Boston housing
Punith Kumar
12/29/2017
Analysis of factors affecting the cause of Boston housing price
Boston.df <- read.csv(paste("Boston.csv", sep = ""))
View(Boston.df)
attach(Boston.df)
dim(Boston.df)## [1] 506 14library(psych)
describe(Boston.df)## vars n mean sd median trimmed mad min max range
## CRIM 1 506 3.61 8.60 0.26 1.68 0.33 0.01 88.98 88.97
## ZN 2 506 11.36 23.32 0.00 5.08 0.00 0.00 100.00 100.00
## INDUS 3 506 11.14 6.86 9.69 10.93 9.37 0.46 27.74 27.28
## CHAS 4 506 0.07 0.25 0.00 0.00 0.00 0.00 1.00 1.00
## NOX 5 506 0.55 0.12 0.54 0.55 0.13 0.38 0.87 0.49
## RM 6 506 6.28 0.70 6.21 6.25 0.51 3.56 8.78 5.22
## AGE 7 506 68.57 28.15 77.50 71.20 28.98 2.90 100.00 97.10
## DIS 8 506 3.80 2.11 3.21 3.54 1.91 1.13 12.13 11.00
## RAD 9 506 9.55 8.71 5.00 8.73 2.97 1.00 24.00 23.00
## TAX 10 506 408.24 168.54 330.00 400.04 108.23 187.00 711.00 524.00
## PT 11 506 18.46 2.16 19.05 18.66 1.70 12.60 22.00 9.40
## B 12 506 356.67 91.29 391.44 383.17 8.09 0.32 396.90 396.58
## LSTAT 13 506 12.65 7.14 11.36 11.90 7.11 1.73 37.97 36.24
## MV 14 506 22.53 9.20 21.20 21.56 5.93 5.00 50.00 45.00
## skew kurtosis se
## CRIM 5.19 36.60 0.38
## ZN 2.21 3.95 1.04
## INDUS 0.29 -1.24 0.30
## CHAS 3.39 9.48 0.01
## NOX 0.72 -0.09 0.01
## RM 0.40 1.84 0.03
## AGE -0.60 -0.98 1.25
## DIS 1.01 0.46 0.09
## RAD 1.00 -0.88 0.39
## TAX 0.67 -1.15 7.49
## PT -0.80 -0.30 0.10
## B -2.87 7.10 4.06
## LSTAT 0.90 0.46 0.32
## MV 1.10 1.45 0.41# Display of the structure of the Boston.f data frames
str(Boston.df)## 'data.frame': 506 obs. of 14 variables:
## $ CRIM : num 0.00632 0.02731 0.02729 0.03237 0.06905 ...
## $ ZN : num 18 0 0 0 0 0 12.5 12.5 12.5 12.5 ...
## $ INDUS: num 2.31 7.07 7.07 2.18 2.18 ...
## $ CHAS : int 0 0 0 0 0 0 0 0 0 0 ...
## $ NOX : num 0.538 0.469 0.469 0.458 0.458 ...
## $ RM : num 6.57 6.42 7.18 7 7.15 ...
## $ AGE : num 65.2 78.9 61.1 45.8 54.2 ...
## $ DIS : num 4.09 4.97 4.97 6.06 6.06 ...
## $ RAD : int 1 2 2 3 3 3 5 5 5 5 ...
## $ TAX : int 296 242 242 222 222 222 311 311 311 311 ...
## $ PT : num 15.3 17.8 17.8 18.7 18.7 ...
## $ B : num 397 397 393 395 397 ...
## $ LSTAT: num 4.98 9.14 4.03 2.94 5.33 ...
## $ MV : num 24 21.6 34.7 33.4 36.2 ...summary(Boston.df)## CRIM ZN INDUS CHAS
## Min. : 0.00632 Min. : 0.00 Min. : 0.46 Min. :0.00000
## 1st Qu.: 0.08205 1st Qu.: 0.00 1st Qu.: 5.19 1st Qu.:0.00000
## Median : 0.25651 Median : 0.00 Median : 9.69 Median :0.00000
## Mean : 3.61352 Mean : 11.36 Mean :11.14 Mean :0.06917
## 3rd Qu.: 3.67708 3rd Qu.: 12.50 3rd Qu.:18.10 3rd Qu.:0.00000
## Max. :88.97620 Max. :100.00 Max. :27.74 Max. :1.00000
## NOX RM AGE DIS
## Min. :0.3850 Min. :3.561 Min. : 2.90 Min. : 1.130
## 1st Qu.:0.4490 1st Qu.:5.886 1st Qu.: 45.02 1st Qu.: 2.100
## Median :0.5380 Median :6.208 Median : 77.50 Median : 3.207
## Mean :0.5547 Mean :6.285 Mean : 68.57 Mean : 3.795
## 3rd Qu.:0.6240 3rd Qu.:6.623 3rd Qu.: 94.08 3rd Qu.: 5.188
## Max. :0.8710 Max. :8.780 Max. :100.00 Max. :12.127
## RAD TAX PT B
## Min. : 1.000 Min. :187.0 Min. :12.60 Min. : 0.32
## 1st Qu.: 4.000 1st Qu.:279.0 1st Qu.:17.40 1st Qu.:375.38
## Median : 5.000 Median :330.0 Median :19.05 Median :391.44
## Mean : 9.549 Mean :408.2 Mean :18.46 Mean :356.67
## 3rd Qu.:24.000 3rd Qu.:666.0 3rd Qu.:20.20 3rd Qu.:396.23
## Max. :24.000 Max. :711.0 Max. :22.00 Max. :396.90
## LSTAT MV
## Min. : 1.73 Min. : 5.00
## 1st Qu.: 6.95 1st Qu.:17.02
## Median :11.36 Median :21.20
## Mean :12.65 Mean :22.53
## 3rd Qu.:16.95 3rd Qu.:25.00
## Max. :37.97 Max. :50.00#number of house near Charles river 1= if tract bounds the river and 0 = otherwise
CharTable <- table(Boston.df$CHAS)
CharTable##
## 0 1
## 471 35#Distance of Radial highways access to boston houses
Acess <- table(Boston.df$RAD)
Acess##
## 1 2 3 4 5 6 7 8 24
## 20 24 38 110 115 26 17 24 132#pupil-teacher ratio by town
population <-table(Boston.df$PT)
population##
## 12.60000038 13 13.60000038 14.39999962 14.69999981 14.80000019
## 3 12 1 1 34 3
## 14.89999962 15.10000038 15.19999981 15.30000019 15.5 15.60000038
## 4 1 13 3 1 2
## 15.89999962 16 16.10000038 16.39999962 16.60000038 16.79999924
## 2 5 5 6 16 4
## 16.89999962 17 17.29999924 17.39999962 17.60000038 17.79999924
## 5 4 1 18 7 23
## 17.89999962 18 18.20000076 18.29999924 18.39999962 18.5
## 11 5 4 4 16 4
## 18.60000038 18.70000076 18.79999924 18.89999962 19 19.10000038
## 17 9 2 3 4 17
## 19.20000076 19.60000038 19.70000076 20.10000038 20.20000076 20.89999962
## 19 8 8 5 140 11
## 21 21.10000038 21.20000076 22
## 27 1 15 2mytab <-xtabs(~RAD + AGE,data=Boston.df)
addmargins(mytab)## AGE
## RAD 2.900000095 6 6.199999809 6.5 6.599999905 6.800000191 7.800000191
## 1 0 0 0 0 0 0 0
## 2 0 0 0 0 0 0 0
## 3 1 0 0 1 1 0 0
## 4 0 0 1 0 1 0 1
## 5 0 1 0 0 0 0 0
## 6 0 0 0 0 0 0 1
## 7 0 0 0 0 0 1 0
## 8 0 0 0 0 0 0 0
## 24 0 0 0 0 0 0 0
## Sum 1 1 1 1 2 1 2
## AGE
## RAD 8.399999619 8.899999619 9.800000191 9.899999619 10 13 13.89999962
## 1 0 0 0 1 0 0 0
## 2 0 0 0 0 0 0 0
## 3 0 0 0 0 0 0 1
## 4 0 0 1 0 0 0 0
## 5 0 0 0 0 1 0 0
## 6 0 0 0 0 0 0 0
## 7 1 1 0 0 0 1 0
## 8 0 0 0 0 0 0 0
## 24 0 0 0 0 0 0 0
## Sum 1 1 1 1 1 1 1
## AGE
## RAD 14.69999981 15.30000019 15.69999981 15.80000019 16.29999924 17
## 1 0 0 0 0 0 0
## 2 0 0 1 0 0 0
## 3 0 1 0 1 1 0
## 4 0 0 0 0 0 0
## 5 1 0 0 0 0 0
## 6 0 0 0 0 0 0
## 7 0 0 0 0 0 0
## 8 0 0 0 0 0 1
## 24 0 0 0 0 0 0
## Sum 1 1 1 1 1 1
## AGE
## RAD 17.20000076 17.5 17.70000076 17.79999924 18.39999962 18.5
## 1 0 0 0 0 0 0
## 2 0 0 0 0 0 0
## 3 0 0 0 0 0 0
## 4 1 1 0 1 1 1
## 5 0 0 0 0 0 0
## 6 0 0 0 0 0 1
## 7 0 1 1 0 1 0
## 8 0 0 0 0 0 0
## 24 0 0 0 0 0 0
## Sum 1 2 1 1 2 2
## AGE
## RAD 18.79999924 19.10000038 19.5 20.10000038 20.79999924 21.10000038
## 1 1 1 0 0 1 0
## 2 0 0 0 0 0 0
## 3 0 0 0 0 0 0
## 4 0 0 1 0 0 1
## 5 0 0 0 1 0 0
## 6 0 0 0 0 0 0
## 7 0 0 0 0 0 0
## 8 0 0 0 0 0 0
## 24 0 0 0 0 0 0
## Sum 1 1 1 1 1 1
## AGE
## RAD 21.39999962 21.5 21.79999924 21.89999962 22.29999924 22.89999962
## 1 0 0 0 0 0 0
## 2 0 0 0 0 0 0
## 3 0 0 1 0 0 0
## 4 2 0 0 1 1 0
## 5 0 1 0 1 0 0
## 6 0 0 0 0 0 1
## 7 0 0 0 0 0 0
## 8 1 0 0 0 0 0
## 24 0 0 0 0 0 0
## Sum 3 1 1 2 1 1
## AGE
## RAD 23.29999924 23.39999962 24.79999924 25.79999924 26.29999924
## 1 1 0 1 0 0
## 2 0 0 0 0 0
## 3 0 0 0 0 0
## 4 0 1 0 1 0
## 5 0 0 0 0 1
## 6 0 0 0 0 0
## 7 0 0 0 0 0
## 8 0 0 0 0 0
## 24 0 0 0 0 0
## Sum 1 1 1 1 1
## AGE
## RAD 27.60000038 27.70000076 27.89999962 28.10000038 28.39999962
## 1 0 0 0 0 1
## 2 0 0 0 0 0
## 3 0 0 0 0 0
## 4 1 2 1 0 0
## 5 0 0 0 1 0
## 6 0 0 0 0 0
## 7 0 0 0 0 0
## 8 0 0 0 0 0
## 24 0 0 0 0 0
## Sum 1 2 1 1 1
## AGE
## RAD 28.79999924 28.89999962 29.10000038 29.20000076 29.29999924
## 1 0 0 0 0 0
## 2 0 0 0 0 0
## 3 0 0 0 0 0
## 4 0 1 0 0 1
## 5 0 1 1 0 0
## 6 1 0 0 0 0
## 7 0 0 0 0 0
## 8 0 0 0 1 0
## 24 0 0 0 0 0
## Sum 1 2 1 1 1
## AGE
## RAD 29.70000076 30.20000076 30.79999924 31.10000038 31.29999924 31.5
## 1 0 0 0 0 0 1
## 2 0 0 0 0 0 0
## 3 0 0 0 0 0 0
## 4 1 0 0 2 0 0
## 5 0 1 1 0 0 0
## 6 0 0 0 0 1 0
## 7 0 0 0 0 0 0
## 8 0 0 0 0 0 0
## 24 0 0 0 0 0 0
## Sum 1 1 1 2 1 1
## AGE
## RAD 31.89999962 32 32.09999847 32.20000076 32.29999924 32.90000153 33
## 1 1 1 0 0 0 0 0
## 2 0 0 0 0 0 0 0
## 3 0 0 0 0 0 0 0
## 4 1 1 1 2 1 1 1
## 5 0 0 0 1 0 0 0
## 6 0 0 0 0 0 0 0
## 7 0 0 0 0 0 0 0
## 8 0 0 0 0 0 0 0
## 24 0 0 0 0 0 0 0
## Sum 2 2 1 3 1 1 1
## AGE
## RAD 33.09999847 33.20000076 33.29999924 33.5 33.79999924 34.09999847
## 1 0 0 0 0 0 0
## 2 0 0 0 0 0 1
## 3 0 0 1 0 1 0
## 4 0 1 0 1 0 0
## 5 1 0 0 0 0 0
## 6 0 0 0 0 0 0
## 7 0 0 0 0 0 0
## 8 0 0 0 0 0 0
## 24 0 0 0 0 0 0
## Sum 1 1 1 1 1 1
## AGE
## RAD 34.20000076 34.5 34.90000153 35.70000076 35.90000153 36.09999847
## 1 0 1 0 0 0 0
## 2 0 0 0 1 0 0
## 3 1 0 0 0 0 0
## 4 0 0 0 0 1 0
## 5 0 1 0 0 0 1
## 6 0 0 0 0 0 0
## 7 0 0 1 0 0 0
## 8 0 0 0 0 0 0
## 24 0 0 0 0 0 0
## Sum 1 2 1 1 1 1
## AGE
## RAD 36.59999847 36.79999924 36.90000153 37.20000076 37.29999924
## 1 0 0 0 0 0
## 2 1 0 1 0 0
## 3 0 0 0 0 0
## 4 1 1 0 0 0
## 5 1 0 0 1 1
## 6 0 0 0 0 0
## 7 0 0 0 0 0
## 8 0 0 0 0 0
## 24 0 0 0 0 0
## Sum 3 1 1 1 1
## AGE
## RAD 37.79999924 38.09999847 38.29999924 38.40000153 38.5 38.90000153 39
## 1 0 0 0 0 0 0 0
## 2 0 0 1 1 0 0 0
## 3 0 0 0 0 0 0 0
## 4 1 0 0 0 0 0 0
## 5 0 1 0 0 1 1 1
## 6 0 0 0 0 0 0 0
## 7 0 0 0 0 0 0 0
## 8 0 0 0 0 0 0 0
## 24 0 0 0 0 0 0 0
## Sum 1 1 1 1 1 1 1
## AGE
## RAD 40 40.09999847 40.29999924 40.40000153 40.5 41.09999847 41.5
## 1 0 0 0 0 0 0 0
## 2 0 0 0 0 0 0 0
## 3 1 0 0 0 0 0 0
## 4 0 0 0 0 0 0 0
## 5 0 1 0 0 1 1 1
## 6 0 0 0 0 0 0 0
## 7 0 0 0 1 0 1 0
## 8 0 0 0 0 0 0 0
## 24 0 0 1 0 0 0 0
## Sum 1 1 1 1 1 2 1
## AGE
## RAD 41.90000153 42.09999847 42.20000076 42.29999924 42.40000153
## 1 0 0 0 0 0
## 2 0 0 0 0 0
## 3 0 1 0 0 0
## 4 0 0 0 1 1
## 5 0 0 0 0 0
## 6 0 0 1 0 0
## 7 0 0 0 0 0
## 8 0 0 0 0 0
## 24 1 0 0 0 0
## Sum 1 1 1 1 1
## AGE
## RAD 42.59999847 42.79999924 43.40000153 43.70000076 44.40000153 45
## 1 0 0 0 0 1 0
## 2 0 0 0 0 0 0
## 3 0 0 0 0 0 0
## 4 0 1 0 0 0 0
## 5 0 0 0 1 0 1
## 6 1 0 0 0 0 0
## 7 0 0 0 0 0 0
## 8 0 0 1 0 0 0
## 24 0 0 0 0 0 0
## Sum 1 1 1 1 1 1
## AGE
## RAD 45.09999847 45.40000153 45.59999847 45.70000076 45.79999924
## 1 0 0 0 0 0
## 2 0 0 0 0 0
## 3 1 0 0 0 1
## 4 0 0 0 1 0
## 5 0 1 0 0 1
## 6 0 0 1 0 0
## 7 0 0 0 0 0
## 8 0 0 0 0 0
## 24 0 0 0 0 0
## Sum 1 1 1 1 2
## AGE
## RAD 46.29999924 46.70000076 47.20000076 47.40000153 47.59999847 48
## 1 0 0 0 0 0 0
## 2 0 0 0 0 0 0
## 3 0 0 0 0 1 1
## 4 0 1 0 0 0 0
## 5 1 0 1 1 0 0
## 6 0 0 0 0 0 0
## 7 0 0 0 0 0 0
## 8 0 0 1 0 0 0
## 24 0 0 0 0 0 0
## Sum 1 1 2 1 1 1
## AGE
## RAD 48.20000076 48.5 49 49.09999847 49.29999924 49.70000076 49.90000153
## 1 0 0 0 0 1 0 0
## 2 0 0 0 0 0 0 0
## 3 0 1 0 0 0 0 0
## 4 0 0 1 0 0 0 0
## 5 0 0 0 0 0 1 1
## 6 0 0 0 0 0 0 0
## 7 0 0 0 1 0 0 0
## 8 0 0 0 0 0 0 0
## 24 1 0 0 0 0 0 0
## Sum 1 1 1 1 1 1 1
## AGE
## RAD 51 51.79999924 51.90000153 52.29999924 52.5 52.59999847 52.79999924
## 1 0 0 0 0 0 0 0
## 2 0 0 0 0 0 0 0
## 3 0 1 0 1 0 0 0
## 4 1 0 0 0 1 0 1
## 5 0 0 0 1 0 1 0
## 6 0 0 0 0 0 0 0
## 7 0 0 0 0 0 0 0
## 8 0 0 0 0 0 0 0
## 24 0 0 1 0 0 0 0
## Sum 1 1 1 2 1 1 1
## AGE
## RAD 52.90000153 53.20000076 53.59999847 53.70000076 53.79999924 54
## 1 0 0 0 0 0 0
## 2 0 0 0 0 0 0
## 3 0 0 1 0 0 0
## 4 0 0 1 0 1 0
## 5 0 0 0 1 0 0
## 6 1 0 0 0 0 1
## 7 0 0 0 0 0 0
## 8 0 0 0 0 0 0
## 24 0 1 0 0 0 0
## Sum 1 1 2 1 1 1
## AGE
## RAD 54.20000076 54.29999924 54.40000153 56 56.09999847 56.40000153 56.5
## 1 0 0 0 0 0 0 0
## 2 0 0 0 0 0 0 0
## 3 1 0 0 0 1 0 0
## 4 0 0 0 0 0 0 1
## 5 0 1 1 1 0 1 0
## 6 0 1 0 0 0 0 0
## 7 0 0 0 0 0 0 0
## 8 0 0 0 0 0 0 0
## 24 0 0 0 0 0 0 0
## Sum 1 2 1 1 1 1 1
## AGE
## RAD 56.70000076 56.79999924 57.79999924 58 58.09999847 58.40000153 58.5
## 1 0 0 0 0 0 0 0
## 2 0 0 1 0 0 0 0
## 3 0 1 0 0 0 1 0
## 4 0 0 0 1 0 0 0
## 5 0 0 0 0 0 0 1
## 6 0 0 0 0 0 0 0
## 7 0 0 0 0 1 0 0
## 8 0 0 0 0 0 0 0
## 24 1 0 0 0 0 0 0
## Sum 1 1 1 1 1 1 1
## AGE
## RAD 58.70000076 58.79999924 59.09999847 59.5 59.59999847 59.70000076
## 1 0 0 0 0 0 1
## 2 0 0 0 0 0 0
## 3 2 0 0 1 0 0
## 4 0 1 1 0 0 0
## 5 0 0 0 0 1 0
## 6 0 0 0 0 0 0
## 7 0 0 0 0 0 0
## 8 0 0 0 0 0 0
## 24 0 0 0 0 0 1
## Sum 2 1 1 1 1 2
## AGE
## RAD 61.09999847 61.40000153 61.5 61.79999924 62 62.20000076 62.5
## 1 0 0 0 0 0 0 0
## 2 1 0 0 0 0 0 1
## 3 0 0 1 0 1 1 0
## 4 0 0 0 1 0 0 0
## 5 0 1 0 0 0 0 0
## 6 0 0 0 0 0 0 0
## 7 0 0 0 0 0 0 0
## 8 0 0 1 0 0 0 0
## 24 0 0 0 0 0 0 0
## Sum 1 1 2 1 1 1 1
## AGE
## RAD 62.79999924 63 63.09999847 64.5 64.69999695 65.09999847 65.19999695
## 1 0 0 0 0 0 0 1
## 2 0 0 1 0 0 0 0
## 3 0 0 0 0 0 0 0
## 4 0 1 0 0 0 0 0
## 5 1 0 0 1 0 0 0
## 6 0 0 0 0 0 1 1
## 7 0 0 0 0 0 0 0
## 8 0 0 0 0 0 0 0
## 24 0 0 0 0 1 0 0
## Sum 1 1 1 1 1 1 2
## AGE
## RAD 65.30000305 65.40000153 66.09999847 66.19999695 66.5 66.59999847 67
## 1 0 0 0 0 0 0 0
## 2 0 0 1 0 0 0 0
## 3 0 0 0 0 0 0 0
## 4 0 0 0 0 0 0 0
## 5 0 0 0 0 0 1 1
## 6 1 0 0 0 0 0 0
## 7 0 0 0 0 0 0 0
## 8 0 0 0 1 1 0 0
## 24 0 1 0 0 0 0 0
## Sum 1 1 1 1 1 1 1
## AGE
## RAD 67.19999695 67.59999847 67.80000305 68.09999847 68.19999695
## 1 0 0 0 0 0
## 2 0 0 0 0 0
## 3 0 0 0 0 0
## 4 1 0 0 0 0
## 5 0 0 0 0 1
## 6 0 0 0 0 0
## 7 0 0 0 0 0
## 8 0 0 1 1 0
## 24 0 1 0 0 0
## Sum 1 1 1 1 1
## AGE
## RAD 68.69999695 68.80000305 69.09999847 69.5 69.59999847 69.69999695
## 1 0 0 1 0 0 0
## 2 0 0 0 0 1 1
## 3 0 1 0 0 0 0
## 4 0 0 0 1 0 0
## 5 1 0 0 0 0 0
## 6 0 0 0 0 0 0
## 7 0 0 0 0 0 0
## 8 0 0 0 0 0 0
## 24 0 0 0 0 0 0
## Sum 1 1 1 1 1 1
## AGE
## RAD 70.19999695 70.30000305 70.40000153 70.59999847 71 71.30000305
## 1 0 0 0 0 0 0
## 2 0 0 0 0 0 0
## 3 0 0 0 0 0 0
## 4 0 0 1 0 0 0
## 5 0 0 0 0 0 1
## 6 0 0 0 1 0 0
## 7 1 1 0 0 0 0
## 8 0 0 1 0 0 0
## 24 0 0 0 1 1 0
## Sum 1 1 2 2 1 1
## AGE
## RAD 71.59999847 71.69999695 71.90000153 72.5 72.69999695 72.90000153
## 1 0 0 0 0 0 0
## 2 0 0 0 0 0 0
## 3 0 0 0 0 0 0
## 4 0 1 0 0 1 0
## 5 0 0 0 0 0 0
## 6 0 0 0 1 0 1
## 7 0 0 1 0 0 0
## 8 1 0 0 0 0 0
## 24 0 0 0 0 0 0
## Sum 1 1 1 1 1 1
## AGE
## RAD 73.09999847 73.30000305 73.40000153 73.5 73.90000153 74.30000305
## 1 0 0 0 0 0 0
## 2 0 0 0 0 1 0
## 3 0 0 0 0 0 0
## 4 0 0 0 0 0 0
## 5 0 0 1 0 0 1
## 6 1 0 0 1 0 0
## 7 0 0 0 0 0 0
## 8 0 1 0 0 0 0
## 24 0 0 0 0 0 0
## Sum 1 1 1 1 1 1
## AGE
## RAD 74.40000153 74.5 74.80000305 74.90000153 75 76 76.5 76.69999695
## 1 0 0 0 0 0 0 0 1
## 2 0 0 0 0 0 1 0 0
## 3 0 0 0 0 0 0 0 0
## 4 0 0 0 0 0 0 0 1
## 5 1 1 0 0 0 0 0 0
## 6 0 0 0 0 0 0 0 0
## 7 0 0 0 0 0 0 1 0
## 8 0 0 0 0 0 0 1 0
## 24 0 0 1 1 1 0 1 0
## Sum 1 1 1 1 1 1 3 2
## AGE
## RAD 76.90000153 77 77.30000305 77.69999695 77.80000305 78.09999847
## 1 0 0 0 0 0 0
## 2 0 0 0 0 0 0
## 3 0 0 0 0 0 0
## 4 0 0 1 1 0 0
## 5 0 0 0 0 0 0
## 6 0 0 0 0 0 0
## 7 0 0 0 0 0 0
## 8 1 0 0 1 0 0
## 24 0 1 0 0 1 1
## Sum 1 1 1 2 1 1
## AGE
## RAD 78.30000305 78.69999695 78.90000153 79.19999695 79.69999695
## 1 0 0 0 0 0
## 2 0 0 1 0 0
## 3 0 0 0 0 0
## 4 0 0 0 0 0
## 5 0 0 0 1 0
## 6 0 0 0 0 1
## 7 0 0 0 1 0
## 8 1 0 0 0 0
## 24 0 1 0 0 0
## Sum 1 1 1 2 1
## AGE
## RAD 79.80000305 79.90000153 80.30000305 80.80000305 81.30000305
## 1 0 0 0 1 0
## 2 0 0 0 0 0
## 3 0 0 0 0 0
## 4 0 0 0 0 0
## 5 0 1 0 0 0
## 6 0 0 0 0 0
## 7 0 0 0 0 0
## 8 0 1 0 1 0
## 24 1 0 1 0 1
## Sum 1 2 1 2 1
## AGE
## RAD 81.59999847 81.69999695 81.80000305 82 82.5 82.59999847 82.80000305
## 1 0 0 0 0 0 0 0
## 2 0 0 0 0 0 0 0
## 3 0 0 0 0 0 0 0
## 4 0 1 0 1 1 0 1
## 5 0 0 1 0 0 1 0
## 6 1 0 0 0 0 1 0
## 7 0 0 0 0 0 0 0
## 8 0 0 0 0 0 0 0
## 24 0 0 0 0 1 0 0
## Sum 1 1 1 1 2 2 1
## AGE
## RAD 82.90000153 83 83.19999695 83.30000305 83.40000153 83.5 83.69999695
## 1 0 0 0 0 0 0 0
## 2 0 0 0 0 0 0 0
## 3 0 0 0 1 0 0 0
## 4 0 0 1 0 0 1 0
## 5 1 0 0 0 0 0 0
## 6 0 0 0 0 0 0 0
## 7 0 0 0 0 0 0 0
## 8 0 1 0 0 0 0 0
## 24 1 1 0 0 1 0 1
## Sum 2 2 1 1 1 1 1
## AGE
## RAD 84 84.09999847 84.19999695 84.40000153 84.5 84.59999847 84.69999695
## 1 0 0 0 0 0 0 0
## 2 0 1 0 0 0 0 0
## 3 0 0 0 0 0 0 0
## 4 0 0 0 0 1 0 0
## 5 0 1 0 0 0 1 0
## 6 0 0 1 0 0 0 0
## 7 0 0 0 0 0 0 0
## 8 0 0 0 0 0 0 0
## 24 1 0 0 1 0 0 1
## Sum 1 2 1 1 1 1 1
## AGE
## RAD 85.09999847 85.19999695 85.40000153 85.5 85.69999695 85.90000153
## 1 0 0 0 0 0 0
## 2 0 0 0 0 0 0
## 3 0 0 0 1 0 0
## 4 0 0 0 0 1 0
## 5 1 1 1 0 0 1
## 6 0 0 0 0 0 0
## 7 0 0 0 0 0 0
## 8 0 0 0 0 0 0
## 24 1 0 1 0 0 0
## Sum 2 1 2 1 1 1
## AGE
## RAD 86.09999847 86.30000305 86.5 86.90000153 87.30000305 87.40000153
## 1 0 0 0 0 0 0
## 2 0 1 0 0 0 0
## 3 0 0 0 0 0 0
## 4 0 0 0 0 2 0
## 5 0 0 0 1 0 1
## 6 0 0 0 0 0 0
## 7 0 0 0 0 0 0
## 8 0 0 1 0 0 0
## 24 1 0 1 0 0 0
## Sum 1 1 2 1 2 1
## AGE
## RAD 87.59999847 87.90000153 88 88.19999695 88.40000153 88.5 88.59999847
## 1 0 0 0 0 0 0 0
## 2 0 0 0 0 1 0 0
## 3 0 0 0 0 0 0 0
## 4 0 0 0 0 0 0 1
## 5 0 0 1 0 0 1 0
## 6 0 0 0 1 0 0 0
## 7 0 0 0 0 0 0 0
## 8 0 0 0 0 0 1 0
## 24 1 4 2 0 1 0 0
## Sum 1 4 3 1 2 2 1
## AGE
## RAD 88.80000305 89 89.09999847 89.19999695 89.30000305 89.40000153 89.5
## 1 0 0 0 0 1 0 0
## 2 0 0 0 0 0 0 0
## 3 0 0 0 0 0 0 0
## 4 1 0 0 1 0 0 0
## 5 0 0 0 0 0 1 0
## 6 0 0 0 0 0 0 0
## 7 0 0 0 0 0 0 0
## 8 0 0 0 0 0 0 0
## 24 0 1 1 0 0 0 1
## Sum 1 1 1 1 1 1 1
## AGE
## RAD 89.59999847 89.80000305 89.90000153 90 90.30000305 90.40000153
## 1 0 0 0 0 0 0
## 2 0 0 0 0 0 0
## 3 0 1 0 0 0 0
## 4 0 0 0 0 1 1
## 5 0 0 0 1 0 0
## 6 0 0 0 0 0 0
## 7 0 0 0 0 0 0
## 8 0 0 0 0 0 0
## 24 1 0 1 1 0 0
## Sum 1 1 1 2 1 1
## AGE
## RAD 90.69999695 90.80000305 91 91.09999847 91.19999695 91.30000305
## 1 0 0 1 0 0 0
## 2 0 0 0 0 0 0
## 3 0 0 0 0 0 0
## 4 0 0 0 0 0 0
## 5 0 1 0 0 1 0
## 6 0 0 0 0 0 0
## 7 0 0 0 0 0 0
## 8 0 0 0 0 0 1
## 24 1 1 1 1 1 0
## Sum 1 2 2 1 2 1
## AGE
## RAD 91.40000153 91.5 91.59999847 91.69999695 91.80000305 91.90000153
## 1 0 0 0 0 0 0
## 2 0 0 0 0 0 0
## 3 0 0 0 0 0 0
## 4 0 0 0 1 0 0
## 5 0 1 1 0 1 1
## 6 0 0 0 0 0 0
## 7 0 0 0 0 0 0
## 8 0 0 0 0 0 0
## 24 1 0 0 0 1 1
## Sum 1 1 1 1 2 2
## AGE
## RAD 92.09999847 92.19999695 92.40000153 92.59999847 92.69999695
## 1 0 0 0 0 0
## 2 0 0 0 0 0
## 3 0 1 0 0 0
## 4 1 0 0 0 1
## 5 0 0 1 1 0
## 6 0 0 0 0 0
## 7 0 0 0 0 0
## 8 0 0 0 0 0
## 24 0 0 1 2 0
## Sum 1 1 2 3 1
## AGE
## RAD 92.90000153 93 93.30000305 93.40000153 93.5 93.59999847 93.80000305
## 1 0 0 0 0 0 0 0
## 2 1 0 0 0 0 0 0
## 3 0 0 0 0 0 0 0
## 4 0 0 0 0 1 1 0
## 5 0 1 0 0 0 0 2
## 6 1 0 0 0 0 0 0
## 7 0 0 0 0 0 0 0
## 8 0 0 0 1 0 0 0
## 24 0 0 2 0 0 1 0
## Sum 2 1 2 1 1 2 2
## AGE
## RAD 93.90000153 94 94.09999847 94.30000305 94.40000153 94.5 94.59999847
## 1 0 0 0 0 0 0 0
## 2 0 0 0 0 0 0 0
## 3 0 0 0 0 0 0 0
## 4 0 0 2 0 1 0 0
## 5 1 1 0 1 0 1 1
## 6 0 0 0 0 0 0 0
## 7 0 0 0 0 0 0 0
## 8 0 0 0 0 0 0 0
## 24 1 0 1 1 0 1 1
## Sum 2 1 3 2 1 2 2
## AGE
## RAD 94.69999695 94.80000305 94.90000153 95 95.19999695 95.30000305
## 1 0 0 0 0 0 0
## 2 0 0 0 0 0 0
## 3 0 0 0 0 0 1
## 4 1 0 0 1 0 0
## 5 0 0 1 0 1 0
## 6 0 0 0 0 0 0
## 7 0 0 0 0 0 0
## 8 0 0 0 0 0 0
## 24 1 1 0 1 0 1
## Sum 2 1 1 2 1 2
## AGE
## RAD 95.40000153 95.59999847 95.69999695 95.80000305 96 96.09999847
## 1 0 0 0 0 0 0
## 2 0 1 0 1 0 0
## 3 0 1 0 0 0 0
## 4 1 0 0 0 1 0
## 5 0 0 1 0 1 2
## 6 1 0 0 0 0 0
## 7 0 0 0 0 0 0
## 8 0 0 0 0 0 0
## 24 2 1 0 0 2 0
## Sum 4 3 1 1 4 2
## AGE
## RAD 96.19999695 96.40000153 96.59999847 96.69999695 96.80000305
## 1 0 0 0 0 0
## 2 0 0 0 0 0
## 3 0 0 0 0 0
## 4 0 0 0 0 0
## 5 1 0 0 1 0
## 6 0 0 0 0 0
## 7 0 0 0 0 0
## 8 0 0 0 0 0
## 24 2 1 2 1 1
## Sum 3 1 2 2 1
## AGE
## RAD 96.90000153 97 97.09999847 97.19999695 97.30000305 97.40000153 97.5
## 1 0 0 0 0 0 0 0
## 2 0 1 0 0 0 0 0
## 3 0 0 0 0 0 0 0
## 4 1 0 0 0 0 0 0
## 5 0 0 1 0 2 1 0
## 6 0 0 0 0 0 0 0
## 7 0 0 0 0 0 0 0
## 8 0 0 0 0 0 0 0
## 24 0 2 0 1 1 2 1
## Sum 1 3 1 1 3 3 1
## AGE
## RAD 97.69999695 97.80000305 97.90000153 98 98.09999847 98.19999695
## 1 0 0 0 0 0 0
## 2 0 0 0 0 0 0
## 3 0 0 0 0 0 0
## 4 1 0 2 1 1 2
## 5 0 1 0 0 0 1
## 6 0 0 0 0 0 0
## 7 0 0 0 0 0 0
## 8 0 0 0 0 0 0
## 24 0 0 2 0 1 1
## Sum 1 1 4 1 2 4
## AGE
## RAD 98.30000305 98.40000153 98.5 98.69999695 98.80000305 98.90000153
## 1 0 0 0 0 0 0
## 2 0 0 0 0 0 0
## 3 0 0 0 0 0 0
## 4 1 2 0 0 2 1
## 5 0 0 1 0 0 0
## 6 0 0 0 0 0 0
## 7 0 0 0 0 0 0
## 8 0 0 0 0 0 0
## 24 1 0 0 1 2 2
## Sum 2 2 1 1 4 3
## AGE
## RAD 99.09999847 99.30000305 100 Sum
## 1 0 0 0 20
## 2 0 0 0 24
## 3 0 0 0 38
## 4 0 0 4 110
## 5 0 0 10 115
## 6 0 0 0 26
## 7 0 0 0 17
## 8 0 0 0 24
## 24 1 1 29 132
## Sum 1 1 43 506boxplot(Boston.df$CRIM, main =" Crime rate distribution in Boston")
boxplot(Boston.df$ZN, main="Proportion of residential land zoned for lots over 25,000 sq.ft in Boston ")
boxplot(Boston.df$INDUS, main = "Proportion of nonretail business acres per town in Boston")
boxplot(Boston.df$CHAS, main = "Charles River Dummy variable")
boxplot(Boston.df$NOX, main = "Nitric oxides Concentration in Boston(parts per million)")
boxplot(Boston.df$RM, main = "Average number of rooms per dwelling in Boston")
boxplot(Boston.df$AGE,main = "Proption of owner-occupied units built prior to 1940 in Boston")
boxplot(Boston.df$DIS, main ="weighted distances to five Boston employment centres")
boxplot(Boston.df$RAD, main = "Index of accessibility to radial highways in Boston")
boxplot(Boston.df$TAX, main = "Full-value property-tax rate per $10,000 in Boston")
boxplot(Boston.df$PT, main ="Pupil-teacher Ration by town")
boxplot(Boston.df$B, main ="1000(BK - 0.063)^2 where Bk is the proportion of blacks by town")
boxplot(Boston.df$LSTAT, main = "% of lower status of the population")
library(lattice)
histogram(~CRIM, data = Boston.df, main = "Crime Distribution in Boston city", xlab = "CRIME RATE in Boston")
histogram(~NOX, data = Boston.df, main = "Nitric Oxide Concentration in Boston city", xlab = "Nitric oxide concentration in Boston")
histogram(~DIS, data = Boston.df, main = "Pupil-teacher Concentration in Boston city", xlab = "Pupil-teacher concentration in Boston")
histogram(~LSTAT, data = Boston.df, main = "Lower status of population in Boston city", xlab = "Lower status population in Boston")
histogram(~RM, data = Boston.df, main = "Average number of rooms per dwelling in Boston city", xlab = "Average number of rooms per dwelling in Boston")
histogram(~B, data = Boston.df, main = "Median value of owner-occupied homes in $1000's Boston city", xlab = "Average number of rooms per dwelling in Boston")
plot(Boston.df[,c(3,5,6,11,13,14)],pch =3)
library(corrplot)## Warning: package 'corrplot' was built under R version 3.4.2## corrplot 0.84 loadedcolnames(Boston.df)## [1] "CRIM" "ZN" "INDUS" "CHAS" "NOX" "RM" "AGE" "DIS"
## [9] "RAD" "TAX" "PT" "B" "LSTAT" "MV"datacolumns <- Boston.df[, c("CRIM","ZN","INDUS","CHAS","NOX","RM","AGE","DIS","RAD","TAX","PT","B","LSTAT","MV")]
N <-cor(datacolumns)
corrplot(N, method = "circle")
library(corrgram)
corrgram(Boston.df, order = TRUE,upper.panel = panel.pie)
data(Boston.df)## Warning in data(Boston.df): data set 'Boston.df' not foundmy_data <- Boston.df[,c(3,5,6,11,13,14)]
head(my_data, 6)## INDUS NOX RM PT LSTAT MV
## 1 2.31 0.538 6.575 15.3 4.98 24.0
## 2 7.07 0.469 6.421 17.8 9.14 21.6
## 3 7.07 0.469 7.185 17.8 4.03 34.7
## 4 2.18 0.458 6.998 18.7 2.94 33.4
## 5 2.18 0.458 7.147 18.7 5.33 36.2
## 6 2.18 0.458 6.430 18.7 5.21 28.7res <-cor(my_data)
round(res, 2)## INDUS NOX RM PT LSTAT MV
## INDUS 1.00 0.76 -0.39 0.38 0.60 -0.48
## NOX 0.76 1.00 -0.30 0.19 0.59 -0.43
## RM -0.39 -0.30 1.00 -0.36 -0.61 0.70
## PT 0.38 0.19 -0.36 1.00 0.37 -0.51
## LSTAT 0.60 0.59 -0.61 0.37 1.00 -0.74
## MV -0.48 -0.43 0.70 -0.51 -0.74 1.00library(car)## Warning: package 'car' was built under R version 3.4.3##
## Attaching package: 'car'## The following object is masked from 'package:psych':
##
## logitpairs(~CRIM+ZN+INDUS+CHAS+NOX+RM+AGE+DIS+RAD+TAX+PT+B+LSTAT, data =Boston.df, main ="Simple sctterplot matrix for Boston Housing prediction")
cor.test(Boston.df$CRIM,Boston.df$MV)##
## Pearson's product-moment correlation
##
## data: Boston.df$CRIM and Boston.df$MV
## t = -9.4597, df = 504, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4599064 -0.3116859
## sample estimates:
## cor
## -0.3883046cor.test(Boston.df$ZN,Boston.df$MV)##
## Pearson's product-moment correlation
##
## data: Boston.df$ZN and Boston.df$MV
## t = 8.6751, df = 504, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.2821414 0.4339786
## sample estimates:
## cor
## 0.3604453cor.test(Boston.df$INDUS,Boston.df$MV)##
## Pearson's product-moment correlation
##
## data: Boston.df$INDUS and Boston.df$MV
## t = -12.408, df = 504, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.5477957 -0.4140137
## sample estimates:
## cor
## -0.4837252cor.test(Boston.df$CHAS,Boston.df$MV)##
## Pearson's product-moment correlation
##
## data: Boston.df$CHAS and Boston.df$MV
## t = 3.9964, df = 504, p-value = 7.391e-05
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.08945817 0.25848001
## sample estimates:
## cor
## 0.1752602cor.test(Boston.df$RM,Boston.df$MV)##
## Pearson's product-moment correlation
##
## data: Boston.df$RM and Boston.df$MV
## t = 21.722, df = 504, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.6474346 0.7378074
## sample estimates:
## cor
## 0.6953599cor.test(Boston.df$NOX,Boston.df$MV)##
## Pearson's product-moment correlation
##
## data: Boston.df$NOX and Boston.df$MV
## t = -10.611, df = 504, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4960135 -0.3533126
## sample estimates:
## cor
## -0.4273208cor.test(Boston.df$AGE,Boston.df$MV)##
## Pearson's product-moment correlation
##
## data: Boston.df$AGE and Boston.df$MV
## t = -9.1366, df = 504, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4493580 -0.2996314
## sample estimates:
## cor
## -0.3769546cor.test(Boston.df$DIS,Boston.df$MV)##
## Pearson's product-moment correlation
##
## data: Boston.df$DIS and Boston.df$MV
## t = 5.7948, df = 504, p-value = 1.207e-08
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.1663849 0.3299100
## sample estimates:
## cor
## 0.2499287cor.test(Boston.df$RAD,Boston.df$MV)##
## Pearson's product-moment correlation
##
## data: Boston.df$RAD and Boston.df$MV
## t = -9.269, df = 504, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.4537021 -0.3045900
## sample estimates:
## cor
## -0.3816262cor.test(Boston.df$TAX,Boston.df$MV)##
## Pearson's product-moment correlation
##
## data: Boston.df$TAX and Boston.df$MV
## t = -11.906, df = 504, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.5338993 -0.3976061
## sample estimates:
## cor
## -0.4685359cor.test(Boston.df$PT,Boston.df$MV)##
## Pearson's product-moment correlation
##
## data: Boston.df$PT and Boston.df$MV
## t = -13.233, df = 504, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.5697371 -0.4400981
## sample estimates:
## cor
## -0.5077867cor.test(Boston.df$B,Boston.df$MV)##
## Pearson's product-moment correlation
##
## data: Boston.df$B and Boston.df$MV
## t = 7.9407, df = 504, p-value = 1.318e-14
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.2536655 0.4087483
## sample estimates:
## cor
## 0.3334608cor.test(Boston.df$LSTAT,Boston.df$MV)##
## Pearson's product-moment correlation
##
## data: Boston.df$LSTAT and Boston.df$MV
## t = -24.528, df = 504, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.7749982 -0.6951959
## sample estimates:
## cor
## -0.7376627t.test(Boston.df$CRIM,Boston.df$MV)##
## Welch Two Sample t-test
##
## data: Boston.df$CRIM and Boston.df$MV
## t = -33.796, df = 1005.5, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -20.01781 -17.82076
## sample estimates:
## mean of x mean of y
## 3.613524 22.532806t.test(Boston.df$ZN,Boston.df$MV)##
## Welch Two Sample t-test
##
## data: Boston.df$ZN and Boston.df$MV
## t = -10.022, df = 658.35, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -13.35760 -8.98074
## sample estimates:
## mean of x mean of y
## 11.36364 22.53281t.test(Boston.df$INDUS,Boston.df$MV)##
## Welch Two Sample t-test
##
## data: Boston.df$INDUS and Boston.df$MV
## t = -22.342, df = 934.12, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -12.39706 -10.39499
## sample estimates:
## mean of x mean of y
## 11.13678 22.53281t.test(Boston.df$CHAS,Boston.df$MV)##
## Welch Two Sample t-test
##
## data: Boston.df$CHAS and Boston.df$MV
## t = -54.921, df = 505.77, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -23.26722 -21.66005
## sample estimates:
## mean of x mean of y
## 0.06916996 22.53280636t.test(Boston.df$RM,Boston.df$MV)##
## Welch Two Sample t-test
##
## data: Boston.df$RM and Boston.df$MV
## t = -39.625, df = 510.89, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -17.05377 -15.44258
## sample estimates:
## mean of x mean of y
## 6.284634 22.532806t.test(Boston.df$NOX,Boston.df$MV)##
## Welch Two Sample t-test
##
## data: Boston.df$NOX and Boston.df$MV
## t = -53.75, df = 505.16, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -22.78145 -21.17477
## sample estimates:
## mean of x mean of y
## 0.5546951 22.5328064t.test(Boston.df$AGE,Boston.df$MV)##
## Welch Two Sample t-test
##
## data: Boston.df$AGE and Boston.df$MV
## t = 34.974, df = 611.61, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 43.45674 48.62744
## sample estimates:
## mean of x mean of y
## 68.57490 22.53281t.test(Boston.df$DIS,Boston.df$MV)##
## Welch Two Sample t-test
##
## data: Boston.df$DIS and Boston.df$MV
## t = -44.673, df = 557.8, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -19.56164 -17.91389
## sample estimates:
## mean of x mean of y
## 3.795043 22.532806t.test(Boston.df$RAD,Boston.df$MV)##
## Welch Two Sample t-test
##
## data: Boston.df$RAD and Boston.df$MV
## t = -23.06, df = 1007, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -14.08824 -11.87855
## sample estimates:
## mean of x mean of y
## 9.549407 22.532806t.test(Boston.df$TAX,Boston.df$MV)##
## Welch Two Sample t-test
##
## data: Boston.df$TAX and Boston.df$MV
## t = 51.403, df = 508.01, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 370.9626 400.4461
## sample estimates:
## mean of x mean of y
## 408.23715 22.53281t.test(Boston.df$PT,Boston.df$MV)##
## Welch Two Sample t-test
##
## data: Boston.df$PT and Boston.df$MV
## t = -9.707, df = 560.79, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -4.902309 -3.252236
## sample estimates:
## mean of x mean of y
## 18.45553 22.53281t.test(Boston.df$B,Boston.df$MV)##
## Welch Two Sample t-test
##
## data: Boston.df$B and Boston.df$MV
## t = 81.916, df = 515.25, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 326.1275 342.1549
## sample estimates:
## mean of x mean of y
## 356.67403 22.53281t.test(Boston.df$LSTAT,Boston.df$MV)##
## Welch Two Sample t-test
##
## data: Boston.df$LSTAT and Boston.df$MV
## t = -19.086, df = 951.59, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -10.895584 -8.863902
## sample estimates:
## mean of x mean of y
## 12.65306 22.53281We see that the number of rooms RM has the strongest positive correlation with the median value of the housing price, while the percentage of lower status population, LSTAT and the pupil-teacher ratio, PTRATIO, have strong negative correlation. The feature with the least correlation to MEDV is the proximity to Charles River, CHAS.