What's wrong with my R code? # Load necessary package

library$($neuralnet$)$

# Load the spam data $($assuming the file is in the current working directory$)$

data $<-$ read.csv$("$spam$\_$train.csv$",$ header $=$ TRUE, stringsAsFactors $=$ FALSE$)$

# $------------------$

# Data processing

# $------------------$

# No specific columns need to be removed

# Ensure the features are scaled for better neural network performance

data$[,1$:$8]<-$ scale$($data$[,1$:$8])$

# Build a formula for the neural network

n $<-$ names$($data$)$

f $<-$ as$.$formula$($paste$("$spam ~$",$ paste$($n$[!$n $\%$in$\%$ "spam"$],$ collapse $="+")))$

# $-------------------$

# Question $1$: One hidden layer with $5$ neurons

# $-------------------$

nn$.$fit$1<-$ neuralnet$($f$,$ data $=$ data, hidden $=5,$ linear.output $=$ FALSE$)$

plot$($nn$.$fit$1)$ # Plot the first network

# $-------------------$

# Question $2$: Two hidden layers with $5$ and $3$ neurons

# $-------------------$

nn$.$fit$2<-$ neuralnet$($f$,$ data $=$ data, hidden $=$ c$(5,3,3),$ linear.output $=$ FALSE, stepmax $=1$e$6)$

plot$($nn$.$fit$2)$ # Plot the second network

# If you encounter issues with convergence, try reducing the complexity of the network:

# Simplified network for better convergence:

# nn$.$fit$2<-$ neuralnet$($f$,$ data $=$ data, hidden $=$ c$(5,3),$ linear.output $=$ FALSE, stepmax $=1$e$6,$ threshold $=0\mathrm{.}01)$

# $-------------------$

# Evaluate the second network on the training data

# $-------------------$

pred $<-$ compute$($nn$.$fit$2,$ data$[,1$:$8])$$net.result

# Convert probabilities to binary output

pred$1<-$ ifelse$($pred $>0\mathrm{.}5,1,0)$

# Calculate True Positive Rate $($TPR$)$ and False Positive Rate $($FPR$)$

TP$.$case $<-$ which$($pred$1+$ data$spam $==2)$

TP $<-$ length$($TP$.$case$)$

T$.$case $<-$ which$($data$spam $==1)$

T$.$actual $<-$ length$($T$.$case$)$

TP$.$rate $<-$ TP $/$ T$.$actual

FP$.$case $<-$ which$($pred$1-$ data$spam $==1)$

FP $<-$ length$($FP$.$case$)$

F$.$case $<-$ which$($data$spam $==0)$

F$.$actual $<-$ length$($F$.$case$)$

FP$.$rate $<-$ FP $/$ F$.$actual

# Output the performance metrics

TP$.$rate

FP$.$rate

Purpose: Question $1.$ Construct an ANN with one hidden layer, and the hidden layer has $5$ nodes. Plot the

constructed network below:

Question $2$

Construct another ANN with two hidden layers. The first hidden layer has $5$ nodes and

the second hidden layer has $5$ nodes. Do you think the second ANN will perform better

than the first ANN constructed in Question $1?$ And why?