Shaun_McKellarJr_HW4.Rmd

---
title: "R Notebook"
output: html_notebook
---

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```{r}
library(caret)
library(e1071)
library(rpart)
library(tidyverse)
library(rpart.plot)
library(readxl)
library(stats)
library(MASS)
library(Rcmdr)
library(neuralnet)
library(sensitivity)
```

```{r}
getwd()
```

```{r}
setwd("/Users/shaunmckellarjr/Desktop/SCM 651-Business Analytics/Week 4 HW")
```


```{r}
Universal_Bank_DS <- read_excel("/Users/shaunmckellarjr/Desktop/SCM 651-Business Analytics/Week 4 HW/universal_bank.xlsx")
```

```{r}
str(Universal_Bank_DS)
```

```{r}
summary(Universal_Bank_DS)
```

```{r}
logit_model <- glm(PersonalLoan ~ Age + Experience + Income + Family + CCAvg + Education + Mortgage + SecuritiesAccount + CDAccount + Online + CreditCard, 
                   data = Universal_Bank_DS, 
                   family = binomial(link = "logit"))
```

```{r}
summary(logit_model)
```

```{r}
logit_model_interactions <- glm(PersonalLoan ~ Income + Family + CCAvg + Education + SecuritiesAccount + CDAccount + Online + CreditCard +
                                  Income:Education + Family:CCAvg + Income:Family + CDAccount:SecuritiesAccount, 
                                data = Universal_Bank_DS, family = "binomial")
```

```{r}
summary(logit_model_interactions)
```

```{r}
plot(logit_model_interactions)
```

```{r}
plot(logit_model)
```


```{r}
# Probit Regression Model - Main Effects Only
probit_model_main <- glm(PersonalLoan ~ Age + Experience + Income + Family + CCAvg + Education + Mortgage + SecuritiesAccount + CDAccount + Online + CreditCard,
                         family = binomial(link = "probit"), 
                         data = Universal_Bank_DS)
```

```{r}
# Summary of Probit Model - Main Effects Only
summary(probit_model_main)
```

```{r}
# Including interactions in the probit model
interaction_model <- glm(PersonalLoan ~ Income + Family + CCAvg + Education + SecuritiesAccount +
                         CDAccount + Online + CreditCard +
                         Income:Education + Family:CCAvg + Income:Family + CDAccount:SecuritiesAccount,
                         family = "binomial", data = Universal_Bank_DS)

```


```{r}
# Summary of the probit interaction model
summary(interaction_model)
```

```{r}
# Building the final logistic regression model
final_model <- glm(PersonalLoan ~ Income + Education + Family + Income:Education + Income:Family,
                   family = binomial(link = "logit"), data = Universal_Bank_DS)
```


```{r}
# View the summary of the model
summary(final_model)
```

```{r}
# Extract coefficients
model_coefficients <- coef(final_model)
print(model_coefficients)
```

```{r}
# Creating a range for each variable
income_range <- seq(from = min(Universal_Bank_DS$Income), to = max(Universal_Bank_DS$Income), length.out = 100)
education_range <- unique(Universal_Bank_DS$Education)
family_range <- unique(Universal_Bank_DS$Family)

# Creating a grid of all combinations
sensitivity_data <- expand.grid(Income = income_range, Education = education_range, Family = family_range)

# Calculating interaction terms
sensitivity_data$Income_Education <- sensitivity_data$Income * sensitivity_data$Education
sensitivity_data$Income_Family <- sensitivity_data$Income * sensitivity_data$Family

```


```{r}
# Predicting probabilities
sensitivity_data$Probability <- predict(final_model, newdata = sensitivity_data, type = "response")

```

```{r}
# Plotting Probability vs. Income for different levels of Education
ggplot(sensitivity_data, aes(x = Income, y = Probability, color = as.factor(Education))) +
    geom_line() +
    labs(title = "Probability of Taking a Loan by Income and Education Level",
         x = "Income",
         y = "Probability",
         color = "Education Level")
```

```{r}
# Select a few representative levels of Income for clarity in the plot
income_levels <- quantile(sensitivity_data$Income, probs = seq(0, 1, 0.25))
```

```{r}
# Plotting
ggplot(sensitivity_data %>% filter(Income %in% income_levels), 
       aes(x = Family, y = Probability, color = as.factor(Income))) +
    geom_line() +
    labs(title = "Probability of Taking a Loan by Family Size and Income Level",
         x = "Family Size",
         y = "Probability",
         color = "Income Level")
```

```{r}
# Preparing data for the neural network. Note that neural networks generally require scaled data.
# For simplicity, we'll use the data as is because the focus here is to demonstrate the steps.
# In practice, you should scale the data before training a neural network.
```

```{r}
# Manually create interaction terms in the data frame
Universal_Bank_DS$Income_Education <- Universal_Bank_DS$Income * Universal_Bank_DS$Education
Universal_Bank_DS$Income_Family <- Universal_Bank_DS$Income * Universal_Bank_DS$Family
```


```{r}
# Training the neural network model
set.seed(123)  # for reproducibility
nn_model <- neuralnet(PersonalLoan ~ Income + Education + Family + Income_Education + Income_Family,
                      data = Universal_Bank_DS,  # using the whole dataset for demonstration
                      hidden = c(5),             # one hidden layer with 5 neurons
                      linear.output = FALSE)     # since it's a classification problem
```

```{r}
# Plotting the neural network
plot(nn_model)
```

```{r}
# Computing predictions on a test set (if available) or the same dataset used for training here
nn_predictions <- compute(nn_model, Universal_Bank_DS[, c("Income", "Education", "Family", "Income_Education", "Income_Family")])

```

```{r}
# The results are probabilities. Converting to binary predictions with threshold 0.5
predicted_classes <- ifelse(nn_predictions$net.result > 0.5, 1, 0)
```

```{r}
# Assuming the actual classes are in the 'PersonalLoan' column of your dataset
actual_classes <- Universal_Bank_DS$PersonalLoan
```

```{r}
# Evaluating the performance using a confusion matrix
conf_matrix <- table(Predicted = predicted_classes, Actual = actual_classes)
print(conf_matrix)
```

```{r}
# Calculating accuracy
accuracy <- sum(diag(conf_matrix)) / sum(conf_matrix)
print(paste("Accuracy of the neural network model:", accuracy))
```

```{r}
# Create a new data frame for sensitivity analysis with ranges for your variables
sensitivity_data_nn <- expand.grid(
  Income = seq(from = min(Universal_Bank_DS$Income), to = max(Universal_Bank_DS$Income), length.out = 100),
  Education = seq(from = min(Universal_Bank_DS$Education), to = max(Universal_Bank_DS$Education), length.out = 100),
  Family = seq(from = min(Universal_Bank_DS$Family), to = max(Universal_Bank_DS$Family), length.out = 100)
)
```

```{r}
# Add interaction terms for the neural network
sensitivity_data_nn$Income_Education <- sensitivity_data_nn$Income * sensitivity_data_nn$Education
sensitivity_data_nn$Income_Family <- sensitivity_data_nn$Income * sensitivity_data_nn$Family
```

```{r}
# Generate predictions
nn_predictions <- compute(nn_model, sensitivity_data_nn)
```

```{r}
# Add the predictions to your data frame
sensitivity_data_nn$Predicted_Probability <- nn_predictions$net.result
```

```{r}
# Plotting the effect of each variable on the predicted probability

# Plotting the effect of Income
ggplot(sensitivity_data_nn, aes(x = Income, y = Predicted_Probability)) +
  geom_line() +
  facet_wrap(~Education) + # Separating plots for each Education level
  labs(title = "Effect of Income on the Probability of Taking a Loan",
       x = "Income",
       y = "Predicted Probability")

```

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