storks=read.table("storks.txt",header=T)
attach(storks)
plot(storks$storks,people,xlab="storks")
storks.lm=lm(people~storks$storks)  
lines(storks$storks,fitted(storks.lm))    # add fitted line to scatterplot
summary(storks.lm)
anova(storks.lm)
plot(fitted(storks.lm),resid(storks.lm))  # check assumptions
qqnorm(resid(storks.lm))                 


oring=read.table("o-ring.txt")            # problem 13.70 on p. 540 of text
oring
names(oring)=c("flight","temp","damage")
attach(oring)
plot(temp[damage>0],damage[damage>0])     # plot of damaged o-rings vs. temp
 # does there look like a relationship between temperature and damage?
plot(temp,damage)                         # plot of all data
 # does this plot look different?
 # how do you feel about predicting for a temp of 31?
oring.lm=lm(damage~temp)  
summary(oring.lm)
 # predicted damage for temp of 31:
coef(oring.lm)
coef(oring.lm)[1] + coef(oring.lm)[2]*31  # should we launch?
lines(temp,fitted(oring.lm))    
 # does a linear fit look reasonable?
plot(fitted(oring.lm),resid(oring.lm))  
qqnorm(resid(oring.lm))                 


olymp=read.table("olympics.txt",header=T)
pairs(olymp)
attach(olymp)
plot(year,long.jump)
long.lm=lm(long.jump~year)
lines(year,fitted(long.lm))
summary(long.lm)
anova(long.lm)
plot(fitted(long.lm),resid(long.lm))
plot(year,resid(long.lm))       # plot looks the same
plot(long.jump,resid(long.lm))  # bad plot
qqnorm(resid(long.lm))
fitted(long.lm)                 # fitted values
hat(year)                       # diagonal of the hat matrix
 # next is a prediction interval, by hand, predicting for 1984 (20th datapoint)
fitted(long.lm)[20]-qt(.975,18)*11.59*sqrt(1+hat(year)[20])
fitted(long.lm)[20]+qt(.975,18)*11.59*sqrt(1+hat(year)[20])
predict(long.lm,data.frame(year=84),interval="predict")  # easier method