# Soft drink bottling data and analysis
# Example 5-3 of the text

 y <- c(-3,-1,0,1,5,4, -1,0,2,1,7,6, -1,0,2,3,7,9, 1,1,6,5,10,11)
 carbon <- as.factor(rep(c(10,12,14),each=2, times=4))
 press <- as.factor(rep(c(25,30), each=12))
 speed <- as.factor(rep(c(200,250), each=6, times=2))
 data <- data.frame(y, carbon, press, speed)
 attach(data)
 data


 par(mfrow=c(2,2))
 plot.design(data)
 interaction.plot(carbon,press,y)
 interaction.plot(carbon,speed,y)
 interaction.plot(press,speed,y)


 g <- lm(y ~ carbon + press + speed + carbon*press + carbon*speed + press*speed + carbon*press*speed)
 anova(g)


 mean(y[press==25])
 mean(y[press==30])
 qt(.975,12)*sqrt(.708/6)