To perform k$-$NN classification and answer the questions, follow these steps in RStudio:

# Load required libraries

library$($caret$)$

library$($mlbench$)$

# Load the UniversalBank dataset

data$("$UniversalBank$")$

# Split the data into training and holdout sets $(60\%$ training, $40\%$ holdout$)$

set.seed$(123)$

index $<-$ createDataPartition$($UniversalBank$PersonalLoan, p $=0\mathrm{.}6,$ list $=$ FALSE$)$

train$\_$data $<-$ UniversalBank$[$index$,]$

holdout$\_$data $<-$ UniversalBank$[-$index, $]$

# Define categorical predictors as factors

categorical$\_$cols $<-$ c$("$Family$",$ "Education", "SecuritiesAccount", "CDAccount", "Online", "CreditCard"$)$

train$\_$data$[$categorical$\_$cols$]<-$ lapply$($train$\_$data$[$categorical$\_$cols$],$ as$.$factor$)$

holdout$\_$data$[$categorical$\_$cols$]<-$ lapply$($holdout$\_$data$[$categorical$\_$cols$],$ as$.$factor$)$

# Define the new customer's data

new$\_$customer $<-$ data.frame$($

Age $=40,$

Experience $=10,$

Income $=84,$

Family $=2,$

CCAvg $=2,$

Education $=2,$

Mortgage $=0,$

SecuritiesAccount $=0,$

CDAccount $=0,$

Online $=1,$

CreditCard $=1$

$)$

# Perform k$-$NN classification with k $=1$

knn$\_$model $<-$ train$($

PersonalLoan ~ $.,$

data $=$ train$\_$data,

method $="$knn$",$

preProcess $=$ c$("$center$",$ "scale"$),$

tuneGrid $=$ expand.grid$($k $=1),$

trControl $=$ trainControl$($method $="$cv$",$ number $=5)$

$)$

# Classify the new customer using the best k

predicted$\_$class $<-$ predict$($knn$\_$model, new$\_$customer$)$

predicted$\_$prob $<-$ predict$($knn$\_$model, new$\_$customer, type $=$ "prob"$)$

# Print the predicted class and probability

print$($predicted$\_$class$)$

print$($predicted$\_$prob$)$

# Confusion matrix for holdout data using the best k

best$\_$k $<-$ knn$\_$model$bestTune$k

predicted$\_$holdout $<-$ predict$($knn$\_$model, holdout$\_$data$)$

confusion$\_$matrix $<-$ confusionMatrix$($predicted$\_$holdout, holdout$\_$data$PersonalLoan$)$

print$($confusion$\_$matrix$)$

Explanation:

The task involves using k$-$NN classification to predict whether customers will accept a personal loan offer based on demographic and banking information. Here are the steps:

Load the UniversalBank dataset and split it into training $(60\%)$ and holdout $(40\%)$ sets.

Define categorical predictors as factors for k$-$NN$.$

Define a new customer's data.

Perform k$-$NN classification with k $=1$ on the training data.

Classify the new customer using the best k obtained from $5-$fold cross$-$validation.

Display the predicted class and probability for the new customer.

Calculate the confusion matrix for the holdout data using the best k$.$

This analysis helps determine if the new customer is likely to accept a personal loan offer based on their attributes and previous campaign