#################
# function form #
#################
# part 1
rm(list = ls())   
ad = "https://www.fsb.miamioh.edu/lij14/400_house.txt"
data = read.table(url(ad), header=T)
attach(data)
mean(rprice)
summary(lm(rprice~age))$coef

logrprice = log(rprice)
summary(lm(logrprice~age))$coef

logarea = log(area)
summary(lm(logrprice~logarea))$coef

# part 2
plot(rprice~age,col=ifelse(age>=100,"blue","red"))
abline(lm(rprice~age))

qm = lm(rprice~poly(age,2,raw=TRUE))
plot(rprice~age, col=ifelse(age>=100,"blue","red"))
curve(predict(qm,newdata=data.frame(age=x)),add=T)

agesq = age^2
summary(lm(rprice~age+agesq))$coef

# part 3
summary(lm(rprice[age<18]~baths[age<18]))$coef
summary(lm(rprice[age>18]~baths[age>18]))$coef
inta = age*baths
summary(lm(rprice~baths+inta))$coef

# part 4
m = lm(rprice~baths+age+area)
yhat = fitted(m)
uhat = resid(m)
rprice[uhat==min(uhat)]
yhat[uhat==min(uhat)]
uhat[uhat==min(uhat)]

############
# optional #
############

#  out-of-sample forecast
ad = "https://www.fsb.miamioh.edu/lij14/400_house.txt"
da = read.table(url(ad), header=T)  
attach(da)
m = lm(rprice~baths+age+area)
summary(m)
m$coef[1]+m$coef[2]*2+m$coef[3]*40+m$coef[4]*1000
predict(m, newdata = data.frame(baths=2, age = 40,area=1000))


# interval forecast
predict(m, newdata = data.frame(baths=2, age = 40,area=1000),interval = "confidence", level = 0.95)
z1 = baths-2
z2 = age-40
z3 = area-1000
lm(rprice~z1+z2+z3)$coef[1]
confint(lm(rprice~z1+z2+z3))[1,]

predict(m, newdata = data.frame(baths=2, age = 40,area=1000),interval = "prediction", level = 0.95)
summary(lm(rprice~z1+z2+z3))
50772.869+qt(0.975,317)*sqrt(2759.982^2+21340^2)
50772.869-qt(0.975,317)*sqrt(2759.982^2+21340^2)


###############
#mini project:#
###############
#  function form
install.packages("ISLR")
library(ISLR)
data(Auto)
head(Auto)
attach(Auto)

plot(weight, mpg)
abline(lm(mpg~weight))

weightsq = weight^2
summary(lm(mpg~weight+weightsq))$coef

qm = lm(mpg~poly(weight,2,raw=TRUE))
plot(mpg~weight)
curve(predict(qm,newdata=data.frame(weight=x)),add=T)

logmpg = log(mpg)
plot(logmpg~weight)
abline(lm(logmpg~weight))

inta = weight*horsepower
summary(lm(mpg~weight+inta))$coef

logweight = log(weight)
summary(lm(logmpg~logweight))$coef



x = 1/weight
summary(lm(mpg~x))
plot(mpg~x)
abline(lm(mpg~x))