Tugas Analisis Multivariat - Review Matrix Algebra
Nama Anda - NIM Anda
2026-02-10
Pendahuluan
Dalam tugas kali ini, saya akan menganalisis dataset Concrete Compressive Strength menggunakan tiga metode analisis multivariat, yaitu:
- Correlation Matrix
- Variance-Covariance Matrix
- Eigenvalue dan Eigenvector
Dataset ini berisi data tentang kekuatan tekan beton yang dipengaruhi oleh berbagai komponen seperti semen, air, agregat, dan umur beton.
Import Data
library(readxl)
library(corrplot)
library(ggplot2)
library(dplyr)
data <- read_excel("Concrete_Data.xls")
head(data)## # A tibble: 6 × 9
## Cement (component 1)(kg in a m…¹ Blast Furnace Slag (…² Fly Ash (component 3…³
## <dbl> <dbl> <dbl>
## 1 540 0 0
## 2 540 0 0
## 3 332. 142. 0
## 4 332. 142. 0
## 5 199. 132. 0
## 6 266 114 0
## # ℹ abbreviated names: ¹`Cement (component 1)(kg in a m^3 mixture)`,
## # ²`Blast Furnace Slag (component 2)(kg in a m^3 mixture)`,
## # ³`Fly Ash (component 3)(kg in a m^3 mixture)`
## # ℹ 6 more variables: `Water (component 4)(kg in a m^3 mixture)` <dbl>,
## # `Superplasticizer (component 5)(kg in a m^3 mixture)` <dbl>,
## # `Coarse Aggregate (component 6)(kg in a m^3 mixture)` <dbl>,
## # `Fine Aggregate (component 7)(kg in a m^3 mixture)` <dbl>, …Dataset ini memiliki 1030 baris data dan 9 variabel.
A. Correlation Matrix
Perhitungan
Correlation matrix digunakan untuk melihat seberapa kuat hubungan antara satu variabel dengan variabel lainnya. Nilainya berkisar dari -1 sampai 1.
cor_matrix <- cor(data)
round(cor_matrix, 3)## Cement (component 1)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) 1.000
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) -0.275
## Fly Ash (component 3)(kg in a m^3 mixture) -0.397
## Water (component 4)(kg in a m^3 mixture) -0.082
## Superplasticizer (component 5)(kg in a m^3 mixture) 0.093
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -0.109
## Fine Aggregate (component 7)(kg in a m^3 mixture) -0.223
## Age (day) 0.082
## Concrete compressive strength(MPa, megapascals) 0.498
## Blast Furnace Slag (component 2)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) -0.275
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) 1.000
## Fly Ash (component 3)(kg in a m^3 mixture) -0.324
## Water (component 4)(kg in a m^3 mixture) 0.107
## Superplasticizer (component 5)(kg in a m^3 mixture) 0.043
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -0.284
## Fine Aggregate (component 7)(kg in a m^3 mixture) -0.282
## Age (day) -0.044
## Concrete compressive strength(MPa, megapascals) 0.135
## Fly Ash (component 3)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) -0.397
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) -0.324
## Fly Ash (component 3)(kg in a m^3 mixture) 1.000
## Water (component 4)(kg in a m^3 mixture) -0.257
## Superplasticizer (component 5)(kg in a m^3 mixture) 0.377
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -0.010
## Fine Aggregate (component 7)(kg in a m^3 mixture) 0.079
## Age (day) -0.154
## Concrete compressive strength(MPa, megapascals) -0.106
## Water (component 4)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) -0.082
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) 0.107
## Fly Ash (component 3)(kg in a m^3 mixture) -0.257
## Water (component 4)(kg in a m^3 mixture) 1.000
## Superplasticizer (component 5)(kg in a m^3 mixture) -0.657
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -0.182
## Fine Aggregate (component 7)(kg in a m^3 mixture) -0.451
## Age (day) 0.278
## Concrete compressive strength(MPa, megapascals) -0.290
## Superplasticizer (component 5)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) 0.093
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) 0.043
## Fly Ash (component 3)(kg in a m^3 mixture) 0.377
## Water (component 4)(kg in a m^3 mixture) -0.657
## Superplasticizer (component 5)(kg in a m^3 mixture) 1.000
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -0.266
## Fine Aggregate (component 7)(kg in a m^3 mixture) 0.223
## Age (day) -0.193
## Concrete compressive strength(MPa, megapascals) 0.366
## Coarse Aggregate (component 6)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) -0.109
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) -0.284
## Fly Ash (component 3)(kg in a m^3 mixture) -0.010
## Water (component 4)(kg in a m^3 mixture) -0.182
## Superplasticizer (component 5)(kg in a m^3 mixture) -0.266
## Coarse Aggregate (component 6)(kg in a m^3 mixture) 1.000
## Fine Aggregate (component 7)(kg in a m^3 mixture) -0.179
## Age (day) -0.003
## Concrete compressive strength(MPa, megapascals) -0.165
## Fine Aggregate (component 7)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) -0.223
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) -0.282
## Fly Ash (component 3)(kg in a m^3 mixture) 0.079
## Water (component 4)(kg in a m^3 mixture) -0.451
## Superplasticizer (component 5)(kg in a m^3 mixture) 0.223
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -0.179
## Fine Aggregate (component 7)(kg in a m^3 mixture) 1.000
## Age (day) -0.156
## Concrete compressive strength(MPa, megapascals) -0.167
## Age (day)
## Cement (component 1)(kg in a m^3 mixture) 0.082
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) -0.044
## Fly Ash (component 3)(kg in a m^3 mixture) -0.154
## Water (component 4)(kg in a m^3 mixture) 0.278
## Superplasticizer (component 5)(kg in a m^3 mixture) -0.193
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -0.003
## Fine Aggregate (component 7)(kg in a m^3 mixture) -0.156
## Age (day) 1.000
## Concrete compressive strength(MPa, megapascals) 0.329
## Concrete compressive strength(MPa, megapascals)
## Cement (component 1)(kg in a m^3 mixture) 0.498
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) 0.135
## Fly Ash (component 3)(kg in a m^3 mixture) -0.106
## Water (component 4)(kg in a m^3 mixture) -0.290
## Superplasticizer (component 5)(kg in a m^3 mixture) 0.366
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -0.165
## Fine Aggregate (component 7)(kg in a m^3 mixture) -0.167
## Age (day) 0.329
## Concrete compressive strength(MPa, megapascals) 1.000Visualisasi
Saya membuat visualisasi heatmap agar lebih mudah melihat pola korelasinya:
corrplot(cor_matrix,
method = "color",
addCoef.col = "black",
number.cex = 0.7,
tl.cex = 0.8,
tl.col = "black")
Penjelasan Hasil
Dari correlation matrix di atas, bisa dilihat beberapa hal menarik:
Cara membaca: - Angka mendekati 1 = kedua variabel bergerak searah (naik bareng, turun bareng) - Angka mendekati -1 = kedua variabel bergerak berlawanan (satu naik, yang lain turun) - Angka mendekati 0 = tidak ada hubungan yang jelas
Temuan penting:
Mari kita lihat korelasi yang paling kuat:
# Cari korelasi tertinggi
cor_data <- data.frame(
Var1 = rep(rownames(cor_matrix), each = ncol(cor_matrix)),
Var2 = rep(colnames(cor_matrix), times = nrow(cor_matrix)),
Nilai = as.vector(cor_matrix)
)
cor_data <- cor_data %>%
filter(Var1 != Var2) %>%
arrange(desc(abs(Nilai))) %>%
head(5)
cor_data## Var1
## 1 Water (component 4)(kg in a m^3 mixture)
## 2 Superplasticizer (component 5)(kg in a m^3 mixture)
## 3 Cement (component 1)(kg in a m^3 mixture)
## 4 Concrete compressive strength(MPa, megapascals)
## 5 Water (component 4)(kg in a m^3 mixture)
## Var2 Nilai
## 1 Superplasticizer (component 5)(kg in a m^3 mixture) -0.6574644
## 2 Water (component 4)(kg in a m^3 mixture) -0.6574644
## 3 Concrete compressive strength(MPa, megapascals) 0.4978327
## 4 Cement (component 1)(kg in a m^3 mixture) 0.4978327
## 5 Fine Aggregate (component 7)(kg in a m^3 mixture) -0.4506350Dari tabel di atas terlihat bahwa beberapa variabel punya hubungan yang cukup kuat. Korelasi positif artinya jika satu variabel naik, variabel lainnya juga cenderung naik. Sebaliknya untuk korelasi negatif.
Hal ini penting karena: - Kita jadi tahu variabel mana yang saling mempengaruhi - Bisa menghindari multikolinearitas saat bikin model - Membantu memahami karakteristik beton
B. Variance-Covariance Matrix
Perhitungan
Variance-covariance matrix menunjukkan dua hal: - Diagonal (angka di garis miring): variance atau seberapa tersebar data tiap variabel - Non-diagonal: covariance atau bagaimana dua variabel berubah bersama-sama
cov_matrix <- cov(data)
round(cov_matrix, 2)## Cement (component 1)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) 10921.74
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) -2481.36
## Fly Ash (component 3)(kg in a m^3 mixture) -2658.35
## Water (component 4)(kg in a m^3 mixture) -181.99
## Superplasticizer (component 5)(kg in a m^3 mixture) 57.91
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -888.61
## Fine Aggregate (component 7)(kg in a m^3 mixture) -1866.15
## Age (day) 540.99
## Concrete compressive strength(MPa, megapascals) 869.15
## Blast Furnace Slag (component 2)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) -2481.36
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) 7444.08
## Fly Ash (component 3)(kg in a m^3 mixture) -1786.61
## Water (component 4)(kg in a m^3 mixture) 197.68
## Superplasticizer (component 5)(kg in a m^3 mixture) 22.36
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -1905.21
## Fine Aggregate (component 7)(kg in a m^3 mixture) -1947.91
## Age (day) -241.15
## Concrete compressive strength(MPa, megapascals) 194.33
## Fly Ash (component 3)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) -2658.35
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) -1786.61
## Fly Ash (component 3)(kg in a m^3 mixture) 4095.55
## Water (component 4)(kg in a m^3 mixture) -351.30
## Superplasticizer (component 5)(kg in a m^3 mixture) 144.25
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -49.64
## Fine Aggregate (component 7)(kg in a m^3 mixture) 405.74
## Age (day) -624.06
## Concrete compressive strength(MPa, megapascals) -113.06
## Water (component 4)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) -181.99
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) 197.68
## Fly Ash (component 3)(kg in a m^3 mixture) -351.30
## Water (component 4)(kg in a m^3 mixture) 456.06
## Superplasticizer (component 5)(kg in a m^3 mixture) -83.87
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -302.72
## Fine Aggregate (component 7)(kg in a m^3 mixture) -771.57
## Age (day) 374.50
## Concrete compressive strength(MPa, megapascals) -103.32
## Superplasticizer (component 5)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) 57.91
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) 22.36
## Fly Ash (component 3)(kg in a m^3 mixture) 144.25
## Water (component 4)(kg in a m^3 mixture) -83.87
## Superplasticizer (component 5)(kg in a m^3 mixture) 35.68
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -123.69
## Fine Aggregate (component 7)(kg in a m^3 mixture) 106.56
## Age (day) -72.72
## Concrete compressive strength(MPa, megapascals) 36.53
## Coarse Aggregate (component 6)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) -888.61
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) -1905.21
## Fly Ash (component 3)(kg in a m^3 mixture) -49.64
## Water (component 4)(kg in a m^3 mixture) -302.72
## Superplasticizer (component 5)(kg in a m^3 mixture) -123.69
## Coarse Aggregate (component 6)(kg in a m^3 mixture) 6045.66
## Fine Aggregate (component 7)(kg in a m^3 mixture) -1112.80
## Age (day) -14.81
## Concrete compressive strength(MPa, megapascals) -214.23
## Fine Aggregate (component 7)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) -1866.15
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) -1947.91
## Fly Ash (component 3)(kg in a m^3 mixture) 405.74
## Water (component 4)(kg in a m^3 mixture) -771.57
## Superplasticizer (component 5)(kg in a m^3 mixture) 106.56
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -1112.80
## Fine Aggregate (component 7)(kg in a m^3 mixture) 6428.10
## Age (day) -790.57
## Concrete compressive strength(MPa, megapascals) -224.01
## Age (day)
## Cement (component 1)(kg in a m^3 mixture) 540.99
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) -241.15
## Fly Ash (component 3)(kg in a m^3 mixture) -624.06
## Water (component 4)(kg in a m^3 mixture) 374.50
## Superplasticizer (component 5)(kg in a m^3 mixture) -72.72
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -14.81
## Fine Aggregate (component 7)(kg in a m^3 mixture) -790.57
## Age (day) 3990.44
## Concrete compressive strength(MPa, megapascals) 347.06
## Concrete compressive strength(MPa, megapascals)
## Cement (component 1)(kg in a m^3 mixture) 869.15
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) 194.33
## Fly Ash (component 3)(kg in a m^3 mixture) -113.06
## Water (component 4)(kg in a m^3 mixture) -103.32
## Superplasticizer (component 5)(kg in a m^3 mixture) 36.53
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -214.23
## Fine Aggregate (component 7)(kg in a m^3 mixture) -224.01
## Age (day) 347.06
## Concrete compressive strength(MPa, megapascals) 279.08Variance Tiap Variabel
Variance yang besar berarti data variabel itu sangat bervariasi (tidak seragam). Sebaliknya variance kecil berarti datanya cenderung mirip-mirip.
variance_data <- data.frame(
Variabel = names(data),
Variance = diag(cov_matrix),
Std_Dev = sqrt(diag(cov_matrix))
)
variance_data <- variance_data %>% arrange(desc(Variance))
variance_data## Variabel
## Cement (component 1)(kg in a m^3 mixture) Cement (component 1)(kg in a m^3 mixture)
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) Blast Furnace Slag (component 2)(kg in a m^3 mixture)
## Fine Aggregate (component 7)(kg in a m^3 mixture) Fine Aggregate (component 7)(kg in a m^3 mixture)
## Coarse Aggregate (component 6)(kg in a m^3 mixture) Coarse Aggregate (component 6)(kg in a m^3 mixture)
## Fly Ash (component 3)(kg in a m^3 mixture) Fly Ash (component 3)(kg in a m^3 mixture)
## Age (day) Age (day)
## Water (component 4)(kg in a m^3 mixture) Water (component 4)(kg in a m^3 mixture)
## Concrete compressive strength(MPa, megapascals) Concrete compressive strength(MPa, megapascals)
## Superplasticizer (component 5)(kg in a m^3 mixture) Superplasticizer (component 5)(kg in a m^3 mixture)
## Variance Std_Dev
## Cement (component 1)(kg in a m^3 mixture) 10921.7427 104.507142
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) 7444.0837 86.279104
## Fine Aggregate (component 7)(kg in a m^3 mixture) 6428.0992 80.175427
## Coarse Aggregate (component 6)(kg in a m^3 mixture) 6045.6562 77.753818
## Fly Ash (component 3)(kg in a m^3 mixture) 4095.5481 63.996469
## Age (day) 3990.4377 63.169912
## Water (component 4)(kg in a m^3 mixture) 456.0602 21.355567
## Concrete compressive strength(MPa, megapascals) 279.0797 16.705679
## Superplasticizer (component 5)(kg in a m^3 mixture) 35.6826 5.973492ggplot(variance_data, aes(x = reorder(Variabel, Variance), y = Variance)) +
geom_bar(stat = "identity", fill = "steelblue") +
coord_flip() +
labs(title = "Variance Tiap Variabel",
x = "Variabel",
y = "Nilai Variance") +
theme_minimal()
Penjelasan Hasil
Interpretasi Variance:
Dari hasil di atas, kita bisa lihat variabel mana yang paling bervariasi. Variabel dengan variance tinggi berarti: - Datanya sangat beragam - Perbedaan antar observasi cukup besar - Mungkin perlu perhatian khusus saat analisis
Interpretasi Covariance:
Untuk bagian non-diagonal di matrix: - Positif: jika satu naik, yang lain ikut naik - Negatif: jika satu naik, yang lain turun - Mendekati 0: tidak ada pola yang jelas
Bedanya dengan correlation adalah covariance masih dalam satuan asli data, sedangkan correlation sudah di-standardisasi. Makanya correlation lebih mudah dibaca karena selalu -1 sampai 1.
C. Eigenvalue dan Eigenvector
Perhitungan
Eigenvalue dan eigenvector ini konsep yang agak rumit, tapi pada dasarnya dipakai untuk: - Mereduksi dimensi data (PCA - Principal Component Analysis) - Mencari komponen utama yang menjelaskan variasi data - Menyederhanakan data tanpa kehilangan banyak informasi
eigen_hasil <- eigen(cor_matrix)Eigenvalue
Eigenvalue menunjukkan seberapa banyak informasi yang bisa dijelaskan oleh tiap komponen.
eigenvalues <- eigen_hasil$values
prop_variance <- eigenvalues / sum(eigenvalues) * 100
kum_variance <- cumsum(prop_variance)
eigen_tabel <- data.frame(
Komponen = paste0("PC", 1:length(eigenvalues)),
Eigenvalue = round(eigenvalues, 4),
Persen_Variance = round(prop_variance, 2),
Kumulatif = round(kum_variance, 2)
)
eigen_tabel## Komponen Eigenvalue Persen_Variance Kumulatif
## 1 PC1 2.2877 25.42 25.42
## 2 PC2 1.9365 21.52 46.94
## 3 PC3 1.4089 15.65 62.59
## 4 PC4 1.0428 11.59 74.18
## 5 PC5 1.0142 11.27 85.45
## 6 PC6 0.8474 9.42 94.86
## 7 PC7 0.2870 3.19 98.05
## 8 PC8 0.1468 1.63 99.68
## 9 PC9 0.0288 0.32 100.00Scree Plot
Scree plot membantu kita lihat komponen mana yang paling penting:
plot(eigenvalues,
type = "b",
main = "Scree Plot",
xlab = "Komponen Principal",
ylab = "Eigenvalue",
col = "blue",
pch = 19)
abline(h = 1, col = "red", lty = 2)
text(x = length(eigenvalues)*0.7, y = 1.3,
"Kriteria Kaiser (eigenvalue > 1)", col = "red")
Eigenvector
Eigenvector menunjukkan kontribusi tiap variabel asli terhadap komponen principal.
eigenvectors <- eigen_hasil$vectors
colnames(eigenvectors) <- paste0("PC", 1:ncol(eigenvectors))
rownames(eigenvectors) <- names(data)
round(eigenvectors, 4)## PC1 PC2 PC3
## Cement (component 1)(kg in a m^3 mixture) -0.0411 0.5365 0.3597
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) -0.1630 0.1363 -0.6990
## Fly Ash (component 3)(kg in a m^3 mixture) 0.3698 -0.2684 0.0198
## Water (component 4)(kg in a m^3 mixture) -0.5641 -0.1181 -0.1203
## Superplasticizer (component 5)(kg in a m^3 mixture) 0.5361 0.2482 -0.1880
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -0.0605 -0.2248 0.5495
## Fine Aggregate (component 7)(kg in a m^3 mixture) 0.3817 -0.1871 0.0012
## Age (day) -0.2619 0.2518 0.1696
## Concrete compressive strength(MPa, megapascals) 0.1072 0.6301 0.0335
## PC4 PC5 PC6
## Cement (component 1)(kg in a m^3 mixture) -0.3098 -0.0547 -0.3899
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) 0.0763 -0.3626 0.2703
## Fly Ash (component 3)(kg in a m^3 mixture) 0.6007 0.2276 -0.3202
## Water (component 4)(kg in a m^3 mixture) 0.0469 0.2961 -0.3062
## Superplasticizer (component 5)(kg in a m^3 mixture) 0.1659 -0.0370 -0.0828
## Coarse Aggregate (component 6)(kg in a m^3 mixture) 0.2216 -0.5455 0.3476
## Fine Aggregate (component 7)(kg in a m^3 mixture) -0.5278 0.3845 0.4091
## Age (day) 0.3595 0.5285 0.5098
## Concrete compressive strength(MPa, megapascals) 0.2253 0.0003 0.1540
## PC7 PC8 PC9
## Cement (component 1)(kg in a m^3 mixture) -0.1338 -0.2984 -0.4725
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) 0.0048 -0.2288 -0.4512
## Fly Ash (component 3)(kg in a m^3 mixture) 0.2472 -0.2553 -0.3865
## Water (component 4)(kg in a m^3 mixture) -0.0098 0.5856 -0.3560
## Superplasticizer (component 5)(kg in a m^3 mixture) -0.6139 0.4476 -0.0528
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -0.0598 0.2431 -0.3372
## Fine Aggregate (component 7)(kg in a m^3 mixture) 0.1747 0.1403 -0.4187
## Age (day) -0.3436 -0.2260 -0.0397
## Concrete compressive strength(MPa, megapascals) 0.6260 0.3469 0.0606Penjelasan Hasil
Bagaimana cara membacanya?
- Eigenvalue:
- Komponen pertama (PC1) punya eigenvalue 2.29, artinya menjelaskan 25.4% variasi data
- Komponen kedua (PC2) menjelaskan 21.5% variasi
- Dan seterusnya…
- Aturan Kaiser:
- Yang penting cuma komponen dengan eigenvalue > 1
- Dari data ini, ada 5 komponen yang signifikan
- Total menjelaskan 85.4% dari keseluruhan data
- Artinya apa?
- Dari 9 variabel asli, kita bisa menyederhanakan jadi 5 komponen saja
- Kita tetap mempertahankan 85.4% informasi
- Ini sangat berguna untuk analisis lanjutan karena data jadi lebih sederhana
- Eigenvector menunjukkan:
- Seberapa besar kontribusi tiap variabel asli ke komponen baru
- Angka besar (positif atau negatif) = kontribusi besar
- Angka kecil = kontribusi kecil
Manfaatnya dalam praktik:
Misalnya kita punya banyak sekali variabel tentang beton. Dengan PCA ini kita bisa: - Mengurangi jumlah variabel yang perlu dianalisis - Tetap menjaga sebagian besar informasi penting - Membuat model yang lebih sederhana dan efisien - Menghindari overfitting dalam machine learning
Contoh: daripada analisis 8 variabel sekaligus, cukup fokus ke 2-3 komponen utama yang sudah merangkum informasi dari semua variabel.
Kesimpulan
Dari ketiga analisis yang sudah dilakukan, saya mendapat beberapa insight:
Correlation Matrix membantu saya memahami hubungan antar variabel. Ada beberapa variabel yang berkorelasi kuat, yang artinya mereka saling mempengaruhi.
Variance-Covariance Matrix menunjukkan variabel mana yang paling bervariasi. Ini penting karena variabel dengan variance tinggi biasanya lebih informatif.
Eigenvalue dan Eigenvector memberikan cara untuk menyederhanakan data. Dari 9 variabel, saya bisa menggunakan hanya 5 komponen principal yang tetap menjelaskan 85.4% informasi.
Ketiga metode ini saling melengkapi dan sangat berguna dalam analisis data multivariat, terutama ketika kita punya banyak variabel dan ingin memahami pola serta struktur datanya.
Referensi:
- Hair, J.F. (2018). Multivariate Data Analysis, 8th Ed.
- Materi Kuliah Analisis Multivariat, S1 Sains Data UNESA