## ----data-scatterplot, echo=FALSE----------------------------------------
# Plot the data
plot(all.x,all.y,xlab="x",ylab="y")
rug(all.x,side=1,col="grey")
rug(all.y,side=2,col="grey")

## ----data-with-mean,echo=FALSE-------------------------------------------
# Plot the data
plot(all.x,all.y,xlab="x",ylab="y")
rug(all.x,side=1,col="grey")
rug(all.y,side=2,col="grey")
# Add a line showing the global mean to the previous plot
abline(h=mean(all.y),lty="dotted")

## ----rapidly-varying-function,echo=FALSE---------------------------------
# Example of a function which varies rapidly but within narrow limits ---
  # we actually do better by fitting a constant than matching the correct
  # functional form!
ugly.func <- function(x) {1 + 0.01*sin(100*x)}
x <- runif(25); y <- ugly.func(x) + rnorm(length(x),0,0.5)
# Plot the data plus the true curve
plot(x,y,xlab="x",ylab="y"); curve(ugly.func,add=TRUE)
# Plot the global sample mean
abline(h=mean(y),col="red")
# Fit the correct functional form
sine.fit = lm(y ~ 1+ sin(100*x))
# Plot the fitted function
curve(sine.fit$coefficients[1]+sine.fit$coefficients[2]*sin(100*x),
      col="blue",add=TRUE)

## ----data-line,echo=FALSE------------------------------------------------
# Go back to the running example data
# Plot the data
plot(all.x,all.y,xlab="x",ylab="y")
rug(all.x,side=1,col="grey")
rug(all.y,side=2,col="grey")
# Add a line showing the global mean to the previous plot
abline(h=mean(all.y),lty="dotted")
# Fit a linear model
fit.all = lm(all.y~all.x)
# Add it to the plot
abline(fit.all)

## ----data-knn-reg,echo=FALSE---------------------------------------------
# Plot the running data + line for global mean
# Plot the data
plot(all.x,all.y,xlab="x",ylab="y")
rug(all.x,side=1,col="grey")
rug(all.y,side=2,col="grey")
# Add a line showing the global mean to the previous plot
abline(h=mean(all.y),lty="dotted")
library(FNN) # For "fast nearest neighbors" methods
# Grid on which to plot fits: knn.reg expects a matrix
plot.seq <- matrix(seq(from=0,to=1,length.out=100),byrow=TRUE)
# kNN regression lines, k from 1 to 20
lines(plot.seq,knn.reg(train=all.x,test=plot.seq,y=all.y,k=1)$pred,col="red")
lines(plot.seq,knn.reg(train=all.x,test=plot.seq,y=all.y,k=3)$pred,col="green")
lines(plot.seq,knn.reg(train=all.x,test=plot.seq,y=all.y,k=5)$pred,col="blue")
lines(plot.seq,knn.reg(train=all.x,test=plot.seq,y=all.y,k=20)$pred,col="purple")
legend("center", legend=c("all","1","3","5","20"), lty=c("dashed",rep("solid",4)), col=c("black","red","green","blue","purple"))

## ----data-ksmooth,echo=FALSE---------------------------------------------
# Plot the running data + line for global mean
# Plot the data
plot(all.x,all.y,xlab="x",ylab="y")
rug(all.x,side=1,col="grey")
rug(all.y,side=2,col="grey")
# Add a line showing the global mean to the previous plot
abline(h=mean(all.y),lty="dotted")
lines(ksmooth(all.x, all.y, "box", bandwidth=2),col="red")
lines(ksmooth(all.x, all.y, "box", bandwidth=1),col="green")
lines(ksmooth(all.x, all.y, "box", bandwidth=0.1),col="blue")
lines(ksmooth(all.x, all.y, "normal", bandwidth=2),col="red",lty="dashed")
lines(ksmooth(all.x, all.y, "normal", bandwidth=1),col="green",lty="dashed")
lines(ksmooth(all.x, all.y, "normal", bandwidth=0.1),col="blue",lty="dashed")