# Compute main effects and interaction effects with the data in Section 6-2

 A <- c(-1, 1, -1,1)
 B <- c(-1, -1, 1, 1)
 I <- c(28, 36, 18, 31)
 II <- c(25, 32, 19, 30)
 III <- c(27, 32, 23, 29)
 
 data <- data.frame(A, B, I, II, III)
 data
 

# compute sums for each combination
 sums <- apply(data[,3:5], 1, sum)
 names(sums) <- c("(1)", "(a)", "(b)", "(ab)")
 sums
 ybar <- sums/3

# Interaction plots


 par(mfrow=c(1,2))
 interaction.plot(A, B, ybar)
 interaction.plot(B, A, ybar)

# Build ANOVA table 

 y <- c(I, II, III)
 y
 [1] 28 36 18 31 25 32 19 30 27 32 23 29
 factorA <- as.factor(rep(A,3))
 factorB <- as.factor(rep(B,3))
 g <- lm(y ~ factorA + factorB + factorA*factorB)
 anova(g)

windows()
# residual analysis
par(mfrow=c(1,2))
# normal plot
 qqnorm(g$residuals)
 qqline(g$residuals)

# residual plot
 plot(g$fitted.values,g$residuals)
 abline(h=0)