#CHOCOLATES: ENERGY V. SIZE, PRICE, UNIT.PRICE, PROTEIN, FAT, CARBOHYDRATES, SODIUM
#USING THE CHOCOLATES DATA SET
#Upload and save data set into your working directory
CHOC=read.table("chocolates.txt",header=TRUE)

#attach the data set into R interpreter
attach(CHOC)
CHOC

#Assign the dependent variable Y to “Energy" and the independent variables Xi to the rest
Y=Energy
X1=Size
X2=Price
X3=Unit.Price
X4=Protein
X5=Fat
X6=Carbo
X7=Sodium

#Test Normality of the data set
par(mfcol=c(2,4))  
qqnorm(Y,main="Y Normal Q-Q Plot")
qqline(Y,lty=2)
qqnorm(X1,main="X1 Normal Q-Q Plot")
qqline(X1,lty=2)
qqnorm(X2,main="X2 Normal Q-Q Plot")
qqline(X2,lty=2)
qqnorm(X3,main="X3 Normal Q-Q Plot")
qqline(X3,lty=2)
qqnorm(X4,main="X4 Normal Q-Q Plot")
qqline(X4,lty=2)
qqnorm(X5,main="X5 Normal Q-Q Plot")
qqline(X5,lty=2)
qqnorm(X6,main="X6 Normal Q-Q Plot")
qqline(X6,lty=2)
qqnorm(X7,main="X7 Normal Q-Q Plot")
qqline(X7,lty=2)
par(mfcol=c(1,1))

#Test the correlations between each Xi to eliminate variables that correlate with each other
par(mfcol=c(3,7))      
plot(X1,X2)
plot(X1,X3)
plot(X1,X4)
plot(X1,X5) 
plot(X1,X6)     
plot(X1,X7)   
plot(X2,X3) 
plot(X2,X4)
plot(X2,X5)
plot(X2,X6)
plot(X2,X7)
plot(X3,X4)
plot(X3,X5)
plot(X3,X6)
plot(X3,X7)
plot(X4,X5)
plot(X4,X6)
plot(X4,X7)
plot(X5,X6)
plot(X5,X7)
plot(X6,X7)
par(mfcol=(1,1))

#Plot X versus Y for correlation
par(mfcol=c(2,4))      
plot(X1,Y,xlab="Size",ylab="Energy")
plot(X2,Y,xlab="Price",ylab="Energy")
plot(X3,Y,xlab="Unit.Price",ylab="Energy")
plot(X4,Y,xlab="Protein",ylab="Energy")   
plot(X5,Y,xlab="Fat",ylab="Energy")       
plot(X6,Y,xlab="Carbo",ylab="Energy")   
plot(X7,Y,xlab="Sodium",ylab="Energy")    
par(mfcol=(1,1)))

#Simple Linear Regression
#Run ANOVA for each X of the simplified model and compare probability values
LM=lm(Y~X4)		
LM
Yhat=fitted(LM)
e=residuals(LM)
RESULTS=data.frame(X4,Y,Yhat,e)	
anova(LM)

#Plot the regression line and points of the correlated variables
par(mfcol=c(1,3))
plot(X4,Y)
abline(LM4,col="blue")
segments(X4,Yhat,X4,Y,col="red")   
plot(X5,Y)
abline(LM5,col="blue")
segments(X5,Yhat,X5,Y,col="red")
plot(X6,Y)
abline(LM6,col="blue")
segments(X6,Yhat,X6,Y,col="red")
par(mfcol=c(1,1)))

#assign X and Y for variables after eliminations
Y=Energy
X4=Protein
X5=Fat
X6=Carbo
X7=Sodium

#full linear model
LM=lm(Y~X4+X5+X6+X7)
LM

#summary to give overall F test p-value and partial t-tests
summary(LM)
anova(LM)

#generate marginal reduced model by removing one variable at a time
RM1=lm(Y~X5+X6+X7)
RM2=lm(Y~X4+X6+X7)
RM3=lm(Y~X4+X5+X7)
RM4=lm(Y~X4+X5+X6)

#run an Anova on each reduced model
Anova(RM1)
Anova(RM2)
Anova(RM3)
Anova(RM4)

#restate full linear model, complete with all variables, and command R to perform the automated backwards stepwise regression
FM=lm(Y~X4+X5+X6+X7)
step(FM,direction="backward")

#restate full model as well as reduced model generated in previous step; run anova on the two to determine appropriateness of full or reduced model
FM=lm(Y~X4+X5+X6+X7)
RM=lm(Y~X4+X5+X6)
anova(RM,FM)