### examples of using non-parametric regression

## Simulating the data

n<-200

x<-runif(n,0,10)
y<-sin(x) + rnorm(n)

## make the first plot to show pattern in the data
plot(x,y)

x
y

## first set of boxplots 
boxplot(split(y,x %/% 1), style.bxp="old")

## make another set of boxplots and add a line joining the medians
# make the plot and get the x coordinate of the middle of each pos
x.midpoints<-boxplot(split(y,x %/% 1), style.bxp="old")
# get information about the location of the boxes
result<-boxplot(split(y,x %/% 1), plot=F)
# medians of the boxes
boxm<-result$stats[3,]
# add a line joining the medians to the plot
# x.midpoints
# boxm
#ael: lines(x.midpoints$stats[3,],boxm)
lines(c(1:length(boxm)),boxm)

## plot the points and add the above line
plot(x,y)
#ael: lines(x.midpoints/10.0,boxm)
#ael: lines(x.midpoints$stats[3,],boxm)
#m<-length(boxm)-1;
#lines(c(0:m),boxm)
lines(c(1:length(boxm)),boxm)
#lea

## now plot the data and add a non-parametric curve
plot(x,y, pch="o")
lines(lowess(x,y, f=.3))

## plots not shown

# par(mfrow=c(2,2))

# see the effect of changing the span
plot(x,y, main="Changing the Span", pch="o")
lines(lowess(x,y))
lines(lowess(x,y, f=.5), lty=2, col=2)
lines(lowess(x,y, f=.25), lty=3, col=3)

# other smoothers
# supersmoother
# plot(x,y, main="Super Smoother", pch=".")
# lines(supsmu(x,y))

# kernel smoothers
# plot(x,y, main="Kernel Smoother", pch=".")
# lines(ksmooth(x,y))

# splines
# plot(x,y, main="Spline Smoother", pch=".")
# lines(smooth.spline(x,y))