The following R code is for a simulation study. You are asked to explain what is illustrated. What can you learn from it in terms of good or bad statistical practice?

Some information that may help you:

$•$ t he error term of the linear regression model is based on a t - distribution with  3  degrees of freedom, which has mean zero and variance  3  and which has heavy tails  ( i . e .  simulations from this t - distribution show more outliers as compared to a normal distribution$).$

$•$ the I QR is the inter - quartile range, which is the difference between the third and the first quartile

set.seed$(156918)$

beta.hat.complete$<-$c$()$

var.beta.hat.complete$<-$c$()$

beta.hat.reduced$<-$c$()$

var.beta.hat.reduced$<-$c$()$

x$<-1$:$200$

db$<-$data.frame$($x$=$x$,$y$=$NA$)$

for$($i in $1$:$10000)\{$

db$y$<-10+\mathrm{.}3*$x$+7*$rt$(200,$ df$=3)$

m$.$complete$<-$lm$($y~x$,$data$=$db$)$

e$<-$residuals$($m$.$complete$)$

iqr$<-$IQR$($e$)$

keep$<-$abs$($e$)<2\mathrm{.}5*$iqr

m$.$reduced$<-$lm$($y~x$,$ data$=$db$,$ subset$=($keep$))$

beta.hat.complete$<-$c$($beta$.$hat.complete,coef$($m$.$complete$)[2])$

var.beta.hat.complete$<-$c$($var$.$beta.hat.complete,summary$($m$.$complete$)$$coef$[2,2]^2)$

beta.hat.reduced$<-$c$($beta$.$hat.reduced,coef$($m$.$reduced$)[2])$

var.beta.hat.reduced$<-$c$($var$.$beta.hat.reduced,summary$($m$.$reduced$)$$coef$[2,2]^2)$

$\}$

mean$($beta$.$hat.complete$)$

## $[1]0\mathrm{.}2997359$

mean$($var$.$beta.hat.complete$)$

## $[1]0\mathrm{.}0002163193$

$10$

mean$($beta$.$hat.reduced$)$

## $[1]0\mathrm{.}2998977$

mean$($var$.$beta.hat.reduced$)$

## $[1]0\mathrm{.}000115903$

X$<-$lm$($y~x$,$data$=$db$,$x$=$T$)$$x

solve$($t$($X$)\%*\%$X$)*49*3$

## $($Intercept$)$ x

## $($Intercept$)2\mathrm{.}9621608-0\mathrm{.}0221608040$

## x $-0\mathrm{.}02216080\mathrm{.}0002205055$