######example 31,31,33
x<-c(0,2,4,6,8,10,12)
y<-c(2.1,5,9,12.6,17.3,21,24.7)

reg<-lm(y~x)
summary(reg)
confint(reg,level=0.95)
anova(reg)
qt(0.975,5)
qf(0.95,1,5)
fitted(reg)
confint(reg)
#normality
resid(reg)
qqnorm(resid(reg))
qqline(resid(reg))
shapiro.test(resid(reg))
#(interval,var(E(y)hat))
predict(reg,interval="confidence",se.fit=T)
#plot


require(graphics)
plot(x,y)
abline(coef(reg))
pred.frame<-data.frame(x=seq(0,12,by=0.5))
pp<-predict(reg,newdata=pred.frame,int="p")
pred.size<-pred.frame$x
plot(x,y,xlim=c(0,16),ylim=c(0,30))
abline(coef(reg))
matlines(pred.size,pp,col=c(1,2,2),lty=c(1,2,2))

##############
# Example 34
coef(reg)
a<-coef(reg)[1]
b<-coef(reg)[2]
y0=c(2.9,13.5,23)
x0=(y0-a)/b
x0
SS=anova(reg)
MSE=SS$"Mean Sq"[2]
n=length(x)
Sx0=(sqrt(MSE)/b)*sqrt(1+1/n+((y0-mean(y))^2/(b^2*var(x)*(n-1))))
Sx0
alpha=0.05
x0+qt(1-alpha/2,n-2)* Sx0
x0-qt(1-alpha/2,n-2)* Sx0


##############
# Example 37
cor.test(x,y)