help.start()
x<- rnorm(50)
y<- rnorm(x)
plot(x,y)
ls()
rm(x,y)

x<- 1:20
w<- 1+sqrt(x)/2
dummy<- data.frame(x=x,y=x+rnorm(x)*w)
dummy
fm<- lm(y~x, data=dummy)
summary(fm)
fm1<- lm(y~x, data=dummy, weight=1/w^2)
summary(fm1)
attach(dummy)
lrf<- lowess(x,y)
plot(x,y)
lines(x,lrf$y)
abline(0,1,lty=3)
abline(coef(fm))
abline(coef(fm1),col="red")
detach()
plot(fitted(fm),resid(fm),xlab="Fitted values",ylab="Residuals",main="Residuals vs Fitted")
qqnorm(resid(fm),main="Residuals Rankit Plot")
rm(fm,fm1,lrf,x,dummy)

filepath<- system.file("data","morley.tab",package="datasets")
filepath
file.show(filepath)
mm<- read.table(filepath)
mm
mm$Expt<- factor(mm$Expt)
mm$Run<- factor(mm$Run)
attach(mm)
plot(Expt,Speed,main="Speed of Light Data", xlab="Experiment No.")
fm<- aov(Speed~Run+Expt, data=mm)
summary(fm)
fm0<- update(fm,.~.-Run)
anova(fm0,fm)
detach()
rm(fm,fm0)

x<- seq(-pi,pi,len=50)
y<- x
f<- outer(x,y,function(x,y) cos(y)/(1+x^2))
oldpar<- par(no.readonly=TRUE)
par(pty="s")
contour(x,y,f)
contour(x,y,f,nlevels=15,add=TRUE)
fa<- (f-t(f))/2
contour(x,y,fa,nlevels=15,add=TRUE)
par(oldpar)
image(x,y,f)
image(x,y,fa)
objects()
rm(x,y,f,fa)

th<- seq(-pi,pi,len=100)
z<- exp(1i*th)
par(pty="s")
plot(z,type="l")
w<- rnorm(100)+rnorm(100)*1i
w<- ifelse(Mod(w)>1, 1/w,w)
plot(w,xlim=c(-1,1),ylim=c(-1,1),pch="+",xlab="x",ylab="y")
lines(z)
w2<- sqrt(runif(100))*exp(2*pi*runif(100)*1i)
plot(w2,xlim=c(-1,1),ylim=c(-1,1),pch="+",xlab="x",ylab="y")
lines(z)
rm(th,w,w2,z)
q()