TUGAS 1 MENCARI EIGEN VECTOR & EIGEN VALUE

NAMA: Muchammad Sandy Kurniawan NIM : 23031554213 KELAS : 2023A deskripsi:

pertama kita buka dataset yaitu: “Housing.csv”

df<-read.csv("Housing.csv")

head(df)
##      price area bedrooms bathrooms stories mainroad guestroom basement
## 1 13300000 7420        4         2       3      yes        no       no
## 2 12250000 8960        4         4       4      yes        no       no
## 3 12250000 9960        3         2       2      yes        no      yes
## 4 12215000 7500        4         2       2      yes        no      yes
## 5 11410000 7420        4         1       2      yes       yes      yes
## 6 10850000 7500        3         3       1      yes        no      yes
##   hotwaterheating airconditioning parking prefarea furnishingstatus
## 1              no             yes       2      yes        furnished
## 2              no             yes       3       no        furnished
## 3              no              no       2      yes   semi-furnished
## 4              no             yes       3      yes        furnished
## 5              no             yes       2       no        furnished
## 6              no             yes       2      yes   semi-furnished

Feature Selection

Selanjutnya kita hapus feature yang tidak kita butuhkan

df_new <- df[, sapply(df, is.numeric)]

head(df_new)
##      price area bedrooms bathrooms stories parking
## 1 13300000 7420        4         2       3       2
## 2 12250000 8960        4         4       4       3
## 3 12250000 9960        3         2       2       2
## 4 12215000 7500        4         2       2       3
## 5 11410000 7420        4         1       2       2
## 6 10850000 7500        3         3       1       2

##Konversi matrix ubah dataset menjadi matrix

cov_matrix <- cov(df_new)

print(cov_matrix)
##                  price         area     bedrooms    bathrooms      stories
## price     3.498544e+12 2.175676e+09 5.059464e+05 4.864093e+05 6.826446e+05
## area      2.175676e+09 4.709512e+06 2.432321e+02 2.113466e+02 1.581294e+02
## bedrooms  5.059464e+05 2.432321e+02 5.447383e-01 1.386738e-01 2.615893e-01
## bathrooms 4.864093e+05 2.113466e+02 1.386738e-01 2.524757e-01 1.421715e-01
## stories   6.826446e+05 1.581294e+02 2.615893e-01 1.421715e-01 7.525432e-01
## parking   6.194673e+05 6.599897e+02 8.856247e-02 7.684161e-02 3.404277e-02
##                parking
## price     6.194673e+05
## area      6.599897e+02
## bedrooms  8.856247e-02
## bathrooms 7.684161e-02
## stories   3.404277e-02
## parking   7.423300e-01

setelah itu kita cari eigen vector dan eigen valuennya

eigen <- eigen(cov_matrix)

berikut adalah hasil eigen valuenya:

print(eigen$vectors)
##              [,1]          [,2]          [,3]          [,4]          [,5]
## [1,] 9.999998e-01  6.218809e-04  2.350022e-07  2.360030e-07 -1.896406e-08
## [2,] 6.218809e-04 -9.999998e-01 -1.068146e-04  4.693651e-05  1.227917e-05
## [3,] 1.446162e-07  2.127405e-05 -4.831235e-01 -3.524835e-01 -7.742078e-01
## [4,] 1.390319e-07  2.715391e-05 -1.156247e-01 -7.418855e-02 -1.559105e-01
## [5,] 1.951224e-07  7.936672e-05 -7.760615e-01 -2.230034e-01  5.897316e-01
## [6,] 1.770643e-07 -8.185750e-05  3.885243e-01 -9.058261e-01  1.688515e-01
##               [,6]
## [1,]  1.167426e-07
## [2,] -2.065080e-05
## [3,]  2.072422e-01
## [4,] -9.781712e-01
## [5,]  1.465063e-02
## [6,] -4.137110e-03

kemudian ada eigen vectornya

eigen$vectors
##              [,1]          [,2]          [,3]          [,4]          [,5]
## [1,] 9.999998e-01  6.218809e-04  2.350022e-07  2.360030e-07 -1.896406e-08
## [2,] 6.218809e-04 -9.999998e-01 -1.068146e-04  4.693651e-05  1.227917e-05
## [3,] 1.446162e-07  2.127405e-05 -4.831235e-01 -3.524835e-01 -7.742078e-01
## [4,] 1.390319e-07  2.715391e-05 -1.156247e-01 -7.418855e-02 -1.559105e-01
## [5,] 1.951224e-07  7.936672e-05 -7.760615e-01 -2.230034e-01  5.897316e-01
## [6,] 1.770643e-07 -8.185750e-05  3.885243e-01 -9.058261e-01  1.688515e-01
##               [,6]
## [1,]  1.167426e-07
## [2,] -2.065080e-05
## [3,]  2.072422e-01
## [4,] -9.781712e-01
## [5,]  1.465063e-02
## [6,] -4.137110e-03

dan terakhir kita buat matriks korelasi nya:

cor_matrix <- cor(df_new)
print(cor_matrix)
##               price       area  bedrooms bathrooms    stories    parking
## price     1.0000000 0.53599735 0.3664940 0.5175453 0.42071237 0.38439365
## area      0.5359973 1.00000000 0.1518585 0.1938195 0.08399605 0.35298048
## bedrooms  0.3664940 0.15185849 1.0000000 0.3739302 0.40856424 0.13926990
## bathrooms 0.5175453 0.19381953 0.3739302 1.0000000 0.32616471 0.17749582
## stories   0.4207124 0.08399605 0.4085642 0.3261647 1.00000000 0.04554709
## parking   0.3843936 0.35298048 0.1392699 0.1774958 0.04554709 1.00000000
library(corrplot)
## corrplot 0.95 loaded
corrplot(cor_matrix, method = "number")

hasilnya:
1. variable "price" berkorelasi positif dengan variable "area" (0.54) → Semakin besar area rumah, semakin mahal harga rumah.
2. variable "bathrooms" berkorelasi positif dengan variable"price" (0.52) → Semakin banyak kamar mandi, semakin tinggi harga rumah.
3 variable "bedrooms" dan  variavble"stories" memiliki korelasi sekitar 0.41 → Rumah dengan lebih banyak kamar tidur cenderung memiliki lebih banyak lantai.