Example Ozone data

library(ElemStatLearn)
data(ozone,package="ElemStatLearn")
ozone<- ozone[order(ozone$ozone),]
head(ozone)

##     ozone radiation temperature wind
## 17      1         8          59  9.7
## 19      4        25          61  9.7
## 14      6        78          57 18.4
## 45      7        48          80 14.3
## 106     7        49          69 10.3
## 7       8        19          61 20.1

#And we wanna find the relationship between temperature and ozone

Bagged Loess

ll<- matrix(NA,nrow=10,ncol=155)
for(i in 1:10){
  ss<- sample(1:dim(ozone)[1],replace=T) #Randomly pick up the ozone data
  ozone0<- ozone[ss,]
  ozone0<- ozone0[order(ozone0$ozone),]
  loess0<- loess(temperature~ozone,data=ozone0,span=0.2) #loess function can built polynomial regression, which is non-linear regression
  ll[i,]<- predict(loess0,newdata=data.frame(ozone=(1:155)))
 #Pass the 1:155 in order and see the preidciotn, and repet it 10 times, which means 10 columns. 
}

## Warning in simpleLoess(y, x, w, span, degree, parametric, drop.square,
## normalize, : pseudoinverse used at 21

## Warning in simpleLoess(y, x, w, span, degree, parametric, drop.square,
## normalize, : neighborhood radius 2

## Warning in simpleLoess(y, x, w, span, degree, parametric, drop.square,
## normalize, : reciprocal condition number 1.7742e-16

plot(ozone$ozone,ozone$temperature,pch=19,cex=0.5)
for(i in 1:10){
  lines(1:155,ll[i,],col="grey",lwd=2)
}
#Add the line of 10 observations, and find it has a little bit overfitting problem
lines(1:155,apply(ll,2,mean),col="red",lwd=2)

#Also, we can use the mean value as a line 

More bagging in caret

Also, we can use caret to do the bagging

library(caret)

## Loading required package: lattice
## Loading required package: ggplot2

library(party)

## Loading required package: grid
## Loading required package: mvtnorm
## Loading required package: modeltools
## Loading required package: stats4
## Loading required package: strucchange
## Loading required package: zoo
## 
## Attaching package: 'zoo'
## 
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
## 
## Loading required package: sandwich

predictors = data.frame(ozone=ozone$ozone)
temperature = ozone$temperature
treebag <- bag(predictors, temperature, B = 10,
                bagControl = bagControl(fit = ctreeBag$fit,
                                        predict = ctreeBag$pred,
                                        aggregate = ctreeBag$aggregate))

## Warning: executing %dopar% sequentially: no parallel backend registered

#Bag function can help you to make the bagging as what loess do, but you should tell what you need in bagControl
plot(ozone$ozone,temperature,col='lightgrey',pch=19)
points(ozone$ozone,predict(treebag$fits[[1]]$fit,predictors),pch=19,col="red")
#treebag$fits[[1]]$fit is one condition the classification tree formular , and we pass the ozone data, it can predict what temperature it should be 
points(ozone$ozone,predict(treebag,predictors),pch=19,col="blue") #This is the all conditions will be used, so the blue will capture better the red line