# Example from book of Box, Hunter, Hunter on lima beans.
# A: depth of planting (0.5 in or 1.5 in)
# B: watering (once or twice daily)
# C: type of bean (baby or large)
# Y: yield

a<-rep(c(-1,1),4)
b<-rep(c(-1,-1,1,1),2)
c<-c(rep(-1,4),rep(1,4))
ab<-a*b; ac<-a*c; bc<-b*c; abc<-a*b*c
y <- c(6,4,10,7,4,3,8,5)
summary(lm(y~a+b+c+ab+ac+bc+abc))
summary(lm(y~(a+b+c)^3)) # easier - using model formula notation
# note: "a:b" in output means entrywise multiplication of columns in design matrix, i.e. the same as the multiplication above.

# Even easier:
library(FrF2)
plan <- FrF2(nruns=8,nfactors=3,randomize=FALSE)
plan
plan <- add.response(plan,y)
plan

# now we have an ordinary data set up to be used with lm
lm3 <- lm(y~.^3,data=plan)
summary(lm3)

MEPlot(lm3)
# dev.copy2pdf(file="LimaME.pdf")
IAPlot(lm3)
# dev.copy2pdf(file="LimaIA.pdf")
effects <- 2*lm3$coeff
effects