## First Example 
x <- rnorm(50)
y <- rnorm(x)
hull <- chull(x,y)
plot(x,y)
polygon(x[hull], y[hull],dens=15)
objects()
rm(x,y)

## Second Example
x <- 1:20
w <- 1+sqrt(x)/2
dummy <- data.frame(x=x,y=x+rnorm(x)*w)
dummy
objects()

fm <- lm(y~x, data=dummy)
summary(fm)
fm1 <- lm(y~x, data=dummy,weight=1/w^2)
lrf <- loess(y~x, data=dummy)
attach(dummy)
plot(x,y)
lines(x, fitted(lrf))
abline(0,1,lty=3)
abline(coef(fm))
abline(coef(fm1), lty=4)
detach()
plot(fitted(fm), resid(fm),xlab="Fitted Values",ylab="Residuals", main="Residuals vs Fitted")
qqnorm(resid(fm), main="Residuals QQ Plot")
rm(fm,fm1,lrf,x,dummy)

##Third Example
x <- seq(-pi,pi,length=50)
y <- x
f <- outer(x,y,function(x,y) cos(y)/(1+x^2))
oldpar <- par()
par(pty="s")
contour(x,y,f)
contour(x,y,f,nlevels=15,add=T)
fa <- (f-t(f))/2
contour(x,y, fa, nlevels=15)
par(oldpar)
persp(x,y,f)
persp(x,y,fa)
image(x,y, f)
image(x,y,fa)
objects(); rm(x,y,f,fa)
q()


sqrt
sqrt(2)
log
log(10)
plot(fdeaths)
mean(fdeaths)
test <- 4
letters
letters[3]
letters[-3]
j <- 1:26
j<5
letters[j<5]
-3.6
"Munich"
c(T, F, T)
c(-2, pi, 2)
c(T, pi, F)
c(T, pi, "Munich")
mode(c(T, pi, "Munich"))