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### Regression - Boston Data
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library(MASS)  # install.packages("MASS")

data(Boston)

Boston

class(Boston)

dim(Boston)
head(Boston)
head(Boston, 100)
names(Boston)

?Boston  # see explanation for variables


#1  crim     per capita crime rate by town.
#2  zn       proportion of residential land zoned for lots over 25,000 sq.ft.
#3  indus    proportion of non-retail business acres per town.
#4  chas     Charles River dummy variable (= 1 if tract bounds river; 0 otherwise).
#5  nox      nitrogen oxides concentration (parts per 10 million).
#6  rm       average number of rooms per dwelling.
#7  age      proportion of owner-occupied units built prior to 1940.
#8  dis      weighted mean of distances to five Boston employment centres.
#9  rad      index of accessibility to radial highways.
#10 tax      full-value property-tax rate per $10,000.
#11 ptratio  pupil-teacher ratio by town.
#12 black    1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town.
#13 lstat    lower status of the population (percent).
#14 medv     median value of owner-occupied homes in \$1000s.


# 13 lstat = lower status of the population (percent)
#      Proportion of population that is lower status
#      = 1/2 (proportion of adults without,
#      some high school education and proportion of male
#      workers classified as laborers). The logarithmic
#      specification implies that socioeconomic status
#      distinctions mean more in the upper brackets of
#      society than in the lower classes. Source: 1970 U. S. Census



library(tidyverse)   # install.packages(tidyverse")
  Boston <- as_tibble(Boston)


class(Boston)
is_tibble(Boston)
is.data.frame(Boston)


Boston
print(Boston, n=100)

fix(Boston)


Boston[ ,1]

Boston[,"zn"]

Boston$age

attach(Boston)  # now you can use their rownames

age
indus



#- Correlaiton Plots
pairs(Boston)   # shows scatterplot matrix (large)

cor(Boston)

library(corrplot)   # install.packages("corrplot")
corrplot(cor(Boston), method="number")
corrplot(cor(Boston))



#- Scatter plots
layout( matrix(1:12, 3, 4) )
plot(crim, medv)
plot(zn, medv)
plot(indus, medv)
plot(nox, medv)
plot(rm, medv)
plot(age, medv)
plot(dis, medv)
plot(rad, medv)
plot(tax, medv)
plot(ptratio, medv)
plot(black, medv)
plot(lstat, medv)

plot(chas, medv)
layout(1)


#- Histogram of the respoonse variable
hist(medv)



#1  crim
#2  zn
#3  indus
#4  chas
#5  nox
#6  rm
#7  age
#8  dis
#9  rad
#10 tax
#11 ptratio
#12 black
#13 lstat
#14 medv  <- response (Y)


#- Regression with all variables
Reg01 <- lm(medv ~ . , data=Boston)
summary(Reg01)

plot(Reg01)



#- Backward stepwise regression
Reg02 <- lm(medv ~ . -age, data=Boston)
summary(Reg02)


Reg03 <- lm(medv ~ . -age-indus, data=Boston)
summary(Reg03)

plot(Reg03)


Reg04 <- lm(medv ~ crim + zn + indus, data=Boston)
summary(Reg04)



#--- Looking at the result
str(Reg03)  # click on environment tab in Rstudio

Reg03$residuals

plot(Reg03$residuals)