Use the bBoston dataset from the ISLR$2$ library $($R Studio$)$ to predict per capita crime rate using the regression methods you learnt in the class particularly best subsets selection, backward subset selection, lasso, and ridge regression. For your ridge and lasso, be sure to use k$-$fold cross validation as we covered in the lab but please choose your k and explain why you$$ve chosen this number.Assume you are submitting this analysis to someone who is seeing this data for the first time. Please provide an overview of what each variable represents and include summary statistics for

both continuous and categorical variables $($tabular and$/$or graphical$).$ Estimate the

models using training and test data $(80-20$ split$).$ Evaluate which model $($or set of models$)$ performs well. Does your chosen model$($s$)$ involve all the features in the data set? Why or why not?

Code from scartch and each part:

$```\{$r$\}$

#Loading the library

library$($ISLR$2)$

$```$

$```\{$r$\}$

#Loading Boston Dataset

data$("$Boston$")$

$```$

$```\{$r$\}$

#Summary of the Boston Dataset

summary$($Boston$)$

$```$

$```\{$r$\}$

# Creating random numbers that can be reproduced

set.seed$(123)$

$```$

$```\{$r$\}$

# Split data into training and test set $(80-20$ split$)$

train$\_$index $<-$ sample$(1$:nrow$($Boston$),0\mathrm{.}8*$ nrow$($Boston$))$

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

test$\_$data $<-$ Boston$[-$train$\_$index,$]$

$```$

$```\{$r$\}$

#Best Subset Selection

library$($leaps$)$

best$\_$subset $<-$ regsubsets$($crim ~ $.,$ data $=$ train$\_$data, nvmax $=13)$

summary$($best$\_$subset$)$

$```$

$```\{$r$\}$

#Backward Subset Selection

backward$\_$subset $<-$ regsubsets$($crim ~ $.,$ data $=$ train$\_$data, method $=$ "backward"$)$

summary$($backward$\_$subset$)$

$```$

$```\{$r$\}$

#LASSO Regression

library$($glmnet$)$

x $<-$ as$.$matrix$($train$\_$data$[,-1])$ # excluding the crim

y $<-$ train$\_$data$crim

lasso$\_$model $<-$ cv$.$glmnet $($x$,$ y$,$ alpha $=1)$

plot$($lasso$\_$model$)$

$```$

$```\{$r$\}$

#Ridge Regression

ridge$\_$model $<-$ cv$.$glmnet$($x$,$ y$,$ alpha $=0)$

plot$($ridge$\_$model$)$

$```$

$```\{$r$\}$

#Predict Using each model

test$\_$x $<-$ as$.$matrix$($test$\_$data$[,-1])$

test$\_$y $<-$ test$\_$data$crim

$```$

COMPLETE THE CODE