2+2
?plot
help(plot)
?par
help(par)
args(pnorm)
q()
qnorm(0.975)
 x <- 2 + 2
 x <- 2 + 2  # The output should be 4!
search()
x <- 5:15
x[1] # Gives the first element of x.
x[2:4] # Gives the elements  x[2], x[3], x[4].
x[-(2:4)] # Gives  all but x[2], x[3], x[4].
a1 <- c(1,3,5,6,8,21)
a2 <- seq(1,21,by=2)
a3 <-seq(min(weld$x),max(weld$x),length=100)
a4 <-rep(2,12)
y <- matrix(1:9, nrow=3) 
y[1, 2]
y[1,]
y[,2]  # Gives the second column  of y. 
z <- kyphosis
?kyphosis
mean(weld$x)
var(weld$x)
weld$x*weld$y
mean(weld$x*weld$y)
weld$x^2
weld$x-1
wmx <- mean(weld$x)
wxy <-weld$x*weld$y
wxm1 <-weld$x-1
rm(a1)
lm(y~x,  data=weld) 
weld.lm1 <-lm(y~x, data=weld)  
resid(weld.lm1)
coef(weld.lm1)
plot(weld.lm1)
deviance(weld.lm1)
fitted(weld.lm1)
print(weld.lm1)
summary(weld.lm1)
anova(weld.lm1)
#We may be interested in whether a quadratic model fits the data any better.
weld.lm2 <-lm(y ~ x + x^2, data=weld)
weld.lm2 <- update(weld.lm1, .~. + x^2)
plot(weld$x,weld$y)
plot(weld$x,weld$y, xlab="Current", ylab="Diameter", las=1)
x <- seq(min(weld$x),max(weld$x),length=100)
y1 <- coef(weld.lm1)[1]+(coef(weld.lm1)[2]*x)
lines(x,y1)
y2 <- coef(weld.lm2)[1]+(coef(weld.lm2)[2]*x)+(coef(weld.lm2)[3]*x*x)
lines(x,y2,lty=2)


y1 <- predict(weld.lm1,data.frame(x))
y2 <- predict(weld.lm2,data.frame(x))
par(mfrow=c(1,1))
dput(y,"h:\\myfile.txt") 
z <- dget("h:\\myfile.txt")