############################################################
# HOUSE PRICE DATA
############################################################
#
# Home: index of the house
# Nbhd: Neighborhood
# Offers: number of offers
# SqFt: size in square feet
# Brick: dummy for brick house
# Bedrooms: number of bedrooms
# Bathrooms: number of bathrooms
# Price: price in dollars
#
############################################################
pdf(file="houseprice-regressionoutput.pdf",width=8,height=8)

data    = read.table("houseprice.txt",header=TRUE)
attach(data)

# Scaling and plotting the variables
size = SqFt/1000
price = Price/1000

# Price against size

# A) Price as a linear function of size
##############################
par(mfrow=c(1,1))
plot(size,price,xlab="Size (1000 square feet)",ylab="Price (1000 dollars)",pch=16)
reg    = lm(price~size)
summary(reg)
abline(reg$coef,lwd=3,col=2)
title("price = -10 + 70*size")
text(1.6,200,"min size = 1.45",cex=1.25,col="blue")
text(1.6,190,"max size = 2.59",cex=1.25,col="blue")
text(1.6,180,"min price = 69.1",cex=1.25,col="blue")
text(1.6,170,"max price= 211.2",cex=1.25,col="blue")

# B) Taking into account  the type of house
###################################
lm(price[Brick=="No"]~size[Brick=="No"])
lm(price[Brick=="Yes"]~size[Brick=="Yes"])

par(mfrow=c(1,1))
plot(size,price,xlab="Size (1000 square feet)",ylab="Price (1000 dollars)",pch=16,col=Brick)
legend("topleft",legend=c("Brick=NO:   price=5+59*size","Brick=YES: price=-23+84*size"),col=1:2,pch=16,cex=1.5)
abline(lm(price[Brick=="No"]~size[Brick=="No"]),lwd=3,col=1)
abline(lm(price[Brick=="No"]~size[Brick=="No"]),lwd=3,col=1)


# C) Taking into account  the neighborhood
###################################
lm(price[Nbhd==1]~size[Nbhd==1])
lm(price[Nbhd==2]~size[Nbhd==2])
lm(price[Nbhd==3]~size[Nbhd==3])

par(mfrow=c(1,1))
plot(size,price,xlab="Size (1000 square feet)",ylab="Price (1000 dollars)",pch=16,
col=Nbhd)
legend("topleft",legend=c("Nbhd=1 - price=33+40*size",
"Nbhd=2 - price=26+49*size","Nbhd=3 - price=57+49*size"),
col=1:3,pch=16,cex=1.5)

abline(lm(price[Nbhd==1]~size[Nbhd==1]),lwd=3,col=1)
abline(lm(price[Nbhd==2]~size[Nbhd==2]),lwd=3,col=2)
abline(lm(price[Nbhd==3]~size[Nbhd==3]),lwd=3,col=3)


# D) Taking into account  the number of bedrooms
#########################################
table(Bedrooms)
bed = Bedrooms
bed[bed<=3]=2
bed[bed>=4]=4
lm(price[bed==2]~size[bed==2])
lm(price[bed==4]~size[bed==4])

par(mfrow=c(1,1))
plot(size,price,xlab="Size (1000 square feet)",ylab="Price (1000 dollars)",pch=16,
col=bed)
legend("topleft",legend=c("2/3 bedrooms: price=27+49*size","4/5 bedrooms: price=24+61*size"),
col=c(2,4),pch=16,cex=1.25)
abline(lm(price[bed==2]~size[bed==2]),lwd=3,col=2)
abline(lm(price[bed==4]~size[bed==4]),lwd=3,col=4)


# E) Taking into account  the number of bathrooms
#########################################
table(Bathrooms)
bath = Bathrooms
bath[bath>=3]=3
lm(price[bath==2]~size[bath==2])
lm(price[bath==3]~size[bath==3])

par(mfrow=c(1,1))
plot(size,price,xlab="Size (1000 square feet)",ylab="Price (1000 dollars)",pch=16,
col=bath)
legend("topleft",legend=c("2 Bathrooms: price=23+50*size","3 Bathrooms: price=36+52*size"),
col=2:3,pch=16,cex=1.25)
abline(lm(price[bath==2]~size[bath==2]),lwd=3,col=2)
abline(lm(price[bath==3]~size[bath==3]),lwd=3,col=3)




dev.off()