Heru

• Konsultan Pengembangan SumberDaya Manusia di pelbagai institusi

• Mengajar di: MM Unair

• Media sosial: @AbuamanyAssundawy

Dengan menyebutkan penulis dan dokumen ini dalam Daftar Pustaka, anda boleh:

memperbanyak, menyebarkan, memodifikasi sebagian atau seluruh dokumen ini,

untuk kegiatan non-komersial.

Beberapa bagian dari paparan ini diadaptasi dari:

• Slide Coursera RD.Peng: R.D. Peng on Github

• Slide Coursera Data Specialization oleh J.T. Leek: Data Specialization

• Slide tutorial Kevin Markham: Kevin Markham on Github

• Website Quick R Tutorial

• Website R Introduction to Statistics

• Website saya R from Dummies

• dll

• Susunan Alfabet ke-18

• R adalah bahasa pemrograman (statistik) yang dikembangkan dari Bahasa S.

• S ditulis pada tahun 1976 (saya kelas 2SD) oleh John Chambers dkk di Bell Labs.

• S awalnya ditulis sebagai library statistik Bahasa Fortran.

• S pada tahun 1988 mulai ditulis ulang dengan Bahasa C++, hingga kemudian menjadi R yang kita kenal sekarang.

• Free dan Lightweight: free as breathing yang diperlukan hanya koneksi internet, ukuran installer R base < 70 MB, R Studio < 60 MB. (Bandingkan dengan SPSS, Matlab) (Bandingkan dengan SPSS, Matlab)

• Cross platform: R tersedia untuk Linux, Mac, dan (tentunya) Windows. (Sebagian besar Windows only)

• Peran komunitas open source: sangat aktif, mailing lists, R Stack Overflow, Youtube, dll.

• Reproducibility: semua yang ditulis dengan R bisa diulang oleh orang lain untuk diperbaiki dan dikembangkan. Karena basisnya open source, maka semangat saling berbagi diantara pemakai R sangat tinggi.

• Terstruktur: basis command line, memang sulit pada awalnya, tapi membuat analisis lebih terstruktur, tiap langkah dapat didokumentasikan dengan memberi komentar dll.

• Visualisasi: R dapat menghasilkan grafis yang sangat bagus dan plot yang fully-customizeable. Banyak output grafik yang tidak dapat dibuat dengan piranti lunak spreadsheet konvensional.

• Mudah: sudah banyak tutorial dilengkapi _code_nya di internet, tinggal mengetik how to .... in R.

• Sederhana: syntax penulisan kode sederhana, berbasis obyek.

• Pengembangan intensif: R dapat dikembangkan melalui > 4000 R packages, bahkan untuk web-authoring, web-scraping, analisis spasial, dll.

• case sensitive

• command line

• what you mean is what you get

• R base telah memiliki perbendaharaan fungsi yang sangat kaya

• Beberapa package juga telah dimasukkan ke dalam R base

• Pengembangan package tujuannya untuk:

• memudahkan dan menyingkat kode, misal: dari 10 baris menjadi tiga baris saja

• meningkatkan kualitas grafis

Jadi jangan heran kalau anda telah fasih menjalankan satu proses, kemudian dengan perkembangan baru, baris kode anda menjadi tidak optimal (terlalu panjang).

Sebelum ke tahap instalasi, kita kenali dulu komponen R yang terdiri dari:

• R base atau R core

• R IDE

• R packages

• Inti dari R, full functionality.

• Jendela script, console, proses, dan output terpisah.

• Unduh installer dari Server CRAN. Mirrors di Indonesia:

• Mirror BPPT

• Mirror Uni Jember

• Ada R Studio atau R Commander.

• Jendela script, console, proses, dan output menyatu.

• Unduh installer dari Website RStudio

Jendela R base

Jendela R Studio

• Pengembangan dari fungsi-fungsi R base dikemas sebagai R packages.

• Saat ini ada lebih dari 4000 packages di sini yang telah terklasifikasi klik menu Task Views, diantaranya:

• Spasial

• Timeseries

• Lingkungan

• bahkan Medis

• Beberapa packages yang sangat fungsional dari pengembang individu dapat dimasukkan ke dalam fungsi dasar R base versi berikutnya, misal: utils, stats, datasets, graphics, grDevices, grid, methods, tools, parallel, compiler, splines, tcltk, stats4.

• Beberapa packages yang sering saya pakai, diantaranya:

  cluster, foreign, mgcv, rpart, spatial, dll.

• Beberapa package yang dikembangkan oleh ahli biologi dan lingkungan, dapat diunduh dari Website Bioconductor Project

• Atau dari individu langsung via repo Github. Perlu menginstalasi devtools package

Package harus diunduh dan diinstalasi terlebih dahulu dengan perintah:

install.packages("packageName")

Kemudian package harus dimuat ke memory dengan perintah:

library(packageName)

atau

require(packageName)

Sekarang mulailah "pekerjaan kotor kita", yaitu menginstalasi R ke dalam PC atau laptop kita. Untuk itu coba perhatikan beberapa hal berikut ini:

• Spesifikasi komputer/laptop: Tidak ada spesifikasi khusus untuk R, tetapi prinsip utamanya adalah makin besar data yang anda gunakan, makin kompleks analisis yang anda lakukan, akan memerlukan spesifikasi prosesor dan RAM yang makin besar. Jadi ini akan sangat bergantung kepada kebutuhan anda. Untuk keperluan pembelajaran gunakan saja komputer yang anda miliki sekarang.

• Sistem operasi (OS): Seperti yang telah saya sampaikan sebelumnya, R berjalan di semua OS: Linux (bisa Ubuntu, Fedora dll), Mac OS, dan tentunya Windows. Jangan kuatir, yang manapun OS yang anda pakai, spesifikasi R nya akan sama persis.

• Apa saja yang perlu anda unduh dan install:

• R base: Inti dari R.

• Kunjungi Situs R Project

• Pilih mirror server. Pilih server yang ada di Indonesia. Klik CRAN mirror di dalam kotak "Getting Started". Cari server di Indonesia. Ada dua, silahkan anda pilih:

• Server BPPT

• Server Universitas Jember

• Setelah server CRAN-BPPT terbuka, klik versi R sesuai dengan OS yang anda miliki.

• R Studio: lingkungan pemrograman.

• Kunjungi Situs R Studio

• Klik menu Products > RStudio > klik tombol Download RStudio Desktop. Secara otomatis R Studio akan membaca OS yang anda pakai dan proses pengunduhan akan segera dimulai.

Atau anda bisa langsung buka halaman http://www.rstudio.com/products/rstudio/download/, Pilih versi RStudio.

• Pilihan installer yang ada per tanggal 04 September 2014 adalah:

• RStudio 0.98.1049 - Windows XP/Vista/7/8 ukuran file 48.2 MB tanggal update 2014-09-02

• RStudio 0.98.1049 - Mac OS X 10.6+ (64-bit) ukuran file 37.8 MB tanggal update 2014-09-02

• RStudio 0.98.1049 - Debian 6+/Ubuntu 10.04+ (32-bit) ukuran file 56.3 MB tanggal update 2014-09-02

• RStudio 0.98.1049 - Debian 6+/Ubuntu 10.04+ (64-bit) ukuran file 58 MB tanggal update 2014-09-02

• RStudio 0.98.1049 - Fedora 13+/openSUSE 11.4+ (32-bit) ukuran file 56.6 MB tanggal update 2014-09-02

• RStudio 0.98.1049 - Fedora 13+/openSUSE 11.4+ (64-bit) ukuran file 57.9 MB tanggal update 2014-09-02

Setelah proses pengunduhan selesai, jalankan file program instalasinya:

• Untuk Linux: jalankan file xRstudioxx.deb dan ikuti perintahnya

• Untuk Mac OSX: jalankan file xRstudioxx.dmg dan ikuti perintahnya

• Untuk Windows: jalankan file xRstudioxx.exe dan ikuti perintahnya

• format database:

• kasus/sampel dalam baris

• variable/parameter/pengukuran dalam kolom

• tanpa judul tabel dan aksesori lainnya

• dulu data harus format text/ASCII bukan binary (xls, xlsx, dll), misal:

• txt

• csv (comma separated values)

• dengan fungsi dasar R

• sekarang dengan fungsi dari package tambahan, seperti foreign, read.table, readxl, R dapat meng-import berbagai format file text maupun binary, misal:

• xls, xlsx (Ms Office)

• sav (SPPS)

• dta (Stata)

• odt (LibreOffice)

format data

data <- read.csv("BandungData.csv", header = TRUE)
attach(data)

## The following object is masked from package:datasets:
## 
##     CO2

dim(data)

## [1] 295  34

str(data)

## 'data.frame':    295 obs. of  34 variables:
##  $ no     : int  16 22 263 17 12 18 13 19 14 20 ...
##  $ code   : int  116 122 8 117 112 118 113 119 114 120 ...
##  $ year   : int  1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 ...
##  $ type   : Factor w/ 2 levels "groundwater",..: 1 1 2 1 1 1 1 1 1 1 ...
##  $ x      : num  785175 785168 799275 785175 785181 ...
##  $ y      : num  10752836 10752843 10753680 10752840 10752843 ...
##  $ distx  : num  6897 6904 0 6897 6891 ...
##  $ elv    : int  1338 1336 1336 1320 1300 1247 1240 1230 1228 1225 ...
##  $ aq     : Factor w/ 3 levels "breccias","clay",..: 3 3 3 3 3 3 3 3 3 3 ...
##  $ zone   : Factor w/ 2 levels "eff","inf": 1 1 1 1 1 1 1 1 1 1 ...
##  $ ec     : num  71.9 71.9 77 71.9 71.9 71.9 71.9 71.9 71.9 71.9 ...
##  $ ph     : num  6.89 6.89 6.39 6.89 6.89 ...
##  $ hard   : num  11 11 26.4 11 11 11 11 11 11 11 ...
##  $ tds    : num  58.7 58.7 50 58.7 58.7 ...
##  $ temp   : num  21 21 16.1 21 21 ...
##  $ eh     : num  30 24 -0.45 34 35 32 30 23 24 21 ...
##  $ Q      : num  1 1 NA 1 1 1 1 1 1 1 ...
##  $ Ca     : num  1.8 1.8 9.44 1.8 1.8 1.8 1.8 1.8 1.8 1.8 ...
##  $ Mg     : num  1.7 1.7 0.72 1.7 1.7 1.7 1.7 1.7 1.7 1.7 ...
##  $ Fe     : num  0.08 0.08 0.216 0.08 0.08 0.08 0.08 0.08 0.08 0.08 ...
##  $ Mn     : num  0.22 0.22 0 0.22 0.22 0.22 0.22 0.22 0.22 0.22 ...
##  $ K      : num  1.7 1.7 0.8 1.7 1.7 1.7 1.7 1.7 1.7 1.7 ...
##  $ Na     : num  5 5 3.2 5 5 5 5 5 5 5 ...
##  $ CO3    : num  7 6 0 6 5.8 6.8 6.7 8 8 8.2 ...
##  $ HCO3   : num  8 7.8 31.4 6.7 7 ...
##  $ CO2    : num  36.3 36.3 7.28 36.3 36.3 36.3 36.3 36.3 36.3 36.3 ...
##  $ Cl     : num  4.8 4.8 5.52 4.8 4.8 4.8 4.8 4.8 4.8 4.8 ...
##  $ SO4    : num  0.6 0.6 0 0.6 0.6 0.6 0.6 0.6 0.6 0.6 ...
##  $ NO2    : num  0 0 0.04 0 0 0 0 0 0 0 ...
##  $ NO3    : num  4.7 4.7 2.24 4.7 4.7 4.7 4.7 4.7 4.7 4.7 ...
##  $ SiO2   : num  23 23 37.8 23 23 ...
##  $ cumrain: num  38.5 38.5 38.5 38.5 38.5 38.5 38.5 38.5 38.5 38.5 ...
##  $ lag1   : num  32.4 32.4 32.4 32.4 32.4 32.4 32.4 32.4 32.4 32.4 ...
##  $ lag1.1 : logi  NA NA NA NA NA NA ...

plot(tds, temp,  
     xlab = "tds (ppm)", 
     ylab = "temp (^oC)", 
     bg = "lightblue", 
     col = "black", 
     cex = 1.1, 
     pch = 21,
     frame = FALSE)

abline(lm(tds~temp), col="red") # regression line (y~x) 
lines(lowess(tds,temp), col="blue") # lowess line (x,y)

Note: semua yang diketik di belakang simbol # tidak dieksekusi oleh R, disebut comment. Biasa digunakan untuk memberi penjelasan baris atau kelompok baris kode.

Mengapa garis regresi tidak diagonal?

hist(tds, col="red")

par(mfrow=c(1,3))  
hist(tds, col="red")
hist(ph, col="green")
hist(hard, col="blue")

par(mfrow=c(2,2))  
hist(tds, col="cyan")
hist(ph, col="magenta")
hist(hard, col="yellow")
hist(eh, col="blue")

Berikut contoh perintah untuk mengetahui koef dan intercept persamaan regresi.

fit <- lm(tds ~ temp, data = data)
coef(fit)

fit <- lm(data$tds ~ data$temp, data = data)
coef(fit)

## (Intercept)   data$temp 
##  -650.96402    37.93123

Untuk memvisualisasikan matriks korelasi.

group1 <- data[,c("x", "y", "elv", "aq", "ec", "ph",
                  "hard", "tds", "temp", "eh", "Q")]
pairs(group1,labels=colnames(group1),
      main="Physical parameter", 
      pch=21, bg=c("red", "blue")
      [unclass(data$type)],
      upper.panel=NULL)
      
legend(x=0.6, y=0.8, levels(data$type), 
        pt.bg=c("red", blue"), 
        pch=21, 
        bty="n", 
        ncol=2, 
        horiz=F)

Misal:

• Apakah tds merupakan fungsi linear dari unsur Ca, Mg, dan Fe?

• atau tds adalah fungsi dari unsur HCO3, CO3, SO4, Cl?

fit <- lm(tds ~ Ca + Mg + Fe, data=data)
summary(fit) 

## 
## Call:
## lm(formula = tds ~ Ca + Mg + Fe, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -352.11  -57.96  -29.36   36.98  835.27 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  77.7128    12.3875   6.273 1.28e-09 ***
## Ca            2.8913     0.4657   6.209 1.84e-09 ***
## Mg           11.2824     1.2024   9.384  < 2e-16 ***
## Fe          -43.5776    33.5691  -1.298    0.195    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 120.8 on 291 degrees of freedom
## Multiple R-squared:  0.543,  Adjusted R-squared:  0.5383 
## F-statistic: 115.3 on 3 and 291 DF,  p-value: < 2.2e-16

fit2 <- lm(tds ~ HCO3 + CO3 + SO4 + Cl, data=data)
summary(fit2)

## 
## Call:
## lm(formula = tds ~ HCO3 + CO3 + SO4 + Cl, data = data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -369.64  -37.61  -23.53   24.36  688.83 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 55.08578   10.67173   5.162 4.55e-07 ***
## HCO3         0.77447    0.06993  11.075  < 2e-16 ***
## CO3          1.13775    0.73530   1.547    0.123    
## SO4          1.47805    0.25607   5.772 2.01e-08 ***
## Cl           2.41691    0.29699   8.138 1.19e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 97.88 on 290 degrees of freedom
## Multiple R-squared:  0.701,  Adjusted R-squared:  0.6969 
## F-statistic:   170 on 4 and 290 DF,  p-value: < 2.2e-16

anova(fit, fit2)

## Analysis of Variance Table
## 
## Model 1: tds ~ Ca + Mg + Fe
## Model 2: tds ~ HCO3 + CO3 + SO4 + Cl
##   Res.Df     RSS Df Sum of Sq     F    Pr(>F)    
## 1    291 4246450                                 
## 2    290 2778559  1   1467891 153.2 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# Prepare Data
mydata <- data[,c("elv", "ph",
                  "hard", "tds", "temp", "Q")]

mydata <- na.omit(mydata) # listwise deletion of missing
mydata <- scale(mydata)

# run PCA
fit <- princomp(mydata, cor=TRUE)

summary(fit) # print variance accounted for 

## Importance of components:
##                           Comp.1    Comp.2    Comp.3    Comp.4    Comp.5
## Standard deviation     1.3597606 1.1297573 0.9700609 0.8708904 0.8527924
## Proportion of Variance 0.3081582 0.2127253 0.1568364 0.1264083 0.1212091
## Cumulative Proportion  0.3081582 0.5208834 0.6777198 0.8041281 0.9253373
##                            Comp.6
## Standard deviation     0.66931040
## Proportion of Variance 0.07466273
## Cumulative Proportion  1.00000000

loadings(fit) # pc loadings 

## 
## Loadings:
##      Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6
## elv   0.488 -0.133         0.800  0.132 -0.294
## ph   -0.111  0.687                0.709       
## hard  0.250  0.368 -0.791        -0.395  0.141
## tds  -0.605        -0.206  0.130 -0.153 -0.737
## temp -0.561 -0.101         0.558 -0.111  0.589
## Q           -0.598 -0.568 -0.159  0.537       
## 
##                Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6
## SS loadings     1.000  1.000  1.000  1.000  1.000  1.000
## Proportion Var  0.167  0.167  0.167  0.167  0.167  0.167
## Cumulative Var  0.167  0.333  0.500  0.667  0.833  1.000

plot(fit,type="lines") # scree plot 

fit$scores # the principal components

##           Comp.1        Comp.2       Comp.3       Comp.4       Comp.5
## 1    2.555170709  4.137174e-01 -0.401835894  0.692409628  0.378888717
## 2    2.550748586  4.149192e-01 -0.401556057  0.685160307  0.377692454
## 4    2.515371607  4.245332e-01 -0.399317361  0.627165736  0.368122347
## 5    2.471150383  4.365508e-01 -0.396518992  0.554672522  0.356159713
## 6    2.353964139  4.683973e-01 -0.389103312  0.362565505  0.324458733
## 7    2.338486711  4.726035e-01 -0.388123883  0.337192881  0.320271811
## 8    2.316376099  4.786123e-01 -0.386724698  0.300946274  0.314290494
## 9    2.311953977  4.798140e-01 -0.386444861  0.293696952  0.313094230
## 10   2.305320793  4.816167e-01 -0.386025106  0.282822970  0.311299835
## 11   2.250044263  4.966386e-01 -0.382527144  0.192206453  0.296346543
## 12   2.227933651  5.026474e-01 -0.381127959  0.155959846  0.290365226
## 13   1.867410026 -2.616254e-01 -0.089218290  0.321085216 -0.257670279
## 14   1.645181935 -7.239144e-01  1.219284576  0.021630346 -0.182046889
## 16   1.105647572 -1.059011e+00  1.265951112  0.539519751 -0.446562492
## 17   0.351155766 -1.836384e+00  0.960274284 -0.048751818  0.158178575
## 18   1.465595962 -6.196960e-01  0.299890164 -0.304720998 -1.177913472
## 19  -0.506573219 -1.511914e+00  0.026146169  0.417734514 -0.462104409
## 20   0.164865384 -7.847679e-01  0.991985755 -0.004910367 -0.720360407
## 21   0.604547067 -3.336723e-01  0.941685813 -0.028105997 -0.228600111
## 22  -0.316973177 -8.740355e-01  0.706829110 -0.050780072 -1.198143500
## 23   0.112829795 -1.087316e-01  1.113450746 -0.236811961 -0.189360571
## 26  -0.422571088 -9.552581e-01  0.281569891 -0.716878176  0.117034146
## 27   0.183249922 -5.443714e-01  1.454311490 -0.671865073  0.519144083
## 28   0.173662027 -3.950843e-01 -0.266312917 -0.736196403  0.213648207
## 30  -0.849718165  1.602827e-01  0.123351495 -0.140031646 -0.092586720
## 31  -1.041995227 -5.897139e-01  0.963761177 -0.431737527 -0.135459601
## 32  -0.493401113 -7.164377e-01  0.572893886 -0.427216979 -0.628634028
## 33  -0.548678826  3.305960e-01  0.752028654 -0.195261029  0.092833351
## 34  -0.597390943  7.297445e-01  0.389409525 -0.311898460  0.053622524
## 35  -1.037871003 -3.012907e-01 -0.290095619 -0.158146149  0.291398886
## 36  -0.569574093  7.840560e-01  0.506503125 -0.267664057 -0.089589587
## 37  -0.858506126 -4.987261e+00 -4.102522220 -1.635829589  1.628323847
## 38  -0.188062864 -1.090072e-01  0.665698772 -0.432650914  0.175386493
## 39  -0.140616531 -2.636812e+00 -1.201290312 -0.997872596  0.716545447
## 40  -0.017171285  1.279101e+00 -0.715900878 -0.409506693 -0.389396937
## 41  -0.540991634 -8.031882e-01  0.836564968 -0.652820891 -0.510649344
## 42   1.127365472 -1.675026e+00  0.414883265 -1.554880662 -1.957106903
## 43  -0.278374427  3.543304e-01 -0.843816716 -0.412079451 -1.244577519
## 44  -1.346496992 -4.068094e-01 -0.414212423 -0.189233327 -0.002247759
## 45   0.009278339  1.365973e-01 -0.692082508 -0.758408638 -1.722412419
## 46  -0.132488469  1.203855e+00 -1.245603597 -0.462077198 -1.469215271
## 47  -0.691031627  4.197883e-01  0.410091548 -0.449287311  0.425443618
## 49  -1.001105077  5.869796e-01  0.625065488 -0.373528736 -0.134504628
## 50  -1.154211997  8.458866e-01  0.199671751 -0.283073840 -0.019113961
## 51  -1.216329222  3.039394e-01  0.543383923 -0.460629834  0.368641941
## 52  -0.245372949  3.438827e-02  1.226586830 -0.864342381  0.113893824
## 53  -0.326510719 -6.741426e-02 -0.506699657 -0.720062174 -1.113630697
## 54  -0.187431576 -1.006845e+00  0.050216158 -1.240234817 -0.331224414
## 56  -0.245897920 -8.310398e-01 -0.179712450 -1.178003338 -0.374601389
## 57  -1.173458819 -6.345535e-01  1.566708467 -0.882815984 -0.394430832
## 58  -0.442846691 -1.173406e+00  1.640855597 -1.055399164 -0.196579936
## 60   2.555170709  4.137174e-01 -0.401835894  0.692409628  0.378888717
## 61   1.561126179 -1.182792e+00  1.237127906  1.286199853 -0.323347362
## 63   1.039076102 -4.424947e-01  0.588044019  1.579035768  0.507349585
## 64   0.613343649  4.625860e-01  0.431646741  1.671529412  0.230410871
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## 66   1.267865427 -5.139358e-01  0.899710270  1.059292210 -0.049160601
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## 68   2.311953977  4.798140e-01 -0.386444861  0.293696952  0.313094230
## 69   1.010972173  9.996923e-01 -0.780962969  1.275960527 -0.111265698
## 70   0.364420679  4.683624e-01  0.328544989  1.264828940  0.313809812
## 71   0.776148155 -2.889951e-01  1.071475204  0.850586245 -0.009921062
## 72   0.340245026 -1.162561e+00  0.233298017  0.533629761  0.323389581
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## 76   0.467425299 -2.802054e+00 -1.239767892 -0.001090907  0.881031663
## 77   1.785721411  6.228231e-01 -0.353144265 -0.568972292  0.170738886
## 78  -0.029078261 -8.426221e-01  0.543511006  0.333961765 -0.503026371
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## 80   1.355042902 -5.896521e-01  0.306886088 -0.485954033 -1.207820057
## 81  -0.278929359  2.572889e-01  0.734958601  0.246947575  0.165805418
## 82   0.194228226  1.747791e+00  0.079820489  0.042912094  1.819433162
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## 91  -1.064105839 -5.837051e-01  0.965160362 -0.467984134 -0.141440918
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## 123  2.471150383  4.365508e-01 -0.396518992  0.554672522  0.356159713
## 124  1.859654871 -7.821996e-01  1.205712484  0.373222433 -0.124028114
## 125  0.540571105 -9.237173e-02  1.437758400  1.412676091  1.670729657
## 126  0.022876147  6.351798e-01  0.538254336  1.462636384  0.806749789
## 127  2.311953977  4.798140e-01 -0.386444861  0.293696952  0.313094230
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## 129  2.250044263  4.966386e-01 -0.382527144  0.192206453  0.296346543
## 130  2.227933651  5.026474e-01 -0.381127959  0.155959846  0.290365226
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## 139 -0.007856376  4.587731e-01  0.385790643  0.283283563  0.757316507
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## 171 -1.225261859  1.582074e-01 -0.309743753 -0.347323304  0.696442388
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## 190  0.336960999  5.376958e-01  0.449136551  1.218446825  0.155644409
## 191  1.645181935 -7.239144e-01  1.219284576  0.021630346 -0.182046889
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## 204  1.409841007  7.249724e-01 -0.329358124 -1.185164609  0.069056498
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## 233 -0.036660681 -1.594176e-01  0.982262170 -1.079257597 -0.402058303
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## 238  0.961811964  2.143884e-01 -0.635177559  2.431681727 -0.662221171
## 240  1.070218894 -6.638544e-01 -0.815469289  2.166268061 -1.068576904
## 241  1.768408313 -7.988054e-01 -1.568017545  1.694558644 -2.051897671
## 242 -1.624745643 -5.221140e+00 -1.909706327  1.219480034  4.418056728
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## 245  0.029532268 -2.502195e-01  1.001427997  1.965821739  0.021001563
## 246 -0.738436690 -1.196834e+00  1.193939075  2.033024108  0.190006611
## 247 -0.089900659  7.734689e-02  0.676020650  1.811198725  0.393321672
## 248 -0.426664529 -2.396249e-01  0.527490634  1.667572898  1.852093891
## 249  0.050765298 -1.105483e+00 -0.039201736  1.511310953  0.303943069
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## 252 -0.903661148 -7.480867e-01 -0.457464240  1.552637319  0.153790377
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## 254 -0.250263710 -1.186830e-01 -1.447342208  0.827199547 -0.330280941
## 255 -0.989263739 -5.506926e-01  0.358489975  1.121894452 -0.288646161
## 256 -0.929300461 -9.598681e-01  0.171382012  0.816583575  0.342117777
## 257 -1.849914785 -7.384507e-01  0.462693030  0.808710752  0.791382525
## 258 -0.305640415 -6.348247e-01  0.717120045  0.399982347 -0.471234240
## 259 -0.814185051  2.392578e-01 -0.743561161  0.776632141  0.703180424
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## 263 -1.009199692 -1.310091e-01  0.137810428  0.394432804 -0.278509574
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## 266 -1.181174376 -3.351984e-01  0.903128361  0.304939424 -0.434794794
## 267 -3.746683288 -9.872953e-01  0.564161560  3.059945329 -1.135764295
## 268 -1.055117206 -3.506738e-01  1.472839703  0.160813045  0.122637791
## 269 -1.751676699 -2.460210e-02 -0.699606573  0.390342105  0.223404682
## 270 -2.969280408 -2.396189e-01 -0.141247808  0.595318332 -0.876021365
## 271 -1.265595157 -5.474094e-02 -0.186727486  0.344348426 -0.591229695
## 272 -1.169388587 -9.193807e-01  0.363566793 -0.014445947  0.310492222
## 273 -1.864228083  2.282846e-01  0.142490685  0.598912030 -0.615766069
## 274 -1.296719215  9.358620e-01 -0.087983852  0.234135643 -0.096019749
## 275 -1.949614079  1.481898e+00 -0.236986954  0.455653518  0.064193184
## 276 -1.935556120  1.335589e+00 -0.626664383  0.383180653 -0.253025287
## 277 -1.739392595 -9.054334e-02 -0.037176775  0.366394729 -0.522231516
## 278 -2.588469447  7.670844e-01 -0.774082317  0.668810888 -1.043419496
## 279 -1.866835054 -9.593011e-01 -3.881629701  0.039501442 -0.177438970
## 280 -0.431317463  5.961279e-01 -0.853422015  0.208361040 -0.512940518
## 281 -2.762732401 -9.127031e-01  1.723470351  0.432824938  0.310070984
## 282 -2.064018066  1.448035e+00 -1.796007295  0.351382775 -0.703330209
## 283 -2.612498257  1.191128e+00 -1.672857266  0.760587179 -1.505304469
## 285 -1.867163784  3.995817e-01  0.427844526  0.081572623  0.417023786
## 286 -3.945507625 -6.895154e-01  0.137368153  0.468044448  0.123102781
## 287 -3.142142913  3.215645e-01  0.002718618  0.454305062 -0.511639157
## 288 -3.373923712 -8.218203e-02 -0.772323498  0.426982222 -0.106842827
## 289 -3.441950172  2.519565e-01  0.626615882  0.683708998 -0.253322560
## 290 -1.336716136 -4.262046e-01  0.469795570  0.022070134 -1.163683415
## 292 -1.305447954  5.873989e-01 -0.843544180  0.039246176 -1.359563642
## 293 -0.989813893  3.847176e-03 -0.717885547 -0.076810710 -1.870002053
## 294 -1.411000643 -1.019845e+00  0.688024610 -0.198551977 -0.926975002
##            Comp.6
## 1   -0.4956718034
## 2   -0.4930099214
## 4   -0.4717148659
## 5   -0.4450960464
## 6   -0.3745561749
## 7   -0.3652395881
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biplot(fit)

# Ward Hierarchical Clustering
d <- dist(as.matrix(mydata), method="euclidean") # distance matrix
fit <- hclust(d, method="complete", members=NULL) 

plot(fit) # display dendogram

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