#getwd

setwd("/Users/hedibert/Desktop")

data = read.table("http://hedibert.org/wp-content/uploads/2014/03/houseprices.txt",header=TRUE)

attach(data)

size = 0.092903*SqFt

price = 3.31*Price/1000


pdf(file="houseprices-analise-de-residuos.pdf",width=9,height=6)
# Regressores potenciais
# ------------------------
par(mfrow=c(2,2))
plot(size,price,xlab="Tamanho (m2)",ylab="Preco (x1000 reais)")
plot(Bedrooms,price,xlab="Numero de quartos",ylab="Preco (x1000 reais)")
plot(Bathrooms,price,xlab="Numero de banheiros",ylab="Preco (x1000 reais)")
plot(Brick,price,xlab="Alvenaria?",ylab="Preco (x1000 reais)")

# 1o modelo de regressao
# --------------------------
reg.simples = lm(price~size)
sighat = summary(reg.simples)$sigma

par(mfrow=c(1,2))
plot(size,price,xlab="Tamanho (m2)",ylab="Preco (x1000 reais)")
abline(reg.simples,col=2,lwd=2)
plot(size,reg.simples$residuals,xlab="Tamanho (m2)",ylab="Residuos")
abline(h=-2*sighat,lty=2,lwd=2,col=2)
abline(h=0,lty=1,lwd=2,col=2)
abline(h=2*sighat,lty=2,lwd=2,col=2)

par(mfrow=c(1,2))
plot(size,reg.simples$residuals,xlab="Tamanho (m2)",ylab="Residuos")
abline(h=-2*sighat,lty=2,lwd=2,col=2)
abline(h=0,lty=1,lwd=2,col=2)
abline(h=2*sighat,lty=2,lwd=2,col=2)
plot(size,reg.simples$residuals/sighat,xlab="Tamanho (m2)",ylab="Residuos padronizados")
abline(h=-2,lty=2,lwd=2,col=2)
abline(h=0,lty=1,lwd=2,col=2)
abline(h=2,lty=2,lwd=2,col=2)


# 2o modelo de regressao 
# --------------------------
reg.multipla = lm(price~size+Bedrooms)
sighat = summary(reg.multipla)$sigma

par(mfrow=c(1,2))
plot(size,reg.multipla$residuals/sighat,xlab="Tamanho (m2)",ylab="Residuos padronizados")
abline(h=-2,lty=2)
abline(h=0,lty=1)
abline(h=2,lty=2)

plot(Bedrooms,reg.multipla$residuals/sighat,xlab="Numero de quartos",ylab="Residuos padronizados")
abline(h=-2,lty=2)
abline(h=0,lty=1)
abline(h=2,lty=2)

par(mfrow=c(1,1))
plot(reg.multipla$fit,reg.multipla$residuals/sighat,xlab="Valores ajustados",ylab="Residuos padronizados")
abline(h=-2,lty=2)
abline(h=0,lty=1)
abline(h=2,lty=2)
title("preco = b0 + b1*tamanho + b2*quartos")


# 3o modelo de regressao
# --------------------------
reg.multipla2 = lm(price~size+Bedrooms+Bathrooms)
sighat = summary(reg.multipla2)$sigma

par(mfrow=c(1,1))
plot(reg.multipla2$fit,reg.multipla2$residuals/sighat,xlab="Valores ajustados",
ylab="Residuos padronizados")
abline(h=-2,lty=2)
abline(h=0,lty=1)
abline(h=2,lty=2)
title("preco = b0 + b1*tamanho + b2*quartos + b3*banheiros")



# 4o modelo de regressao
# --------------------------
n = nrow(data)
brick=rep(0,n)
brick[Brick=="Yes"]=1
reg.multipla3 = lm(price~size+Bedrooms+Bathrooms+brick)
sighat = summary(reg.multipla3)$sigma

par(mfrow=c(1,1))
plot(reg.multipla3$fit,reg.multipla3$residuals/sighat,xlab="Valores ajustados",
ylab="Residuos padronizados")
abline(h=-2,lty=2)
abline(h=0,lty=1)
abline(h=2,lty=3)
title("preco = b0 + b1*tamanho + b2*quartos + b3*banheiros + b4*alvenaria")



# Comparing fitted values with observed values
# -------------------------------------------------------
par(mfrow=c(2,2))

plot(reg.simples$fit,price,xlab="Valores ajustados",ylab="Preco (x1000 reais)")
title("Tamanho")
abline(0,1)
legend("topleft",paste("R2=",round(summary(reg.simples)$adj.r,4),sep=""))

plot(reg.multipla$fit,price,xlab="Valores ajustados",ylab="Preco (x1000 reais)")
title("Tamanho e quartos")
abline(0,1)
legend("topleft",paste("R2=",round(summary(reg.multipla)$adj.r,4),sep=""))

plot(reg.multipla2$fit,price,xlab="Valores ajustados",ylab="Preco (x1000 reais)")
title("Tamanho, quartos e banheiros")
abline(0,1)
legend("topleft",paste("R2=",round(summary(reg.multipla2)$adj.r,4),sep=""))

plot(reg.multipla3$fit,price,xlab="Valores ajustados",ylab="Preco (x1000 reais)")
title("Tamanho, quartos, banheiros e alvenaria")
abline(0,1)
legend("topleft",paste("R2=",round(summary(reg.multipla3)$adj.r,4),sep=""))


dev.off()