## General Factorial Example
## AHW3
## April 10, 2008

rm(list = ls())

## 
y <- c(196.6, 197.7, 199.8, 
       196.0, 196.0, 199.4,
	   198.5, 196.0, 198.4,
	   197.2, 196.9, 197.6,
	   197.5, 195.6, 197.4,
	   196.6, 196.2, 198.1,
	   198.4, 199.6, 200.6,
	   198.6, 200.4, 200.9,
	   197.5, 198.7, 199.6,
	   198.1, 198.0, 199.0,
	   197.6, 197.0, 198.5,
	   198.4, 197.8, 199.8)

hard <- as.factor(c(rep(c(2,4,8), each=6), rep(c(2,4,8), each=6)))
cook <- as.factor(rep(c(3,4), each=18))
pressure <- as.factor(rep(c(400, 500, 650), 12))

data <- data.frame(y,hard, cook, pressure)

## model
full <- lm(y~hard*cook*pressure)
anova(full)

sub <- lm(y~hard + cook + pressure + hard:pressure)
anova(sub)

## normality check
qqnorm(sub$res); qqline(sub$res)