#####################
# simple regression #
#####################

# part 1
# if necessary, run search(), then run detach(data_that_you_attahed_before) 
ad = "https://www.fsb.miamioh.edu/lij14/400_house.txt"
data = read.table(url(ad), header=T)  
head(data)
attach(data)
plot(baths, rprice)

mean(rprice[baths==1])
mean(rprice[baths==2])
mean(rprice[baths==3])

plot(baths, rprice)
abline(lm(rprice ~ baths))

# part 2
summary(lm(rprice~baths))
beta1hat = cov(rprice, baths)/var(baths)
beta1hat

beta0hat = mean(rprice)-beta1hat*mean(baths)
beta0hat

uhat = rprice-beta0hat-beta1hat*baths
RSE = sqrt(sum(uhat^2)/(length(rprice)-2))
RSE

R_squared = 1 - sum(uhat^2)/sum((rprice-mean(rprice))^2)
R_squared

confint(lm(rprice~baths))

# part 3
n = nrow(data)
betahat1.v = rep(0,n)
for (j in 1:n) {
	subsample = data[-j,]
	betahat1.v[j] = coef(lm(rprice~baths,data=subsample))[2]
}
betahat1.v[1:5]
hist(betahat1.v, main="Sampling Distribution of Beta1hat", xlab="Beta1hat")

# part 4
my_mod=lm(rprice~baths)
yhat = fitted(my_mod)           
head(yhat)
uhat = resid(my_mod)
head(uhat)
mean(uhat)

R_squared = cor(rprice, yhat)^2
R_squared


################
# mini project #
################
# check out https://fsb.miamioh.edu/lij14/311r_BasicR.pdf
# Learn R at https://stats.oarc.ucla.edu/r/
# google "R, HistData" to learn more about the HistData package

install.packages("HistData", repos = "https://cloud.r-project.org/")
library(HistData)
ls("package:HistData")
data(GaltonFamilies)
attach(GaltonFamilies)
head(GaltonFamilies)

plot(father, childHeight)
abline(lm(childHeight~father))

summary(lm(childHeight~father))
yhat = 40.13929+0.38451*70
yhat

newdata = data.frame(father=70)
m = lm(childHeight~father)
predict(m,newdata)

names(m)
head(m$residuals)
names(summary(m))
summary(m)$r.squared
summary(m)$coefficients

summary(lm(childHeight~mother))$r.squared
summary(lm(childHeight~mother))$coefficients