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)
par(oldpar)
image(x, y, f)
image(x, y, fa)
contour(x,y,fa,add=T)

image(x, y, fa)
contour(x,y,fa,add=T,nlevels=100)

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)
w <- sqrt(runif(100))*exp(2*pi*runif(100)*1i)
plot(w, xlim=c(-1,1), ylim=c(-1,1), pch="+", xlab="x", ylab="y")
lines(z)
rm(th, w, z)