# Illustration of one-way layout
# (cf. slides 18-20 to chapter 1)

# Bread were baked from flour that were fortified with a fixed amount 
# of vitamines and vitamin C content (mg/100 g) was measured for two loaves 
# immediately after baking (group 1), after one day of storage (goup 2), and 
# after three days of storage (group 3). From Moore & McCabe:
# Introduction to the practice of statistics, 5th edition, 2006.

# Read data:
group=c(1,1, 2,2, 3,3)
vitc=c(47.62,49.79, 40.45,43.46, 21.25,22.34)
group=factor(group)

# a)
fit.a=lm(vitc~group-1)
summary(fit.a)
Xa=model.matrix(fit.a)
Xa

# b)
fit.b=lm(vitc~group)
summary(fit.b)
Xb=model.matrix(fit.b)
Xb

# c)
newgroup=relevel(group,ref="3")
fit.c=lm(vitc~newgroup)
summary(fit.c)
Xc=model.matrix(fit.c)
Xc

# d)
contrasts(group)=contr.sum
fit.d=lm(vitc~group)
summary(fit.d)
Xd=model.matrix(fit.d)
Xd

# e)
x1=as.numeric(group==1)
x2=as.numeric(group==2)
x3=as.numeric(group==3)
fit.e=lm(vitc~x1+x2+x3)
summary(fit.e)
Xe=model.matrix(fit.e)
Xe