Analisis Concrete
Yanaka Sofia Pardede
2026-02-12
Import Dataset
library(readxl)
data <- read_excel("C:/Users/Yanaka Sofia/Downloads/Tugas_Analisis Multivariat/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>, …Pada tahap awal, dataset Concrete Compressive Strength diimpor dari
file Excel menggunakan package readxl. Dataset ini berisi
berbagai komposisi material penyusun beton serta nilai kuat tekan yang
dihasilkan.
Data yang telah dibaca kemudian disimpan dalam objek
data sehingga dapat digunakan untuk analisis berikutnya.
Untuk melakukan pengecekan awal, ditampilkan beberapa observasi pertama
menggunakan fungsi head() guna memastikan tidak terdapat
kesalahan dalam proses pembacaan data.
Data Understanding
Setelah dataset berhasil diimpor, langkah selanjutnya adalah memahami struktur data. Proses ini dilakukan untuk mengetahui jumlah variabel, tipe data, serta memastikan bahwa seluruh data numerik dapat digunakan dalam analisis statistik lanjutan.
str(data)## tibble [1,030 × 9] (S3: tbl_df/tbl/data.frame)
## $ Cement (component 1)(kg in a m^3 mixture) : num [1:1030] 540 540 332 332 199 ...
## $ Blast Furnace Slag (component 2)(kg in a m^3 mixture): num [1:1030] 0 0 142 142 132 ...
## $ Fly Ash (component 3)(kg in a m^3 mixture) : num [1:1030] 0 0 0 0 0 0 0 0 0 0 ...
## $ Water (component 4)(kg in a m^3 mixture) : num [1:1030] 162 162 228 228 192 228 228 228 228 228 ...
## $ Superplasticizer (component 5)(kg in a m^3 mixture) : num [1:1030] 2.5 2.5 0 0 0 0 0 0 0 0 ...
## $ Coarse Aggregate (component 6)(kg in a m^3 mixture) : num [1:1030] 1040 1055 932 932 978 ...
## $ Fine Aggregate (component 7)(kg in a m^3 mixture) : num [1:1030] 676 676 594 594 826 ...
## $ Age (day) : num [1:1030] 28 28 270 365 360 90 365 28 28 28 ...
## $ Concrete compressive strength(MPa, megapascals) : num [1:1030] 80 61.9 40.3 41.1 44.3 ...Berdasarkan struktur data di atas, seluruh variabel memiliki tipe numerik sehingga analisis korelasi dan perhitungan statistik multivariat dapat dilakukan tanpa perlu proses konversi data tambahan.
Summary Statistics
Ringkasan statistik digunakan untuk memberikan gambaran umum mengenai distribusi data pada setiap variabel. Informasi yang ditampilkan meliputi nilai minimum, maksimum, rata-rata (mean), median, dan kuartil.
summary(data)## Cement (component 1)(kg in a m^3 mixture)
## Min. :102.0
## 1st Qu.:192.4
## Median :272.9
## Mean :281.2
## 3rd Qu.:350.0
## Max. :540.0
## Blast Furnace Slag (component 2)(kg in a m^3 mixture)
## Min. : 0.0
## 1st Qu.: 0.0
## Median : 22.0
## Mean : 73.9
## 3rd Qu.:142.9
## Max. :359.4
## Fly Ash (component 3)(kg in a m^3 mixture)
## Min. : 0.00
## 1st Qu.: 0.00
## Median : 0.00
## Mean : 54.19
## 3rd Qu.:118.27
## Max. :200.10
## Water (component 4)(kg in a m^3 mixture)
## Min. :121.8
## 1st Qu.:164.9
## Median :185.0
## Mean :181.6
## 3rd Qu.:192.0
## Max. :247.0
## Superplasticizer (component 5)(kg in a m^3 mixture)
## Min. : 0.000
## 1st Qu.: 0.000
## Median : 6.350
## Mean : 6.203
## 3rd Qu.:10.160
## Max. :32.200
## Coarse Aggregate (component 6)(kg in a m^3 mixture)
## Min. : 801.0
## 1st Qu.: 932.0
## Median : 968.0
## Mean : 972.9
## 3rd Qu.:1029.4
## Max. :1145.0
## Fine Aggregate (component 7)(kg in a m^3 mixture) Age (day)
## Min. :594.0 Min. : 1.00
## 1st Qu.:731.0 1st Qu.: 7.00
## Median :779.5 Median : 28.00
## Mean :773.6 Mean : 45.66
## 3rd Qu.:824.0 3rd Qu.: 56.00
## Max. :992.6 Max. :365.00
## Concrete compressive strength(MPa, megapascals)
## Min. : 2.332
## 1st Qu.:23.707
## Median :34.443
## Mean :35.818
## 3rd Qu.:46.136
## Max. :82.599Dari hasil ringkasan statistik tersebut dapat diperoleh gambaran mengenai rentang nilai pada masing-masing variabel. Perbedaan nilai minimum dan maksimum menunjukkan variasi data yang nantinya dapat memengaruhi hubungan antar variabel dalam analisis korelasi.
Correlation Matrix
Matriks korelasi digunakan untuk mengetahui kekuatan hubungan linear antar variabel dalam dataset. Nilai korelasi berada pada rentang -1 hingga 1. Nilai yang mendekati 1 menunjukkan hubungan positif yang kuat, sedangkan nilai yang mendekati 0 menunjukkan hubungan yang lemah.
cor_matrix <- cor(data)
cor_matrix## Cement (component 1)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) 1.00000000
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) -0.27519344
## Fly Ash (component 3)(kg in a m^3 mixture) -0.39747544
## Water (component 4)(kg in a m^3 mixture) -0.08154361
## Superplasticizer (component 5)(kg in a m^3 mixture) 0.09277137
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -0.10935604
## Fine Aggregate (component 7)(kg in a m^3 mixture) -0.22272017
## Age (day) 0.08194726
## Concrete compressive strength(MPa, megapascals) 0.49783272
## Blast Furnace Slag (component 2)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) -0.27519344
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) 1.00000000
## Fly Ash (component 3)(kg in a m^3 mixture) -0.32356947
## Water (component 4)(kg in a m^3 mixture) 0.10728594
## Superplasticizer (component 5)(kg in a m^3 mixture) 0.04337574
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -0.28399823
## Fine Aggregate (component 7)(kg in a m^3 mixture) -0.28159326
## Age (day) -0.04424580
## Concrete compressive strength(MPa, megapascals) 0.13482445
## Fly Ash (component 3)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) -0.397475440
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) -0.323569468
## Fly Ash (component 3)(kg in a m^3 mixture) 1.000000000
## Water (component 4)(kg in a m^3 mixture) -0.257043997
## Superplasticizer (component 5)(kg in a m^3 mixture) 0.377339559
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -0.009976788
## Fine Aggregate (component 7)(kg in a m^3 mixture) 0.079076351
## Age (day) -0.154370165
## Concrete compressive strength(MPa, megapascals) -0.105753348
## Water (component 4)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) -0.08154361
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) 0.10728594
## Fly Ash (component 3)(kg in a m^3 mixture) -0.25704400
## Water (component 4)(kg in a m^3 mixture) 1.00000000
## Superplasticizer (component 5)(kg in a m^3 mixture) -0.65746444
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -0.18231167
## Fine Aggregate (component 7)(kg in a m^3 mixture) -0.45063498
## Age (day) 0.27760443
## Concrete compressive strength(MPa, megapascals) -0.28961348
## Superplasticizer (component 5)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) 0.09277137
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) 0.04337574
## Fly Ash (component 3)(kg in a m^3 mixture) 0.37733956
## Water (component 4)(kg in a m^3 mixture) -0.65746444
## Superplasticizer (component 5)(kg in a m^3 mixture) 1.00000000
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -0.26630276
## Fine Aggregate (component 7)(kg in a m^3 mixture) 0.22250149
## Age (day) -0.19271652
## Concrete compressive strength(MPa, megapascals) 0.36610230
## Coarse Aggregate (component 6)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) -0.109356039
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) -0.283998230
## Fly Ash (component 3)(kg in a m^3 mixture) -0.009976788
## Water (component 4)(kg in a m^3 mixture) -0.182311668
## Superplasticizer (component 5)(kg in a m^3 mixture) -0.266302755
## Coarse Aggregate (component 6)(kg in a m^3 mixture) 1.000000000
## Fine Aggregate (component 7)(kg in a m^3 mixture) -0.178505755
## Age (day) -0.003015507
## Concrete compressive strength(MPa, megapascals) -0.164927821
## Fine Aggregate (component 7)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) -0.22272017
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) -0.28159326
## Fly Ash (component 3)(kg in a m^3 mixture) 0.07907635
## Water (component 4)(kg in a m^3 mixture) -0.45063498
## Superplasticizer (component 5)(kg in a m^3 mixture) 0.22250149
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -0.17850575
## Fine Aggregate (component 7)(kg in a m^3 mixture) 1.00000000
## Age (day) -0.15609405
## Concrete compressive strength(MPa, megapascals) -0.16724896
## Age (day)
## Cement (component 1)(kg in a m^3 mixture) 0.081947264
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) -0.044245801
## Fly Ash (component 3)(kg in a m^3 mixture) -0.154370165
## Water (component 4)(kg in a m^3 mixture) 0.277604429
## Superplasticizer (component 5)(kg in a m^3 mixture) -0.192716518
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -0.003015507
## Fine Aggregate (component 7)(kg in a m^3 mixture) -0.156094049
## Age (day) 1.000000000
## Concrete compressive strength(MPa, megapascals) 0.328876976
## Concrete compressive strength(MPa, megapascals)
## Cement (component 1)(kg in a m^3 mixture) 0.4978327
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) 0.1348244
## Fly Ash (component 3)(kg in a m^3 mixture) -0.1057533
## Water (component 4)(kg in a m^3 mixture) -0.2896135
## Superplasticizer (component 5)(kg in a m^3 mixture) 0.3661023
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -0.1649278
## Fine Aggregate (component 7)(kg in a m^3 mixture) -0.1672490
## Age (day) 0.3288770
## Concrete compressive strength(MPa, megapascals) 1.0000000Dari matriks korelasi di atas terlihat bahwa beberapa variabel memiliki hubungan yang cukup kuat, baik positif maupun negatif. Informasi ini penting untuk memahami keterkaitan antar komponen penyusun beton terhadap kuat tekan yang dihasilkan.
Visualisasi Correlation Matrix
Untuk mempermudah interpretasi hubungan antar variabel, matriks korelasi divisualisasikan dalam bentuk heatmap. Warna yang semakin gelap menunjukkan tingkat korelasi yang semakin kuat.
library(corrplot)## corrplot 0.95 loadedcorrplot(cor_matrix,
method = "square",
type = "upper",
col = colorRampPalette(c("white","lightblue","darkblue"))(200),
tl.col = "black",
tl.srt = 45,
addCoef.col = "black",
number.cex = 0.6)
title("Correlation Matrix of Concrete Variables")
Berdasarkan heatmap di atas, dapat terlihat dengan lebih jelas pasangan
variabel yang memiliki hubungan kuat. Visualisasi ini membantu dalam
mengidentifikasi pola keterkaitan yang mungkin tidak langsung terlihat
dari tabel numerik.
Variance – Covariance Matrix
Matriks kovarians digunakan untuk melihat bagaimana dua variabel berubah secara bersama-sama. Nilai positif menunjukkan bahwa variabel bergerak searah, sedangkan nilai negatif menunjukkan pergerakan yang berlawanan. Berbeda dengan korelasi, kovarians masih dipengaruhi oleh skala masing-masing variabel.
cov_matrix <- cov(data)
cov_matrix## Cement (component 1)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) 10921.74265
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) -2481.35943
## Fly Ash (component 3)(kg in a m^3 mixture) -2658.35075
## Water (component 4)(kg in a m^3 mixture) -181.98979
## Superplasticizer (component 5)(kg in a m^3 mixture) 57.91462
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -888.60851
## Fine Aggregate (component 7)(kg in a m^3 mixture) -1866.15111
## Age (day) 540.99182
## Concrete compressive strength(MPa, megapascals) 869.14762
## Blast Furnace Slag (component 2)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) -2481.35943
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) 7444.08373
## Fly Ash (component 3)(kg in a m^3 mixture) -1786.60759
## Water (component 4)(kg in a m^3 mixture) 197.67855
## Superplasticizer (component 5)(kg in a m^3 mixture) 22.35531
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -1905.21057
## Fine Aggregate (component 7)(kg in a m^3 mixture) -1947.91126
## Age (day) -241.15038
## Concrete compressive strength(MPa, megapascals) 194.32935
## Fly Ash (component 3)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) -2658.3508
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) -1786.6076
## Fly Ash (component 3)(kg in a m^3 mixture) 4095.5481
## Water (component 4)(kg in a m^3 mixture) -351.2971
## Superplasticizer (component 5)(kg in a m^3 mixture) 144.2503
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -49.6442
## Fine Aggregate (component 7)(kg in a m^3 mixture) 405.7364
## Age (day) -624.0647
## Concrete compressive strength(MPa, megapascals) -113.0614
## Water (component 4)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) -181.98979
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) 197.67855
## Fly Ash (component 3)(kg in a m^3 mixture) -351.29712
## Water (component 4)(kg in a m^3 mixture) 456.06024
## Superplasticizer (component 5)(kg in a m^3 mixture) -83.87096
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -302.72431
## Fine Aggregate (component 7)(kg in a m^3 mixture) -771.57347
## Age (day) 374.49650
## Concrete compressive strength(MPa, megapascals) -103.32229
## Superplasticizer (component 5)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) 57.91462
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) 22.35531
## Fly Ash (component 3)(kg in a m^3 mixture) 144.25026
## Water (component 4)(kg in a m^3 mixture) -83.87096
## Superplasticizer (component 5)(kg in a m^3 mixture) 35.68260
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -123.68745
## Fine Aggregate (component 7)(kg in a m^3 mixture) 106.56203
## Age (day) -72.72060
## Concrete compressive strength(MPa, megapascals) 36.53380
## Coarse Aggregate (component 6)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) -888.60851
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) -1905.21057
## Fly Ash (component 3)(kg in a m^3 mixture) -49.64420
## Water (component 4)(kg in a m^3 mixture) -302.72431
## Superplasticizer (component 5)(kg in a m^3 mixture) -123.68745
## Coarse Aggregate (component 6)(kg in a m^3 mixture) 6045.65623
## Fine Aggregate (component 7)(kg in a m^3 mixture) -1112.79516
## Age (day) -14.81127
## Concrete compressive strength(MPa, megapascals) -214.22975
## Fine Aggregate (component 7)(kg in a m^3 mixture)
## Cement (component 1)(kg in a m^3 mixture) -1866.1511
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) -1947.9113
## Fly Ash (component 3)(kg in a m^3 mixture) 405.7364
## Water (component 4)(kg in a m^3 mixture) -771.5735
## Superplasticizer (component 5)(kg in a m^3 mixture) 106.5620
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -1112.7952
## Fine Aggregate (component 7)(kg in a m^3 mixture) 6428.0992
## Age (day) -790.5656
## Concrete compressive strength(MPa, megapascals) -224.0107
## Age (day)
## Cement (component 1)(kg in a m^3 mixture) 540.99182
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) -241.15038
## Fly Ash (component 3)(kg in a m^3 mixture) -624.06475
## Water (component 4)(kg in a m^3 mixture) 374.49650
## Superplasticizer (component 5)(kg in a m^3 mixture) -72.72060
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -14.81127
## Fine Aggregate (component 7)(kg in a m^3 mixture) -790.56558
## Age (day) 3990.43773
## Concrete compressive strength(MPa, megapascals) 347.06265
## Concrete compressive strength(MPa, megapascals)
## Cement (component 1)(kg in a m^3 mixture) 869.1476
## Blast Furnace Slag (component 2)(kg in a m^3 mixture) 194.3294
## Fly Ash (component 3)(kg in a m^3 mixture) -113.0614
## Water (component 4)(kg in a m^3 mixture) -103.3223
## Superplasticizer (component 5)(kg in a m^3 mixture) 36.5338
## Coarse Aggregate (component 6)(kg in a m^3 mixture) -214.2298
## Fine Aggregate (component 7)(kg in a m^3 mixture) -224.0107
## Age (day) 347.0626
## Concrete compressive strength(MPa, megapascals) 279.0797Dari matriks kovarians tersebut dapat dilihat kecenderungan hubungan antar variabel berdasarkan arah perubahannya. Nilai yang besar menunjukkan adanya variasi yang tinggi antar pasangan variabel.
Visualisasi Covariance Matrix
Karena nilai kovarians tidak berada pada rentang -1 hingga 1, visualisasi dilakukan menggunakan heatmap untuk memperlihatkan besar kecilnya nilai secara relatif.
library(reshape2)
library(ggplot2)
melted_cov <- melt(cov_matrix)
ggplot(melted_cov, aes(Var1, Var2, fill = value)) +
geom_tile(color = "white") +
scale_fill_gradient(low = "white", high = "blue") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1)) +
labs(title = "Covariance Matrix of Concrete Variables",
x = "", y = "", fill = "Cov")
Berdasarkan heatmap matriks kovarians, terlihat bahwa setiap variabel
memiliki tingkat perubahan bersama yang berbeda-beda. Warna yang semakin
gelap menunjukkan nilai kovarians yang semakin besar, yang berarti dua
variabel tersebut cenderung meningkat atau menurun secara bersamaan
dengan kekuatan yang lebih tinggi.
Sebaliknya, warna yang lebih terang menunjukkan hubungan perubahan yang relatif lebih kecil. Visualisasi ini membantu dalam memahami pola keterkaitan antar variabel sebelum dilakukan analisis lanjutan seperti Principal Component Analysis (PCA).
Eigen Value dan Proporsi Keragaman
eigen_result <- eigen(cor_matrix)
eigen_value <- eigen_result$values
eigen_vector <- eigen_result$vectors
eigen_value## [1] 2.28771185 1.93651535 1.40892580 1.04278807 1.01415431 0.84741063 0.28695777
## [8] 0.14678093 0.02875528proporsi <- eigen_value / sum(eigen_value)
proporsi## [1] 0.254190206 0.215168373 0.156547311 0.115865342 0.112683812 0.094156736
## [7] 0.031884197 0.016308992 0.003195031round(proporsi, 3)## [1] 0.254 0.215 0.157 0.116 0.113 0.094 0.032 0.016 0.003kumulatif <- cumsum(proporsi)
round(kumulatif, 3)## [1] 0.254 0.469 0.626 0.742 0.854 0.949 0.980 0.997 1.000Eigen value menunjukkan besar kontribusi masing-masing komponen utama dalam menjelaskan keragaman data. Semakin besar eigen value, semakin penting komponen tersebut.
Berdasarkan hasil perhitungan, komponen utama pertama memiliki kontribusi keragaman terbesar dibandingkan komponen lainnya. Jika dilihat dari proporsi kumulatif, beberapa komponen awal sudah mampu menjelaskan sebagian besar variasi data.
Scree Plot
plot(eigen_value, type = "b",
xlab = "Principal Component",
ylab = "Eigen Value",
main = "Scree Plot")
Scree plot menunjukkan penurunan nilai eigen dari setiap komponen utama.
Terlihat bahwa penurunan terbesar terjadi pada beberapa komponen
pertama, kemudian grafik mulai melandai.
Hal ini menunjukkan bahwa sebagian besar informasi data sudah dapat dijelaskan oleh komponen-komponen awal, sehingga komponen berikutnya memberikan tambahan informasi yang relatif kecil.
Penentuan Jumlah Komponen Utama
kumulatif## [1] 0.2541902 0.4693586 0.6259059 0.7417712 0.8544550 0.9486118 0.9804960
## [8] 0.9968050 1.0000000Berdasarkan hasil perhitungan proporsi kumulatif keragaman, terlihat bahwa hingga komponen utama keempat telah mampu menjelaskan sekitar 74,2% variasi data. Sementara itu, hingga komponen kelima, proporsi kumulatif meningkat menjadi sekitar 85,4%.
Dengan demikian, lima komponen utama dianggap telah cukup merepresentasikan sebagian besar informasi yang terdapat pada variabel asli.
Kesimpulan
Berdasarkan hasil analisis Principal Component Analysis (PCA) terhadap data karakteristik campuran beton, diperoleh bahwa terdapat hubungan antar variabel yang dapat direduksi menjadi beberapa komponen utama tanpa kehilangan sebagian besar informasi penting.
Dari perhitungan eigen value dan proporsi keragaman, diketahui bahwa komponen utama pertama memberikan kontribusi variasi terbesar dibandingkan komponen lainnya. Melalui perhitungan proporsi kumulatif, diperoleh bahwa hingga komponen utama keempat telah mampu menjelaskan sekitar 74,2% variasi data. Sementara itu, sampai komponen kelima, keragaman yang dapat dijelaskan meningkat menjadi sekitar 85,4%.
Oleh karena itu, struktur data dari sembilan variabel awal dapat digambarkan, cukup dengan menggunakan lima komponen utama. Reduksi dimensi ini memungkinkan analisis menjadi lebih sederhana tanpa menghilangkan informasi penting dari data.