################################################################################################
# 
# USED CARS 
#
################################################################################################
#
# Data taken from the advertising pages of the Sunday Times a few years ago, presenting cars 
# for sale in the UK of car, age of car (in six-month units based on date of registration), 
# recorded mileage, and vendor.
#
# 1. Case number 1:54;
# 2. Asking price in pounds;
# 3. Type/Model:  0=model 500, 1=450, 2=380, 3=280, 4=200;
# 4. Age of car in six-month units, based on registration;
# 5. Recorded mileage (in thousands);
# 6. Vendor (0,1,2,3 are dealerships, 4="sale by owner").
#
################################################################################################
names = c("case","price","model","age","mileage","vendor")
data     = read.table("usedcars.txt",header=TRUE)
n        = nrow(data)
attach(data)

# Question a)
reg.a = lm(price~mileage)
summary(reg.a)

# Question b)
reg.b = lm(price~age)
summary(reg.b)

# Question d)
reg.d = lm(price~mileage+age)
summary(reg.d)




# Question g)
# Model can be 0, 1, 2, 3 and 4
# Therefore we need 4 dummy variables
M0=rep(0,n)
M1=rep(0,n)
M2=rep(0,n)
M3=rep(0,n)
M0[model==0]=1
M1[model==1]=1
M2[model==2]=1
M3[model==3]=1
reg.g = lm(price~M0+M1+M2+M3)
summary(reg.g)

# Question h)
# Vendor can be 0, 1, 2, 3 and 4
# Therefore we need 4 dummy variables
V0=rep(0,n)
V1=rep(0,n)
V2=rep(0,n)
V3=rep(0,n)
V0[vendor==0]=1
V1[vendor==1]=1
V2[vendor==2]=1
V3[vendor==3]=1
reg.h = lm(price~V0+V1+V2+V3)
summary(reg.h)

# Question i)
reg.i = lm(price~mileage+age+M0+M1+M2+M3+V0+V1+V2+V3)
summary(reg.i)

# Residual plots 
pdf(file="hw5-fig1.pdf",width=10,height=10)
par(mfrow=c(3,2))
plot(reg.a$fit,reg.a$res,xlab="fitted value",ylab="residuals")
abline(h=0,col=2)
title("price on milage")
plot(reg.b$fit,reg.b$res,xlab="fitted value",ylab="residuals")
abline(h=0,col=2)
title("price on age")
plot(reg.d$fit,reg.d$res,xlab="fitted value",ylab="residuals")
abline(h=0,col=2)
title("price on mileage and age")

plot(reg.g$fit,reg.g$res,xlab="fitted value",ylab="residuals")
abline(h=0,col=2)
title("price on type")
plot(reg.h$fit,reg.h$res,xlab="fitted value",ylab="residuals")
abline(h=0,col=2)
title("price on vendor")
plot(reg.i$fit,reg.i$res,xlab="fitted value",ylab="residuals")
abline(h=0,col=2)
title("price on mileage, age, type and vendor")
dev.off()


# Excluding mileage and vendor from the regression
reg= lm(price~age+M0+M1+M2+M3)
summary(reg)