midterm

library(ISLR2)
library(GGally)

## Loading required package: ggplot2

## Registered S3 method overwritten by 'GGally':
##   method from   
##   +.gg   ggplot2

library(ggplot2)
# Load Boston data
data(Boston)
# (a) View dataset
head(Boston)

##      crim zn indus chas   nox    rm  age    dis rad tax ptratio lstat medv
## 1 0.00632 18  2.31    0 0.538 6.575 65.2 4.0900   1 296    15.3  4.98 24.0
## 2 0.02731  0  7.07    0 0.469 6.421 78.9 4.9671   2 242    17.8  9.14 21.6
## 3 0.02729  0  7.07    0 0.469 7.185 61.1 4.9671   2 242    17.8  4.03 34.7
## 4 0.03237  0  2.18    0 0.458 6.998 45.8 6.0622   3 222    18.7  2.94 33.4
## 5 0.06905  0  2.18    0 0.458 7.147 54.2 6.0622   3 222    18.7  5.33 36.2
## 6 0.02985  0  2.18    0 0.458 6.430 58.7 6.0622   3 222    18.7  5.21 28.7

# (b) Pairwise scatterplots (first 6 variables for simplicity)
ggpairs(Boston[, 1:6])

# (c) Correlation of crim with other predictors
cor(Boston$crim, Boston)

##      crim         zn     indus        chas       nox         rm       age
## [1,]    1 -0.2004692 0.4065834 -0.05589158 0.4209717 -0.2192467 0.3527343
##             dis       rad       tax   ptratio     lstat       medv
## [1,] -0.3796701 0.6255051 0.5827643 0.2899456 0.4556215 -0.3883046

# (d) Summary of key predictors
summary(Boston$crim)

##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
##  0.00632  0.08204  0.25651  3.61352  3.67708 88.97620

summary(Boston$tax)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   187.0   279.0   330.0   408.2   666.0   711.0

summary(Boston$ptratio)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   12.60   17.40   19.05   18.46   20.20   22.00

sum(Boston$chas == 1)

## [1] 35

median(Boston$ptratio)

## [1] 19.05

Boston[which.min(Boston$medv), ]

##        crim zn indus chas   nox    rm age    dis rad tax ptratio lstat medv
## 399 38.3518  0  18.1    0 0.693 5.453 100 1.4896  24 666    20.2 30.59    5

sum(Boston$rm > 7)

## [1] 64