggplot2)
library(dplyr)
library(caTools)
library(tidyr)

```

## Visualizations of EDA (will include unknown data) - Masters v/s PhD:



1.What is the annual total no. of applicants, which term recorded the highest and lowest number of applicants?

```{r no.Of applicants, echo=FALSE}

noOfApp <- applicantData %>% 
  group_by(Entry.Term, Degree) %>% 
  summarise(no_of_application = n(), .groups = 'drop')


ggplot(data = noOfApp, aes(x = Entry.Term, y = no_of_application, group = Degree, color = Degree)) + 
  geom_line() +
  geom_point() +
  xlab("Term") + ylab("Number of Applicants") +
  ggtitle("U of R Student Application - Number of Applicants by Program (2015 - 2022)") +
  theme(plot.title = element_text(size = 12, hjust = 0.5)) +
  scale_color_brewer(palette = "Set1")


```
```{r applicants by sub-program, echo=FALSE}

masters<-subset(applicantData,Degree=="Master's")

noOfAppM <- masters %>% 
  group_by(Entry.Term, Program..ASE.) %>% 
  summarise(no_of_application = n(), .groups = 'drop')


ggplot(data = noOfAppM, aes(x = Entry.Term, y = no_of_application, group = Program..ASE., color = Program..ASE.)) +
  geom_line() +
  geom_point() +
  xlab("Term") + ylab("Number of Applicants") +
  labs(color = "Program") +
  ggtitle("U of R Student Application - Number of Master's Sub-Program Applicants by Program (2015 - 2022)") +
  theme(plot.title = element_text(size = 8, hjust = 0.5), axis.text.x = element_text(angle = 30, hjust = 1))

  
```

```{r no.Of Applicants by Phd program, echo=FALSE}

phd<-subset(applicantData,Degree=="PhD")

#no.Of Applicants by Phd program
noOfAppP<-phd %>% group_by(Entry.Term,Program..ASE.) %>% 
  summarise(no_of_application = n(),
            .groups='drop')

#plotting
ggplot(data=noOfAppP, aes(x=Entry.Term, y = no_of_application, group = Program..ASE., color = Program..ASE.)) + 
  geom_line() +
  geom_point()+
  xlab("Term Year") + ylab("No.Of Applicants") + 
  labs(title = "U of R Student Application - Total No.of PhD Sub Program Applicants Every Fall Term By Program (2015 - 2022)",color = "Program") +
  theme(plot.title = element_text(size = 8, hjust = 0.5), axis.text.x = element_text(angle = 30, hjust = 1))
```

2.Identify the top 10 undergraduate institutes from which applicants are applying.

```{r masters top 10 undergrad institutes, echo=FALSE}

mTopIns <- masters %>% group_by(Institution.1.Name) %>% summarize(applicants=n(), 
            .groups = 'drop') %>% 
            arrange(desc(applicants)) %>%
            slice_head(n = 10)

ggplot(mTopIns, aes(x = reorder(Institution.1.Name, -applicants), y = applicants)) +
  geom_col(fill = "steelblue") +
  labs(title = "U of R Student Application - Top 10 Institution of Master Applicants (2015 - 2022)",
       x = "Institution",
       y = "Number of Applicants") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, hjust = 1),
        plot.title = element_text(size = 10))

```


```{r phd top 10 undergrad institutes, echo=FALSE}
pTopIns <- phd %>% group_by(Institution.1.Name) %>% summarize(applicants=n(), 
            .groups = 'drop') %>% 
            arrange(desc(applicants)) %>%
            slice_head(n = 10)

ggplot(pTopIns, aes(x = reorder(Institution.1.Name, -applicants), y = applicants)) +
  geom_col(fill = "skyblue") +
  labs(title = "U of R Student Application - Top 10 Institution of PhD Applicants (2015 - 2022)",
       x = "Institution",
       y = "Number of Applicants") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 60, hjust = 1),
        plot.title = element_text(size = 10))
```


3.How do the numbers of applicants vary by gender across different terms?

```{r masters applicants by gender, echo=FALSE}

# Grouping Term and Gender
mByGender <- masters %>% 
  group_by(Degree, Entry.Term, Sex) %>% 
  summarise(applicants = n(), .groups = 'drop')

# Create a grouped bar chart for No. Of Applicants for Master's by Gender and Term
ggplot(mByGender, aes(x = Entry.Term, y = applicants, fill = Sex)) +
  geom_bar(stat = "identity", position = "dodge") +
  labs(title = "U of R Student Application - No. Of Applicants for Master's by Gender and Term (2015 - 2022)",
       x = "Term (Years)",
       y = "Number of Applicants",
       fill = "Gender") +
  theme_minimal() +
  theme(plot.title = element_text(size = 10))


```

```{r phd applicants by gender, echo=FALSE}
pByGender<- phd %>% group_by(Degree,Entry.Term,Sex) %>% 
  summarise(applicants = n(),
            .groups='drop')

# Create a grouped bar chat for No. Of Applicants for PhD by Gender and Term
ggplot(pByGender, aes(x = Entry.Term, y = applicants, fill = Sex)) +
  geom_bar(stat = "identity", position = "dodge") +
  labs(title = "U of R Student Application - No. Of Applicants for PhD by Gender and Term (2015 - 2022)",
       x = "Term (Years)",
       y = "Number of Applicants",
       fill = "Gender") +
  theme_minimal() +
  theme(plot.title = element_text(size = 10))

```

4.What are the top 10 countries from which applicants have applied to the university?

```{r  masters top country of applicants, echo=FALSE}

# Master Applicants
appCountryM <- masters %>%
  group_by(Citizenship, Entry.Term) %>%
  summarise(Count = n(), .groups = "drop") %>%
  arrange(desc(Count)) %>%
  top_n(50, wt = Count)

# Create a stacked bar plot
ggplot(appCountryM, beside=TRUE, aes(x = reorder(Citizenship, Count), y = Count, fill = Entry.Term)) +
geom_bar(stat = "identity", position = "stack", width = 0.9) +
  
# Improve the appearance
  theme_minimal() +
  labs(title = "U of R Student Application - No. Of Master's Applicants based on Citizenship By Term (2015 - 2022)", 
  x = "Citizenship Status", 
  y = "No. Of Applicants") +
  
  coord_flip() +
  
  # Adjust text size and angle
  theme(axis.text.y = element_text(size = 10, angle = 45),
        plot.title = element_text(size = 10, hjust = 0.5),  # Center the title
        legend.title = element_text(size = 10),
        legend.text = element_text(size = 8))
```


```{r phdtop country of applicants, echo = FALSE}

#PhD Applicants
appCountryP <- phd %>%
  group_by(Citizenship, Entry.Term) %>%
  summarise(Count = n(), .groups = "drop") %>%
  arrange(desc(Count)) %>%
  top_n(50, wt = Count)

# Create a stacked bar plot
ggplot(appCountryM, beside = TRUE, aes(x = reorder(Citizenship, Count), y = Count, fill = Entry.Term)) +
  geom_bar(stat = "identity", position = "stack", width = 0.9) +
  
theme_minimal() +
  labs(title = "U of R Student Application - No. Of PhD Applicants based on Citizenship By Term (2015 - 2022)", 
       x = "Citizenship Status", 
       y = "No. Of Applicants") +
  
  coord_flip() +
  
  # Adjust text size and angle
  theme(axis.text.y = element_text(size = 10, angle = 45),
        plot.title = element_text(size = 10, hjust = 0.5),  # Center the title
        legend.title = element_text(size = 10),
        legend.text = element_text(size = 7.5))


```


5.Determine the total number of applicants who were placed on probation.

```{r  masters applicants placed on probation, echo=FALSE}

#Masters students
mProb <- subset(masters,Ever.Placed.on.Academic.Probation==1 | Ever.Placed.on.Academic.Probation==0)
mProb$probationStatus = ifelse(mProb$Ever.Placed.on.Academic.Probation==1,"probation","not on probation")

nProbM<-mProb %>% group_by(Entry.Term,probationStatus) %>% 
  summarise(applicant= n(),
            .groups='drop')

#no.Of Applicants by Masters program
ggplot(nProbM, aes(x=Entry.Term, y = applicant, color = probationStatus, group = probationStatus)) + 
    geom_line() +
    geom_point()+
    labs(color = "Ever Placed on Probation",x="Term Year",y="No.Of Applicants",fill="Probation Status") +
    ggtitle("U of R Student Application - Total No.of Masters Applicants By Probation Status and Term (2015 - 2022)") +
    theme(plot.title = element_text(size = 8), axis.text.x = element_text(angle = 30, hjust = 1))
```

```{r phd applicants placed on probation, echo=FALSE}

#PhD students
pProb <- subset(phd,Ever.Placed.on.Academic.Probation==1 | Ever.Placed.on.Academic.Probation==0)
pProb$probationStatus = ifelse(pProb$Ever.Placed.on.Academic.Probation==1,"probation","not on probation")

nProbP<-pProb %>% group_by(Entry.Term,probationStatus) %>% 
  summarise(applicant= n(),
            .groups='drop')

#no.Of Applicants by PhD program
ggplot(nProbP, aes(x=Entry.Term, y = applicant, color = probationStatus, group = probationStatus)) + 
    geom_line() +
    geom_point()+
    labs(color = "Ever Placed on Probation",x="Term Year",y="No.Of Applicants",fill="Probation Status") +
    ggtitle("U of R Student Application - Total No.of PhD Applicants By Probation Status and Term (2015 - 2022)") +
    theme(plot.title = element_text(size = 8), axis.text.x = element_text(angle = 30, hjust = 1))
```


6.Determine the total number of applicants who failed a course.

```{r  masters applicants failed a course, echo=FALSE}
#Masters students
mCourse <- subset(masters,Have.you.ever.failed.a.course.==1 | Have.you.ever.failed.a.course.==0)
mCourse$courseStatus = ifelse(mCourse$Have.you.ever.failed.a.course.==1,"failed","not failed")

nCourseM<-mCourse %>% group_by(Entry.Term,courseStatus) %>% 
  summarise(applicant= n(),
            .groups='drop')

#no.Of Applicants by Masters program
ggplot(nCourseM, aes(x=Entry.Term, y = applicant, color = courseStatus, group = courseStatus)) + 
    geom_line() +
    geom_point()+
    labs(color = "Ever failed a Test",x="Term Year",y="No.Of Applicants",fill="Course Status") +
    ggtitle("U of R Student Application - Total No.of Masters Applicants By Failed A course Status and Term (2015 - 2022)") +
    theme(plot.title = element_text(size = 8))

```


```{r phd applicants failed a course, echo=FALSE}
#PhD students
pCourse <- subset(phd,Have.you.ever.failed.a.course.==1 | Have.you.ever.failed.a.course.==0)
pCourse$courseStatus = ifelse(pCourse$Have.you.ever.failed.a.course.==1,"failed","not failed")

nCourseP<-pCourse %>% group_by(Entry.Term,courseStatus) %>% 
  summarise(applicant= n(),
            .groups='drop')

#no.Of Applicants by PhD program
ggplot(nCourseP, aes(x=Entry.Term, y = applicant, color = courseStatus, group = courseStatus)) + 
    geom_line() +
    geom_point()+
    labs(color = "Ever failed a Test",x="Term Year",y="No.Of Applicants",fill="Course Status") +
    ggtitle("U of R Student Application - Total No.of PhD Applicants By Failed A course Status and Term (2015 - 2022)") +
    theme(plot.title = element_text(size = 8))
```

## Data Cleaning: (code in rmd file)


1.Apply a filter to the dataset based on the 24 specified dimensions.

```{r  filter dimensions, echo=FALSE}

#Column to Remove
column_to_remove <- c("Any.Relatives.Listed.","Spouse.Studying.Applying","Current.Student.","Type","Citizenship2","Institution.3.Degree","Institution.3.Major","Institution.3.Location","Institution.3.Level.of.Study","Institution.3.Name","Job.3.Title","Institution.2.Degree","Institution.2.Major","Institution.2.Location","Institution.2.Level.of.Study","Institution.2.Name","Job.2.Title","Job.1.Title","Sub.Category","Previously.Applied.","How.Applicant.Heard...Other")

applicantData <- applicantData[, !colnames(applicantData) %in% column_to_remove]
column_names <- colnames(applicantData)
#print(column_names)

```


2.Change column names to lowercase and use underscores or simpler terms for better interpretability.
```{r  change the column names, echo=FALSE}
# Renaming column names
# Define new column names
new_column_names <- c(
  "reference", "program", "degree", "entry_term",
  "time_status", "decision", "sex", "birth_country",
  "age", "native_language", "citizenship_status",
  "citizenship", "failed_course", "academic_probation",
  "inst_1_name", "inst_1_location",
  "inst_1_study_level", "inst_1_degree",
  "inst_1_major", "currently_employed",
  "heard_about_UR", "other_schools_applying"
)

# Rename specified columns
colnames(applicantData)[colnames(applicantData) %in% c(
  "Ref", "Program..ASE.", "Degree", "Entry.Term",
  "Time.Status", "Decision.1", "Sex", "Birth.Country",
  "Age.at.App.Submission", "Native.Language", "Citizenship",
  "Citizenship1", "Have.you.ever.failed.a.course.",
  "Ever.Placed.on.Academic.Probation", "Institution.1.Name",
  "Institution.1.Location", "Institution.1.Level.of.Study",
  "Institution.1.Degree", "Institution.1.Major",
  "Currently.Employed.", "How.Applicant.Heard.About.UR",
  "Other.Schools.Applying.To"
)] <- new_column_names

#handling recommender 1,2,3 columns 
applicantData <- applicantData %>%
  mutate(num_two_recs = (Recommender.1.Relationship != "" & Recommender.2.Relationship != "") +
                        (Recommender.1.Relationship != "" & Recommender.3.Relationship != "") +
                        (Recommender.2.Relationship != "" & Recommender.3.Relationship != ""),
         num_three_recs = (Recommender.1.Relationship != "" & Recommender.2.Relationship != "" & Recommender.3.Relationship != ""))

#dropping recommender 1,2,3 columns 
column_to_remove <- c("Recommender.1.Relationship","Recommender.2.Relationship","Recommender.3.Relationship")
applicantData <- applicantData[, !colnames(applicantData) %in% column_to_remove]

# Updated column names
#print(colnames(applicantData))

# printing the number of missing values present in each column
#print("Count of missing values by column") 
empty_or_na_counts <- sapply(applicantData, function(x) sum(x == "" | is.na(x)))
sorted_counts <- sort(empty_or_na_counts, decreasing = TRUE)
#print(sorted_counts)

#applicantData
```


3.Segment the dataset into two parts: one for master's programs and another for Ph.D. programs.
```{r  segment dataset into masters and phd program, echo=FALSE}
# Create a DataFrame for applicants with a phd degree
phd_data <- subset(applicantData, degree == 'PhD')

# Save the master's dataset to a CSV file
#write.csv(phd_data, file = 'phd_data.csv', row.names = FALSE)

# Create a DataFrame for applicants with a master's degree
masters_data <- subset(applicantData, degree == "Master's")

# Save the master's dataset to a CSV file
#write.csv(masters_data, file = 'masters_data.csv', row.names = FALSE)


```
  
  
4.For empty values, categorize them as "Unknown" for categorical data. For age, fill in with the average age corresponding to the respective program.
```{r  deal with null values, echo=FALSE}
#mean age in masters
mean_age <- mean(masters_data$age , na.rm = TRUE)
masters_mean_age <- round(mean_age)
#cat("The masters mean age is:", masters_mean_age, "\n")

#mean age in phd
mean_age <- mean(phd_data$age , na.rm = TRUE)
phd_mean_age <- round(mean_age)
#cat("The phd mean age is:", phd_mean_age, "\n")

#Replacing missing age values with the rounded value in the masters_data 
masters_data$age <- ifelse(is.na(masters_data$age), masters_mean_age, masters_data$age)

#Replacing missing age values with the rounded value in the phd_data 
phd_data$age <- ifelse(is.na(phd_data$age), phd_mean_age, phd_data$age)

# Fill missing values in 'sex' column in masters_data with the mode
masters_data$sex[is.na(masters_data$sex) | masters_data$sex == ""] <- "unknown"

# Fill missing values in 'sex' column in phd_data with the mode
phd_data$sex[is.na(phd_data$sex) | phd_data$sex == ""] <- "unknown"

# Fill missing values in 'academic_probation' column in masters_data with the mode
masters_data$academic_probation[is.na(masters_data$academic_probation) | masters_data$academic_probation == ""] <- "unknown"

# Fill missing values in 'academic_probation' column in phd_data with the mode
phd_data$academic_probation[is.na(phd_data$academic_probation) | phd_data$academic_probation == ""] <- "unknown"

# Fill missing values in 'failed_course' column in masters_data with the mode
masters_data$failed_course [is.na(masters_data$failed_course ) | masters_data$failed_course  == ""] <- "unknown"

# Fill missing values in 'failed_course' column in phd_data with the mode
phd_data$failed_course [is.na(phd_data$failed_course ) | phd_data$failed_course  == ""] <- "unknown"


##HANDLING OTHER CATEGORICAL FEATURES
# Columns to replace missing values with 'unknown'
columns_to_replace <- c('time_status', 'decision', 'inst_1_name', 'inst_1_location', 'inst_1_study_level', 'inst_1_degree', 'inst_1_major')

# Replace missing values with 'unknown' in masters_data
masters_data[, columns_to_replace] <- lapply(masters_data[, columns_to_replace], function(x) ifelse(is.na(x) | x == "", "unknown", x))

# Replace missing values with 'unknown' in phd_data
phd_data[, columns_to_replace] <- lapply(phd_data[, columns_to_replace], function(x) ifelse(is.na(x) | x == "", "unknown", x))

# Replace missing values with 'unknown sources' in masters_data
masters_data$heard_about_UR <- ifelse(is.na(masters_data$heard_about_UR) | masters_data$heard_about_UR == "", "unknown", masters_data$heard_about_UR)

# Replace missing values with 'unknown sources' in phd_data
phd_data$heard_about_UR <- ifelse(is.na(phd_data$heard_about_UR) | phd_data$heard_about_UR == "", "unknown", phd_data$heard_about_UR)

# Columns to replace missing values with 'not mentioned'
columns_to_replace <- c('birth_country', 'other_schools_applying','native_language','citizenship_status','citizenship')

# Replace missing values with 'not mentioned' in masters_data
masters_data[, columns_to_replace] <- lapply(masters_data[, columns_to_replace], function(x) ifelse(is.na(x) | x == "", "unknown", x))

# Replace missing values with 'not mentioned' in phd_data
phd_data[, columns_to_replace] <- lapply(phd_data[, columns_to_replace], function(x) ifelse(is.na(x) | x == "", "unknown", x))

# Find unique values in the 'Num_Two_Recs' column
unique_values_Num_Two_Recs <- unique(masters_data$num_two_recs)

# Find unique values in the 'Num_Three_Recs' column
unique_values_Num_Three_Recs <- unique(masters_data$num_three_recs)

# Identify and replace missing values
missing_indices_Num_Two_Recs <- which(is.na(masters_data$num_two_recs))
missing_indices_Num_Three_Recs <- which(is.na(masters_data$num_three_recs))

# Replace missing values with any unique value from the respective columns
if (length(missing_indices_Num_Two_Recs) > 0) {
  masters_data$num_two_recs[missing_indices_Num_Two_Recs] <- unique_values_Num_Two_Recs[1]
}

if (length(missing_indices_Num_Three_Recs) > 0) {
  masters_data$num_three_recs[missing_indices_Num_Three_Recs] <- unique_values_Num_Three_Recs[1]
}

# Creating a column called accept_reject for masters and phd dataset
masters_data$decision_status<-ifelse(masters_data$decision=="Deny","deny",
                                   ifelse(masters_data$decision=="unknown","unknown",
                                          ifelse(masters_data$decision=="Withdraw","withdraw","accept")))

phd_data$decision_status<-ifelse(phd_data$decision=="Deny","deny",
                                   ifelse(phd_data$decision=="unknown","unknown",
                                          ifelse(phd_data$decision=="Withdraw","withdraw","accept")))

```

## Descriptive Analysis: Master's and PhD


1.Calculate the mean, variance, and standard deviation of age, and visualize the distribution using histograms and box plots.
```{r  descriptive analysis of age Masters - mean variance and standard deviation, echo=FALSE,warning=FALSE}

# mean , var, sd of age in masters dataset
mastMeanAge<- mean(masters_data$age)
mastVarAge<- var(masters_data$age)
mastSdAge<-sd(masters_data$age)

cat("The Mean age of Masters applicant is:", mastMeanAge)
cat("\nThe Variance in age of Masters applicant is:", mastVarAge)
cat("\nThe Standard Deviation in age of Masters applicant is:",mastSdAge)
```

```{r descriptive analysis of age Masters - histogram of age, echo=FALSE,warning=FALSE}
bin <-ceiling((log2(length(masters_data$age))) + 1)

ggplot(data = masters_data, aes(x=age)) + geom_histogram(
  bins = bin) + labs(x = 'age', y = 'frequency', title = "U of R Student Application - Histogram of Master's Applicant Age (2015 - 2022)" ) +
  geom_vline(xintercept =  mean(masters_data$age),col = "red") + 
  geom_vline(xintercept = median(masters_data$age), col = "blue") +
  annotate("text",x = 30, y = 8000 , label = substitute(paste(tilde(x), "=",m),list(m=sprintf("%.02f",median(masters_data$age)))),color = "blue") + 
  annotate("text",x = 30, y = 7000, label = substitute(paste(bar(x),"=",m),list(m=sprintf("%.02f", mean(masters_data$age)))),color = "red") + theme(plot.title = element_text(size = 10))
  
```

```{r descriptive analysis of age Masters - box plot of age, echo=FALSE,warning=FALSE}

ggplot(masters_data, aes(y = age,x =entry_term))+geom_boxplot(outlier.size = 1.5 )+labs(title = "U of R Student Application - Box Plot of Master's Applicant Age By Term (2015 - 2022)", x = "Term By Year", y = "Age")+theme(plot.title = element_text(size = 10))
```
```{r  descriptive analysis of age PhDs - mean variance and standard deviation, echo=FALSE}

# mean , var, sd of age in phd dataset
phdMeanAge<- mean(phd_data$age)
phdVarAge<- var(phd_data$age)
phdSdAge<-sd(phd_data$age)

cat("The Mean age of PhD applicant is:", phdMeanAge)
cat("\nThe Variance in age of PhD applicant is:",phdVarAge)
cat("\nThe Standard Deviation in age of PhD applicant is:",phdSdAge)

```

```{r descriptive analysis of age PhDs - histogram of age, echo=FALSE,warning=FALSE}
bin <-ceiling((log2(length(phd_data$age))) + 1)

ggplot(data = phd_data, aes(x=age)) + geom_histogram(
  bins = bin) + labs(x = 'age', y = 'frequency', title = "U of R Student Application - Histogram of PhD Applicant's Age (2015 - 2022)" ) +
  geom_vline(xintercept =  mean(phd_data$age),col = "red") + 
  geom_vline(xintercept = median(phd_data$age), col = "blue") +
  annotate("text",x = 30, y = 8000 , label = substitute(paste(tilde(x), "=",m),list(m=sprintf("%.02f",median(phd_data$age)))),color = "blue") + 
  annotate("text",x = 30, y = 7000, label = substitute(paste(bar(x),"=",m),list(m=sprintf("%.02f", mean(phd_data$age)))),color = "red") + theme(plot.title = element_text(size = 10))
  
```

```{r descriptive analysis of age PhDs - box plot of age, echo=FALSE,warning=FALSE}

ggplot(phd_data, aes(y = age,x=entry_term))+geom_boxplot(outlier.size = 1.5 )+labs(title = "U of R Student Application - Box Plot of PhD's Applicant Age By Term (2015 -2022)", x = "Term By Year", y = "Age")+theme(plot.title = element_text(size = 10))
```

2.Examine the acceptance rate based on gender across different terms.

```{r  master acceptance rate by gender, echo=FALSE,warning=FALSE}
#masters data
m_contingency_table <- table(masters_data$sex, masters_data$entry_term, masters_data$decision_status)
m_proportions_by_gender <- prop.table(m_contingency_table, margin = 1)
m_proportions_df <- as.data.frame(as.table(m_proportions_by_gender))

m_merged_proportions <- m_proportions_df %>%
  filter(Var3 == "accept", Var1 %in% c("M", "F")) %>%
  arrange(Var1)

ggplot(m_merged_proportions, aes(x = Var2, y = Freq , fill=Var1)) +
  geom_col(position = "fill")+ labs(title="U of R Student Application - Master's Acceptance Rate Based On Gender Across Terms (2015 - 2022)", x = "Term Year", y = "Proportion", fill="Gender") + theme(plot.title = element_text(size=8))

#print(m_merged_proportions)
```

```{r phd acceptance rate by gender, echo=FALSE,warning=FALSE }
#Phd data
p_contingency_table <- table(phd_data$sex, phd_data$entry_term, phd_data$decision_status)
p_proportions_by_gender <- prop.table(p_contingency_table, margin = 1)
p_proportions_df <- as.data.frame(as.table(p_proportions_by_gender))
p_merged_proportions <- p_proportions_df %>%
  filter(Var3 == "accept", Var1 %in% c("M", "F")) %>%
  arrange(Var1)

#print(p_merged_proportions)

ggplot(p_merged_proportions, aes(x = Var2, y = Freq , fill=Var1)) +
  geom_col(position = "fill")+ labs(title="U of R Student Application - PhD Acceptance Rate Based On Gender Across Terms (2015 - 2022)", x = "Term Year", y = "Proportion", fill="Gender") + theme(plot.title = element_text(size=8))

```


3.Explore the acceptance rate by country in relation to different terms.

```{r  acceptance rate by country, echo=FALSE,warning=FALSE}

#masters data
m_citizen_contingency_table <- table(masters_data$citizenship_status, masters_data$entry_term, masters_data$decision_status)
m_proportions_by_citizen <- prop.table(m_citizen_contingency_table, margin = 1)
m_citizen_proportions_df <- as.data.frame(as.table(m_proportions_by_citizen))

m_merged_citizen <- m_citizen_proportions_df %>%
  filter(Var3 == "accept", Var1 %in% c("FN", "US", "PR", "unknown")) %>%
  arrange(Var1)

#print(m_merged_citizen)

ggplot(m_merged_citizen, aes(x = Var2, y = Freq , fill=Var1)) +
  geom_col(position = "fill")+ labs(title="U of R Student Application - Master's Acceptance Rate Based On Citizenship (2015 - 2022)", x = "Term Year", y = "Proportion", fill="Citizenship Status") + theme(plot.title = element_text(size=9))


#Phd data
p_citizen_contingency_table <- table(phd_data$citizenship_status, phd_data$entry_term, phd_data$decision_status)
p_proportions_by_citizen <- prop.table(p_citizen_contingency_table, margin = 1)
p_citizen_proportions_df <- as.data.frame(as.table(p_proportions_by_citizen))
p_merged_citizen <- p_citizen_proportions_df %>%
  filter(Var3 == "accept") %>%
  filter(Var1 %in% c("FN", "US", "PR", "unknown")) %>%
  arrange(Var1)

#print(p_merged_citizen)

ggplot(p_merged_citizen, aes(x = Var2, y = Freq , fill=Var1)) +
  geom_col(position = "fill")+ labs(title="U of R Student Application - PhD Acceptance Rate Based On Citizenship (2015 - 2022)", x = "Term Year", y = "Proportion", fill="Citizenship Status") + theme(plot.title = element_text(size=9))

```
  
4.Investigate the acceptance decision for applicants who were placed on probation.

```{r  masters acceptance rate of probation applicants, echo=FALSE,warning=FALSE}

mProbAccept<- masters_data %>% filter(academic_probation==1)

mProAccG<- mProbAccept %>% group_by(decision_status,entry_term) %>% summarise(count=n(), .groups = 'drop')

ggplot(mProAccG, aes(x=entry_term , y=count,fill=decision_status)) +
  geom_col() +
labs(title = "U of R Student Application - Acceptance Decision of Master's Applicants On Academic Probation (2015 -2022)", x = "Term Year", y = "No. Of Applicants", fill="Decision Status") + theme(plot.title = element_text(size=8))

```

```{r  phd acceptance rate of probation applicants, echo=FALSE,warning=FALSE}
pProbAccept<- phd_data %>% filter(academic_probation==1)

pProAccG<- pProbAccept %>% group_by(decision_status,entry_term) %>% summarise(count=n(), .groups = 'drop')

ggplot(pProAccG, aes(x=entry_term , y=count,fill=decision_status)) +
  geom_col() +
labs(title = "U of R Student Application - Acceptance Decision of PhD's Applicants On Academic Probation (2015 -2022)", x = "Term Year", y = "No. Of Applicants", fill="Decision Status") + theme(plot.title = element_text(size=8))
```


5.Investigate the acceptance decision for applicants who failed a course.

```{r  masters acceptance rate applicants who failed a course, echo=FALSE,warning=FALSE}
mFailedc<- masters_data %>% filter(failed_course==1)

mFailedcTable <- mFailedc %>% group_by(decision_status,entry_term) %>% summarise(applicants=n(), .groups='drop') 

ggplot(mFailedcTable, aes(x=entry_term , y=applicants, fill=decision_status)) +
  geom_col() +
  labs(title = "U of R Student Application - Acceptance Decision of Master's Applicants who failed a course (2015 - 2022)", x = "Term Year", y = "No. Of Applicants", fill="Decision Status") + theme(plot.title = element_text(size=8))

```

```{r  phd acceptance rate applicants who failed a course, echo=FALSE,warning=FALSE}
pFailedc<- phd_data %>% filter(failed_course==1)

pFailedcTable <- pFailedc %>% group_by(decision_status,entry_term) %>% summarise(applicants=n(), .groups='drop') 

ggplot(pFailedcTable, aes(x=entry_term , y=applicants, fill=decision_status)) +
  geom_col() +
  labs(title = "U of R Student Application - Acceptance Decision of Master's Applicants who failed a course (2015 -2022)", x = "Term Year", y = "No. Of Applicants", fill="Decision Status") + theme(plot.title = element_text(size=8))
```


6.Investigate the age distribution between applicants who failed a course v/s applicants who did not fail a course.
```{r  age distribution failed vs not failed a course, echo=FALSE,warning=FALSE} 
# Function to see distributions
create_filtered_histogram <- function(data, plot_column, filter_column, filter_value, binwidth = 0.5, fill_color = "pink", text) {
  # Filter the data based on the filter_column and filter_value
  filtered_data <- data %>% filter(!!sym(filter_column) == filter_value)
  
  # Create the histogram using the filtered data
  ggplot(filtered_data, aes_string(x = plot_column)) +
    geom_histogram(binwidth = binwidth, fill = fill_color, color = "black") +
    theme_minimal() +
    labs(title = text, 
         x = plot_column, 
         y = "Frequency") +
    theme(axis.text.x = element_text(angle = 45, hjust = 1))+
    theme(plot.title = element_text(size = 8))
}


# To help respond 3rd sub question of th primary question
create_filtered_histogram(masters_data, "age", "failed_course", 0, 0.5, "green","U of R Student Application - Distribution of age of Master's Applicants Never Failed a Course (2015 - 2022)")
create_filtered_histogram(masters_data, "age", "failed_course", 1, 0.5, "yellow","U of R Student Application - Distribution of age of Master's Applicants Failed a Course (2015 - 2022)")


ggplot(applicantData, aes(x = degree, y = age)) +
  geom_boxplot() +
  theme_minimal() +
  labs(title = "U of R Student Application - Age Distribution by Degree (2015 - 2022)", 
       x = "Degree", 
       y = "Age at Application Submission") +
  theme(axis.text.x = element_text(angle = 45, hjust = 1))

```
_______________________________________


## Inferential Analysis:

1.Is there a notable distinction in age variance between applicants who have experienced course failure and those who haven't, considering each degree type?
$$
\begin{aligned}
H_0&:\text{There is no difference in the variance of ages between Master's applicants who have experienced course failure}\\
    &\text{and those who haven't. (i.e., the variances are equal)} \\
H_A&:\text{There is a significant difference in the variance of ages between Master's applicants}\\
&\text{who have experienced course failure and those who haven't.}
\end{aligned}
$$

```{r  age variance hypothesis test, echo=FALSE,warning=FALSE}
# For Master's applicants 
masters_failed <- masters_data$age[masters_data$failed_course == 1] 
masters_not_failed <- masters_data$age[masters_data$failed_course == 0] 
length(masters_failed) 
length(masters_not_failed) 

# Variance test for Master's applicants 
var.test(masters_failed, masters_not_failed) 

# For Ph.D. applicants 
phd_failed <- phd_data$age[phd_data$failed_course == 1] 
phd_not_failed <- phd_data$age[phd_data$failed_course == 0] 

# Variance test for Ph.D. applicants 
var.test(phd_failed, phd_not_failed)

```

\begin{equation}
\begin{split}
\text{Conclusion}: &\text{ Given that the p-value is much less than the significance level } \\
&(\alpha = 0.05), \text{ we reject the null hypothesis. This suggests that} \\
&\text{there is a statistically significant difference in the variance of the} \\
&\text{ages between Master’s applicants who have experienced course} \\
&\text{failure and those who haven’t.}
\end{split}
\end{equation}

_______________________________________



2. Is there a discernible difference in the average age between master's and Ph.D. students?


$$
\begin{aligned}
H_0&:\text{The average age of Master's students is equal to the average age of Ph.D. students. (no difference in means)}\\
H_A&:\text{The average age of Master's students is not equal to the average age of Ph.D. students.}\\
\end{aligned}
$$

```{r  age variance hypothesis test by program, echo=FALSE,warning=FALSE}

# T-test to compare average age 
t.test(masters_data$age, phd_data$age)
```

\begin{equation}
\begin{split}
Conclusion&: \text{The extremely small p-value (p < 2.2e-16) is much lower than our alpha level of significance } \\
&(\alpha = 0.05) \text{indicating that the difference in average ages between Master's and Ph.D. students} \\
&\text{is statistically significant. Therefore, we reject the null hypothesis, H0, which stated that we don’t} \\
&\text{have enough evidence to conclude that the average of Master’s students is equal} \\
&\text{ to the average of PhD students.}
\end{split}
\end{equation}


_______________________________________



3. Compare the acceptance rate for students who learned about the university through family/friends versus those who found it through an internet search.
$$
\begin{aligned}
H_0&:\text{Applicants who learnt about U of R through Family/Friend or}\\&\text{Internet Search is independent of Acceptance status }\\
H_A&:\text{Applicants who learnt about U of R through Family/Friend or}\\&\text{ Internet Search and Acceptance status are associated }\\
\end{aligned}
$$

```{r  hypothesis test based on how they hear about U of R, echo=FALSE,warning=FALSE}
#masters data
family_friend<- subset(masters_data, heard_about_UR=="Family/Friend")
n_accept_frnd_fam<-length(family_friend$heard_about_UR[family_friend$decision_status=="accept"])
n_not_accept_frnd_fam<-length(family_friend$heard_about_UR[family_friend$decision_status=="deny"])

internet_search<- subset(masters_data, heard_about_UR=="Internet search")
n_accept_internet<-length(internet_search$heard_about_UR[internet_search$decision_status=="accept"])
n_not_internet<-length(internet_search$heard_about_UR[internet_search$decision_status=="deny"])

chiMaster<-matrix(c(n_accept_frnd_fam,n_not_accept_frnd_fam, n_accept_internet, n_not_internet), nrow = 2, byrow = TRUE)
colnames(chiMaster) <- c("Accepted", "NotAccepted")
rownames(chiMaster) <- c("FamilyFriends", "InternetSearch")
print(chiMaster)

result <- chisq.test(chiMaster, correct = F)

print(result)

#phd data
family_friend_p<- subset(phd_data, heard_about_UR=="Family/Friend")
n_accept_frnd_fam_p<-length(family_friend_p$heard_about_UR[family_friend_p$decision_status=="accept"])
n_not_accept_frnd_fam_p<-length(family_friend_p$heard_about_UR[family_friend_p$decision_status=="deny"])

internet_search_p<- subset(phd_data, heard_about_UR=="Internet search")
n_accept_internet_p<-length(internet_search_p$heard_about_UR[internet_search_p$decision_status=="accept"])
n_not_internet_p<-length(internet_search_p$heard_about_UR[internet_search_p$decision_status=="deny"])

chiPhd<-matrix(c(n_accept_frnd_fam_p,n_not_accept_frnd_fam_p, n_accept_internet_p, n_not_internet_p), nrow = 2, byrow = TRUE)
colnames(chiPhd) <- c("Accepted", "NotAccepted")
rownames(chiPhd) <- c("FamilyFriends", "InternetSearch")
print(chiPhd)

result <- chisq.test(chiPhd, correct = F)

print(result)


```

\begin{equation}
\begin{aligned}
&\alpha = 0.05 \\
\text{Master Conclusion}: &\text{ Since the p-value is less than the significance level, we reject the null hypothesis} \\
&\text{and suggest that there is an association between how students learned about the university} \\
&\text{and the acceptance rate for the Master’s Program.} \\
\\
\text{PhD Conclusion}: &\text{ Since the p-value is greater than the significance level, we accept the null hypothesis} \\
&\text{and conclude that there is no association between how students learned about the university} \\
&\text{and the acceptance rate for the PhD program.}
\end{aligned}
\end{equation}

_______________________________________


## Logistic Regression:

1. Can we use factors such as age, citizenship, gender, recommender relationships, current employment status, and program choice to predict the likelihood of a candidate being accepted?
```{r merge data, echo=FALSE,warning=FALSE}
rows_to_keep_masters <- nrow(masters_data)
rows_to_keep_phd <- nrow(phd_data)


# Randomly sample rows from df1
reduced_masters <- sample_n(masters_data, size = rows_to_keep_masters)
reduced_phd <- sample_n(phd_data, size = rows_to_keep_phd )

# Merge the reduced df1 with df2
merged_data_masters_phd <- rbind(reduced_masters, reduced_phd)
```

```{r  logistic regression - preparing data, echo=FALSE}

merged_data_masters_phd <- na.omit(merged_data_masters_phd)
categorical_vars <- c("program", "degree", "entry_term", "time_status",
                      "sex","citizenship_status","failed_course",
                      "academic_probation",
                      "inst_1_degree","heard_about_UR")
#print(categorical_vars)
categorical_vars <- categorical_vars[categorical_vars %in% colnames(merged_data_masters_phd)]
print(categorical_vars)
merged_data_masters_phd[categorical_vars] <- lapply(merged_data_masters_phd[categorical_vars], factor)
```

```{r logistic regression - model building, echo=FALSE}
modelTrainingfeatures  <- select(merged_data_masters_phd, program, degree, entry_term, time_status,
               sex, citizenship_status, inst_1_degree, heard_about_UR,
               age, failed_course, academic_probation, decision_status)

modelTrainingfeatures$decision_status <- ifelse(merged_data_masters_phd$decision_status == "accept", 1, 0)


#Splitting the dataset into 70% Training and 30% Testing
set.seed(123) # for reproducible results
split <- sample.split(modelTrainingfeatures$decision_status, SplitRatio = 0.7)
train <- subset(modelTrainingfeatures, split == TRUE)
test <- subset(modelTrainingfeatures, split == FALSE)

```

```{r logistic regression - prediction and accuracy, echo=FALSE}
 model <- glm(decision_status ~ ., data = train, family = "binomial")
 print(summary(model))
  
  
 predictions <- predict(model, newdata = test, type = "response")
 predicted_classes <- ifelse(predictions > 0.50, 1, 0)
 # Confusion matrix for the test set
 conf_matrix <- table(Predicted = predicted_classes, Actual = test$decision_status)
 print(conf_matrix)
 # Calculate accuracy on the test set
 accuracy <- sum(diag(conf_matrix)) / sum(conf_matrix)
 print(paste("Accuracy:", accuracy))

```