library(ISLR)
library(MASS)
data("Boston")
dim(Boston)
str(Boston)
attach(Boston)
#b Scatter plot
pairs(Boston)
library(ggplot2)
#c
Boston.corr=cor(Boston)
Boston.corr.crim<-Boston.corr[-1,1]
print(
  Boston.corr.crim[order(abs(Boston.corr.crim), decreasing = T)]
)
par(mfrow=c(2,2))
# get the four most correlated variables
aux = names(Boston.corr.crim[order(abs(Boston.corr.crim), decreasing = T)][1:4])
for(i in aux){
  plot(get(i), crim, xlab=i)
}
#Crime Rate
summary(crim)
length(crim[crim>30])
#Tax Rate
par(mfrow=c(1,1))
hist(tax)
length(tax[tax>500])
#Pupil Teacher Ratio
hist(ptratio)
length(ptratio[ptratio<14])
#e
table(chas)
#f
median(ptratio)
#g
subs.lw<-which(medv<median(medv))
print(subs.lw)
#Compare with the rest of the other predictors.

Boston.corr.subs.lw = cor(Boston[subs.lw, ])
corr.compare = data.frame('lower'=Boston.corr.subs.lw[, "medv"], 'all'=Boston.corr[, "medv"])
corr.compare$diff = corr.compare$lower - corr.compare$all

#Check how much vary the differences.

hist(corr.compare$diff, xlab="Correlation Differences")
hist(abs(corr.compare$diff), xlab="Correlation Differences")
#The main correlation diffences were at the variables:
  
  main.diffs = head(corr.compare[order(abs(corr.compare$diff), decreasing = T), ], 5)

print(main.diffs)
print(rownames(main.diffs))
#h
hist(rm, main="Distribution of Rooms by Dwelling", xlab="Rooms")
#More than 7 rooms per dweling
length(rm[rm>7])
#More than 8 rooms per dweling
length(rm[rm>8])
#Let's see the prices of these houses compared over all others suburb houses.

frm =as.factor(as.character(lapply(rm, function(x) ifelse(x>8, "]8, +Inf[", ifelse(x>7,"]7,8]","[0,7]")))))
plot(frm, medv, varwidth=T, xlab="Number of Rooms", 
     ylab="Median Values by $1000s",
     title="Median Value of Owner-Occupied Homes")

Boston[rm>8 & medv<30, ]