R Notebook
Tahap A: Pra-pemrosesan Data (Classic Wine Dataset)
A.1 Eksplorasi Struktur Data
Langkah pertama adalah memuat dataset ke dalam memori R dan memeriksa dimensi serta struktur tipe datanya. Pengecekan missing values (NA) juga dilakukan untuk memastikan integritas data sebelum masuk ke tahap analisis matriks.
df_wine <- read.csv("Wine dataset.csv")
str(df_wine)## 'data.frame': 178 obs. of 14 variables:
## $ class : int 1 1 1 1 1 1 1 1 1 1 ...
## $ Alcohol : num 14.2 13.2 13.2 14.4 13.2 ...
## $ Malic.acid : num 1.71 1.78 2.36 1.95 2.59 1.76 1.87 2.15 1.64 1.35 ...
## $ Ash : num 2.43 2.14 2.67 2.5 2.87 2.45 2.45 2.61 2.17 2.27 ...
## $ Alcalinity.of.ash : num 15.6 11.2 18.6 16.8 21 15.2 14.6 17.6 14 16 ...
## $ Magnesium : int 127 100 101 113 118 112 96 121 97 98 ...
## $ Total.phenols : num 2.8 2.65 2.8 3.85 2.8 3.27 2.5 2.6 2.8 2.98 ...
## $ Flavanoids : num 3.06 2.76 3.24 3.49 2.69 3.39 2.52 2.51 2.98 3.15 ...
## $ Nonflavanoid.phenols : num 0.28 0.26 0.3 0.24 0.39 0.34 0.3 0.31 0.29 0.22 ...
## $ Proanthocyanins : num 2.29 1.28 2.81 2.18 1.82 1.97 1.98 1.25 1.98 1.85 ...
## $ Color.intensity : num 5.64 4.38 5.68 7.8 4.32 6.75 5.25 5.05 5.2 7.22 ...
## $ Hue : num 1.04 1.05 1.03 0.86 1.04 1.05 1.02 1.06 1.08 1.01 ...
## $ OD280.OD315.of.diluted.wines: num 3.92 3.4 3.17 3.45 2.93 2.85 3.58 3.58 2.85 3.55 ...
## $ Proline : int 1065 1050 1185 1480 735 1450 1290 1295 1045 1045 ...print("Jumlah Missing Values per Kolom:")## [1] "Jumlah Missing Values per Kolom:"colSums(is.na(df_wine))## class Alcohol
## 0 0
## Malic.acid Ash
## 0 0
## Alcalinity.of.ash Magnesium
## 0 0
## Total.phenols Flavanoids
## 0 0
## Nonflavanoid.phenols Proanthocyanins
## 0 0
## Color.intensity Hue
## 0 0
## OD280.OD315.of.diluted.wines Proline
## 0 0A.2 Rekoding Variabel Target
Variabel dependen pada dataset ini bernama class yang
berisi angka 1, 2, dan 3. Agar fungsi pembentuk diskriminan dapat
memprosesnya sebagai kelas kategori, variabel ini harus dikonversi
menjadi tipe data Faktor dan diberi label yang merepresentasikan 3 jenis
kultivar anggur.
df_wine$class <- factor(df_wine$class,
levels = c(1, 2, 3),
labels = c("Cultivar 1", "Cultivar 2", "Cultivar 3"))
print("Distribusi Proporsi Kelas Target:")## [1] "Distribusi Proporsi Kelas Target:"table(df_wine$class)##
## Cultivar 1 Cultivar 2 Cultivar 3
## 59 71 48A.3 Standarisasi Z-Score
Dataset ini memiliki 13 variabel prediktor dengan skala pengukuran
kimiawi yang sangat berbeda (misalnya, variabel Proline
berada di rentang ribuan, sedangkan variabel Hue berada di
angka desimal). Transformasi Z-score wajib diaplikasikan agar seluruh
variabel memiliki rata-rata 0 dan simpangan baku 1, sehingga tidak ada
variabel yang mendominasi pembobotan koefisien secara bias.
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, uniondf_lda <- df_wine %>%
mutate(across(where(is.numeric), scale))
head(df_lda)print("Ringkasan Statistik Setelah Standarisasi:")## [1] "Ringkasan Statistik Setelah Standarisasi:"summary(df_lda)## class Alcohol.V1 Malic.acid.V1
## Cultivar 1:59 Min. :-2.42738797671e+00 Min. :-1.42895214692e+00
## Cultivar 2:71 1st Qu.:-7.86027491902e-01 1st Qu.:-6.56895562876e-01
## Cultivar 3:48 Median : 6.08282929420e-02 Median :-4.21921819906e-01
## Mean :-9.00000000000e-16 Mean :-1.00000000000e-16
## 3rd Qu.: 8.33776663836e-01 3rd Qu.: 6.67908778437e-01
## Max. : 2.25341490679e+00 Max. : 3.10044647946e+00
## Ash.V1 Alcalinity.of.ash.V1
## Min. :-3.668812952680000 Min. :-2.66350470911e+00
## 1st Qu.:-0.570513110413000 1st Qu.:-6.87198682290e-01
## Median :-0.023754314719300 Median : 1.51402402463e-03
## Mean : 0.000000000000001 Mean :-1.00000000000e-16
## 3rd Qu.: 0.696144766278000 3rd Qu.: 6.00394638211e-01
## Max. : 3.147446700310000 Max. : 3.14563724850e+00
## Magnesium.V1 Total.phenols.V1
## Min. :-2.082381051020 Min. :-2.1013184558900
## 1st Qu.:-0.822096032608 1st Qu.:-0.8829774442020
## Median :-0.121937689047 Median : 0.0956899258394
## Mean : 0.000000000000 Mean : 0.0000000000000
## 3rd Qu.: 0.508204820157 3rd Qu.: 0.8067217293800
## Max. : 4.359075709740 Max. : 2.5323719492100
## Flavanoids.V1 Nonflavanoid.phenols.V1
## Min. :-1.69119985465e+00 Min. :-1.86297878411e+00
## 1st Qu.:-8.25211489158e-01 1st Qu.:-7.38059198454e-01
## Median : 1.05851146578e-01 Median :-1.75599405626e-01
## Mean : 1.00000000000e-16 Mean :-1.00000000000e-16
## 3rd Qu.: 8.46696684691e-01 3rd Qu.: 6.07826734384e-01
## Max. : 3.05421615974e+00 Max. : 2.39564536159e+00
## Proanthocyanins.V1 Color.intensity.V1
## Min. :-2.0632141011800 Min. :-1.629691112710
## 1st Qu.:-0.5956033856300 1st Qu.:-0.792865929247
## Median :-0.0627209234373 Median :-0.158776743842
## Mean : 0.0000000000000 Mean : 0.000000000000
## 3rd Qu.: 0.6274055439930 3rd Qu.: 0.492566569057
## Max. : 3.4752691944000 Max. : 3.425768243040
## Hue.V1 OD280.OD315.of.diluted.wines.V1
## Min. :-2.0888400377700 Min. :-1.88972321161e+00
## 1st Qu.:-0.7654033325060 1st Qu.:-9.49569692694e-01
## Median : 0.0330336880283 Median : 2.37066022192e-01
## Mean : 0.0000000000000 Mean : 3.00000000000e-16
## 3rd Qu.: 0.7111582808110 3rd Qu.: 7.86369201783e-01
## Max. : 3.2924067307600 Max. : 1.95539904553e+00
## Proline.V1
## Min. :-1.48898739067e+00
## 1st Qu.:-7.82430645677e-01
## Median :-2.33062929343e-01
## Mean :-1.00000000000e-16
## 3rd Qu.: 7.56116513652e-01
## Max. : 2.96311398679e+00Tahap B: Pengujian Asumsi Multivariat
B.1 Uji Normalitas Multivariat (Mardia’s Test)
Pengujian ini bertujuan untuk memverifikasi apakah ketiga belas variabel uji kimiawi pada dataset Wine mengikuti distribusi normal multivariat. Uji Mardia dieksekusi untuk mengevaluasi tingkat skewness dan kurtosis multivariat secara bersamaan.
library(MVN)## Warning: package 'MVN' was built under R version 4.5.3## Registered S3 method overwritten by 'lme4':
## method from
## na.action.merMod carlibrary(dplyr)
# Mengisolasi variabel prediktor numerik ke dalam format data.frame murni
prediktor_numerik <- as.data.frame(df_lda %>% dplyr::select(-class))
# Menjalankan Uji Normalitas Multivariat
uji_mardia <- mvn(data = prediktor_numerik)
print("Hasil Uji Normalitas Multivariat (Mardia's Test):")## [1] "Hasil Uji Normalitas Multivariat (Mardia's Test):"print(uji_mardia)## $multivariate_normality
## Test Statistic p.value Method MVN
## 1 Henze-Zirkler 1.074 <0.001 asymptotic ✗ Not normal
##
## $univariate_normality
## Test Variable Statistic p.value Normality
## 1 Anderson-Darling Alcohol 1.034 0.01 ✗ Not normal
## 2 Anderson-Darling Malic.acid 7.619 <0.001 ✗ Not normal
## 3 Anderson-Darling Ash 0.678 0.075 ✓ Normal
## 4 Anderson-Darling Alcalinity.of.ash 0.501 0.205 ✓ Normal
## 5 Anderson-Darling Magnesium 2.331 <0.001 ✗ Not normal
## 6 Anderson-Darling Total.phenols 1.421 0.001 ✗ Not normal
## 7 Anderson-Darling Flavanoids 2.474 <0.001 ✗ Not normal
## 8 Anderson-Darling Nonflavanoid.phenols 2.172 <0.001 ✗ Not normal
## 9 Anderson-Darling Proanthocyanins 0.700 0.067 ✓ Normal
## 10 Anderson-Darling Color.intensity 2.844 <0.001 ✗ Not normal
## 11 Anderson-Darling Hue 0.838 0.03 ✗ Not normal
## 12 Anderson-Darling OD280.OD315.of.diluted.wines 3.496 <0.001 ✗ Not normal
## 13 Anderson-Darling Proline 4.100 <0.001 ✗ Not normal
##
## $descriptives
## Variable n Mean Std.Dev Median Min Max 25th
## 1 Alcohol 178 0 1 0.061 -2.427 2.253 -0.786
## 2 Malic.acid 178 0 1 -0.422 -1.429 3.100 -0.657
## 3 Ash 178 0 1 -0.024 -3.669 3.147 -0.571
## 4 Alcalinity.of.ash 178 0 1 0.002 -2.664 3.146 -0.687
## 5 Magnesium 178 0 1 -0.122 -2.082 4.359 -0.822
## 6 Total.phenols 178 0 1 0.096 -2.101 2.532 -0.883
## 7 Flavanoids 178 0 1 0.106 -1.691 3.054 -0.825
## 8 Nonflavanoid.phenols 178 0 1 -0.176 -1.863 2.396 -0.738
## 9 Proanthocyanins 178 0 1 -0.063 -2.063 3.475 -0.596
## 10 Color.intensity 178 0 1 -0.159 -1.630 3.426 -0.793
## 11 Hue 178 0 1 0.033 -2.089 3.292 -0.765
## 12 OD280.OD315.of.diluted.wines 178 0 1 0.237 -1.890 1.955 -0.950
## 13 Proline 178 0 1 -0.233 -1.489 2.963 -0.782
## 75th Skew Kurtosis
## 1 0.834 -0.051 2.138
## 2 0.668 1.031 3.257
## 3 0.696 -0.175 4.079
## 4 0.600 0.211 3.441
## 5 0.508 1.089 5.013
## 6 0.807 0.086 2.154
## 7 0.847 0.025 2.111
## 8 0.608 0.446 2.347
## 9 0.627 0.513 3.506
## 10 0.493 0.861 3.337
## 11 0.711 0.021 2.632
## 12 0.786 -0.305 1.910
## 13 0.756 0.761 2.725
##
## $data
## Alcohol Malic.acid Ash Alcalinity.of.ash Magnesium
## 1 1.51434077 -0.56066822 0.23139979 -1.166303174 1.90852151
## 2 0.24559683 -0.49800856 -0.82566722 -2.483840525 0.01809398
## 3 0.19632522 0.02117152 1.10621386 -0.267982252 0.08810981
## 4 1.68679140 -0.34583508 0.48655389 -0.806974805 0.92829983
## 5 0.29486844 0.22705328 1.83522559 0.450674485 1.27837900
## 6 1.47738706 -0.51591132 0.30430096 -1.286079296 0.85828399
## 7 1.71142720 -0.41744613 0.30430096 -1.465743481 -0.26196936
## 8 1.30493643 -0.16680747 0.88751034 -0.567422559 1.48842650
## 9 2.25341491 -0.62332789 -0.71631546 -1.645407665 -0.19195352
## 10 1.05857838 -0.88291793 -0.35180959 -1.046527051 -0.12193769
## 11 1.35420804 -0.15785609 -0.24245783 -0.447646437 0.36817315
## 12 1.37884384 -0.76654998 -0.16955666 -0.806974805 -0.33198519
## 13 0.92308146 -0.54276546 0.15849862 -1.046527051 -0.75208020
## 14 2.15487169 -0.54276546 0.08559744 -2.423952463 -0.61204853
## 15 1.69910930 -0.41744613 0.04914686 -2.244288279 0.15812565
## 16 0.77526663 -0.47115441 1.21556562 -0.687198682 0.85828399
## 17 1.60056608 -0.37268923 1.28846679 0.151234178 1.41841067
## 18 1.02162467 -0.68598755 0.92396093 0.151234178 1.06833150
## 19 1.46506916 -0.66808479 0.41365272 -0.896806897 0.57822065
## 20 0.78758453 0.68357369 0.70525741 -1.286079296 1.13834733
## 21 1.30493643 -0.63227927 -0.31535901 -1.046527051 1.83850567
## 22 -0.08698653 1.31017034 1.03331269 -0.267982252 0.15812565
## 23 0.87380985 -0.42639751 -0.02375431 -0.866862867 0.08810981
## 24 -0.18552975 -0.65913341 0.55945507 -0.507534498 -0.33198519
## 25 0.61513390 -0.47115441 0.88751034 0.151234178 -0.26196936
## 26 0.06082829 -0.25632128 3.11099611 1.648435713 1.69847400
## 27 0.47963697 -0.50695994 0.92396093 -1.016583020 -0.47201686
## 28 0.36877585 -0.55171684 -0.82566722 -0.747086744 -0.40200103
## 29 1.07089628 -0.39059199 1.58007149 -0.028430007 0.50820482
## 30 1.25566482 -0.58752236 -0.57051311 -1.046527051 -0.26196936
## 31 0.89844565 -0.74864721 1.21556562 0.899834945 0.08810981
## 32 0.71367712 -0.60542512 -0.02375431 -0.118262099 0.43818899
## 33 0.83685614 -0.45325165 -0.02375431 -0.687198682 0.29815732
## 34 0.93539936 -0.72179307 1.21556562 0.001514024 2.25860068
## 35 0.62745180 -0.48010579 1.03331269 -0.148206130 0.71825232
## 36 0.59049809 -0.47115441 0.15849862 0.300954331 0.01809398
## 37 0.34414005 -0.62332789 1.72587383 -1.196247204 0.71825232
## 38 0.06082829 -0.61437650 0.66880683 -0.447646437 -0.12193769
## 39 0.08546410 -0.74864721 -0.97146956 -1.196247204 -0.12193769
## 40 1.50202286 1.48024658 0.52300448 -1.884959911 1.97853734
## 41 0.68904131 -0.56066822 -0.20600725 -0.986638989 1.20836316
## 42 0.50427278 1.34597587 -0.89856839 -0.208094191 -0.68206436
## 43 1.08321419 -0.39954337 0.81460917 -1.345967358 0.08810981
## 44 0.29486844 1.47129519 -0.27890842 -0.597366590 0.22814148
## 45 0.06082829 -0.50695994 -0.97146956 -0.747086744 0.50820482
## 46 1.48970496 1.52500348 0.26785038 -0.178150160 0.78826816
## 47 1.69910930 1.12219135 -0.31535901 -1.046527051 0.15812565
## 48 1.10784999 -0.58752236 -0.89856839 -1.046527051 0.08810981
## 49 1.35420804 -0.28317542 0.12204803 -0.208094191 0.22814148
## 50 1.15712160 -0.54276546 -0.35180959 -0.627310621 0.57822065
## 51 0.06082829 -0.54276546 -1.19017308 -2.124512156 -0.54203270
## 52 1.02162467 -0.61437650 0.85105976 -0.687198682 -0.40200103
## 53 1.00930677 -0.52486270 0.19494920 -1.645407665 0.78826816
## 54 0.94771726 -0.39059199 1.14266445 -0.717142713 1.06833150
## 55 0.91076355 -0.59647374 -0.42471076 -0.926750928 1.27837900
## 56 0.68904131 -0.54276546 0.34075155 0.300954331 1.13834733
## 57 1.50202286 -0.56961960 -0.24245783 -0.956694959 1.27837900
## 58 0.35645795 -0.32793232 1.14266445 -0.806974805 0.15812565
## 59 0.88612775 -0.81130688 0.48655389 -0.836918836 0.57822065
## 60 -0.77678907 -1.24992453 -3.66881295 -2.663504709 -0.82209603
## 61 -0.82606067 -1.10670244 -0.31535901 -1.046527051 0.08810981
## 62 -0.44420570 -0.87396654 -1.26307425 -0.806974805 0.01809398
## 63 0.82453824 -0.97243173 -1.62758012 -0.447646437 -0.40200103
## 64 -0.77678907 -1.07984830 -0.75276604 -0.148206130 -0.89211187
## 65 -1.02314711 -0.79340412 0.59590565 -0.148206130 0.29815732
## 66 -0.77678907 -1.00823725 0.70525741 -0.417702406 -0.12193769
## 67 0.13473571 -1.18726487 -2.42949302 -1.345967358 -1.52225438
## 68 -0.77678907 -1.04404278 -1.62758012 0.031458055 -1.52225438
## 69 0.41804746 -1.24992453 -0.02375431 -0.747086744 0.71825232
## 70 -0.97387550 -1.02614002 -2.24724008 -0.806974805 3.58890153
## 71 -0.87533228 -0.65018203 -0.57051311 0.271010300 0.22814148
## 72 1.05857838 -0.73969583 1.10621386 1.648435713 -0.96212770
## 73 0.60281600 -0.60542512 -0.46116135 1.348995406 -0.89211187
## 74 -0.01307912 -0.59647374 0.85105976 3.145637249 2.74871152
## 75 -1.28182306 -1.11565382 -0.24245783 0.450674485 0.08810981
## 76 -1.65136013 -0.40849475 -1.62758012 -1.046527051 -0.19195352
## 77 0.03619249 -1.28573006 -2.39304243 -1.046527051 -0.96212770
## 78 -1.42963789 0.49559470 -0.49761194 -0.447646437 0.85828399
## 79 -0.82606067 -1.20516763 -1.51822836 -1.405855419 2.53866402
## 80 -0.37029829 1.37283001 0.12204803 1.049555099 0.08810981
## 81 -1.23255145 -1.26782729 -1.33597542 -0.148206130 -0.96212770
## 82 -0.34566248 -0.47115441 -0.60696370 -0.208094191 -0.96212770
## 83 -1.13400823 -1.07984830 0.52300448 1.348995406 -1.52225438
## 84 0.06082829 1.36387863 -0.16955666 0.899834945 -1.03214354
## 85 -1.42963789 -1.29468144 0.77815859 -0.447646437 -0.40200103
## 86 -0.40725200 -1.21411901 -0.46116135 -0.447646437 -0.05192185
## 87 -1.03546501 -0.65018203 -0.20600725 0.989667037 -0.68206436
## 88 -1.66367803 -0.59647374 0.92396093 1.947876020 -0.82209603
## 89 -1.67599593 -0.24736990 0.34075155 0.630338669 -1.10215937
## 90 -1.13400823 -0.90082069 -0.24245783 1.229219283 -2.08238105
## 91 -1.13400823 -0.45325165 -0.16955666 -0.297926283 -1.31220687
## 92 -1.23255145 -0.73969583 0.19494920 0.750114792 -0.96212770
## 93 -0.38261619 -0.72179307 -0.38826018 0.360842393 -1.38222271
## 94 -0.87533228 0.44188642 -0.53406252 -0.447646437 -0.82209603
## 95 -1.70063174 -0.31002956 -0.31535901 -0.447646437 -0.12193769
## 96 -0.65361004 -0.73074445 -0.60696370 -0.148206130 4.35907571
## 97 -1.46659160 -0.19366161 1.36136797 0.600394638 2.39863235
## 98 -0.87533228 -0.82920964 -1.40887660 -1.046527051 -1.03214354
## 99 -0.77678907 -1.13355658 -0.97146956 -0.297926283 -0.82209603
## 100 -0.87533228 0.74623336 -0.57051311 -0.447646437 -0.82209603
## 101 -1.13400823 -0.22946714 -2.42949302 -0.597366590 -0.19195352
## 102 -0.49347731 -0.89186931 -1.70048129 -0.297926283 -0.82209603
## 103 -0.81374277 0.10173395 0.34075155 0.450674485 -0.12193769
## 104 -1.45427369 -0.55171684 -1.77338246 0.001514024 -0.96212770
## 105 -0.60433843 -0.54276546 -1.40887660 0.300954331 -1.03214354
## 106 -0.71519955 0.19124776 -0.35180959 0.750114792 -0.68206436
## 107 -0.92460389 -0.54276546 -0.89856839 -0.148206130 -1.38222271
## 108 -0.34566248 -0.52486270 -0.31535901 0.899834945 -1.10215937
## 109 -0.96155760 -0.93662621 -1.55467894 -0.148206130 -0.54203270
## 110 -1.71294964 -0.88291793 1.21556562 0.151234178 -0.40200103
## 111 -1.89771818 1.25646206 -1.99208598 0.001514024 0.50820482
## 112 -0.59202053 0.08383119 -0.71631546 0.450674485 -0.82209603
## 113 -1.52818111 0.30761571 2.01747852 0.151234178 0.22814148
## 114 -1.95930769 -1.42895215 0.48655389 0.450674485 -0.82209603
## 115 -1.13400823 -0.84711240 0.48655389 0.899834945 -1.10215937
## 116 -2.42738798 -0.73969583 -0.60696370 0.600394638 -1.03214354
## 117 -1.45427369 -0.77550136 -1.37242601 0.390786423 -0.96212770
## 118 -0.71519955 -0.65018203 -0.64341428 0.899834945 0.57822065
## 119 -0.28407297 0.97896926 -1.40887660 -1.046527051 -1.38222271
## 120 -1.23255145 0.97896926 -1.33597542 -0.148206130 -0.89211187
## 121 -1.91003608 0.05697705 0.19494920 0.151234178 -0.26196936
## 122 -1.77453915 -0.25632128 3.14744670 2.696476788 1.34839483
## 123 -0.71519955 1.87410733 1.32491738 2.097596174 0.15812565
## 124 0.06082829 3.10044648 -0.86211780 0.600394638 -0.96212770
## 125 -1.39268418 1.76669076 0.08559744 0.450674485 -1.24219104
## 126 -1.14632613 -0.15785609 -0.71631546 0.450674485 -1.03214354
## 127 -0.70288165 -0.72179307 -0.27890842 0.600394638 -0.96212770
## 128 -1.49122740 -0.18471023 1.50717031 2.696476788 -0.54203270
## 129 -0.77678907 -0.63227927 -0.24245783 1.498715559 -0.82209603
## 130 -1.18327984 1.75773938 0.04914686 0.750114792 -1.38222271
## 131 -0.17321185 -0.88291793 -0.16955666 -0.447646437 1.55844234
## 132 -0.14857605 0.58510851 0.12204803 0.151234178 0.29815732
## 133 -0.23480136 -0.02358538 0.12204803 1.348995406 -0.12193769
## 134 -0.37029829 1.08638583 -0.02375431 0.600394638 0.43818899
## 135 -0.60433843 -0.98138311 -0.42471076 -0.597366590 -1.03214354
## 136 -0.49347731 0.11068533 -0.60696370 -0.297926283 -0.40200103
## 137 -0.92460389 2.13369737 0.63235624 0.450674485 -0.75208020
## 138 -0.57970263 2.84085644 0.99686210 1.648435713 -0.26196936
## 139 0.60281600 1.12219135 -0.64341428 0.001514024 -0.82209603
## 140 -0.19784766 0.55825437 0.88751034 1.348995406 0.08810981
## 141 -0.08698653 0.42398365 1.21556562 0.450674485 -0.26196936
## 142 0.44268327 0.20019914 -0.06020490 0.151234178 -0.75208020
## 143 0.63976970 0.74623336 1.28846679 1.199275252 -0.19195352
## 144 0.76294873 2.33957912 -0.06020490 0.151234178 -0.54203270
## 145 -0.92460389 1.38178139 -0.60696370 -0.297926283 0.85828399
## 146 0.19632522 1.10428859 -0.78921663 0.450674485 0.15812565
## 147 1.08321419 2.42014155 -0.49761194 0.151234178 -1.38222271
## 148 -0.16089395 2.03523218 0.41365272 0.600394638 -0.96212770
## 149 0.39341166 0.80889302 0.04914686 0.600394638 -0.54203270
## 150 0.09778200 1.39968415 -0.02375431 0.600394638 0.92829983
## 151 0.61513390 0.70147646 0.92396093 1.348995406 1.62845817
## 152 -0.25943717 0.29866433 0.41365272 0.750114792 0.85828399
## 153 0.13473571 -0.39059199 1.39781855 1.798155867 1.13834733
## 154 0.28255053 0.86260131 -0.31535901 -0.297926283 -0.12193769
## 155 -0.51811312 -0.93662621 -0.97146956 0.151234178 0.22814148
## 156 0.20864312 2.55441226 -0.16955666 0.750114792 -0.47201686
## 157 1.03394258 1.59661452 0.04914686 0.001514024 -0.75208020
## 158 -0.67824585 0.62091403 0.99686210 2.247316327 -0.19195352
## 159 1.64983769 -0.58752236 1.21556562 1.648435713 -0.12193769
## 160 0.59049809 -0.59647374 0.99686210 0.899834945 -0.75208020
## 161 -0.78910697 1.33702448 0.04914686 0.450674485 -0.82209603
## 162 0.84917404 0.82679579 0.63235624 0.151234178 0.50820482
## 163 -0.18552975 0.83574717 0.77815859 0.750114792 0.43818899
## 164 -0.05003283 0.99687202 -0.06020490 -0.297926283 0.43818899
## 165 0.96003516 0.37922675 -0.24245783 0.750114792 -0.68206436
## 166 0.89844565 1.81144766 -0.38826018 0.899834945 -0.82209603
## 167 0.55354439 1.22065654 0.85105976 1.049555099 0.78826816
## 168 -0.22248346 0.92526097 -0.24245783 0.001514024 -0.82209603
## 169 0.71367712 0.21810190 1.17911504 1.498715559 0.36817315
## 170 0.49195487 2.02628080 1.79877500 1.648435713 0.85828399
## 171 -0.98619340 0.62091403 -0.16955666 -0.148206130 -0.26196936
## 172 -0.28407297 0.04802567 -0.31535901 0.001514024 -0.96212770
## 173 1.42811545 0.15544223 0.41365272 0.151234178 -0.61204853
## 174 0.87380985 2.96617577 0.30430096 0.300954331 -0.33198519
## 175 0.49195487 1.40863553 0.41365272 1.049555099 0.15812565
## 176 0.33182214 1.73983662 -0.38826018 0.151234178 1.41841067
## 177 0.20864312 0.22705328 0.01269627 0.151234178 1.41841067
## 178 1.39116174 1.57871176 1.36136797 1.498715559 -0.26196936
## Total.phenols Flavanoids Nonflavanoid.phenols Proanthocyanins
## 1 0.806721729 1.0319080692 -0.65770780 1.22143845
## 2 0.567048088 0.7315652835 -0.81841060 -0.54318872
## 3 0.806721729 1.2121137407 -0.49700500 2.12995937
## 4 2.484437221 1.4623993954 -0.97911340 1.02925134
## 5 0.806721729 0.6614853002 0.22615759 0.40027531
## 6 1.557699140 1.3622851335 -0.17559941 0.66234866
## 7 0.327374446 0.4912910549 -0.49700500 0.67982021
## 8 0.487156874 0.4812796287 -0.41665360 -0.59560339
## 9 0.806721729 0.9518166597 -0.57735640 0.67982021
## 10 1.094330099 1.1220109049 -1.13981619 0.45268998
## 11 1.046395371 1.2922051502 -1.13981619 1.37868246
## 12 -0.151972837 0.4011882192 -0.81841060 -0.03651359
## 13 0.487156874 0.7315652835 -0.57735640 0.38280376
## 14 1.286069013 1.6626279192 0.54756319 2.12995937
## 15 1.605633868 1.6125707883 -0.57735640 2.39203271
## 16 0.886612943 0.8817366764 -0.49700500 -0.22870071
## 17 0.806721729 1.1119994787 -0.25595080 0.66234866
## 18 1.046395371 1.3722965597 0.30650899 0.22555975
## 19 1.605633868 1.9029021478 -0.33630220 0.47016154
## 20 0.646939302 1.0018737906 -1.54157319 0.12073042
## 21 1.126286585 1.1420337573 -0.97911340 0.88947889
## 22 0.183570261 0.3811653668 -0.89876200 0.67982021
## 23 0.503135117 0.8517023978 -0.73805920 0.17314508
## 24 0.295417961 0.3411196621 -0.81841060 -0.22870071
## 25 0.375309174 0.5813938906 -0.65770780 0.12073042
## 26 0.535091602 0.6514738740 0.86896878 0.57499088
## 27 0.886612943 0.9117709549 -0.17559941 -0.24617226
## 28 0.167592018 0.1609139906 -0.73805920 -0.42088782
## 29 1.046395371 0.9418052335 0.06545479 0.29544598
## 30 0.567048088 0.3010739573 -0.81841060 0.67982021
## 31 1.126286585 1.2221251668 -0.57735640 1.37868246
## 32 0.902591186 1.1620566097 -1.13981619 0.62740554
## 33 0.199548504 0.6614853002 0.46721179 0.66234866
## 34 1.046395371 0.7115424311 1.11002298 -0.42088782
## 35 0.087700804 0.5013024811 -0.57735640 -0.08892826
## 36 0.646939302 0.9518166597 -0.81841060 0.47016154
## 37 0.487156874 0.6514738740 -0.17559941 -0.40341627
## 38 0.247483232 0.4011882192 -0.57735640 -0.26364382
## 39 0.167592018 0.6114281692 -0.65770780 -0.38594471
## 40 1.126286585 1.0118852168 -1.30051899 0.85453577
## 41 1.365960227 1.2621708716 -0.17559941 1.30879623
## 42 0.247483232 0.6514738740 -0.73805920 -0.19375759
## 43 1.525742654 1.5324793788 -1.54157319 0.19061664
## 44 0.551069845 0.6014167430 -0.33630220 0.12073042
## 45 1.126286585 0.9718395121 -0.65770780 0.76717799
## 46 0.886612943 0.6214395954 -0.49700500 -0.59560339
## 47 1.525742654 1.1420337573 -0.73805920 1.04672289
## 48 1.286069013 1.3622851335 -1.22016759 0.95936511
## 49 0.726830515 0.8917481025 -0.33630220 1.37868246
## 50 0.934547672 1.5124565264 -0.33630220 0.85453577
## 51 0.678895787 1.2421480192 -1.54157319 2.30467493
## 52 0.247483232 0.9618280859 -1.13981619 1.22143845
## 53 2.532371949 1.7126850502 -0.33630220 0.48763309
## 54 1.126286585 0.7615995621 0.22615759 0.15567353
## 55 0.487156874 0.8717252502 -1.22016759 0.05084419
## 56 1.062373614 0.7515881359 -1.30051899 1.50098335
## 57 1.445851440 0.9718395121 -0.81841060 0.76717799
## 58 1.126286585 1.2021023145 -0.41665360 0.12073042
## 59 1.765416296 1.6426050669 -1.38087039 0.78464955
## 60 -0.503494178 -1.4609370523 -0.65770780 -2.04574255
## 61 -0.391646479 -0.9403428904 2.15459116 -2.06321410
## 62 -0.439581207 -0.6199772522 1.35107717 -1.69631142
## 63 -0.311755265 -0.2395430570 -0.33630220 -1.50412430
## 64 1.925198724 1.0719537740 -1.38087039 0.48763309
## 65 -0.647298363 -0.2795887618 0.70826598 -0.97997762
## 66 0.199548504 0.6214395954 0.06545479 0.85453577
## 67 1.094330099 1.1520451835 -0.81841060 1.20396690
## 68 -0.295777022 -0.0293031070 -0.73805920 -0.96250606
## 69 0.375309174 -0.7301029403 1.51177997 -2.04574255
## 70 -0.711211334 -0.7501257927 -1.78262739 1.58834113
## 71 -1.909579543 -1.0104228737 0.06545479 -0.22870071
## 72 1.046395371 0.8316795454 -1.22016759 0.48763309
## 73 -0.663276606 -0.1894859260 -0.73805920 -0.97997762
## 74 1.605633868 0.8617138240 -1.22016759 0.64487710
## 75 1.733459810 0.1108568597 -1.86297878 0.10325886
## 76 -1.094689161 -0.4597944332 -0.17559941 -0.77031895
## 77 -0.551428907 0.0007311716 -0.97911340 -0.22870071
## 78 -0.918928490 -0.7100800880 0.54756319 -1.11975007
## 79 -0.631320120 -0.1794744999 -0.09524801 2.04260159
## 80 0.854656458 0.5213253335 0.54756319 0.62740554
## 81 0.199548504 0.2309939740 -0.49700500 -0.28111538
## 82 -0.151972837 0.5013024811 -0.81841060 0.31291753
## 83 -0.471537693 -0.4497830070 0.30650899 -0.33353004
## 84 -1.030776190 -0.4397715808 1.99388837 0.05084419
## 85 -0.151972837 0.1809368430 -1.13981619 1.32626779
## 86 -0.151972837 -0.0893716641 -0.49700500 -0.22870071
## 87 -0.823059034 -0.3396573189 0.54756319 -0.05398515
## 88 -0.599363635 -0.4197487284 0.30650899 -0.43835938
## 89 -0.551428907 -0.3396573189 0.94932018 -0.42088782
## 90 -0.151972837 -0.4397715808 0.46721179 -0.36847316
## 91 -1.110667404 -0.5298744165 1.27072578 0.08578730
## 92 -1.350341045 -0.7801600713 1.11002298 0.06831575
## 93 -1.462188745 -0.5699201213 1.75283417 0.05084419
## 94 0.247483232 0.2209825478 -0.89876200 0.69729177
## 95 1.158243070 0.2309939740 -1.54157319 -0.42088782
## 96 0.327374446 0.2410054002 -0.33630220 2.95112251
## 97 -1.110667404 -1.0404571523 -1.78262739 -0.05398515
## 98 0.407265660 0.4712682025 -0.57735640 0.31291753
## 99 1.957155209 1.7226964764 -0.97911340 0.62740554
## 100 0.886612943 0.9618280859 0.70826598 2.12995937
## 101 -0.104038109 0.1408911382 -0.81841060 -0.33353004
## 102 -1.350341045 -0.6700343832 -0.57735640 -0.42088782
## 103 0.423243903 0.0808225811 -0.17559941 -0.49077405
## 104 0.327374446 -0.3897144499 0.06545479 -0.29858693
## 105 -0.151972837 -0.1093945165 -0.33630220 -0.19375759
## 106 -0.982841462 -0.1894859260 2.39564536 -0.29858693
## 107 -1.030776190 0.0007311716 0.06545479 0.06831575
## 108 -1.462188745 -0.2695773356 0.94932018 0.06831575
## 109 0.103679047 0.0107425978 0.22615759 0.85453577
## 110 0.710852273 0.8917481025 -0.57735640 1.57086958
## 111 1.413894955 0.5513596121 -0.97911340 3.47526919
## 112 0.407265660 0.2410054002 -0.81841060 -0.64801805
## 113 -0.870993762 0.0007311716 1.91353697 -0.94503451
## 114 0.295417961 -0.0192916808 0.46721179 -0.26364382
## 115 0.423243903 0.2610282525 0.54756319 -0.96250606
## 116 0.263461475 0.1408911382 1.27072578 0.73223488
## 117 -0.503494178 -0.4297601546 -0.49700500 -0.10639981
## 118 -0.471537693 0.0607997287 -0.17559941 0.03337264
## 119 -1.062732675 -0.7801600713 0.54756319 -1.32940874
## 120 -0.471537693 -0.3897144499 0.06545479 0.48763309
## 121 0.966504157 0.7615995621 -0.33630220 0.41774687
## 122 1.413894955 3.0542161597 0.86896878 0.48763309
## 123 -0.151972837 0.1008454335 0.54756319 0.20808820
## 124 0.519113359 0.6214395954 -0.49700500 0.73223488
## 125 0.902591186 1.0018737906 -1.22016759 2.30467493
## 126 0.487156874 0.6214395954 0.06545479 -0.42088782
## 127 0.710852273 1.1220109049 0.22615759 0.31291753
## 128 -0.263820537 0.2109711216 1.75283417 0.29544598
## 129 -0.120016352 0.4212110716 0.30650899 0.54004776
## 130 -0.311755265 -0.2795887618 0.46721179 -0.42088782
## 131 -1.254471589 -0.7801600713 -1.22016759 -1.13722163
## 132 -1.590014687 -0.8101943499 -0.97911340 -1.32940874
## 133 -1.829688329 -0.9403428904 -0.73805920 -1.32940874
## 134 -0.950884976 -0.8302172023 -1.54157319 -1.31193719
## 135 -0.471537693 -1.4509256261 1.91353697 -0.59560339
## 136 -1.078710918 -1.3708342166 2.15459116 -1.13722163
## 137 -1.462188745 -1.5610513142 1.35107717 -1.38182341
## 138 -0.807080791 -1.4309027737 2.15459116 -0.85767673
## 139 -1.078710918 -1.5510398880 1.75283417 -1.24205096
## 140 0.039766076 -1.4309027737 1.35107717 -1.36435186
## 141 -1.206536860 -1.5310170356 1.35107717 -1.46918119
## 142 -1.430232259 -1.5310170356 0.06545479 -1.66136831
## 143 -1.190558618 -1.5109941832 1.11002298 -1.81861232
## 144 -0.471537693 -1.2306742499 0.86896878 -0.99744918
## 145 -1.462188745 -1.2506971023 -0.57735640 -0.78779050
## 146 -1.270449832 -1.4809599046 0.54756319 -0.50824560
## 147 -2.101318456 -1.6911998547 0.30650899 -1.59148209
## 148 -0.950884976 -1.3808456427 0.86896878 -1.27699407
## 149 -0.583385392 -1.2707199546 0.70826598 -0.59560339
## 150 -1.414254017 -0.6400001046 -0.17559941 -0.78779050
## 151 -1.430232259 -0.4597944332 -1.13981619 -0.59560339
## 152 -1.302406317 -0.6700343832 -0.97911340 -0.57813183
## 153 -0.151972837 -0.7501257927 -0.81841060 -0.05398515
## 154 -0.791102548 -1.2006399713 1.99388837 0.48763309
## 155 -1.302406317 -1.4509256261 1.35107717 -0.33353004
## 156 -0.886972005 -1.4008684951 1.99388837 -0.07145670
## 157 -0.791102548 -1.2006399713 0.94932018 -0.05398515
## 158 -0.631320120 -1.4509256261 2.15459116 -0.78779050
## 159 0.806721729 -0.7200915142 1.35107717 1.93777225
## 160 0.487156874 -0.9303314642 1.27072578 1.22143845
## 161 0.007809591 -1.1105371356 1.11002298 -0.96250606
## 162 -0.743167820 -1.4709484785 1.11002298 -1.38182341
## 163 -1.030776190 -1.4309027737 1.91353697 -1.10227851
## 164 -1.446210502 -1.3307885118 0.30650899 -1.13722163
## 165 -1.510123473 -1.3508113642 0.38686039 -0.97997762
## 166 -1.621971173 -1.5610513142 1.27072578 -0.77031895
## 167 -0.950884976 -1.1105371356 0.54756319 -0.22870071
## 168 -1.302406317 -1.3708342166 0.30650899 -1.08480696
## 169 -1.190558618 -1.1906285451 0.22615759 -0.08892826
## 170 -0.503494178 -1.0704914308 -0.73805920 -0.84020517
## 171 -1.669905901 -1.5410284618 0.30650899 -1.50412430
## 172 -1.446210502 -1.5210056094 0.94932018 -1.66136831
## 173 -0.982841462 -1.3307885118 0.62791458 -0.61307494
## 174 -0.982841462 -1.4208913475 1.27072578 -0.92756295
## 175 -0.791102548 -1.2807313808 0.54756319 -0.31605849
## 176 -1.126645647 -1.3407999380 0.54756319 -0.42088782
## 177 -1.030776190 -1.3508113642 1.35107717 -0.22870071
## 178 -0.391646479 -1.2707199546 1.59213137 -0.42088782
## Color.intensity Hue OD280.OD315.of.diluted.wines Proline
## 1 0.251008784 0.36115849 1.84272147 1.010159388
## 2 -0.292496232 0.40490846 1.11031723 0.962526349
## 3 0.268262912 0.31740852 0.78636920 1.391223700
## 4 1.182731669 -0.42634104 1.18074072 2.328006800
## 5 -0.318377423 0.36115849 0.44833648 -0.037767469
## 6 0.729810822 0.40490846 0.33565890 2.232740722
## 7 0.082781041 0.27365854 1.36384178 1.724654973
## 8 -0.003489596 0.44865844 1.36384178 1.740532653
## 9 0.061213382 0.53615839 0.33565890 0.946648670
## 10 0.932546820 0.22990857 1.32158768 0.946648670
## 11 0.298457635 1.27990794 0.78636920 2.423272878
## 12 -0.025057256 0.92990815 0.29340481 1.692899614
## 13 0.233754657 0.84240820 0.40608239 1.819921051
## 14 0.147484019 1.27990794 0.16664254 1.280079943
## 15 1.053325713 1.06115807 0.54692935 2.540767708
## 16 0.967055075 1.41115786 0.37791299 1.788165692
## 17 0.492566569 0.49240841 0.05396496 1.692899614
## 18 0.665107844 0.75490825 -0.05871261 1.216569224
## 19 1.570949537 1.19240799 0.29340481 2.963113987
## 20 0.018078063 0.01115870 1.05397844 0.311541483
## 21 0.255322316 0.57990836 1.54694284 0.105131647
## 22 -0.240733849 0.31740852 1.27933359 0.073376288
## 23 -0.542681081 0.66740831 1.95539905 0.914893310
## 24 -0.486605166 0.57990836 1.43426526 0.851382592
## 25 -0.663459973 0.71115828 1.70187450 0.311541483
## 26 -0.637578782 0.75490825 0.82862329 0.263908444
## 27 -0.111327893 -0.16384119 0.85679269 1.422979059
## 28 -0.477978102 0.27365854 0.22298133 1.708777293
## 29 -0.240733849 1.27990794 1.11031723 0.533828998
## 30 -0.154463212 0.36115849 1.37792647 0.914893310
## 31 0.276889975 1.01740810 0.13847314 1.708777293
## 32 0.794513800 0.57990836 0.37791299 2.439150558
## 33 -0.525426953 1.19240799 0.36382829 0.771994193
## 34 0.147484019 1.27990794 0.54692935 1.550000497
## 35 -0.370139806 0.62365833 0.36382829 1.105425466
## 36 0.018078063 0.36115849 1.20891011 0.549706678
## 37 -0.197598531 0.57990836 0.23706602 0.422685241
## 38 -0.348572146 0.71115828 -0.14322079 1.137180826
## 39 -0.585816399 0.97365812 0.11030375 0.867260271
## 40 0.018078063 -0.29509111 1.29341829 0.041620929
## 41 0.462371846 -0.03259127 1.08214784 0.152764686
## 42 -0.335631551 -0.20759117 0.54692935 0.914893310
## 43 0.160424615 -0.33884109 1.33567238 1.105425466
## 44 -0.301123296 -0.60134093 0.54692935 -0.212421946
## 45 -0.007803128 -0.33884109 1.03989375 0.438562920
## 46 0.078467509 -0.38259106 1.01172435 1.057792427
## 47 -0.068192574 0.36115849 1.16665602 1.010159388
## 48 0.449431250 -0.20759117 1.01172435 0.756116514
## 49 0.492566569 0.49240841 0.19481193 0.994281709
## 50 1.657220175 0.71115828 0.68777632 1.629388895
## 51 0.923919756 0.71115828 0.42016708 1.280079943
## 52 0.233754657 1.23615797 1.06806314 1.645266575
## 53 0.859216778 0.22990857 0.91313147 1.407101380
## 54 0.535701888 0.75490825 0.44833648 1.994575527
## 55 0.341592953 -0.16384119 0.82862329 0.994281709
## 56 0.514134228 0.09865865 0.58918345 1.184813865
## 57 0.570210143 -0.07634125 0.98355496 0.708483475
## 58 0.406295932 0.49240841 0.32157420 1.661144254
## 59 0.751378481 -0.29509111 0.36382829 1.708777293
## 60 -1.340684477 0.40490846 -1.11506488 -0.720507695
## 61 -0.771298270 1.27990794 -1.32633534 -0.212421946
## 62 0.298457635 0.09865865 -1.43901291 -0.942795210
## 63 -0.542681081 1.19240799 -0.21364428 -0.371198742
## 64 -0.262301509 1.14865802 0.36382829 -1.038061288
## 65 -0.909331290 2.15490741 -0.53759231 -1.244471124
## 66 -0.197598531 1.01740810 -0.43899943 -0.218773018
## 67 0.104348700 0.71115828 0.80045390 -0.777667342
## 68 -0.163090276 0.71115828 1.22299481 -0.752263054
## 69 -0.814433589 0.27365854 -0.96013322 0.009865569
## 70 -0.952466609 1.41115786 0.64552223 -0.091751580
## 71 -0.866195971 -0.22509116 -1.11506488 0.390929881
## 72 -0.723849419 1.76115765 0.77228450 -1.069816648
## 73 -0.568562272 0.09865865 0.23706602 -0.872933420
## 74 -0.736790015 1.54240778 1.25116420 0.756116514
## 75 -0.797179461 0.14240862 0.73003041 0.441738456
## 76 -0.542681081 1.19240799 -0.66435458 -1.012657001
## 77 -0.197598531 1.01740810 -0.18547489 -1.126976294
## 78 -1.038737246 0.01115870 -0.12913610 -0.784018414
## 79 -0.715222356 0.44865844 -0.42491473 0.009865569
## 80 -1.073245501 1.01740810 0.73003041 -0.901513243
## 81 -1.103440224 1.84865760 0.71594572 -1.488987391
## 82 -0.499545762 0.88615818 0.74411511 -0.104453724
## 83 -1.232846180 1.54240778 0.15255784 -0.371198742
## 84 -0.111327893 -0.51384098 -0.84745564 -0.736385375
## 85 -0.866195971 -0.73259085 0.65960693 -0.720507695
## 86 -1.051677842 1.19240799 0.77228450 -0.942795210
## 87 -1.125007884 1.62990773 -0.49533822 -0.799896093
## 88 -1.060304905 1.76115765 0.84270799 -0.587135186
## 89 -0.974034268 0.18615860 0.19481193 -0.212421946
## 90 -1.431268647 0.49240841 0.84270799 -0.387076422
## 91 -1.146575543 0.53615839 -0.48125352 -0.847529132
## 92 -0.628951718 0.40490846 0.05396496 -0.942795210
## 93 -0.866195971 0.01115870 -0.77703216 -0.799896093
## 94 -1.254413840 0.84240820 0.96947026 -1.450880959
## 95 -0.779925334 0.88615818 0.49059057 -1.276226483
## 96 -1.060304905 0.88615818 0.02579557 0.603690789
## 97 -1.103440224 -0.03259127 -0.49533822 -0.387076422
## 98 -0.930898949 1.19240799 0.18072723 -1.012657001
## 99 -0.240733849 0.36115849 0.22298133 -0.275932664
## 100 -1.189710862 2.02365749 0.30748951 -1.082518791
## 101 -0.758357674 1.36740789 0.49059057 -0.117155868
## 102 -1.125007884 0.36115849 0.22298133 -0.587135186
## 103 -0.974034268 -0.68884088 1.08214784 -0.980901641
## 104 -1.293235627 -0.07634125 -0.24181367 -1.053938968
## 105 -0.913644822 0.36115849 1.34975708 -0.237826233
## 106 -1.017169587 -0.42634104 0.96947026 -1.371492561
## 107 -0.715222356 0.18615860 0.78636920 -0.752263054
## 108 -0.758357674 -0.33884109 -0.26998307 -0.822124845
## 109 -1.017169587 -0.42634104 0.57509875 -1.381019169
## 110 -1.038737246 0.01115870 0.91313147 -0.212421946
## 111 -0.930898949 -0.90759075 0.27932011 -0.587135186
## 112 -1.319116818 -0.25134114 0.23706602 -1.339737202
## 113 -0.542681081 1.19240799 -0.15730549 -0.444236069
## 114 -0.853255375 0.62365833 -0.42491473 -0.993603785
## 115 -0.930898949 -0.12009122 0.81453860 -1.149205046
## 116 -1.362252137 3.29240673 0.36382829 -1.079343255
## 117 -1.340684477 -0.03259127 1.01172435 -0.799896093
## 118 -1.293235627 0.44865844 0.49059057 -1.276226483
## 119 -0.715222356 -1.12634062 -0.69252397 -1.190487013
## 120 -1.629691113 -0.12009122 0.61735284 -0.580784114
## 121 -0.779925334 -0.68884088 1.09623253 -0.387076422
## 122 0.406295932 -0.12009122 1.51877344 -0.895162171
## 123 -1.284608563 -0.16384119 0.71594572 -1.212715765
## 124 -1.060304905 -0.99509069 0.68777632 -1.165082726
## 125 -0.974034268 -0.90759075 1.44834996 -1.165082726
## 126 -0.991288395 -0.42634104 0.94130087 -1.171433797
## 127 -0.482291634 -1.17009059 0.32157420 -1.253997732
## 128 -0.887763630 0.05490867 -0.24181367 -0.891986635
## 129 -1.267354435 -0.29509111 0.23706602 -1.285753091
## 130 -1.060304905 -0.73259085 -0.05871261 -0.529975539
## 131 -0.413275124 -0.86384077 -1.86155382 -0.371198742
## 132 0.147484019 -0.95134072 -1.67845276 -0.688752336
## 133 0.276889975 -1.30134051 -1.76296094 -0.593486258
## 134 -0.025057256 -0.77634083 -1.86155382 -0.466464820
## 135 0.169051679 -0.90759075 -1.55169049 -0.307688024
## 136 0.880784438 -0.99509069 -1.45309761 -0.164788907
## 137 -0.521113421 -0.90759075 -1.88972321 -0.085400508
## 138 -0.025057256 -0.60134093 -1.29816594 -0.736385375
## 139 0.276889975 -0.64509090 -1.11506488 -0.529975539
## 140 -0.059565511 -0.29509111 -0.65026988 -0.498220180
## 141 -0.197598531 -0.82009080 -0.42491473 -0.466464820
## 142 0.233754657 -1.12634062 -0.19955958 0.105131647
## 143 -0.305436828 -0.29509111 -0.77703216 -0.720507695
## 144 -0.283869168 -0.20759117 -0.79111685 -0.625241617
## 145 1.359586476 -1.34509048 -0.86154034 0.343296842
## 146 -0.456410443 -1.56384035 -1.31225064 0.263908444
## 147 -0.068192574 -1.65134030 -1.80521503 -1.053938968
## 148 1.118028691 -1.82634020 -1.05872609 -0.387076422
## 149 1.450170645 -1.78259022 -1.39675882 -0.307688024
## 150 1.872896769 -1.69509027 -1.80521503 -0.625241617
## 151 1.527814219 -1.60759033 -1.84746912 -0.784018414
## 152 2.476791231 -2.08884004 -1.60802927 -0.847529132
## 153 0.880784438 -1.52009038 -1.80521503 -1.022183609
## 154 2.356012338 -1.73884025 -1.55169049 -0.228299625
## 155 1.096461031 -1.65134030 -1.49535170 -0.339443383
## 156 1.225866988 -1.56384035 -1.59394458 -0.069522829
## 157 1.704669026 -1.69509027 -1.36858943 -0.847529132
## 158 1.053325713 -1.25759054 -1.24182715 0.422685241
## 159 3.425768243 -1.69509027 -0.91787912 -0.275932664
## 160 2.886576759 -1.69509027 -1.17140367 -0.402954102
## 161 1.118028691 -1.73884025 -1.45309761 -0.720507695
## 162 0.354533549 0.01115870 -1.11506488 -0.212421946
## 163 0.225127593 -0.38259106 -0.70660867 -0.561730898
## 164 0.095721637 -1.21384056 -1.21365776 -0.228299625
## 165 1.950540342 -1.12634062 -1.31225064 -0.418831781
## 166 0.673734908 -0.77634083 -1.21365776 -0.720507695
## 167 2.425028848 -0.47009101 -1.48126700 -0.164788907
## 168 2.243860510 -1.03884067 -1.21365776 -0.196544266
## 169 1.553695410 -0.95134072 -1.14323428 0.009865569
## 170 1.484678900 -1.25759054 -0.97421791 -0.371198742
## 171 0.190619338 -1.30134051 -1.10098018 -0.752263054
## 172 2.088572931 -1.69509027 -1.38267412 -0.879284492
## 173 2.002302725 -1.47634041 -1.26999655 -0.275932664
## 174 1.139596350 -1.38884046 -1.22774246 -0.021889790
## 175 0.967055075 -1.12634062 -1.48126700 0.009865569
## 176 2.217979318 -1.60759033 -1.48126700 0.279786124
## 177 1.829761450 -1.56384035 -1.39675882 0.295663803
## 178 1.786626131 -1.52009038 -1.42492821 -0.593486258
##
## $subset
## NULL
##
## $outlierMethod
## [1] "none"
##
## attr(,"class")
## [1] "mvn"Interpretasi Hasil: B.1 Uji Normalitas Multivariat
Berdasarkan pengujian normalitas multivariat menggunakan metode
Henze-Zirkler, didapatkan nilai p-value < 0.001. Angka yang
jauh di bawah taraf signifikansi 0.05 ini mengindikasikan penolakan
Hipotesis Nol (\(H_0\)), yang berarti
ke-13 variabel metrik kimiawi anggur tersebut secara simultan tidak
mengikuti distribusi normal multivariat. Pada tingkat univariat, hanya
fitur Ash, Alcalinity of ash, dan
Proanthocyanins yang menunjukkan sebaran normal.
Meskipun asumsi normalitas ini tidak terpenuhi, pemodelan Analisis Diskriminan Linier (LDA) tetap sangat valid untuk dilanjutkan. Algoritma LDA secara empiris terbukti memiliki sifat robust (tangguh) terhadap pelanggaran normalitas ringan hingga sedang, dan tidak akan merusak integritas pembentukan fungsi linier pemisahnya.
B.2 Uji Kesamaan Matriks Kovarians (Box’s M Test)
Analisis Diskriminan Linier mensyaratkan adanya homoskedastisitas, yaitu matriks varians-kovarians antar kelompok (Cultivar 1, 2, dan 3) harus bernilai homogen. Asumsi ini diuji secara statistik menggunakan Box’s M Test.
library(heplots)## Warning: package 'heplots' was built under R version 4.5.3## Loading required package: broom## Warning: package 'broom' was built under R version 4.5.3# Menjalankan Uji Box's M secara langsung menggunakan data yang sudah distandarisasi
uji_boxm <- boxM(Y = prediktor_numerik, group = df_lda$class)
print("Hasil Uji Kesamaan Matriks Kovarians (Box's M Test):")## [1] "Hasil Uji Kesamaan Matriks Kovarians (Box's M Test):"print(uji_boxm)##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: prediktor_numerik by df_lda$class
## Chi-Sq (approx.) = 684.2031, df = 182, p-value = < 2.2e-16Interpretasi Hasil: B.2 Uji Kesamaan Matriks Kovarians
Hasil Uji Box’s M menghasilkan nilai signifikansi (p-value) sebesar < 2.2e-16. Karena nilai ini sangat kecil, kita menolak Hipotesis Nol, yang berarti terdapat perbedaan matriks varians-kovarians antar ketiga kelas target (Cultivar 1, 2, dan 3) atau dengan kata lain, asumsi homoskedastisitas terlanggar.
Pelanggaran asumsi kesamaan matriks pada data saintifik riil adalah hal yang sangat lazim. Meskipun secara teoritis kondisi ini merupakan indikasi untuk menggunakan Quadratic Discriminant Analysis (QDA), metode LDA tetap dipertahankan dan dilanjutkan. Hal ini dikarenakan prioritas utama proyek ini adalah kapabilitas reduksi dimensi spasial (menghasilkan sumbu LD1 dan LD2) yang mudah diinterpretasikan secara visual, sebuah fitur unggulan LDA yang tidak dimiliki oleh algoritma QDA.
B.3 Uji Multikolinieritas (VIF dan Matriks Korelasi)
Tahap ini mengevaluasi ada tidaknya redundansi informasi antar variabel kimiawi. Multikolinieritas dideteksi menggunakan perhitungan Variance Inflation Factor (VIF) melalui model regresi linear bayangan, serta diinspeksi secara visual menggunakan corrplot.
library(car)## Warning: package 'car' was built under R version 4.5.3## Loading required package: carData## Warning: package 'carData' was built under R version 4.5.3##
## Attaching package: 'car'## The following object is masked from 'package:dplyr':
##
## recodelibrary(corrplot)## corrplot 0.95 loaded# Membangun model bayangan untuk menghitung VIF
model_dummy <- lm(as.numeric(class) ~ ., data = df_lda)
nilai_vif <- vif(model_dummy)
print("Nilai Variance Inflation Factor (VIF):")## [1] "Nilai Variance Inflation Factor (VIF):"print(nilai_vif)## Alcohol Malic.acid
## 2.460372 1.656647
## Ash Alcalinity.of.ash
## 2.185448 2.238732
## Magnesium Total.phenols
## 1.417855 4.334519
## Flavanoids Nonflavanoid.phenols
## 7.029350 1.796380
## Proanthocyanins Color.intensity
## 1.975683 3.026304
## Hue OD280.OD315.of.diluted.wines
## 2.551447 3.785473
## Proline
## 2.823849# Mengkalkulasi dan memvisualisasikan matriks korelasi Pearson
matriks_korelasi <- cor(prediktor_numerik)
corrplot(matriks_korelasi, method = "circle", type = "upper",
tl.col = "black", tl.cex = 0.7, tl.srt = 45)
Interpretasi Hasil: B.3 Uji Multikolinieritas
Pengujian multikolinieritas memberikan hasil komputasi yang sangat
memuaskan. Evaluasi nilai Variance Inflation Factor (VIF)
menunjukkan bahwa seluruh variabel prediktor berada jauh di bawah ambang
batas bahaya (VIF < 10). Nilai VIF tertinggi hanya tercatat pada
fitur Flavanoids sebesar 7.02, sementara fitur lainnya
rata-rata berada di angka 1 hingga 3.
Temuan angka ini selaras dengan visualisasi matriks korelasi
(corrplot), di mana meskipun terdapat hubungan yang cukup kuat
antara Total phenols dan Flavanoids (ditandai
dengan titik biru gelap), tidak ditemukan adanya korelasi linear yang
bernilai sempurna (+1 atau -1). Dengan demikian, dapat disimpulkan bahwa
asumsi non-multikolinieritas terpenuhi dengan sangat
baik, memastikan model terbebas dari redundansi matematis dan
risiko singular covariance matrix.
Tahap C: Analisis Diskriminan Linier (LDA)
C.1 Pembentukan Model LDA
Pada tahap ini, fungsi lda() dari pustaka
MASS digunakan untuk membentuk model diskriminan. Model ini
akan mencari kombinasi linier dari 13 variabel kimiawi yang dapat
menghasilkan pemisahan (separasi) maksimum antar kelompok Cultivar 1, 2,
dan 3.
library(MASS)##
## Attaching package: 'MASS'## The following object is masked from 'package:dplyr':
##
## select# Membentuk model LDA: class sebagai target, sisanya sebagai prediktor
model_lda <- lda(class ~ ., data = df_lda)
# Menampilkan ringkasan model
print("Ringkasan Model LDA:")## [1] "Ringkasan Model LDA:"print(model_lda)## Call:
## lda(class ~ ., data = df_lda)
##
## Prior probabilities of groups:
## Cultivar 1 Cultivar 2 Cultivar 3
## 0.3314607 0.3988764 0.2696629
##
## Group means:
## Alcohol Malic.acid Ash Alcalinity.of.ash Magnesium
## Cultivar 1 0.9166093 -0.2915199 0.3246886 -0.7359212 0.46192317
## Cultivar 2 -0.8892116 -0.3613424 -0.4437061 0.2225094 -0.36354162
## Cultivar 3 0.1886265 0.8928122 0.2572190 0.5754413 -0.03004191
## Total.phenols Flavanoids Nonflavanoid.phenols Proanthocyanins
## Cultivar 1 0.87090552 0.95419225 -0.57735640 0.5388633
## Cultivar 2 -0.05790375 0.05163434 0.01452785 0.0688079
## Cultivar 3 -0.98483874 -1.24923710 0.68817813 -0.7641311
## Color.intensity Hue OD280.OD315.of.diluted.wines Proline
## Cultivar 1 0.2028288 0.4575567 0.7691811 1.1711967
## Cultivar 2 -0.8503999 0.4323908 0.2446043 -0.7220731
## Cultivar 3 1.0085728 -1.2019916 -1.3072623 -0.3715295
##
## Coefficients of linear discriminants:
## LD1 LD2
## Alcohol -0.3274906 0.707744750
## Malic.acid 0.1846135 0.341153776
## Ash -0.1012536 0.643569825
## Alcalinity.of.ash 0.5169574 -0.488847900
## Magnesium -0.0309001 -0.006609312
## Total.phenols 0.3868085 -0.020160425
## Flavanoids -1.6592953 -0.491436530
## Nonflavanoid.phenols -0.1861596 -0.202977648
## Proanthocyanins 0.0767491 -0.175764297
## Color.intensity 0.8231206 0.587061123
## Hue -0.1869798 -0.346430951
## OD280.OD315.of.diluted.wines -0.8218561 0.036340126
## Proline -0.8474810 0.898426186
##
## Proportion of trace:
## LD1 LD2
## 0.6875 0.3125Interpretasi Hasil: C.1 Ringkasan Model LDA
Model LDA berhasil mengekstraksi dua fungsi diskriminan (LD1 dan
LD2). Nilai Proportion of Trace menunjukkan bahwa LD1
memegang peranan kunci dengan menjelaskan 68,75% daya pemisah
antar kelompok, sementara LD2 melengkapinya dengan 31,25%. Secara total,
kedua sumbu ini menangkap 100% informasi perbedaan antar kelas.
Berdasarkan koefisien linier, variabel Flavanoids dan
Color intensity menjadi fitur yang paling berpengaruh dalam
membentuk garis pemisah pada sumbu LD1.
C.2 Ekstraksi Nilai Diskriminan (Proyeksi Data)
Setelah model terbentuk, kita perlu menghitung skor atau nilai koordinat baru untuk setiap observasi pada sumbu diskriminan (LD1 dan LD2). Proses ini mentransformasi data asli yang memiliki 13 dimensi menjadi data baru dengan dimensi yang lebih rendah untuk keperluan klasifikasi dan visualisasi.
# Melakukan prediksi untuk mendapatkan nilai koordinat pada sumbu LD (Linear Discriminant)
prediksi_lda <- predict(model_lda)
# Mengambil nilai koordinat LD1 dan LD2 ke dalam dataframe baru
df_proyeksi <- as.data.frame(prediksi_lda$x)
# Menambahkan kembali label class asli untuk keperluan plotting
df_proyeksi$class <- df_lda$class
head(df_proyeksi)Interpretasi Hasil: C.2 Proyeksi Data
Data asli yang awalnya memiliki 13 dimensi (fitur kimiawi) kini telah berhasil dikompresi menjadi hanya 2 dimensi baru (LD1 dan LD2) tanpa kehilangan informasi penting. Nilai skor pada sumbu LD yang dihasilkan menunjukkan koordinat setiap sampel dalam ruang diskriminan, yang nantinya akan memudahkan kita untuk melihat sebaran dan pengelompokan data secara visual pada tahap berikutnya.
C.3 Evaluasi Akurasi Re-substitusi
Untuk melihat seberapa baik model LDA dalam mengenali data yang digunakan saat pelatihan, dilakukan perhitungan matriks klasifikasi (Confusion Matrix). Tahap ini memberikan gambaran awal mengenai performa model dalam mengelompokkan anggur ke kategori yang tepat.
# Membuat tabel klasifikasi antara data aktual dan data prediksi model
tabel_klasifikasi <- table(Aktual = df_lda$class, Prediksi = prediksi_lda$class)
print("Matriks Klasifikasi (Confusion Matrix):")## [1] "Matriks Klasifikasi (Confusion Matrix):"print(tabel_klasifikasi)## Prediksi
## Aktual Cultivar 1 Cultivar 2 Cultivar 3
## Cultivar 1 59 0 0
## Cultivar 2 0 71 0
## Cultivar 3 0 0 48# Menghitung total akurasi
akurasi <- sum(diag(tabel_klasifikasi)) / sum(tabel_klasifikasi)
print(paste("Total Akurasi Model: ", round(akurasi * 100, 2), "%", sep=""))## [1] "Total Akurasi Model: 100%"Interpretasi Hasil: C.3 Matriks Klasifikasi dan Akurasi
Hasil evaluasi menunjukkan performa model yang sangat impresif dengan Total Akurasi mencapai 100%. Melalui Confusion Matrix, terlihat bahwa seluruh sampel (59 Cultivar 1, 71 Cultivar 2, dan 48 Cultivar 3) berhasil diklasifikasikan ke dalam kelompok yang benar tanpa ada satu pun kesalahan (misclassification). Hal ini membuktikan bahwa batas-batas linier yang dibentuk oleh model LDA sangat efektif dalam membedakan karakteristik kimiawi ketiga jenis kultivar anggur tersebut.
Tahap D: Visualisasi dan Kesimpulan
D.1 Visualisasi Skor Diskriminan (Scatter Plot)
Untuk mengonfirmasi pemisahan antar kelas secara visual, kita memetakan nilai LD1 dan LD2 ke dalam grafik sebaran (scatter plot). Penggunaan elips kepercayaan (confidence ellipses) ditambahkan untuk mempertegas batas wilayah koordinat dari masing-masing kultivar anggur.
library(ggplot2)
# Membuat visualisasi scatter plot LD1 vs LD2
plot_lda <- ggplot(df_proyeksi, aes(x = LD1, y = LD2, color = class, fill = class)) +
geom_point(size = 3, alpha = 0.7) +
stat_ellipse(geom = "polygon", alpha = 0.1, level = 0.95) +
theme_minimal() +
labs(title = "Visualisasi Pemisahan Kultivar Anggur (LDA)",
subtitle = "Proyeksi Data pada Sumbu LD1 dan LD2",
x = "Linear Discriminant 1 (68.75%)",
y = "Linear Discriminant 2 (31.25%)",
color = "Kultivar",
fill = "Kultivar") +
theme(legend.position = "bottom")
# Menampilkan plot
print(plot_lda)
D.2 Kesimpulan Akhir
Berdasarkan seluruh rangkaian analisis yang telah dilakukan pada Wine Dataset, berikut adalah poin-poin kesimpulan utamanya:
# (Opsional) Kode untuk menampilkan kembali ringkasan akurasi sebagai penutup
cat("Ringkasan Akhir Proyek Analisis Diskriminan Linier:\n",
"- Dataset: Classic Wine Dataset (178 observasi, 13 fitur)\n",
"- Akurasi Klasifikasi: ", akurasi * 100, "%\n",
"- Status Pemisahan: Sempurna (Linearly Separable)\n")## Ringkasan Akhir Proyek Analisis Diskriminan Linier:
## - Dataset: Classic Wine Dataset (178 observasi, 13 fitur)
## - Akurasi Klasifikasi: 100 %
## - Status Pemisahan: Sempurna (Linearly Separable)