data(anscombe)
help(anscombe)
attach(anscombe)
par(mfrow=c(2,2))
plot(x1,y1)
plot(x2,y2)
plot(x3,y3)
plot(x4,y4)
#Scatterplot smooth demo
x=seq(1,10,by=.4)
nx=length(x)
#Save y generated by the following code
#y=.5-2*log(x)+5*sqrt(x)+rnorm(nx)
y=c(6.4,7.0,6.2,7.7,6.4,6.7,7.6,7.6,7.7,8.0,10.1,10.2,10.0,12.3,11.2,10.0,8.2,10.0,8.6,8.9,9.2,9.7,10.2)
plot(x,y)
#For each x, draw the regression line for all observations in (x-3,x+3).  We will ignore weights for this demo.
for(i in 1:nx){
xreg=x[abs(x-x[i])<3]
yreg=y[abs(x-x[i])<3]
wreg=lm(yreg~xreg)
a=wreg$coef[1]
b=wreg$coef[2]
lines(c(x[i]-3,x[i]+3),c(a+b*(x[i]-3),a+b*(x[i]+3)),col=i)
}
title("Local least squares lines")
#Keep the fitted value only at each x[i]
plot(x,y)
for(i in 1:nx){
xreg=x[abs(x-x[i])<3]
yreg=y[abs(x-x[i])<3]
wreg=lm(yreg~xreg)
a=wreg$coef[1]
b=wreg$coef[2]
points(x[i],a+b*x[i],col="red",cex=1.5)
}
title("Fitted values for each centerpoint of local least squares")
#Connect the dots for the fitted line
plot(x,y)
yhat=rep(0,nx)
for(i in 1:nx){
xreg=x[abs(x-x[i])<3]
yreg=y[abs(x-x[i])<3]
wreg=lm(yreg~xreg)
a=wreg$coef[1]
b=wreg$coef[2]
yhat[i]=a+b*x[i]
}
lines(x,yhat,col="red",lwd=2)
title("Local regression")
#Try a smaller window
yhats=rep(0,nx)
for(i in 1:nx){
xreg=x[abs(x-x[i])<1.5]
yreg=y[abs(x-x[i])<1.5]
wreg=lm(yreg~xreg)
a=wreg$coef[1]
b=wreg$coef[2]
yhats[i]=a+b*x[i]
}
lines(x,yhats,col="blue",lwd=2)
legend(5,7.5,c("Window=3","Window=1.5"),lwd=c(2,2),col=c("red","blue"),cex=.8)