Unsupervised Learning : In-class materials
Team Algoritma
October 13, 2022
Introduction
Supervised vs Unsupervised Learning
Supervised Learning
- Memiliki target variabel
- Tujuannya untuk membuat model prediksi dengan training data
- Model di-evaluasi dengan testing data
Unsupervised Learning
- Tidak memiliki target variabel
- Tujuannya untuk mencari pola dalam data, yang berguna untuk menghasilkan informasi. Digunakan pada tahap pre-processing maupun Exploratory Data Analysis (EDA)
- Tidak perlu melakukan evaluasi model, karena tidak ada label aktual
Mindmap
Secara umum, unsupervised learning yang akan kita pelajari terbagi menjadi dua cabang:
- Dimensionality Reduction: mereduksi dimensi dengan tetap mempertahankan informasi sebanyak-banyaknya. Algoritma: Principal Component Analysis (PCA)
- Clustering: pengelompokkan data berdasarkan kemiripan karakteristik data. Algoritma: K-means Clustering
Dimensionality Reduction
Tujuan dimensionality reduction adalah untuk mereduksi banyaknya variabel (dimensi) pada data dengan tetap mempertahankan informasi sebanyak mungkin.
Dimensionality reduction dapat mengatasi masalah high-dimensional data. Kesulitan yang dihadapi pada high-dimensional data:
- Memerlukan waktu dan komputasi yang besar dalam melakukan pemodelan
- Melakukan visualisasi lebih dari tiga dimensi
Dimensionality reduction bertujuan untuk mereduksi dimensi data dengan tetap mempertahankan sebanyak mungkin informasi (informasi inti) dari data.
Dimensi: banyaknya variabel/kolom yang menjelaskan data.
Informasi: direpresentasikan oleh variance. Semakin tinggi variance (semakin beragam data) maka informasi yang diperoleh semakin banyak.
Note: Nilai variansi akan bergantung pada skala variabel.
Real Case: Image Compression
Foto berukuran 40x40 pixel memiliki 1600 kolom (dimensi).
Image compression adalah salah satu contoh nyata dimensionality reduction dimana data berupa gambar direduksi dimensinya namun tetap menghasilkan gambar yang serupa (informasi inti tidak hilang).
Algoritma yang akan kita gunakan untuk melakukan dimensionality reduction adalah Principal Component Analysis (PCA).
Principal Component Analysis (PCA)
Ide dasar dari PCA adalah untuk membuat sumbu (axis) baru yang dapat menangkap informasi (variance) sebesar mungkin. Sumbu baru ini adalah yang dinamakan sebagai Principal Component (PC). Untuk melakukan dimensionality reduction, kita akan memilih beberapa PC untuk dapat merangkum informasi yang dibutuhkan.
Kunjungi link berikut untuk ilustrasi PCA secara visual untuk data 2D dan 3D: https://setosa.io/ev/principal-component-analysis/
Figure 1A (kiri):
- Sumbu: X1 dan X2
- Variance data dijelaskan oleh X1 dan X2
- Dibuatlah sumbu baru untuk menangkap informasi X1 dan X2, yang dinamakan PC1 dan PC2
Figure 1B (kanan):
- Sumbu baru: PC1 dan PC2
- PC1 menangkap variance lebih banyak daripada PC2
[Optional] Mathematics of PCA
Video: 3Blue1Brown: Eigenvectors and eigenvalues
Untuk membentuk PC dan nilai pada PC dibutuhkan eigen values & eigen vector. Secara manual, eigen values dan eigen vector didapatkan dari operasi matrix.
- eigen values: variance/informasi yang dirangkum oleh setiap PC
- eigen vector: arah sumbu PC
Teori Matrix
- skalar: nilai yang memiliki magnitude/besaran
- vektor: nilai yang memiliki besaran dan arah (umum digambarkan dalam suatu koordinat)
- matrix: kumpulan nilai/bentukan data dalam baris dan kolom
Perkalian skalar-vektor: mengubah besaran vektor (tidak merubah arah kecuali berbalik arah)
\[2\left(\begin{array}{cc}2\\3\end{array}\right) = \left(\begin{array}{cc}4\\6\end{array}\right)\]
\[-2\left(\begin{array}{cc}2\\3\end{array}\right) = \left(\begin{array}{cc}-4\\-6\end{array}\right)\]
Perkalian matrix-vektor: mengubah besaran dan arah
\[\left(\begin{array}{cc}1 & 2\\-1 & 2\end{array}\right)\left(\begin{array}{cc}2\\3 \end{array}\right) = \left(\begin{array}{cc}8\\4\end{array}\right)\]
Perkalian Matrix-Vektor Spesial
- Matrix Rotasi: mengubah arah vektor tanpa mengubah besaran
\[ \left(\begin{array}{cc} 0 & -1\\ 1 & 0 \end{array}\right) \left(\begin{array}{cc} 2\\ 3 \end{array}\right)= \left(\begin{array}{cc} -3\\ 2 \end{array}\right) \]
# perkalian matrix di R
matrix(c(0,1,-1,0), nrow=2) %*% as.vector(c(2,3))#> [,1]
#> [1,] -3
#> [2,] 2- Matrix Identitas: tidak mengubah besaran maupun arah vektor
\[ \left(\begin{array}{cc} 1 & 0\\ 0 & 1 \end{array}\right) \left(\begin{array}{cc} 2\\ 3 \end{array}\right)= \left(\begin{array}{cc} 2\\ 3 \end{array}\right) \]
# perkalian matrix di R
matrix(c(1,0,0,1), nrow=2) %*% as.vector(c(2,3))#> [,1]
#> [1,] 2
#> [2,] 3Eigen dari suatu Matrix
Untuk setiap matrix, terdapat vektor spesial (eigen vector) yang jika dikalikan dengan matrixnya, hasilnya akan sama dengan vektor tersebut dikalikan suatu skalar (eigen value). Sehingga didapatkan rumus:
\[Ax = \lambda x\]
- \(x\) adalah eigen vector
- \(\lambda\) adalah eigen value dari matrix \(A\).
\[ \left(\begin{array}{cc} 2 & 3\\ 2 & 1 \end{array}\right) \left(\begin{array}{cc} 3\\ 2 \end{array}\right) = \left(\begin{array}{cc} 12\\ 8 \end{array}\right) =4 \left(\begin{array}{cc} 3\\ 2 \end{array}\right) \]
Teori eigen dipakai untuk menentukan PC dan nilai-nilai pada PC.
Penerapan Eigen dalam PCA:
Matrix covariance adalah matrix yang dapat merangkum informasi (variance) dari data. Kita menggunakan matrix covariance untuk mendapatkan mendapatkan eigen vector dan eigen value dari matrix tersebut, dimana:
- eigen vector: arah sumbu tiap PC, yang menjadi formula untuk mentransformasi data awal ke PC baru.
- eigen value: variansi yang ditangkap oleh setiap PC.
Hasil dari perhitungan matrix covariance (data kita yang terdiri dari baris & kolom), memungkinkan kita untuk merangkumnya ke dalam sebuah sumbu (Eigen Vector) yang berisikan informasi/variance (Eigen Value).
Eigen vector akan menjadi formula untuk kalkulasi nilai di setiap PC. Contohnya, untuk data yang terdiri dari 2 variabel, bila diketahui eigen vector dari PC1 adalah:
Notes:
- PC dibuat untuk merangkum sebanyak mungkin informasi (variance) data
- PC1 menangkap variance paling besar, daripada PC2, dan seterusnya
- Banyaknya PC yang dibentuk = Banyaknya dimensi data asli
- Antar PC tidak saling berkorelasi, karena saling tegak lurus
- Sehingga di dalam satu PC -> akan terdiri dari rangkuman kesulurhan variable yang ada
- Metode PCA cocok untuk data numerik yang saling berkorelasi
PCA Workflow
Business Question: New York Property Market
Terdapat data unit bangunan/tempat tinggal yang terjual di New York Property Market selama periode 12 bulan (sumber: New York City Department of Finance). Ingin dilakukan eksploratory data analysis untuk data ini:
# Please run the code down below
library(dplyr)
property <- read.csv("data_input/nyc.csv")
glimpse(property)#> Rows: 84,548
#> Columns: 22
#> $ X <int> 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 1…
#> $ BOROUGH <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
#> $ NEIGHBORHOOD <chr> "ALPHABET CITY", "ALPHABET CITY", "ALPH…
#> $ BUILDING.CLASS.CATEGORY <chr> "07 RENTALS - WALKUP APARTMENTS …
#> $ TAX.CLASS.AT.PRESENT <chr> "2A", "2", "2", "2B", "2A", "2", "2B", …
#> $ BLOCK <int> 392, 399, 399, 402, 404, 405, 406, 407,…
#> $ LOT <int> 6, 26, 39, 21, 55, 16, 32, 18, 34, 153,…
#> $ EASE.MENT <lgl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,…
#> $ BUILDING.CLASS.AT.PRESENT <chr> "C2", "C7", "C7", "C4", "C2", "C4", "C4…
#> $ ADDRESS <chr> "153 AVENUE B", "234 EAST 4TH STREET"…
#> $ APARTMENT.NUMBER <chr> " ", " ", " ", " ", " ", " ", " ", " ",…
#> $ ZIP.CODE <int> 10009, 10009, 10009, 10009, 10009, 1000…
#> $ RESIDENTIAL.UNITS <int> 5, 28, 16, 10, 6, 20, 8, 44, 15, 24, 30…
#> $ COMMERCIAL.UNITS <int> 0, 3, 1, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, …
#> $ TOTAL.UNITS <int> 5, 31, 17, 10, 6, 20, 8, 46, 15, 24, 34…
#> $ LAND.SQUARE.FEET <chr> "1633", "4616", "2212", "2272", "2369",…
#> $ GROSS.SQUARE.FEET <chr> "6440", "18690", "7803", "6794", "4615"…
#> $ YEAR.BUILT <int> 1900, 1900, 1900, 1913, 1900, 1900, 192…
#> $ TAX.CLASS.AT.TIME.OF.SALE <int> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …
#> $ BUILDING.CLASS.AT.TIME.OF.SALE <chr> "C2", "C7", "C7", "C4", "C2", "C4", "C4…
#> $ SALE.PRICE <chr> "6625000", " - ", " - ", "3936272", "…
#> $ SALE.DATE <chr> "2017-07-19 00:00:00", "2016-12-14 00:0…Deskripsi data:
X: ID barisBOROUGH: Kode digit untuk wilayah dimana properti berada; Manhattan (1), Bronx (2), Brooklyn (3), Queens (4), dan Staten Island (5)NEIGHBORHOOD: Nama lingkunganBUILDING.CLASS.CATEGORY: Kategori kelas propertiTAX.CLASS.AT.PRESENT,TAX.CLASS.AT.TIME.OF.SALE: Jenis pajak bangunanBLOCK,LOT: Kombinasi borough, blok, dan lot membentuk kode unik untuk properti di New York CityEASE.MENT: Ragam hak yang dimiliki bangunan (contoh: hak jalan, dsb.)BUILDING.CLASS.AT.PRESENT,BUILDING.CLASS.AT.TIME.OF.SALE: Kategori kepemilikan bangunan (A: rumah satu keluarga; O: gedung kantor; R: kondominium (kepemilikan bersama); dsb.)ADDRESS: Alamat propertiAPARTMENT.NUMBER: Nomor apartemenZIP.CODE: Kode pos propertiRESIDENTIAL.UNITS: Jumlah unit hunian di properti yang terdaftarCOMMERCIAL.UNITS: Jumlah unit komersial di properti yang terdaftarTOTAL.UNITS: Jumlah unit hunian dan komersialLAND.SQUARE.FEET: Luas tanah properti (square feet)GROSS.SQUARE.FEET: Total area semua lantai bangunan yang diukur dari permukaan luar dinding luar bangunan, termasuk area tanah dan ruang di dalam setiap bangunan atau struktur pada propertiYEAR.BUILT: Tahun properti dibangunSALE.PRICE: Harga properti terjual; bila 0 maka properti merupakan warisanSALE.DATE: Tanggal properti dijual
Data Cleansing
1. Buang kolom yang tidak diperlukan:
- Kolom yang tidak relevan, karena berisikan nomer ID:
X - Kolom dengan semua nilai NA:
EASE.MENT
# Please run the code down below
unique(property$EASE.MENT)#> [1] NA2. Memperbaiki tipe data yang belum tepat:
Perhatikan kolom yang dideteksi sebagai integer:
BOROUGH,BLOCK,LOT: int -> factor- Diubah menjadi factor karena adanya sifat pengulangan
ZIP.CODE: int -> factor- Diubah menjadi factor karena adanya sifat pengulangan
RESIDENTIAL.UNITS,COMMERCIAL.UNITS,TOTAL.UNITS: int -> tetap int- Tidak akan diubah menjadi tipe data lainnya karena berisikan sebuah value dari penjumlahan
YEAR.BUILT: int -> int- Tergantung kebutuhan, kalau misalnya kita mau cek hubungan antara year built dengan sale price, maka lebih cocok integer. kalau untuk visualisasi bar plot, factor lebih cocok
TAX.CLASS.AT.TIME.OF.SALE: int -> factor- Diubah menjadi factor karena adanya sifat pengulangan
Perhatikan kolom yang dideteksi sebagai character:
NEIGHBORHOOD: chr -> factor- Diubah menjadi factor karena adanya sifat pengulangan
BUILDING.CLASS.CATEGORY,BUILDING.CLASS.AT.PRESENT,BUILDING.CLASS.AT.TIME.OF.SALE: chr -> factor- Diubah menjadi factor karena adanya sifat pengulangan
TAX.CLASS.AT.PRESENT: chr -> factor- Diubah menjadi factor karena adanya sifat pengulangan
ADDRESS: chr -> tetap chrAPARTMENT.NUMBER: chr -> chrLAND.SQUARE.FEET,GROSS.SQUARE.FEET: chr -> int- Diubah menjadi int karena berisikan informasi mengenai luas bangunan
SALE.PRICE: chr -> int- Diubah menjadi int karena berisikan informasi mengenai luas bangunan
SALE.DATE: chr -> Date- Diubah menjadi date karena berisikan informasi mengenai tanggal
# Please run the code down below
property_clean <- property %>%
# hapus kolom
select(-c(X, EASE.MENT)) %>%
# mengubah int -> factor dan chr -> factor
mutate_at(vars(BOROUGH, BLOCK, LOT, ZIP.CODE, TAX.CLASS.AT.TIME.OF.SALE,
NEIGHBORHOOD, BUILDING.CLASS.CATEGORY, BUILDING.CLASS.AT.PRESENT,
BUILDING.CLASS.AT.TIME.OF.SALE, TAX.CLASS.AT.PRESENT), as.factor) %>%
# mengubah chr -> int
mutate_at(vars(LAND.SQUARE.FEET, GROSS.SQUARE.FEET, SALE.PRICE), as.integer) %>%
# mengubah chr -> date
mutate(SALE.DATE = lubridate::ymd_hms(SALE.DATE))
glimpse(property_clean)#> Rows: 84,548
#> Columns: 20
#> $ BOROUGH <fct> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
#> $ NEIGHBORHOOD <fct> ALPHABET CITY, ALPHABET CITY, ALPHABET …
#> $ BUILDING.CLASS.CATEGORY <fct> 07 RENTALS - WALKUP APARTMENTS …
#> $ TAX.CLASS.AT.PRESENT <fct> 2A, 2, 2, 2B, 2A, 2, 2B, 2, 2, 2, 2, 2B…
#> $ BLOCK <fct> 392, 399, 399, 402, 404, 405, 406, 407,…
#> $ LOT <fct> 6, 26, 39, 21, 55, 16, 32, 18, 34, 153,…
#> $ BUILDING.CLASS.AT.PRESENT <fct> C2, C7, C7, C4, C2, C4, C4, C7, D5, D9,…
#> $ ADDRESS <chr> "153 AVENUE B", "234 EAST 4TH STREET"…
#> $ APARTMENT.NUMBER <chr> " ", " ", " ", " ", " ", " ", " ", " ",…
#> $ ZIP.CODE <fct> 10009, 10009, 10009, 10009, 10009, 1000…
#> $ RESIDENTIAL.UNITS <int> 5, 28, 16, 10, 6, 20, 8, 44, 15, 24, 30…
#> $ COMMERCIAL.UNITS <int> 0, 3, 1, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, …
#> $ TOTAL.UNITS <int> 5, 31, 17, 10, 6, 20, 8, 46, 15, 24, 34…
#> $ LAND.SQUARE.FEET <int> 1633, 4616, 2212, 2272, 2369, 2581, 175…
#> $ GROSS.SQUARE.FEET <int> 6440, 18690, 7803, 6794, 4615, 9730, 42…
#> $ YEAR.BUILT <int> 1900, 1900, 1900, 1913, 1900, 1900, 192…
#> $ TAX.CLASS.AT.TIME.OF.SALE <fct> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, …
#> $ BUILDING.CLASS.AT.TIME.OF.SALE <fct> C2, C7, C7, C4, C2, C4, C4, C7, D5, D9,…
#> $ SALE.PRICE <int> 6625000, NA, NA, 3936272, 8000000, NA, …
#> $ SALE.DATE <dttm> 2017-07-19, 2016-12-14, 2016-12-09, 20…3. Cek missing values:
# Please run the code down below
colSums(is.na(property_clean))#> BOROUGH NEIGHBORHOOD
#> 0 0
#> BUILDING.CLASS.CATEGORY TAX.CLASS.AT.PRESENT
#> 0 0
#> BLOCK LOT
#> 0 0
#> BUILDING.CLASS.AT.PRESENT ADDRESS
#> 0 0
#> APARTMENT.NUMBER ZIP.CODE
#> 0 0
#> RESIDENTIAL.UNITS COMMERCIAL.UNITS
#> 0 0
#> TOTAL.UNITS LAND.SQUARE.FEET
#> 0 26252
#> GROSS.SQUARE.FEET YEAR.BUILT
#> 27612 0
#> TAX.CLASS.AT.TIME.OF.SALE BUILDING.CLASS.AT.TIME.OF.SALE
#> 0 0
#> SALE.PRICE SALE.DATE
#> 14562 0Kolom dengan missing values: ada 3, LAND.SQUARE.FEET, GROSS.SQUARE.FEET, dan SALE.PRICE
Beberapa cara untuk handle missing values:
- Imputasi: mengisi nilai NA dengan suatu nilai
- Drop column: hapus kolom apabila NA pada kolom tersebut terlalu banyak (di atas 5%)
- Drop row: hapus baris apabila mengandung nilai NA
Catatan: Pembahasan mengenai Missing Value akan dijelaskan pada materi Time Series.
Untuk menghilangkan missing value kita bisa mengunakan bantuan fungsi
filter() & complete.cases().
# Please type your code down here
property_clean <- property_clean %>%
filter(complete.cases(.))colSums(is.na(property_clean))#> BOROUGH NEIGHBORHOOD
#> 0 0
#> BUILDING.CLASS.CATEGORY TAX.CLASS.AT.PRESENT
#> 0 0
#> BLOCK LOT
#> 0 0
#> BUILDING.CLASS.AT.PRESENT ADDRESS
#> 0 0
#> APARTMENT.NUMBER ZIP.CODE
#> 0 0
#> RESIDENTIAL.UNITS COMMERCIAL.UNITS
#> 0 0
#> TOTAL.UNITS LAND.SQUARE.FEET
#> 0 0
#> GROSS.SQUARE.FEET YEAR.BUILT
#> 0 0
#> TAX.CLASS.AT.TIME.OF.SALE BUILDING.CLASS.AT.TIME.OF.SALE
#> 0 0
#> SALE.PRICE SALE.DATE
#> 0 04. Memilih kolom numerik:
Dikarenakan analisis PCA menggunakan nilai variance, kita hanya dapat mereduksi kolom bertipe data numerik.
# Please type your code down here
property_num <- property_clean %>%
select_if(is.numeric)
glimpse(property_num)#> Rows: 48,243
#> Columns: 7
#> $ RESIDENTIAL.UNITS <int> 5, 10, 6, 8, 24, 10, 24, 3, 4, 5, 0, 1, 1, 1, 1, 2, …
#> $ COMMERCIAL.UNITS <int> 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1…
#> $ TOTAL.UNITS <int> 5, 10, 6, 8, 24, 10, 24, 4, 5, 6, 1, 1, 1, 1, 1, 3, …
#> $ LAND.SQUARE.FEET <int> 1633, 2272, 2369, 1750, 4489, 3717, 4131, 1520, 2201…
#> $ GROSS.SQUARE.FEET <int> 6440, 6794, 4615, 4226, 18523, 12350, 16776, 3360, 5…
#> $ YEAR.BUILT <int> 1900, 1913, 1900, 1920, 1920, 2009, 1928, 1910, 1900…
#> $ SALE.PRICE <int> 6625000, 3936272, 8000000, 3192840, 16232000, 103500…Exploratory Data Analysis
Apakah antar variable memiliki skala yang sama? Mari kita cek range
untuk tiap kolom dengan menggunakan fungsi summary():
# Please type your code down here
summary(property_num)#> RESIDENTIAL.UNITS COMMERCIAL.UNITS TOTAL.UNITS LAND.SQUARE.FEET
#> Min. : 0.000 Min. : 0.0000 Min. : 0.000 Min. : 0
#> 1st Qu.: 1.000 1st Qu.: 0.0000 1st Qu.: 1.000 1st Qu.: 1413
#> Median : 1.000 Median : 0.0000 Median : 1.000 Median : 2140
#> Mean : 2.567 Mean : 0.2485 Mean : 2.834 Mean : 3357
#> 3rd Qu.: 2.000 3rd Qu.: 0.0000 3rd Qu.: 2.000 3rd Qu.: 3071
#> Max. :1844.000 Max. :2261.0000 Max. :2261.000 Max. :4228300
#> GROSS.SQUARE.FEET YEAR.BUILT SALE.PRICE
#> Min. : 0 Min. : 0 Min. : 0
#> 1st Qu.: 828 1st Qu.:1920 1st Qu.: 80280
#> Median : 1620 Median :1931 Median : 480000
#> Mean : 3637 Mean :1828 Mean : 1107496
#> 3rd Qu.: 2520 3rd Qu.:1961 3rd Qu.: 830000
#> Max. :3750565 Max. :2017 Max. :1040000000Mari kita cek juga matriks covariance dari property_num,
dengan menggunakan fungsi cov():
# Please type your code down here
cov(property_num)#> RESIDENTIAL.UNITS COMMERCIAL.UNITS TOTAL.UNITS
#> RESIDENTIAL.UNITS 305.049227 2.453481 307.4475
#> COMMERCIAL.UNITS 2.453481 120.715187 123.1605
#> TOTAL.UNITS 307.447502 123.160464 430.5673
#> LAND.SQUARE.FEET 220200.789429 18207.148349 238340.8764
#> GROSS.SQUARE.FEET 318448.577564 21369.667678 339744.6630
#> YEAR.BUILT 220.670165 27.677915 242.5530
#> SALE.PRICE 28836512.816272 5362349.231994 34181339.6879
#> LAND.SQUARE.FEET GROSS.SQUARE.FEET YEAR.BUILT
#> RESIDENTIAL.UNITS 220200.79 318448.58 220.67016
#> COMMERCIAL.UNITS 18207.15 21369.67 27.67792
#> TOTAL.UNITS 238340.88 339744.66 242.55301
#> LAND.SQUARE.FEET 988110040.59 545385900.86 138633.73804
#> GROSS.SQUARE.FEET 545385900.86 816829031.72 425290.83095
#> YEAR.BUILT 138633.74 425290.83 215635.35375
#> SALE.PRICE 13967140344.87 107371730683.06 41381457.84525
#> SALE.PRICE
#> RESIDENTIAL.UNITS 28836513
#> COMMERCIAL.UNITS 5362349
#> TOTAL.UNITS 34181340
#> LAND.SQUARE.FEET 13967140345
#> GROSS.SQUARE.FEET 107371730683
#> YEAR.BUILT 41381458
#> SALE.PRICE 78460695562213Variance dari masing-masing variabel berbeda jauh karena range dari tiap variabel berbeda, begitu pula dengan covariance. Nilai variance dan covariance dipengaruhi oleh skala dari data. Semakin tinggi skala, nilai variance atau covariance akan semakin tinggi.
Notes: Data dengan perbedaan skala antar variabel yang tinggi tidak baik untuk langsung dianalisis PCA karena dapat menimbulkan bias.
Data Preprocessing: Scaling
Scaling dilakukan agar antar variabel memiliki skala yang tidak jauh
berbeda. Nilai scaling yang digunakan adalah Z-score (mean = 0, standar
deviasi = 1) atau kita bisa langsung menggunakan fungsi
scale().
\[Z = \frac{x-mean}{sd}\]
# Please type your code down here
property_num_z <- scale(property_num)
summary(property_num_z)#> RESIDENTIAL.UNITS COMMERCIAL.UNITS TOTAL.UNITS
#> Min. : -0.14695 Min. : -0.02261 Min. : -0.13658
#> 1st Qu.: -0.08970 1st Qu.: -0.02261 1st Qu.: -0.08838
#> Median : -0.08970 Median : -0.02261 Median : -0.08838
#> Mean : 0.00000 Mean : 0.00000 Mean : 0.00000
#> 3rd Qu.: -0.03244 3rd Qu.: -0.02261 3rd Qu.: -0.04019
#> Max. :105.43166 Max. :205.76518 Max. :108.82667
#> LAND.SQUARE.FEET GROSS.SQUARE.FEET YEAR.BUILT SALE.PRICE
#> Min. : -0.10678 Min. : -0.12725 Min. :-3.9360 Min. : -0.12503
#> 1st Qu.: -0.06183 1st Qu.: -0.09828 1st Qu.: 0.1986 1st Qu.: -0.11597
#> Median : -0.03870 Median : -0.07057 Median : 0.2223 Median : -0.07084
#> Mean : 0.00000 Mean : 0.00000 Mean : 0.0000 Mean : 0.00000
#> 3rd Qu.: -0.00908 3rd Qu.: -0.03908 3rd Qu.: 0.2869 3rd Qu.: -0.03133
#> Max. :134.40587 Max. :131.10214 Max. : 0.4075 Max. :117.28556Dikarenakan kita tidak membagi data, maka dari itu kita cukup melakukan scalling sekali saja.
- Pada materi K-NN -> kita membagi data menjadi data train & test
- Scaling 2x, yang pertama untuk data train & yang kedua untuk data test
- Pada scaling data test, kita akan memanfaatkan nilai mean & SD dari scaling data train kita
Principal Component Analysis using prcomp()
PCA dapat dilakukan dengan menggunakan fungsi
prcomp().
Cara 1: menggunakan data yang di-scale secara terpisah,
yaitu property_num_z
# Please type your code down here
prcomp(property_num_z)#> Standard deviations (1, .., p=7):
#> [1] 1.705249835 1.085811853 0.999591384 0.987849523 0.840500004 0.481289277
#> [7] 0.005136074
#>
#> Rotation (n x k) = (7 x 7):
#> PC1 PC2 PC3 PC4 PC5
#> RESIDENTIAL.UNITS -0.50138338 0.08936884 -0.019241647 0.16910059 0.56011546
#> COMMERCIAL.UNITS -0.18548792 -0.81557172 0.014975088 -0.14893618 -0.36170475
#> TOTAL.UNITS -0.52014300 -0.35665390 -0.008860518 0.06344165 0.27995828
#> LAND.SQUARE.FEET -0.37554855 0.26238205 -0.074578580 0.39235388 -0.66005834
#> GROSS.SQUARE.FEET -0.50070661 0.28523938 -0.004506179 -0.08135536 -0.18003718
#> YEAR.BUILT -0.02601345 0.01616302 0.994397509 0.09723184 -0.02509751
#> SALE.PRICE -0.22636182 0.22178116 0.070130740 -0.88044527 -0.09134236
#> PC6 PC7
#> RESIDENTIAL.UNITS -0.20433374 -0.59680907352
#> COMMERCIAL.UNITS 0.07891239 -0.37546407004
#> TOTAL.UNITS -0.13009145 0.70911598103
#> LAND.SQUARE.FEET -0.44151829 0.00005541206
#> GROSS.SQUARE.FEET 0.79301891 -0.00002543141
#> YEAR.BUILT -0.01231074 0.00042440835
#> SALE.PRICE -0.33335840 0.00005903831Cara 2: menggunakan data yang belum discale, lalu tambahkan
parameter scale = T
# Please type your code down here
pca <- prcomp(x = property_num,
scale. = TRUE)
pca#> Standard deviations (1, .., p=7):
#> [1] 1.705249835 1.085811853 0.999591384 0.987849523 0.840500004 0.481289277
#> [7] 0.005136074
#>
#> Rotation (n x k) = (7 x 7):
#> PC1 PC2 PC3 PC4 PC5
#> RESIDENTIAL.UNITS -0.50138338 0.08936884 -0.019241647 0.16910059 0.56011546
#> COMMERCIAL.UNITS -0.18548792 -0.81557172 0.014975088 -0.14893618 -0.36170475
#> TOTAL.UNITS -0.52014300 -0.35665390 -0.008860518 0.06344165 0.27995828
#> LAND.SQUARE.FEET -0.37554855 0.26238205 -0.074578580 0.39235388 -0.66005834
#> GROSS.SQUARE.FEET -0.50070661 0.28523938 -0.004506179 -0.08135536 -0.18003718
#> YEAR.BUILT -0.02601345 0.01616302 0.994397509 0.09723184 -0.02509751
#> SALE.PRICE -0.22636182 0.22178116 0.070130740 -0.88044527 -0.09134236
#> PC6 PC7
#> RESIDENTIAL.UNITS -0.20433374 -0.59680907352
#> COMMERCIAL.UNITS 0.07891239 -0.37546407004
#> TOTAL.UNITS -0.13009145 0.70911598103
#> LAND.SQUARE.FEET -0.44151829 0.00005541206
#> GROSS.SQUARE.FEET 0.79301891 -0.00002543141
#> YEAR.BUILT -0.01231074 0.00042440835
#> SALE.PRICE -0.33335840 0.00005903831Additional Notes: Hasil scaling pada fungsi prcomp()
akan sama saja dengan hasil scaling pada fungsi
scale().
Terdapat tiga komponen utama dalam objek pca:
pca$sdev: standar deviasi (akar variance) yang ditangkap oleh masing-masing PC, disebut juga sebagai eigen value. Digunakan untuk mengetahui seberapa besaran informasi yang ditangkap masing-masing PC.
# Please run the code down below
pca$sdev#> [1] 1.705249835 1.085811853 0.999591384 0.987849523 0.840500004 0.481289277
#> [7] 0.005136074# Nilai dari variance
pca$sdev ^ 2#> [1] 2.90787699968 1.17898738072 0.99918293523 0.97584668055 0.70644025663
#> [6] 0.23163936792 0.00002637926Atau kita bisa juga untuk menggunakan bantuan fungsi
plot().
# Please run the code down below
plot(pca)
pca$rotation: matrix rotasi, dimana matrix ini terdiri dari eigen vectors. Digunakan untuk mengetahui kontribusi masing-masing variabel ke PC.
# Please run the code down below
pca$rotation#> PC1 PC2 PC3 PC4 PC5
#> RESIDENTIAL.UNITS -0.50138338 0.08936884 -0.019241647 0.16910059 0.56011546
#> COMMERCIAL.UNITS -0.18548792 -0.81557172 0.014975088 -0.14893618 -0.36170475
#> TOTAL.UNITS -0.52014300 -0.35665390 -0.008860518 0.06344165 0.27995828
#> LAND.SQUARE.FEET -0.37554855 0.26238205 -0.074578580 0.39235388 -0.66005834
#> GROSS.SQUARE.FEET -0.50070661 0.28523938 -0.004506179 -0.08135536 -0.18003718
#> YEAR.BUILT -0.02601345 0.01616302 0.994397509 0.09723184 -0.02509751
#> SALE.PRICE -0.22636182 0.22178116 0.070130740 -0.88044527 -0.09134236
#> PC6 PC7
#> RESIDENTIAL.UNITS -0.20433374 -0.59680907352
#> COMMERCIAL.UNITS 0.07891239 -0.37546407004
#> TOTAL.UNITS -0.13009145 0.70911598103
#> LAND.SQUARE.FEET -0.44151829 0.00005541206
#> GROSS.SQUARE.FEET 0.79301891 -0.00002543141
#> YEAR.BUILT -0.01231074 0.00042440835
#> SALE.PRICE -0.33335840 0.00005903831Intuisi dari hasil pca$rotation sama seperti membuat
interpretasi pada saat membuat regresi linear, namun tanpa
intercept:
Contoh: Residental Units: 10, Commercial Units: 30, Sale Price: 2000
PC1 = -0.501 * RESIDENTIAL.UNITS - 0.185 * COMMERCIAL.UNITS + ... - 0.226 * SALE.PRICEPC2 = 0.089 * RESIDENTIAL.UNITS - 0.816 * COMMERCIAL.UNITS + ... + 0.222 * SALE.PRICEPC3 = -0.019 * RESIDENTIAL.UNITS + 0.015 * COMMERCIAL.UNITS + ... + 0.070 * SALE.PRICE- dan seterusnya sampai PC7
Notes:
- Semakin besar koefisiennya, semakin banyak informasi variable awal yang terangkum pada PC tersebut.
- Simbol +/- tidak mempengarhui besarana informasi yang ditangkap. Simbol tersebut hanya menunjukan arah dar sumbu PC nya saja
pca$x: nilai hasil proyeksi titik ke PC untuk tiap baris. Digunakan untuk mendapatkan nilai data yang baru.
# Please run the code down below
pca$x#> PC1 PC2 PC3 PC4
#> [1,] -0.29352086896 0.1479146616219 0.1980775582 -0.52924261332
#> [2,] -0.50824356888 0.0295576579825 0.1954128431 -0.18860257924
#> [3,] -0.35925318568 0.1581999613924 0.2059768446 -0.63879359544
#> [4,] -0.33086357198 0.0053431505723 0.2092174164 -0.13792555567
#> [5,] -1.80765829377 0.3042283848435 0.2792419499 -1.23666889116
#> [6,] -0.79212575107 0.2609976555396 0.4474640224 -0.80379059786
#> [7,] -1.66251852198 0.1756186595336 0.2631998917 -0.80389853213
#> [8,] -0.08820266025 -0.0339468939965 0.1979133975 -0.22527126779
#> [9,] -0.28898384451 0.0797774072183 0.2039970663 -0.60166678539
#> [10,] -0.24208375579 -0.0160993803741 0.2056660892 -0.34169137796
#> [11,] 0.06316159967 0.0116337926866 0.1827917902 -0.30996430908
#> [12,] -0.05772414885 0.1933202532380 0.2122638328 -0.64788146692
#> [13,] 0.10520178284 0.0220933000060 0.1519705206 0.07998744172
#> [14,] 0.10520178284 0.0220933000060 0.1519705206 0.07998744172
#> [15,] 0.10520178284 0.0220933000060 0.1519705206 0.07998744172
#> [16,] -0.18458209703 0.1112979698656 0.2543388144 -0.67497865904
#> [17,] -0.19125681176 0.1939120136981 0.2149826313 -0.70283980666
#> [18,] -0.57993109347 0.2510443309879 0.2746773879 -1.45314426963
#> [19,] -0.16592950860 0.1115423780817 0.2152298905 -0.45739705761
#> [20,] -1.30845430758 -0.0763958132802 0.1736771879 -0.34780912284
#> [21,] -0.22042015085 0.1640390916507 0.2100224752 -0.66368886199
#> [22,] -1.60988838065 0.0210034601320 0.2319933288 -1.08345938871
#> [23,] -0.37711732016 -0.0282127164347 0.1543676336 0.02248047926
#> [24,] -0.34729327432 -0.0574332423993 0.1451276371 0.13848255235
#> [25,] -0.35275132642 -0.0520856395241 0.1468186344 0.11725319390
#> [26,] -1.13327489751 0.6948290589613 0.4138390599 -2.73891505581
#> [27,] -0.52596422137 0.0365863253976 0.2334301811 -0.47155223327
#> [28,] -0.84797988671 -0.0896905275630 0.1759240661 -0.29447522999
#> [29,] -0.47086564806 -0.0031071276715 0.2296475715 -0.40499994662
#> [30,] -0.33854889279 0.0131394042276 0.1895431859 -0.16558034595
#> [31,] -0.58953923054 0.1389244439384 0.4214685856 -0.32970834775
#> [32,] -2.98842884011 0.3533028450855 0.3405441136 0.11672204728
#> [33,] -1.28668489834 -0.1597421619220 0.0037942975 0.35345148173
#> [34,] -0.36497864135 0.1578800693426 0.2529014380 -0.93720566567
#> [35,] 0.00096495031 -0.1199032121874 0.1726767080 0.09813171762
#> [36,] -0.34117518527 0.0055300208707 0.2340153138 -0.70591083367
#> [37,] -0.37869325753 0.1754634261148 0.2940669265 -1.68219369611
#> [38,] -1.20370141241 1.1359140709447 0.5896229564 -4.09994045958
#> [39,] -6.20070393258 3.7427719751134 1.3295284212 -15.17993466777
#> [40,] -0.40289759294 -0.1145149762394 0.2999678685 -0.98993606300
#> [41,] -0.23160583738 0.2579783229899 0.4755683651 -0.96502790362
#> [42,] -0.07936867621 0.1472035939111 0.2457348034 -0.81161170425
#> [43,] -0.38859889101 0.4438228531013 0.3292412503 -1.89622469042
#> [44,] -3.56135660930 2.8443256316457 1.0264823875 -10.49809959304
#> [45,] -0.28023910948 0.0794739559478 0.2792889352 -0.97378746197
#> [46,] -0.47495387466 -0.1134718249162 0.2596265369 -1.02639695373
#> [47,] -0.17628317423 -0.0241861183928 0.2714081094 -0.86389017714
#> [48,] -2.21976731863 -0.4506708537811 0.4633060365 -3.47942376268
#> [49,] -5.60069566111 4.6772974873326 1.4583221499 -14.03759473651
#> [50,] 0.00586483896 0.0521878086806 0.1869214302 -0.36101540286
#> [51,] -5.69165515857 3.2023694105724 0.8280566112 -9.45715607873
#> [52,] -1.57135847850 1.4488686206138 0.5679390669 -4.85370092405
#> [53,] -1.94199887935 -0.1783875412678 0.2039448565 -0.26646281606
#> [54,] -0.82032672030 -0.1356673695815 0.2348884280 -0.64012986366
#> [55,] -1.85498658755 -0.1950041210018 0.1741351361 -0.01723450240
#> [56,] -0.28921811866 -0.0806790408772 0.1210257876 0.13057091309
#> [57,] -0.71465706323 0.5034900157020 0.3413519071 -1.85838269083
#> [58,] -0.83418710218 -0.9142720517817 0.2686472623 -1.01740782145
#> [59,] -0.02233427146 -0.2207753613090 0.2236200446 -0.24318546268
#> [60,] -0.10035308206 -0.0888499515503 0.2304985990 -0.35253475748
#> [61,] 0.06261650786 -0.1139900114680 0.2104954430 -0.21672455555
#> [62,] -0.11784909525 0.1489592895704 0.2270272725 -0.61255876244
#> [63,] -0.86345650317 -0.1405786678900 0.2768385797 -1.57756753249
#> [64,] -3.99995306458 3.4737054605134 1.2926868680 -13.92072987480
#> [65,] -0.90696363068 0.4314328761688 0.2869213135 -1.36561642434
#> [66,] -1.75066727995 0.4642441203050 0.3297175798 -1.84742565505
#> [67,] -0.48683624792 0.1861124910661 0.2626316178 -0.94804484317
#> [68,] -0.80960720483 0.2013797029063 0.3324251227 -1.75849309678
#> [69,] -0.43394765825 -0.1666779910051 0.2160394077 -0.29734706667
#> [70,] -0.49244602331 -0.1646097206645 0.2791939423 -1.13906058791
#> [71,] -0.24839356161 -0.0747007483796 0.1833620388 0.18329798110
#> [72,] -0.51323797084 0.0239708460022 0.1623124129 -0.10895215831
#> [73,] -0.85844774267 0.2326812491368 0.2328868015 -1.00787206376
#> [74,] -0.26906326925 0.1386769917531 0.2431516017 -0.54999587469
#> [75,] -1.21757173818 0.0276766075215 0.2381832963 -0.88812385364
#> [76,] -0.85959873907 0.2232375678467 0.2443095765 -0.91429618393
#> [77,] -0.56230280065 -0.1385893889300 0.1368873198 0.19610121400
#> [78,] -0.61607660550 -0.1506606007428 0.1353586247 0.20884051569
#> [79,] -0.69770859125 0.3830391162366 0.5080463803 -1.32196828224
#> [80,] -0.42699412897 0.4833838884016 0.4026086612 -2.02116635150
#> [81,] -0.63577381003 0.4594327548487 0.3719158971 -1.73683335337
#> [82,] -0.22716806834 0.1127719322616 0.2315548792 -0.71407383372
#> [83,] 0.03161337073 -0.0729523979721 0.4010919618 -0.37375320629
#> [84,] -0.02237906042 -0.0324061768863 0.1764119724 -0.21427928538
#> [85,] -0.16523759220 0.0889205300280 0.2037632328 -0.59848854824
#> [86,] 0.00578919001 0.0774555019554 0.1811875719 -0.30040250195
#> [87,] -2.07476340030 0.0298486981335 0.2127916707 -0.97678542991
#> [88,] -1.14553527384 -0.0172990893361 0.2009858533 -0.17770892994
#> [89,] -1.14782957847 -0.0608713729624 0.2052218348 -0.19423944577
#> [90,] -1.32757069084 -0.0760238321923 0.1649193992 -0.25196764002
#> [91,] -1.32757069084 -0.0760238321923 0.1649193992 -0.25196764002
#> [92,] -1.21808415945 -0.2051929069184 0.1359043184 0.37097439033
#> [93,] -1.32182235203 0.0815137165124 0.2201373648 -0.93073139337
#> [94,] -1.56540525187 -0.1327820114500 0.1954418452 -0.64842951052
#> [95,] -0.72532512296 0.0402307734046 0.2024144775 -0.63077631012
#> [96,] -3.63845739370 0.4780713091325 0.3435243890 -2.30914955221
#> [97,] -0.27468030803 -0.0597347573701 0.1962911011 -0.48449417357
#> [98,] -0.43553077134 0.1549134677151 0.2617110579 -0.83093993457
#> [99,] -0.11749854887 0.0396844357637 0.1857449590 -0.36183139510
#> [100,] -1.50369206697 -0.0721129175894 0.2486626286 -0.76853742100
#> [101,] -0.49929049377 0.0263542737807 0.2829071653 -1.17316607061
#> [102,] -6.61733622867 1.0030652880152 1.0510402166 -11.32439565505
#> [103,] -28.15717834610 15.7890382711097 4.6559170237 -58.11412775025
#> [104,] -3.01402563602 0.4540000938394 0.6009690477 -5.58920125709
#> [105,] -1.28838026249 -0.5076962300685 0.2138028682 -0.26875001017
#> [106,] -1.86701983755 -0.1342993058065 0.1938974517 -0.69892803361
#> [107,] -1.83433939122 -0.5493596124800 0.1726551389 -0.25200347484
#> [108,] -3.97693469611 3.3908429110005 1.1939021017 -10.55837616526
#> [109,] -6.23612323686 4.9145411554429 1.3640054025 -13.07592465435
#> [110,] -42.49960466501 2.9608984514985 0.9827068095 -15.51805636175
#> [111,] -5.58086115965 4.6615557557591 1.4591481957 -14.06328339525
#> [112,] -2.86838006955 1.2606012958395 0.5738490876 -5.26414089645
#> [113,] -0.33829429952 0.2613066991573 0.3491035094 -1.57978191011
#> [114,] -38.91084112066 3.8025516521968 1.2864188367 -18.61709896891
#> [115,] -27.13952364883 3.2838511228971 1.0916410395 -14.79765863582
#> [116,] -34.34907688857 26.4737559727848 5.2408651628 -67.03140355643
#> [117,] -11.03668498054 3.8345289697334 0.2071836238 -1.75857332726
#> [118,] -55.32024251416 42.5034361787686 8.1972634683 -107.23641387259
#> [119,] -12.77678883715 2.0028377278036 0.5282238355 -7.09629692018
#> [120,] -0.68903702251 0.0767354177748 0.3498545735 -1.22296214881
#> [121,] -4.92890679812 3.8747874697281 1.1419378170 -10.19883449967
#> [122,] -20.61725566825 -22.6622638201771 2.2748798118 -23.75701786860
#> [123,] -4.36830653772 3.3705705203982 0.8707347083 -9.51468797934
#> [124,] -2.53373149130 1.7639571492982 0.5403460438 -5.18982699036
#> [125,] -1.17654016130 0.0488610474568 0.1242910364 0.16550422130
#> [126,] -1.17874926943 0.0510254520384 0.1249754557 0.15691178806
#> [127,] -0.25621684453 0.0537100005680 0.2227365465 -0.54963120079
#> [128,] -5.56181096477 2.8966756614962 1.1509334467 -12.79671134129
#> [129,] -1.20210745866 0.0507753611702 0.3927275077 -2.69599174125
#> [130,] -5.17868845573 -0.9336164407999 0.1661556607 -0.89277326123
#> [131,] -0.72361070703 0.7325596646948 0.4125187340 -2.87054087335
#> [132,] -0.29971520707 0.0919748266483 0.3691761487 -1.28544164722
#> [133,] -0.08849922895 -0.2382702664352 0.2279012582 -0.43597205841
#> [134,] -0.15428293182 0.0685927688886 0.2343106587 -0.43454076904
#> [135,] 0.00355396842 0.0758201356613 0.2019853275 -0.26788484118
#> [136,] -0.10733120356 0.1777426241966 0.2106712102 -0.63056689513
#> [137,] -0.07349972676 0.1546259285385 0.2276980508 -0.59165701101
#> [138,] -0.37932631408 0.3562978143078 0.3060590267 -1.21704092459
#> [139,] -0.80698346324 0.5722443131449 0.3237492357 -2.14169983180
#> [140,] -0.53556796388 -0.1551049008678 0.3514878406 0.20736409738
#> [141,] -0.43317172402 -0.1265238210831 0.1591330646 0.17789877832
#> [142,] -0.35023361254 0.1301593090953 0.2585755331 -0.74991442072
#> [143,] -1.33250430965 0.1684286558041 0.2667548830 -0.97619695600
#> [144,] -2.19323429464 0.0349115548705 0.2998656412 -1.49943413123
#> [145,] -1.12002905445 0.1738711333871 0.2346476705 -0.96079826956
#> [146,] -0.27093060946 0.1174908761688 0.2517698382 -0.66060641865
#> [147,] -0.34432620821 0.2489880371715 0.2930067649 -1.43425511353
#> [148,] -2.00167315576 1.1248361664707 0.5951623048 -5.27029136095
#> [149,] -0.19215262233 0.1806044429399 0.2326207365 -0.92789558572
#> [150,] -0.18238838621 0.3175594347882 0.2481448776 -1.15155538311
#> [151,] -0.23078558782 0.3612351414358 0.2593641410 -1.29868149145
#> [152,] -0.45267965201 0.5571608115389 0.3139473910 -1.96954320341
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#> [1897,] 0.02979574212 0.0394814662301 0.2108767185 0.07940590896
#> [1898,] 0.08009468499 -0.0000614398763 0.2805322555 0.08324076070
#> [1899,] 0.10211527533 -0.0172886262375 0.2666375611 0.12613400072
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#> [1904,] 0.03961981539 -0.0943346893943 0.2211442814 0.05727350979
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#> [1908,] 0.10160586529 -0.0131552892113 0.2054307879 0.08377952322
#> [1909,] 0.09400623631 -0.0102931646445 0.2042217605 0.09587909349
#> [1910,] 0.08255279111 -0.0025777209392 0.1943460564 0.08197245322
#> [1911,] 0.09149706603 -0.0113409993657 0.1915749680 0.11676164441
#> [1912,] 0.08315728055 -0.0005117087475 0.1962253945 0.06016421246
#> [1913,] 0.08785299277 -0.0031027197461 0.2933105259 0.06549343800
#> [1914,] 0.10719630943 -0.0201542183748 0.2881024409 0.12914445785
#> [1915,] 0.07034496422 0.0079637289239 0.3788963704 0.06819617926
#> [1916,] 0.10528839712 -0.0145574684243 0.2167030854 0.07927935183
#> [1917,] 0.08907084970 -0.0036040466857 0.2071918752 0.05983636137
#> [1918,] 0.08743768321 -0.0034107780232 0.2814924198 0.07483773866
#> [1919,] 0.10261508295 -0.0133813988454 0.2699010120 0.08811702069
#> [1920,] 0.05606855831 0.0182740996336 0.2862164263 0.10736683572
#> [1921,] 0.10335776886 -0.0151812374354 0.2616713763 0.07052895584
#> [1922,] 0.10599317010 -0.0155680575379 0.2602689846 0.07964792690
#> [1923,] 0.08923392377 -0.0034567061631 0.2576684046 0.09009573472
#> [1924,] 0.10151976038 -0.0137871427721 0.2380345596 0.08509711939
#> [1925,] 0.10166116276 -0.0113276698754 0.2700276627 0.08276435737
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#> [1927,] 0.09732345857 -0.0114711874068 0.2274933008 0.08179375610
#> [1928,] 0.10528058242 -0.0166239542642 0.1949880775 0.08504781153
#> [1929,] 0.08274453419 -0.0024321634930 0.2172342426 0.07153198720
#> [1930,] 0.10298368244 -0.0166074271264 0.2112628386 0.13249545814
#> [1931,] 0.13641865447 -0.0377067036358 0.1962977201 0.09070743534
#> [1932,] 0.07086531593 0.0095417289809 0.2156826799 0.06736989382
#> [1933,] 0.06589005807 0.0115708342031 0.2014981366 0.09576777261
#> [1934,] 0.10022574159 -0.0123903465772 0.3836461392 0.06309418895
#> [1935,] 0.09621616841 -0.0096608397744 0.3827199725 0.06854414869
#> [1936,] 0.11505622661 -0.0252145853014 0.2568372019 0.12209619367
#> [1937,] 0.09816550782 -0.0108826321771 0.2819165057 0.07757406523
#> [1938,] 0.10205231220 -0.0168049103905 0.2552479157 0.12935820583
#> [1939,] 0.11709335349 -0.0266207110830 0.2464857105 0.11917130667
#> [1940,] 0.09397940727 -0.0082133607064 0.2503513843 0.06779299085
#> [1941,] 0.07886472239 0.0035248964514 0.2373601200 0.07335430095
#> [1942,] 0.08777192771 -0.0044099689038 0.2589851731 0.08377469160
#> [1943,] 0.09605840718 -0.0148593083843 0.2788147135 0.11655011005
#> [1944,] 0.07976801024 -0.0005235301719 0.2920950982 0.07904487322
#> [1945,] 0.10645040933 -0.0200905061726 0.2778957789 0.12468566210
#> [1946,] 0.11406072844 -0.0254075579953 0.2794070796 0.11673479075
#> [1947,] 0.08530023240 -0.0018906636464 0.2621574929 0.05414113617
#> [1948,] 0.09092234806 -0.0073990100859 0.2604156659 0.07600862778
#> [1949,] 0.09076901763 -0.0072487824558 0.2604631702 0.07541224164
#> [1950,] 0.10073923272 -0.0132759149761 0.2156437218 0.09044588280
#> [1951,] 0.08974315294 -0.0074839405731 0.2605751952 0.07646822886
#> [1952,] 0.09357641362 -0.0112396313273 0.2593875858 0.09137788223
#> [1953,] 0.09681113848 -0.0102681470917 0.2613552175 0.06837353522
#> [1954,] 0.05900828857 0.0158009516561 0.4021698994 0.06663441437
#> [1955,] 0.07169334984 0.0069189961172 0.4046539443 0.05372166817
#> [1956,] 0.07188000408 0.0067361190154 0.4045961156 0.05444766889
#> [1957,] 0.07153723391 0.0070719528826 0.4047023116 0.05311444769
#> [1958,] 0.05394953609 0.0205222131611 0.1876187750 0.11201840318
#> [1959,] 0.08376353360 -0.0052149745032 0.3928627377 0.14979020598
#> [1960,] 0.06554851773 0.0126314420122 0.3985060594 0.07894201812
#> [1961,] 0.11196253708 -0.0229220681892 0.2560301968 0.12655501440
#> [1962,] 0.07205468892 0.0086798718203 0.3750311045 0.09575642378
#> [1963,] 0.05271540279 0.0193035500705 0.2462059201 0.08121790194
#> [1964,] 0.08052043006 0.0008222924774 0.1907966838 0.10456080505
#> [1965,] 0.09786074708 -0.0146605730033 0.2555680645 0.12639833334
#> [1966,] 0.11205358177 -0.0229242793722 0.2344963484 0.12512049153
#> [1967,] 0.09682470567 -0.0135811709089 0.2119163578 0.12698036484
#> [1968,] 0.10606338966 -0.0206165029362 0.2682585989 0.11667944597
#> [1969,] 0.10122436627 -0.0133993781878 0.2050686335 0.08791109979
#> [1970,] 0.01773568659 0.0347283475492 0.3308988560 0.15569135098
#> [1971,] 0.08607327410 -0.0024763117495 0.2816023513 0.07318736588
#> [1972,] 0.09664771219 -0.0095072152267 0.2719756181 0.06839113223
#> [1973,] 0.10002098159 -0.0128122230904 0.2709305219 0.08151162720
#> [1974,] 0.09614792120 -0.0089093405102 0.2607093548 0.07086376140
#> [1975,] 0.10355186121 -0.0181070114206 0.2666504899 0.12636741876
#> [1976,] 0.07846895908 0.0031533221639 0.1697276669 0.09579259323
#> [1977,] 0.09047666345 -0.0097686252712 0.2759558690 0.13352761133
#> [1978,] 0.08049742942 0.0002869120229 0.1960772138 0.06269144478
#> [1979,] 0.09555921605 -0.0104038385515 0.1838737119 0.08309535236
#> [1980,] 0.07508926826 0.0041238360378 0.2398425005 0.05628376014
#> [1981,] 0.07122599187 0.0097340679715 0.2457629887 0.08658898709
#> [1982,] 0.10508645174 -0.0154315420941 0.2497588162 0.07769354077
#> [1983,] 0.10659420094 -0.0169087804574 0.2492916899 0.08355800443
#> [1984,] 0.11569180629 -0.0258222865140 0.2464730971 0.11894358176
#> [1985,] 0.08842378364 -0.0044640772562 0.2276275183 0.07334556734
#> [1986,] 0.10626385166 -0.0155591292171 0.2628812652 0.05782596684
#> [1987,] 0.08635474001 -0.0037711747150 0.2496668157 0.07134362141
#> [1988,] 0.09274951187 -0.0073996383482 0.2604339425 0.07347509350
#> [1989,] 0.09823430931 -0.0146494349873 0.2144650705 0.12491829805
#> [1990,] 0.01461770824 -0.0052571697423 0.2044179138 0.08159757346
#> [1991,] -0.02185236370 0.0213102920401 0.1999344401 0.09410878057
#> [1992,] 0.00769496259 0.0006777147855 0.2059036141 0.06237611827
#> [1993,] 0.02824135748 -0.0178713248291 0.2004870495 0.13022101571
#> [1994,] 0.02824135748 -0.0178713248291 0.2004870495 0.13022101571
#> [1995,] 0.00669938310 -0.0018716121219 0.1948141234 0.16160991188
#> [1996,] 0.01834014655 -0.0115251173482 0.3581771315 0.14938132004
#> [1997,] 0.03452995848 -0.0167054537054 0.2045156430 0.08578539230
#> [1998,] 0.02546372854 -0.0101896703438 0.2396571763 0.05864858732
#> [1999,] -0.00069148090 0.0019075575283 0.3327361866 0.16862313066
#> [2000,] 0.00328127829 0.0000173614534 0.2294165248 0.14404781161
#> [2001,] 0.01155272356 -0.0028508321064 0.3386018414 0.08174688886
#> [2002,] 0.04125462082 -0.0209225832947 0.2363708484 0.09406041492
#> [2003,] 0.02585938049 -0.0126682371985 0.2112450626 0.11998276140
#> [2004,] 0.04151734298 -0.0213382361357 0.2254680995 0.09529655108
#> [2005,] -0.10109725490 0.0617211776123 0.3816431871 0.18156913306
#> [2006,] 0.00974529419 -0.0005024308325 0.3809570736 0.06843309126
#> [2007,] 0.02801717010 -0.0184045567608 0.3752961358 0.13950243898
#> [2008,] 0.01777739969 -0.0122129886319 0.2974156120 0.13429900887
#> [2009,] 0.03318143980 -0.0208798397329 0.1493090087 0.12461170420
#> [2010,] 0.03402027028 -0.0191288835403 0.1760870586 0.14828739341
#> [2011,] 0.03826345913 -0.0230000707386 0.3800020874 0.15336107408
#> [2012,] 0.00104021077 0.0013233301501 0.1733440405 0.15850551822
#> [2013,] 0.01219931066 -0.0080441370885 0.3796089688 0.15013574771
#> [2014,] -0.01078231251 0.0137044691759 0.1990237912 0.10771789323
#> [2015,] 0.02734056228 -0.0167218717626 0.3068521665 0.14559999299
#> [2016,] 0.00497006349 0.0024713155565 0.3698374061 0.08666291962
#> [2017,] 0.04081569760 -0.0230389903627 0.1720687227 0.09393832751
#> [2018,] 0.00985135057 -0.0009439621076 0.1739552078 0.05907497905
#> [2019,] 0.04161213412 -0.0262292680782 0.3390512268 0.13770860022
#> [2020,] 0.34463491753 -0.0720363748320 -3.9136911898 -0.33779992076
#> [2021,] 0.35355363737 -0.0807746153201 -3.9164543609 -0.30311012725
#> [2022,] 0.35355363737 -0.0807746153201 -3.9164543609 -0.30311012725
#> [2023,] 0.37985539541 -0.0991255500027 -3.9111857344 -0.33103019314
#> [2024,] 0.32972501045 -0.0605346525193 -3.9146902520 -0.34126335799
#> [2025,] 0.32801068251 -0.0629286862825 -3.9215268270 -0.27642415715
#> [2026,] 0.33575242000 -0.0683375553266 -3.9199894285 -0.28451232770
#> [2027,] 0.35355363737 -0.0807746153201 -3.9164543609 -0.30311012725
#> [2028,] 0.38103202661 -0.0999727616188 -3.9109975452 -0.33181813999
#> [2029,] 0.38103202661 -0.0999727616188 -3.9109975452 -0.33181813999
#> [2030,] 0.35338594847 -0.0801905268429 -3.9156431641 -0.31113119513
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#> [2033,] -0.73917457660 -0.0461927619141 0.4038830752 -0.07248615014
#> [2034,] -47.82120421304 -4.6598661702453 -0.9930454361 5.68183957937
#> [2035,] -46.51150681424 -5.9430605112630 -1.3988119597 10.77597114692
#> [2036,] -43.75929247835 -3.6509492407332 -1.3823501784 10.67647289461
#> [2037,] -43.75929247835 -3.6509492407332 -1.3823501784 10.67647289461
#> [2038,] -0.03564556322 -0.0201697236110 0.2019203100 0.10539788307
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#> [2091,] 0.27401063781 -0.0331578091122 0.2185529747 0.06391568262
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#> [2100,] 0.21678313449 -0.0424877413229 0.2860640647 0.07689450041
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#> [2104,] 0.21337348254 -0.0390868499781 0.2807482669 0.06235066463
#> [2105,] 0.21509844984 -0.0407769108175 0.2802138427 0.06906000865
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#> [2108,] 0.21810117071 -0.0437188685750 0.2792835487 0.08073923712
#> [2109,] 0.22001780105 -0.0455967139521 0.2786897440 0.08819406380
#> [2110,] 0.21835672142 -0.0439692479586 0.2792043747 0.08173321401
#> [2111,] 0.21996152616 -0.0455616568974 0.2808312343 0.08840245626
#> [2112,] 0.21996152616 -0.0455616568974 0.2808312343 0.08840245626
#> [2113,] 0.21996178171 -0.0455619072768 0.2808311551 0.08840345024
#> [2114,] 0.21740627459 -0.0430581134407 0.2816228947 0.07846368132
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#> [2328,] 0.13779959676 0.0142741056279 0.2031633805 0.08358643735
#> [2329,] 0.15817308066 -0.0026095560840 0.2823569927 0.07590964807
#> [2330,] 0.14614068531 0.0037165497368 0.1987247976 0.13770769872
#> [2331,] 0.17237774949 -0.0148900256040 0.2043403175 0.10771627464
#> [2332,] 0.11322989776 0.0280935243429 0.2346535323 0.08689591385
#> [2333,] 0.13924512016 0.0106707719111 0.2069093949 0.06070016831
#> [2334,] 0.15284123343 -0.0006722931067 0.3927805757 0.15067199721
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#> [3415,] 0.26977266860 -0.0299292360563 0.3175725150 0.06708660879
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#> [3422,] 0.26984640748 -0.0293187948837 0.2453317881 0.05284602320
#> [3423,] 0.26362747869 -0.0232257124317 0.2472585180 0.02865719796
#> [3424,] 0.27039957255 -0.0298607660974 0.2451604081 0.05499758558
#> [3425,] 0.27071901094 -0.0301737403270 0.2450614407 0.05624005670
#> [3426,] 0.27039957255 -0.0298607660974 0.2451604081 0.05499758558
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#> [3787,] 0.07417945005 0.0048960724154 0.1754088845 0.05003794269
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#> [3853,] 0.09742808657 -0.0147092658453 0.1916364924 0.11763007762
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#> [3858,] 0.09345880662 -0.0124874906873 0.1701734706 0.11489550499
#> [3859,] 0.08480032955 -0.0008568471125 0.2073978635 0.05628511841
#> [3860,] 0.10207782511 -0.0133066956323 0.2400454820 0.06656048479
#> [3861,] 0.11163390155 -0.0238332859854 0.2361800030 0.11430722105
#> [3862,] 0.10258892654 -0.0138074543995 0.2398871341 0.06854843857
#> [3863,] 0.10207782511 -0.0133066956323 0.2400454820 0.06656048479
#> [3864,] 0.09401288298 -0.0067427800835 0.2390799218 0.06725026764
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#> [4727,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
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#> [4729,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
#> [4730,] 0.32683658908 -0.1109592042378 -3.9111808211 -0.33250893303
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#> [4985,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
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#> [5361,] 0.27038383587 -0.0298051897562 0.2409171730 0.05408182427
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#> [5363,] 0.26955033692 -0.0289483993873 0.2369272944 0.04998533690
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#> [5365,] 0.27305528178 -0.0322619437958 0.2230970709 0.06105433175
#> [5366,] 0.27389859913 -0.0330881957617 0.2228357969 0.06433445549
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#> [5368,] 0.27374526870 -0.0329379681315 0.2228833012 0.06373806936
#> [5369,] 0.27218640936 -0.0314106538915 0.2233662624 0.05767481032
#> [5370,] 0.27351527306 -0.0327126266863 0.2229545578 0.06284349016
#> [5371,] 0.21329291722 -0.0391283893101 0.2935175594 0.06460096012
#> [5372,] 0.21239848973 -0.0382520614675 0.2937946682 0.06112204100
#> [5373,] 0.21273070565 -0.0385775546662 0.2936917421 0.06241421096
#> [5374,] 0.21597619969 -0.0417573728381 0.2926862329 0.07503771748
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#> [5610,] 0.26048723220 -0.0204501978501 0.2800922497 0.02285220245
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#> [5625,] 0.26962404299 -0.0289804558304 0.2326563484 0.04941746750
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#> [5628,] 0.27098242999 -0.0304519078812 0.2471038843 0.05769191424
#> [5629,] 0.26585567908 -0.0253887438677 0.2444441283 0.03689661511
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#> [5631,] 0.26453703740 -0.0240967862482 0.2448526659 0.03176769435
#> [5632,] 0.26702610134 -0.0265354814446 0.2440815115 0.04144902927
#> [5633,] 0.26989338033 -0.0293447381288 0.2431931798 0.05260144999
#> [5634,] 0.26994449047 -0.0293948140055 0.2431773450 0.05280024537
#> [5635,] 0.26968893976 -0.0291444346219 0.2432565189 0.05180626847
#> [5636,] 0.26678063896 -0.0265359349120 0.2696462240 0.04562160788
#> [5637,] 0.27037112647 -0.0300537652518 0.2685338299 0.05958698320
#> [5638,] 0.26933614608 -0.0290397287481 0.2688544844 0.05556137679
#> [5639,] 0.26968113954 -0.0293777409160 0.2687475996 0.05690324560
#> [5640,] 0.26751994717 -0.0272602824688 0.2694171737 0.04849718303
#> [5641,] 0.26995319883 -0.0296442948078 0.2686633110 0.05796143340
#> [5642,] 0.26607787450 -0.0258473916071 0.2698639523 0.04288817143
#> [5643,] 0.26965558447 -0.0293527029777 0.2687555170 0.05680384791
#> [5644,] 0.27412772193 -0.0337343421909 0.2673699727 0.07419844350
#> [5645,] 0.27039668154 -0.0300788031901 0.2685259125 0.05968638089
#> [5646,] 0.27085472276 -0.0305878126542 0.2747561695 0.06274978358
#> [5647,] 0.26245988188 -0.0223628499025 0.2773570340 0.03009764270
#> [5648,] 0.26297098330 -0.0228636086697 0.2771986861 0.03208559648
#> [5649,] 0.26979028720 -0.0296653913592 0.2878302818 0.06117326804
#> [5650,] 0.26332485419 -0.0233307929538 0.2898333828 0.03602565269
#> [5651,] 0.26416817154 -0.0241570449198 0.2895721088 0.03930577643
#> [5652,] 0.27055693934 -0.0304165295101 0.2875927599 0.06415519871
#> [5653,] 0.26574175847 -0.0256385515554 0.2827124188 0.04414449003
#> [5654,] 0.26751487678 -0.0273356308995 0.2779149659 0.05018656696
#> [5655,] 0.26866485498 -0.0284623381257 0.2775586831 0.05465946297
#> [5656,] 0.26777042749 -0.0275860102831 0.2778357920 0.05118054385
#> [5657,] 0.26649267393 -0.0263341133650 0.2782316618 0.04621065939
#> [5658,] 0.27390552650 -0.0332756944515 0.2419501486 0.06820688718
#> [5659,] 0.27038195395 -0.0301246107945 0.2749026413 0.06091092633
#> [5660,] 0.26373763544 -0.0236147468205 0.2769611642 0.03506752716
#> [5661,] 0.27146118522 -0.0312623189498 0.2830644985 0.06681775421
#> [5662,] 0.26948658549 -0.0294079934710 0.2921724844 0.06084655824
#> [5663,] 0.27003601952 -0.0299463091458 0.2920022604 0.06298360856
#> [5664,] 0.26776161819 -0.0277179326316 0.2927069086 0.05413721422
#> [5665,] 0.26842605004 -0.0283689190290 0.2925010563 0.05672155414
#> [5666,] 0.27067583727 -0.0304125470856 0.2748115913 0.06205399975
#> [5667,] 0.26393716681 -0.0238303195289 0.2790234013 0.03627089048
#> [5668,] 0.25900503807 -0.0189979974251 0.2805514587 0.01708713648
#> [5669,] 0.26828152891 -0.0280867690503 0.2776774441 0.05316849763
#> [5670,] 0.26720821592 -0.0270351756391 0.2780099747 0.04899379469
#> [5671,] 0.26743821156 -0.0272605170844 0.2779387181 0.04988837389
#> [5672,] 0.26636489857 -0.0262089236732 0.2782712487 0.04571367095
#> [5673,] 0.26061500755 -0.0205753875419 0.2800526627 0.02334919090
#> [5674,] 0.26240386254 -0.0223280432272 0.2794984451 0.03030702913
#> [5675,] 0.26750429435 -0.0273453416786 0.2800422999 0.05057268248
#> [5676,] 0.27052546598 -0.0303053768276 0.2791062895 0.06232367609
#> [5677,] 0.26490335032 -0.0247970303881 0.2808481166 0.04045618448
#> [5678,] 0.25359805421 -0.0132386111057 0.2333733615 -0.01377094605
#> [5679,] 0.27143549390 -0.0307150920819 0.2278470194 0.05560864096
#> [5680,] 0.27018431761 -0.0294892346197 0.2282346551 0.05074213010
#> [5681,] 0.26800217009 -0.0273512450631 0.2289107215 0.04225456143
#> [5682,] 0.27148660404 -0.0307651679586 0.2278311846 0.05580743634
#> [5683,] 0.26654869327 -0.0263689200403 0.2760902507 0.04600127296
#> [5684,] 0.26884864968 -0.0286223344928 0.2753776851 0.05494706498
#> [5685,] 0.26635703023 -0.0261811355026 0.2761496311 0.04525579029
#> [5686,] 0.26578204113 -0.0256177818894 0.2763277726 0.04301934229
#> [5687,] 0.26189276111 -0.0218272844600 0.2796567930 0.02831907535
#> [5688,] 0.26463206293 -0.0244910746632 0.2766840554 0.03854644628
#> [5689,] 0.26437651222 -0.0242406952796 0.2767632293 0.03755246938
#> [5690,] 0.26667646862 -0.0264941097321 0.2760506637 0.04649826141
#> [5691,] 0.26233210652 -0.0222376602107 0.2773966210 0.02960065426
#> [5692,] 0.26488761364 -0.0247414540468 0.2766048814 0.03954042317
#> [5693,] 0.26427429193 -0.0241405435261 0.2767948989 0.03715487863
#> [5694,] 0.26623813231 -0.0261851179270 0.2889307998 0.04735698925
#> [5695,] 0.26864030900 -0.0285386841330 0.2881865646 0.05670037203
#> [5696,] 0.26522231823 -0.0251898598772 0.2892455162 0.04340593111
#> [5697,] 0.27362354788 -0.0334210821134 0.2866426724 0.07608292141
#> [5698,] 0.26938140606 -0.0292647843455 0.2879569601 0.05958290501
#> [5699,] 0.27009694806 -0.0299658466196 0.2877352730 0.06236604031
#> [5700,] 0.26991806256 -0.0297905810511 0.2877906948 0.06167025649
#> [5701,] 0.26979028720 -0.0296653913592 0.2878302818 0.06117326804
#> [5702,] 0.26991806256 -0.0297905810511 0.2877906948 0.06167025649
#> [5703,] 0.26416817154 -0.0241570449198 0.2895721088 0.03930577643
#> [5704,] 0.27362354788 -0.0334210821134 0.2866426724 0.07608292141
#> [5705,] 0.27030138863 -0.0301661501265 0.2876719339 0.06316122182
#> [5706,] 0.26772133553 -0.0277387022976 0.2990915548 0.05526236197
#> [5707,] 0.26746578481 -0.0274883229140 0.2991707288 0.05426838508
#> [5708,] 0.26110257209 -0.0212538762620 0.3011421603 0.02951836049
#> [5709,] 0.27037314464 -0.0302565331430 0.2897737580 0.06386759670
#> [5710,] 0.27144645763 -0.0313081265542 0.2894412273 0.06804229965
#> [5711,] 0.27014314900 -0.0300311916978 0.2898450145 0.06297301750
#> [5712,] 0.26717876074 -0.0271267908478 0.2907634324 0.05144288556
#> [5713,] 0.27057267602 -0.0304721058513 0.2918359951 0.06507096003
#> [5714,] 0.27044490066 -0.0303469161595 0.2918755821 0.06457397158
#> [5715,] 0.26801716890 -0.0279683120152 0.2926277346 0.05513119112
#> [5716,] 0.26888012303 -0.0287334871753 0.2838641554 0.05677858761
#> [5717,] 0.27105761692 -0.0308869963128 0.2853135861 0.06567533207
#> [5718,] 0.26893590713 -0.0288082214804 0.2859709279 0.05742283893
#> [5719,] 0.27093347038 -0.0307653620083 0.2853520488 0.06519245810
#> [5720,] 0.26865604568 -0.0285942604743 0.2924297997 0.05761613334
#> [5721,] 0.26875826596 -0.0286944122277 0.2923981302 0.05801372410
#> [5722,] 0.26725051676 -0.0272171738644 0.2928652565 0.05214926044
#> [5723,] 0.26903937175 -0.0289698295497 0.2923110388 0.05910709868
#> [5724,] 0.26916714710 -0.0290950192415 0.2922714518 0.05960408713
#> [5725,] 0.26680236205 -0.0269387204622 0.3099965451 0.05382435191
#> [5726,] 0.25773031178 -0.0180502523439 0.3128072206 0.01853817227
#> [5727,] 0.26744123883 -0.0275646689212 0.3097986102 0.05630929414
#> [5728,] 0.26744123883 -0.0275646689212 0.3097986102 0.05630929414
#> [5729,] 0.26864232718 -0.0287414520242 0.3094264926 0.06098098553
#> [5730,] 0.25517480466 -0.0155464585078 0.3135989601 0.00859840336
#> [5731,] 0.26654681134 -0.0266883410786 0.3100757191 0.05283037502
#> [5732,] 0.25990249283 -0.0201784771047 0.3121342419 0.02698697585
#> [5733,] 0.26428924165 -0.0241551907201 0.2767902672 0.03721302628
#> [5734,] 0.26423212606 -0.0240992309278 0.2768079626 0.03699087244
#> [5735,] 0.26405451832 -0.0239252172562 0.2768629885 0.03630005850
#> [5736,] 0.26897642503 -0.0287475241846 0.2753380981 0.05544405343
#> [5737,] 0.25824329513 -0.0182315900729 0.2786634042 0.01369702400
#> [5738,] 0.26233607475 -0.0223821015284 0.2922637789 0.03260702347
#> [5739,] 0.26015111617 -0.0202413577985 0.2929407162 0.02410852105
#> [5740,] 0.26140331465 -0.0214682167782 0.2925527638 0.02897900782
#> [5741,] 0.26799652302 -0.0279280048754 0.2905100757 0.05462361161
#> [5742,] 0.26035555674 -0.0204416613054 0.2928773770 0.02490370257
#> [5743,] 0.26756208681 -0.0275023599233 0.2906446715 0.05293385090
#> [5744,] 0.26129416699 -0.0211805663350 0.2734700816 0.02470898538
#> [5745,] 0.26512742767 -0.0249362570892 0.2722824723 0.03961863875
#> [5746,] 0.26768293479 -0.0274400509253 0.2714907327 0.04955840766
#> [5747,] 0.26563852910 -0.0254370158564 0.2721241244 0.04160659253
#> [5748,] 0.26844958693 -0.0281911890761 0.2712532108 0.05254033833
#> [5749,] 0.26819403622 -0.0279408096925 0.2713323848 0.05154636144
#> [5750,] 0.26118212832 -0.0211109529844 0.2777529038 0.02512775824
#> [5751,] 0.25977659940 -0.0197338663745 0.2781883605 0.01966088534
#> [5752,] 0.26271543259 -0.0226132292861 0.2772778600 0.03109161959
#> [5753,] 0.26251099202 -0.0224129257792 0.2773411992 0.03029643808
#> [5754,] 0.26194878045 -0.0218620911353 0.2775153819 0.02810968892
#> [5755,] 0.26617027640 -0.0259780817634 0.2740834353 0.04410212581
#> [5756,] 0.25656156963 -0.0165638169396 0.2770603761 0.00672859470
#> [5757,] 0.25849097750 -0.0184541812858 0.2764626127 0.01423312023
#> [5758,] 0.26617027640 -0.0259780817634 0.2740834353 0.04410212581
#> [5759,] 0.26864911830 -0.0284067617845 0.2733154480 0.05374370166
#> [5760,] 0.26826579223 -0.0280311927090 0.2734342089 0.05225273632
#> [5761,] 0.26443253155 -0.0242755019548 0.2746218182 0.03734308295
#> [5762,] 0.26391262083 -0.0239066655361 0.2896512827 0.03831179954
#> [5763,] 0.26685145402 -0.0267860284477 0.2887407823 0.04974253379
#> [5764,] 0.26621257724 -0.0261600799887 0.2889387171 0.04725759156
#> [5765,] 0.27088915526 -0.0307420227088 0.2874898338 0.06544736867
#> [5766,] 0.26774588151 -0.0276623562903 0.2884636734 0.05322145291
#> [5767,] 0.26672367866 -0.0266608387559 0.2887803692 0.04924554535
#> [5768,] 0.25656553786 -0.0167082582573 0.2919275340 0.00973496392
#> [5769,] 0.26186821513 -0.0219036304672 0.2902846744 0.03035998441
#> [5770,] -4.59844944633 0.3344806367524 0.0674373277 1.14221277151
#> [5771,] 0.26959956513 -0.0293178963024 0.2708969280 0.05701323434
#> [5772,] 0.26461632625 -0.0244354983219 0.2724408202 0.03763068496
#> [5773,] 0.26947178978 -0.0291927066106 0.2709365150 0.05651624590
#> [5774,] 0.26551075374 -0.0253118261646 0.2721637113 0.04110960408
#> [5775,] 0.26998800222 -0.0296984729655 0.2707765836 0.05852407922
#> [5776,] 0.27004677888 -0.0297560602237 0.2707583736 0.05875269390
#> [5777,] -13.57728437680 1.2598347746132 -0.3018310091 3.03773760978
#> [5778,] 0.26583806047 -0.0256525885647 0.2741863615 0.04280995585
#> [5779,] 0.26634916189 -0.0261533473319 0.2740280136 0.04479790964
#> [5780,] 0.27324903112 -0.0329135906895 0.2718903168 0.07163528570
#> [5781,] 0.26609361118 -0.0259029679483 0.2741071875 0.04380393274
#> [5782,] 0.26366587942 -0.0235243638040 0.2748593401 0.03436115228
#> [5783,] 0.26024149988 -0.0201692800636 0.2759202711 0.02104186193
#> [5784,] 0.26228590557 -0.0221723151325 0.2752868795 0.02899367706
#> [5785,] 0.26123814766 -0.0211457596597 0.2756114927 0.02491837181
#> [5786,] 0.26302700264 -0.0228984153450 0.2750572750 0.03187621005
#> [5787,] 0.26781857849 -0.0275930287877 0.2735727633 0.05051327676
#> [5788,] 0.26749914010 -0.0272800545582 0.2736717308 0.04927080565
#> [5789,] 0.26072704623 -0.0206450008925 0.2757698406 0.02293041803
#> [5790,] 0.26558250976 -0.0254022091811 0.2742655354 0.04181597896
#> [5791,] 0.27401568325 -0.0336647288403 0.2716527949 0.07461721637
#> [5792,] 0.26456030691 -0.0244006916467 0.2745822313 0.03784007140
#> [5793,] 0.26540362426 -0.0252269436126 0.2743209572 0.04112019514
#> [5794,] 0.26739691981 -0.0271799028048 0.2737034003 0.04887321489
#> [5795,] 0.26808690674 -0.0278559271405 0.2734896307 0.05155695250
#> [5796,] 0.26162147372 -0.0215213287351 0.2754927317 0.02640933715
#> [5797,] 0.26431753373 -0.0241628312322 0.2746574465 0.03689579335
#> [5798,] 0.26686026332 -0.0266541060992 0.2738696656 0.04678586342
#> [5799,] 0.26123814766 -0.0211457596597 0.2756114927 0.02491837181
#> [5800,] 0.26894206066 -0.0288544085948 0.2902171321 0.05830132611
#> [5801,] 0.26462325363 -0.0246229970117 0.2915551720 0.04150311665
#> [5802,] 0.26385660149 -0.0238718588609 0.2917926938 0.03852118598
#> [5803,] 0.26848206938 -0.0284037257043 0.2903596452 0.05651216771
#> [5804,] 0.26469991884 -0.0246981108268 0.2915314198 0.04180130972
#> [5805,] 0.26551768112 -0.0254993248544 0.2912780631 0.04498203577
#> [5806,] 0.26799652302 -0.0279280048754 0.2905100757 0.05462361161
#> [5807,] 0.26743431146 -0.0273771702315 0.2906842584 0.05243686245
#> [5808,] 0.26334550007 -0.0233711000936 0.2919510417 0.03653323219
#> [5809,] 0.26500657969 -0.0249985660871 0.2914364110 0.04299408199
#> [5810,] 0.26500657969 -0.0249985660871 0.2914364110 0.04299408199
#> [5811,] 0.26507046737 -0.0250611609330 0.2914166175 0.04324257621
#> [5812,] 0.26890372805 -0.0288168516872 0.2902290082 0.05815222958
#> [5813,] 0.27037314464 -0.0302565331430 0.2897737580 0.06386759670
#> [5814,] 0.26321772471 -0.0232459104018 0.2919906287 0.03603624375
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#> [5821,] 0.25262810684 -0.0129107423232 0.2995195831 -0.00429803592
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#> [5827,] 0.26634553045 -0.0261698684303 0.2761531940 0.04521106133
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#> [5832,] 0.26769867147 -0.0274956272665 0.2757339679 0.05047416897
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#> [5838,] 0.26667646862 -0.0264941097321 0.2760506637 0.04649826141
#> [5839,] 0.26629314256 -0.0261185406567 0.2761694246 0.04500729607
#> [5840,] 0.26604451922 -0.0260556599628 0.2953629504 0.04788575086
#> [5841,] 0.27000555525 -0.0299365404089 0.2941357541 0.06329239268
#> [5842,] 0.26719449742 -0.0271823671891 0.2950066676 0.05235864688
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#> [5844,] 0.26949445383 -0.0294357816416 0.2942941020 0.06130443890
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#> [5846,] 0.26723478008 -0.0271615975231 0.2886220213 0.05123349913
#> [5847,] 0.26460534214 -0.0245853689313 0.2894366659 0.04100617270
#> [5848,] 0.27005666540 -0.0299866162856 0.2941199193 0.06349118806
#> [5849,] 0.27345548987 -0.0333166620876 0.2930669057 0.07671108071
#> [5850,] 0.26862558141 -0.0285844917373 0.2945632934 0.05792491747
#> [5851,] 0.26908846371 -0.0288171375352 0.2710552759 0.05502528056
#> [5852,] 0.26832181157 -0.0280659993843 0.2712927978 0.05204334989
#> [5853,] 0.26855180721 -0.0282913408296 0.2712215413 0.05293792909
#> [5854,] 0.26669899643 -0.0262149958336 0.2441828542 0.04017673885
#> [5855,] 0.26683954932 -0.0263527044946 0.2441393085 0.04072342614
#> [5856,] 0.27198889616 -0.0313978490744 0.2425439533 0.06075206049
#> [5857,] 0.27105613607 -0.0304839643242 0.2428329383 0.05712404484
#> [5858,] 0.26521680230 -0.0247627954086 0.2446420631 0.03441167288
#> [5859,] 0.27032781654 -0.0297703830809 0.2430585840 0.05429121070
#> [5860,] 0.26905006298 -0.0285184861628 0.2434544538 0.04932132625
#> [5861,] 0.26630289282 -0.0258269077890 0.2443055738 0.03863607467
#> [5862,] 0.27071114260 -0.0301459521563 0.2429398231 0.05578217604
#> [5863,] 0.26905006298 -0.0285184861628 0.2434544538 0.04932132625
#> [5864,] 0.26917783833 -0.0286436758546 0.2434148668 0.04981831469
#> [5865,] 0.26726120799 -0.0267658304775 0.2440086715 0.04236348801
#> [5866,] 0.26743431146 -0.0273771702315 0.2906842584 0.05243686245
#> [5867,] 0.27055203014 -0.0304317987115 0.2897183362 0.06456338053
#> [5868,] 0.25874558725 -0.0188642711886 0.2933761729 0.01864164815
#> [5869,] 0.26638655354 -0.0263506147586 0.2910088717 0.04836155720
#> [5870,] 0.26891650559 -0.0288293706564 0.2902250495 0.05820192842
#> [5871,] 0.26935094180 -0.0292550156086 0.2900904538 0.05989168914
#> [5872,] 0.26756208681 -0.0275023599233 0.2906446715 0.05293385090
#> [5873,] 0.26494269202 -0.0249359712412 0.2914562045 0.04274558776
#> [5874,] 0.26360105078 -0.0236214794773 0.2918718678 0.03752720909
#> [5875,] 0.26845651430 -0.0283786877659 0.2903675626 0.05641277002
#> [5876,] 0.26385660149 -0.0238718588609 0.2917926938 0.03852118598
#> [5877,] 0.26748542160 -0.0274272461082 0.2906684237 0.05263565783
#> [5878,] -0.61967714684 0.8417826862310 0.5655264722 -3.39802618942
#> [5879,] 0.26866095487 -0.0285789912728 0.2903042235 0.05720795153
#> [5880,] 0.26730653610 -0.0272519805396 0.2907238454 0.05193987401
#> [5881,] 0.26679543468 -0.0267512217724 0.2908821933 0.04995192023
#> [5882,] 0.26615655790 -0.0261252733134 0.2910801282 0.04746697800
#> [5883,] 0.26717876074 -0.0271267908478 0.2907634324 0.05144288556
#> [5884,] 0.26822651866 -0.0281533463207 0.2904388192 0.05551819082
#> [5885,] 0.26827762881 -0.0282034221974 0.2904229844 0.05571698619
#> [5886,] 0.26257884793 -0.0226199619428 0.2921885636 0.03355130152
#> [5887,] 0.25504010193 -0.0152337701262 0.2945241953 0.00422898323
#> [5888,] 0.26871206502 -0.0286290671495 0.2902883887 0.05740674691
#> [5889,] 0.27356752854 -0.0333862754382 0.2887840835 0.07629230784
#> [5890,] 0.26935094180 -0.0292550156086 0.2900904538 0.05989168914
#> [5891,] 0.27356752854 -0.0333862754382 0.2887840835 0.07629230784
#> [5892,] 0.26449547827 -0.0244978073199 0.2915947589 0.04100612820
#> [5893,] 0.26531324055 -0.0252990213475 0.2913414023 0.04418685426
#> [5894,] 0.26883984037 -0.0287542568413 0.2902488017 0.05790373536
#> [5895,] 0.26903150341 -0.0289420413790 0.2901894212 0.05864921802
#> [5896,] 0.26807318824 -0.0280031186905 0.2904863236 0.05492180468
#> [5897,] 0.26942760701 -0.0293301294236 0.2900667016 0.06018988221
#> [5898,] 0.27078202578 -0.0306571401568 0.2896470796 0.06545795973
#> [5899,] 0.26952982729 -0.0294302811771 0.2900350320 0.06058747296
#> [5900,] 0.26845651430 -0.0283786877659 0.2903675626 0.05641277002
#> [5901,] 0.26717876074 -0.0271267908478 0.2907634324 0.05144288556
#> [5902,] 0.26372882613 -0.0237466691691 0.2918322808 0.03802419753
#> [5903,] 0.26771541724 -0.0276525875534 0.2905971671 0.05353023703
#> [5904,] 0.26705098539 -0.0270016011560 0.2908030194 0.05094589712
#> [5905,] 0.27356752854 -0.0333862754382 0.2887840835 0.07629230784
#> [5906,] 0.26168442044 -0.0217436341002 0.2924656725 0.03007238240
#> [5907,] 0.26628433325 -0.0262504630052 0.2910405412 0.04796396644
#> [5908,] 0.25881734327 -0.0189546542051 0.2954779970 0.01934802303
#> [5909,] 0.26456723429 -0.0245881903364 0.2936965830 0.04171250308
#> [5910,] 0.26970380360 -0.0296208159471 0.2921051865 0.06169143860
#> [5911,] 0.26354503144 -0.0235866728020 0.2940132789 0.03773659552
#> [5912,] 0.26679052548 -0.0267664909739 0.2930077696 0.05036010204
#> [5913,] 0.26643275448 -0.0264159598368 0.2931186132 0.04896853439
#> [5914,] 0.26944825288 -0.0293704365635 0.2921843605 0.06069746171
#> [5915,] 0.26277837930 -0.0228355346511 0.2942508007 0.03475466485
#> [5916,] 0.26822160947 -0.0281686155221 0.2925643955 0.05592637263
#> [5917,] 0.26546166178 -0.0254645181791 0.2934194742 0.04519142220
#> [5918,] 0.26857938046 -0.0285191466592 0.2924535519 0.05731794028
#> [5919,] 0.26725051676 -0.0272171738644 0.2928652565 0.05214926044
#> [5920,] 0.26980602388 -0.0297209677005 0.2920735169 0.06208902935
#> [5921,] 0.26303393001 -0.0230859140348 0.2941716268 0.03574864174
#> [5922,] 0.26533388642 -0.0253393284873 0.2934590612 0.04469443376
#> [5923,] 0.26694385591 -0.0269167186040 0.2929602652 0.05095648817
#> [5924,] 0.26277837930 -0.0228355346511 0.2942508007 0.03475466485
#> [5925,] 0.27351150921 -0.0333514687629 0.2909254946 0.07650169428
#> [5926,] 0.27008712966 -0.0299963850225 0.2919864256 0.06318240393
#> [5927,] 0.26175617645 -0.0218340171167 0.2945674966 0.03077875728
#> [5928,] 0.26737829212 -0.0273423635562 0.2928256695 0.05264624889
#> [5929,] 0.26930769999 -0.0292327279025 0.2922279062 0.06015077442
#> [5930,] 0.26814494425 -0.0280935017070 0.2925881477 0.05562817956
#> [5931,] 0.26270171409 -0.0227604208361 0.2942745529 0.03445647178
#> [5932,] 0.27010084816 -0.0298491934725 0.2749897327 0.05981755175
#> [5933,] 0.27178748286 -0.0315016974044 0.2744671846 0.06637779923
#> [5934,] 0.27011873671 -0.0298667200294 0.2749841905 0.05988713013
#> [5935,] 0.26923197574 -0.0289979035682 0.2752589241 0.05643803032
#> [5936,] 0.26644647298 -0.0262687682868 0.2761219203 0.04560368220
#> [5937,] 0.26999862788 -0.0297490417191 0.2750214023 0.05941996099
#> [5938,] 0.26884864968 -0.0286223344928 0.2753776851 0.05494706498
#> [5939,] -33.09504154369 -0.5456000892442 -0.8223579365 6.49352554138
#> [5940,] 0.26861764495 -0.0282956091019 0.2648289776 0.05191217903
#> [5941,] 0.26933318694 -0.0289966713761 0.2646072905 0.05469531433
#> [5942,] 0.26817043120 -0.0278574451806 0.2649675320 0.05017271947
#> [5943,] 0.27155647813 -0.0311749720135 0.2639184771 0.06334291328
#> [5944,] 0.27155647813 -0.0311749720135 0.2639184771 0.06334291328
#> [5945,] 0.27130092742 -0.0309245926299 0.2639976511 0.06234893639
#> [5946,] 0.27202924695 -0.0316381738732 0.2637720053 0.06518177053
#> [5947,] 0.17555714100 0.0628817209827 0.2936607041 -0.31005116556
#> [5948,] 0.27068760571 -0.0303236821092 0.2641876686 0.05996339185
#> [5949,] 0.26898819348 -0.0286586592082 0.2647141754 0.05335344552
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#> [5951,] 0.27104537671 -0.0306742132463 0.2640768250 0.06135495950
#> [5952,] 0.27015094922 -0.0297978854036 0.2643539339 0.05787604038
#> [5953,] 0.27109648685 -0.0307242891230 0.2640609902 0.06155375487
#> [5954,] 0.27040649993 -0.0300482647872 0.2642747599 0.05887001727
#> [5955,] 0.21727285345 -0.0438911868638 0.3836188868 0.09845399906
#> [5956,] 0.20895924634 -0.0344205964019 0.2460069316 0.03791758054
#> [5957,] 0.20258937874 -0.0290430289192 0.3393148043 0.03151455538
#> [5958,] 0.20285770699 -0.0293059272720 0.3392316716 0.03255823112
#> [5959,] 0.20425045837 -0.0306704949127 0.3388001736 0.03797540517
#> [5960,] 0.21006423707 -0.0363666258899 0.3369989661 0.06058837945
#> [5961,] 0.21019201243 -0.0364918155817 0.3369593791 0.06108536789
#> [5962,] 0.21000034939 -0.0363040310440 0.3370187596 0.06033988523
#> [5963,] 0.20948924797 -0.0358032722768 0.3371771075 0.05835193144
#> [5964,] 0.21044756314 -0.0367421949653 0.3368802051 0.06207934479
#> [5965,] 0.20987257404 -0.0361788413522 0.3370583465 0.05984289678
#> [5966,] 0.18664301432 -0.0134193553818 0.3442552591 -0.03050960263
#> [5967,] 0.19843667968 -0.0249743639355 0.3406013811 0.01536243090
#> [5968,] 0.21839324023 -0.0445873203692 0.3407906653 0.09426627038
#> [5969,] 0.21839324023 -0.0445873203692 0.3407906653 0.09426627038
#> [5970,] 0.21062725335 -0.0362355610851 0.2646066527 0.04825086202
#> [5971,] 0.21350219886 -0.0390523291508 0.2637159457 0.05943310205
#> [5972,] 0.22046595576 -0.0458751673543 0.2615584554 0.08651897233
#> [5973,] 0.21024392728 -0.0358599920097 0.2647254136 0.04675989668
#> [5974,] 0.21217972392 -0.0377566158406 0.2641256709 0.05428927163
#> [5975,] 0.20743286945 -0.0331058187900 0.2655963272 0.03582615088
#> [5976,] 0.22046595576 -0.0458751673543 0.2615584554 0.08651897233
#> [5977,] 0.21018003960 -0.0357973971638 0.2647452071 0.04651140246
#> [5978,] 0.20909394908 -0.0347332847835 0.2650816964 0.04228700067
#> [5979,] 0.20832729694 -0.0339821466326 0.2653192183 0.03930507000
#> [5980,] 0.22046595576 -0.0458751673543 0.2615584554 0.08651897233
#> [5981,] 0.20796952594 -0.0336316154956 0.2654300618 0.03791350235
#> [5982,] 0.21055866085 -0.0369715188350 0.3495901172 0.06507512295
#> [5983,] 0.21732887279 -0.0439259935391 0.3814774757 0.09824461263
#> [5984,] 0.20202138514 -0.0289282684606 0.3862199957 0.03870539684
#> [5985,] 0.18967337656 -0.0168502134336 0.3921696741 -0.00889550519
#> [5986,] 0.18916227514 -0.0163494546664 0.3923280220 -0.01088345898
#> [5987,] 0.20561382270 -0.0323877722269 0.3787348315 0.05139652788
#> [5988,] 0.19628622171 -0.0232489247250 0.3816246808 0.01511637135
#> [5989,] 0.20007919973 -0.0270253851452 0.3868217178 0.03115117247
#> [5990,] 0.21564889296 -0.0414166104379 0.2906635827 0.07333736571
#> [5991,] 0.21513779154 -0.0409158516707 0.2908219306 0.07134941193
#> [5992,] 0.19404329373 -0.0211317008934 0.3908157994 0.00810149965
#> [5993,] 0.19312331117 -0.0202303351124 0.3911008256 0.00452318284
#> [5994,] 0.19249721193 -0.0196169056225 0.3912948018 0.00208793946
#> [5995,] 0.18972262118 -0.0168984615408 0.3921544172 -0.00870396585
#> [5996,] 0.18532901446 -0.0125937639122 0.3935156313 -0.02579311234
#> [5997,] 0.17127372530 0.0011771021866 0.3978701989 -0.08046184136
#> [5998,] 0.18629719388 -0.0135423512449 0.3932156729 -0.02202733149
#> [5999,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
#> [6000,] 0.31508125633 -0.0994417525916 -3.9075388191 -0.37823187003
#> [6001,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
#> [6002,] 0.31048134351 -0.0949349236866 -3.9061136879 -0.39612345407
#> [6003,] 0.32198112555 -0.1062019959492 -3.9096765159 -0.35139449397
#> [6004,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
#> [6005,] 0.30986802180 -0.0943340131659 -3.9059236704 -0.39850899861
#> [6006,] 0.27180090385 -0.0316754792449 0.2914554692 0.06984821176
#> [6007,] 0.26878382103 -0.0287194501661 0.2923902128 0.05811312179
#> [6008,] 0.26648386463 -0.0264660357135 0.2931027784 0.04916732977
#> [6009,] -0.64450259357 -0.7549783795705 0.2276772470 0.10725748792
#> [6010,] -0.02296358655 -0.1839470737648 0.3172810719 -0.08213798212
#> [6011,] 0.04197443472 -0.1251853900861 0.2534312984 0.09357968200
#> [6012,] -0.16500273901 -0.4515650639552 0.3201477702 -0.07532303671
#> [6013,] -1.01278223339 0.8748929966563 -4.1858744197 1.10578411781
#> [6014,] -1.01123934597 0.8733813311277 -4.1863524324 1.11178525330
#> [6015,] 0.34787468047 -0.0763759230334 -3.9168025846 -0.30474282320
#> [6016,] 0.36317107361 -0.0874939665246 -3.9145444754 -0.31315793171
#> [6017,] 0.36427385220 -0.0882285199062 -3.9142605180 -0.31494053986
#> [6018,] 0.34985002839 -0.0781870390799 -3.9171898448 -0.29924078640
#> [6019,] -1.73240603659 1.2059926177070 0.3137908344 -1.16963030962
#> [6020,] -11.29873654145 7.9144308243084 0.0048750406 -4.74674636231
#> [6021,] 0.24710005226 -0.0497041524373 0.3418923499 0.08458438033
#> [6022,] 0.24710005226 -0.0497041524373 0.3418923499 0.08458438033
#> [6023,] 0.24710005226 -0.0497041524373 0.3418923499 0.08458438033
#> [6024,] 0.24710005226 -0.0497041524373 0.3418923499 0.08458438033
#> [6025,] 0.24710005226 -0.0497041524373 0.3418923499 0.08458438033
#> [6026,] 0.24710005226 -0.0497041524373 0.3418923499 0.08458438033
#> [6027,] 0.24710005226 -0.0497041524373 0.3418923499 0.08458438033
#> [6028,] 0.24624395738 -0.0488653815022 0.3421575826 0.08125455774
#> [6029,] 0.24710005226 -0.0497041524373 0.3418923499 0.08458438033
#> [6030,] 0.24710005226 -0.0497041524373 0.3418923499 0.08458438033
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#> [7105,] 0.21749693081 -0.0440304135649 0.3750532425 0.09761645332
#> [7106,] 0.21749693081 -0.0440304135649 0.3750532425 0.09761645332
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#> [7109,] 0.21749693081 -0.0440304135649 0.3750532425 0.09761645332
#> [7110,] 0.21749693081 -0.0440304135649 0.3750532425 0.09761645332
#> [7111,] 0.21419144919 -0.0406713474000 0.3633330049 0.08219596402
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#> [7125,] 0.35916878648 -0.0846977147811 -3.9153392725 -0.30897654725
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#> [7784,] 0.10447335791 -0.0153048577970 0.1487661299 0.08797227431
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#> [8921,] 0.27379160590 -0.0335255021393 0.2802184392 0.07545476211
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#> [8925,] 0.26871481978 -0.0278888411273 0.2116974878 0.04160823604
#> [8926,] 0.26355269540 -0.0228311775783 0.2132968017 0.02152990284
#> [8927,] 0.26797372272 -0.0271627409148 0.2119270923 0.03872570305
#> [8928,] 0.27100697598 -0.0303755618739 0.2364760029 0.05565100518
#> [8929,] 0.26817036307 -0.0275963507158 0.2373548338 0.04461786169
#> [8930,] 0.26616646217 -0.0256330007792 0.2379756764 0.03682359190
#> [8931,] 0.26784218351 -0.0276763932996 0.2799376161 0.05188691873
#> [8932,] 0.26643665459 -0.0262993066897 0.2803730728 0.04642004583
#> [8933,] 0.27112782396 -0.0303132528760 0.2173220641 0.05227556194
#> [8934,] 0.27087227324 -0.0300628734924 0.2174012381 0.05128158505
#> [8935,] 0.26780566470 -0.0270583208890 0.2183513255 0.03935386236
#> [8936,] 0.26836787627 -0.0276091555329 0.2181771428 0.04154061152
#> [8937,] 0.27134504206 -0.0305260753520 0.2172547663 0.05312044230
#> [8938,] 0.26857231684 -0.0278094590398 0.2181138037 0.04233579303
#> [8939,] 0.26908341826 -0.0283102178071 0.2179554558 0.04432374681
#> [8940,] 0.26473905616 -0.0240537682856 0.2193014130 0.02742613966
#> [8941,] 0.26742233863 -0.0266827518136 0.2184700865 0.03786289702
#> [8942,] 0.26742233863 -0.0266827518136 0.2184700865 0.03786289702
#> [8943,] 0.26706456764 -0.0263322206765 0.2185809300 0.03647132937
#> [8944,] 0.26490523225 -0.0244776093498 0.2468626482 0.03362708242
#> [8945,] 0.26487114178 -0.0244442087400 0.2468732100 0.03349448590
#> [8946,] 0.26579965974 -0.0253539371924 0.2465855393 0.03710600154
#> [8947,] 0.26464968153 -0.0242272299661 0.2469418221 0.03263310553
#> [8948,] 0.26123693547 -0.0206425956223 0.2225104849 0.01423174772
#> [8949,] 0.26706954825 -0.0263571795601 0.2207034423 0.03691797809
#> [8950,] 0.26746853958 -0.0267480968917 0.2205798280 0.03846987421
#> [8951,] 0.26731520915 -0.0265978692616 0.2206273323 0.03787348807
#> [8952,] 0.26283715341 -0.0221301153042 0.2135184888 0.01874676754
#> [8953,] 0.26554599095 -0.0247841367705 0.2126792449 0.02928292259
#> [8954,] 0.26617809564 -0.0254034501758 0.2124834081 0.03174152443
#> [8955,] 0.26232605198 -0.0216293565370 0.2136768367 0.01675881376
#> [8956,] 0.26733296401 -0.0268562134941 0.2461104956 0.04306986289
#> [8957,] 0.26618298581 -0.0257295062678 0.2464667784 0.03859696688
#> [8958,] 0.26636187130 -0.0259047718364 0.2464113566 0.03929275070
#> [8959,] 0.26554410903 -0.0251035578088 0.2466647133 0.03611202465
#> [8960,] 0.26141689690 -0.0207988362987 0.2203306744 0.01450444007
#> [8961,] 0.26011358827 -0.0195219014422 0.2207344616 0.00943515793
#> [8962,] 0.26908341826 -0.0283102178071 0.2179554558 0.04432374681
#> [8963,] 0.26933896897 -0.0285605971907 0.2178762818 0.04531772370
#> [8964,] 0.26767788935 -0.0269331311972 0.2183909125 0.03885687391
#> [8965,] 0.26626355113 -0.0256879669358 0.2336974859 0.03634667138
#> [8966,] 0.26575244970 -0.0251872081686 0.2338558338 0.03435871760
#> [8967,] 0.26741352933 -0.0268146741621 0.2333412031 0.04081956739
#> [8968,] 0.26741352933 -0.0268146741621 0.2333412031 0.04081956739
#> [8969,] 0.26680424398 -0.0266192994239 0.2760110767 0.04699524985
#> [8970,] 0.26629314256 -0.0261185406567 0.2761694246 0.04500729607
#> [8971,] 0.27524810871 -0.0344304756963 0.2245417512 0.07001071483
#> [8972,] 0.26740270185 -0.0267438286194 0.2269723916 0.03949562427
#> [8973,] 0.26249612818 -0.0219365444540 0.2284925316 0.02041126796
#> [8974,] 0.26131683105 -0.0214236413660 0.2968276686 0.02949717838
#> [8975,] 0.26272235996 -0.0228007279759 0.2963922118 0.03496405128
#> [8976,] 0.25467251254 -0.0149137773921 0.2988861914 0.00365377921
#> [8977,] 0.27102083073 -0.0307505592535 0.2747047065 0.06339586856
#> [8978,] 0.27508005069 -0.0343260556705 0.2309659844 0.07063887413
#> [8979,] 0.26268584116 -0.0221826555653 0.2348059213 0.02243099490
#> [8980,] 0.26650336516 -0.0258827699782 0.2293750768 0.03642488696
#> [8981,] 0.25640911204 -0.0159927843255 0.2325024480 -0.00283720024
#> [8982,] 0.26484228553 -0.0242553039847 0.2298897075 0.02996403717
#> [8983,] 0.26162840110 -0.0217088274249 0.2946070835 0.03028176883
#> [8984,] 0.27351150921 -0.0333514687629 0.2909254946 0.07650169428
#> [8985,] 0.27019815925 -0.0299646144274 0.2770836394 0.06062332432
#> [8986,] 0.26830708398 -0.0281118069887 0.2776695267 0.05326789532
#> [8987,] 0.26662044929 -0.0264593030568 0.2781920748 0.04670764784
#> [8988,] 0.26779598256 -0.0276110482214 0.2778278746 0.05127994154
#> [8989,] 0.26547047108 -0.0253325958306 0.2785483576 0.04223475183
#> [8990,] 0.27390364458 -0.0335951154898 0.2759356170 0.07503598924
#> [8991,] 0.27089782832 -0.0300879114307 0.2173933207 0.05138098274
#> [8992,] 0.27061672253 -0.0298124941087 0.2174804120 0.05028760816
#> [8993,] 0.27048894718 -0.0296873044169 0.2175199990 0.04979061971
#> [8994,] 0.27074449789 -0.0299376838005 0.2174408251 0.05078459660
#> [8995,] 0.27412772193 -0.0337343421909 0.2673699727 0.07419844350
#> [8996,] 0.26684452664 -0.0265985297579 0.2696264305 0.04587010210
#> [8997,] 0.26083908491 -0.0207146142430 0.2714870184 0.02251164516
#> [8998,] 0.26035353856 -0.0202388934141 0.2716374489 0.02062308907
#> [8999,] 0.26638453536 -0.0261478468674 0.2697689436 0.04408094370
#> [9000,] 0.26748340342 -0.0272244782169 0.2694284956 0.04835504433
#> [9001,] 0.26160573704 -0.0214657523938 0.2712494966 0.02549357583
#> [9002,] 0.26211683847 -0.0219665111611 0.2710911487 0.02748152962
#> [9003,] 0.26633342522 -0.0260977709907 0.2697847784 0.04388214832
#> [9004,] 0.27362354788 -0.0334210821134 0.2866426724 0.07608292141
#> [9005,] 0.25754940810 -0.0176722188842 0.2916227142 0.01356177495
#> [9006,] 0.26276264262 -0.0227799583099 0.2900075656 0.03383890353
#> [9007,] 0.26393817590 -0.0239317034745 0.2896433654 0.03841119723
#> [9008,] 0.26340151940 -0.0234059067689 0.2898096307 0.03632384576
#> [9009,] 0.27362354788 -0.0334210821134 0.2866426724 0.07608292141
#> [9010,] 0.26838475829 -0.0282883047494 0.2882657385 0.05570639514
#> [9011,] 0.26467927296 -0.0246578036870 0.2894137609 0.04129373022
#> [9012,] 0.26212376584 -0.0221540098508 0.2902055004 0.03135396130
#> [9013,] 0.26757075986 -0.0268482486452 0.2205481584 0.03886746497
#> [9014,] 0.25880537044 -0.0182602357873 0.2232638251 0.00477405760
#> [9015,] 0.26736631929 -0.0266479451383 0.2206114976 0.03807228345
#> [9016,] 0.27395966391 -0.0336299221651 0.2737942060 0.07482660281
#> [9017,] 0.26463206293 -0.0244910746632 0.2766840554 0.03854644628
#> [9018,] 0.26669408723 -0.0262302650350 0.2463084305 0.04058492066
#> [9019,] 0.25915534123 -0.0188440732185 0.2486440622 0.01126260237
#> [9020,] 0.25762203696 -0.0173417969168 0.2491191059 0.00529874102
#> [9021,] 0.27474393466 -0.0341172156189 0.2438144509 0.07189519273
#> [9022,] 0.26337192797 -0.0229753330481 0.2473376919 0.02766322107
#> [9023,] 0.26666752307 -0.0261038431511 0.2356963838 0.03834521622
#> [9024,] 0.26965746640 -0.0290332819393 0.2347700486 0.04997474585
#> [9025,] 0.26610531150 -0.0255530085071 0.2358705665 0.03615846706
#> [9026,] 0.26352929476 -0.0235310964607 0.2897700437 0.03682083421
#> [9027,] 0.26273708755 -0.0227549203715 0.2900154829 0.03373950584
#> [9028,] 0.27362354788 -0.0334210821134 0.2866426724 0.07608292141
#> [9029,] 0.25565575177 -0.0158168826137 0.2922094012 0.00619630679
#> [9030,] 0.26391262083 -0.0239066655361 0.2896512827 0.03831179954
#> [9031,] 0.26365707012 -0.0236562861525 0.2897304567 0.03731782265
#> [9032,] 0.25880160659 -0.0188990778639 0.2912347619 0.01843226172
#> [9033,] 0.26429594690 -0.0242822346116 0.2895325218 0.03980276488
#> [9034,] 0.25870819561 -0.0186670037619 0.2763953148 0.01507800059
#> [9035,] 0.27005464722 -0.0297838483943 0.2728799912 0.05921057456
#> [9036,] 0.26605521045 -0.0256043165760 0.2465063654 0.03809997843
#> [9037,] 0.27474393466 -0.0341172156189 0.2438144509 0.07189519273
#> [9038,] 0.26047149552 -0.0203946215088 0.2758490145 0.02193644114
#> [9039,] 0.27401568325 -0.0336647288403 0.2716527949 0.07461721637
#> [9040,] 0.25996039410 -0.0198938627416 0.2760073625 0.01994848735
#> [9041,] 0.25663823484 -0.0166389307546 0.2770366239 0.00702678777
#> [9042,] 0.26839356759 -0.0281563824009 0.2733946219 0.05274972477
#> [9043,] 0.27067375096 -0.0299486847296 0.2259589650 0.05221852847
#> [9044,] 0.26788939354 -0.0278431223234 0.2926673216 0.05463420267
#> [9045,] 0.26137285039 -0.0214584480413 0.2946862575 0.02928779194
#> [9046,] 0.26712274141 -0.0270919841726 0.2929048435 0.05165227200
#> [9047,] 0.26725051676 -0.0272171738644 0.2928652565 0.05214926044
#> [9048,] 0.25971177076 -0.0198309820478 0.2952008882 0.02282694215
#> [9049,] 0.26265060395 -0.0227103449593 0.2942903877 0.03425767640
#> [9050,] 0.27019224097 -0.0298784996832 0.2685892517 0.05889119938
#> [9051,] 0.26205849624 -0.0219093495478 0.2711092241 0.02725460469
#> [9052,] 0.26085679457 -0.0207319655343 0.2714815317 0.02258052776
#> [9053,] 0.26154381711 -0.0214050854692 0.2712686804 0.02525273523
#> [9054,] 0.26569454844 -0.0254718225316 0.2699827133 0.04139720609
#> [9055,] 0.26576832263 -0.0257649734394 0.2933244654 0.04638419447
#> [9056,] 0.26966627570 -0.0289013595908 0.2198989320 0.04701807547
#> [9057,] 0.27056070319 -0.0297776874335 0.2196218231 0.05049699459
#> [9058,] 0.26953850035 -0.0287761698990 0.2199385189 0.04652108703
#> [9059,] 0.26457886648 -0.0239771364305 0.2278472638 0.02851217962
#> [9060,] 0.26548607151 -0.0248659832423 0.2275661963 0.03204079758
#> [9061,] 0.27524810871 -0.0344304756963 0.2245417512 0.07001071483
#> [9062,] 0.26760714242 -0.0269441321263 0.2269090525 0.04029080578
#> [9063,] 0.26809268877 -0.0274198529551 0.2267586219 0.04217936187
#> [9064,] 0.26280292528 -0.0227591886439 0.2836229193 0.03271375578
#> [9065,] 0.26459178027 -0.0245118443292 0.2830687016 0.03967159402
#> [9066,] 0.26331402671 -0.0232599474111 0.2834645714 0.03470170957
#> [9067,] 0.26471955562 -0.0246370340210 0.2830291146 0.04016858247
#> [9068,] 0.27328050447 -0.0330247433720 0.2803767871 0.07346680833
#> [9069,] 0.26791393952 -0.0277667763162 0.2820394402 0.05259329361
#> [9070,] 0.26740283810 -0.0272660175489 0.2821977881 0.05060533983
#> [9071,] 0.26677673886 -0.0266525880591 0.2823917643 0.04817009644
#> [9072,] 0.25916132764 -0.0191912824274 0.2847511482 0.01854958508
#> [9073,] 0.27379160590 -0.0335255021393 0.2802184392 0.07545476211
#> [9074,] 0.25909743996 -0.0191286875815 0.2847709417 0.01830109086
#> [9075,] 0.25526417928 -0.0153729968273 0.2859585510 0.00339143749
#> [9076,] 0.26574754051 -0.0252024773701 0.2359814101 0.03476689941
#> [9077,] 0.26518532894 -0.0246516427261 0.2361555928 0.03258015025
#> [9078,] 0.26850748820 -0.0279065747131 0.2351263314 0.04550184984
#> [9079,] 0.26657424834 -0.0263939579786 0.2760823333 0.04610067065
#> [9080,] 0.26682979905 -0.0266443373623 0.2760031593 0.04709464754
#> [9081,] 0.26700868455 -0.0268196029308 0.2759477376 0.04779043136
#> [9082,] 0.26583315127 -0.0256678577662 0.2763119378 0.04321813766
#> [9083,] 0.26565426578 -0.0254925921976 0.2763673595 0.04252235384
#> [9084,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
#> [9085,] 0.30792583639 -0.0924311298505 -3.9053219484 -0.40606322298
#> [9086,] 0.20105419255 -0.0278601736558 0.3737753164 0.03237979609
#> [9087,] 0.30958691602 -0.0940585958440 -3.9058365791 -0.39960237319
#> [9088,] 0.18988272633 -0.0170352477390 0.3899807586 -0.00850850549
#> [9089,] 0.19813109604 -0.0250363870856 0.3789290521 0.02186482316
#> [9090,] 0.21828120155 -0.0445177070187 0.3450734874 0.09468504325
#> [9091,] 0.21138018698 -0.0371338907860 0.2813658237 0.05459764488
#> [9092,] 0.17746787092 -0.0048515404940 0.3917030366 -0.05722396422
#> [9093,] 0.16883025686 0.0036112826722 0.3943791163 -0.09082038314
#> [9094,] 0.19887320219 -0.0258638712437 0.3893194116 0.02688766289
#> [9095,] 0.19478439080 -0.0218578011058 0.3905861949 0.01098403263
#> [9096,] 0.20109736622 -0.0276213668972 0.3440251658 0.02656585303
#> [9097,] 0.20179008754 -0.0283000702923 0.3438105490 0.02926022619
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#> [10406,] 0.22265070997 -0.0472326276898 0.1780434234 0.07835290141
#> [10407,] 0.20430271386 -0.0313441436646 0.4046296993 0.05142422286
#> [10408,] 0.20430271386 -0.0313441436646 0.4046296993 0.05142422286
#> [10409,] 0.21749693081 -0.0440304135649 0.3750532425 0.09761645332
#> [10410,] 0.20333653035 -0.0303774328054 0.4028049840 0.04723892886
#> [10411,] 0.19970656026 -0.0268209188509 0.4039296105 0.03311998411
#> [10412,] 0.20395020983 -0.0309786938572 0.4026148557 0.04962586497
#> [10413,] 0.21727285345 -0.0438911868638 0.3836188868 0.09845399906
#> [10414,] 0.21727285345 -0.0438911868638 0.3836188868 0.09845399906
#> [10415,] 0.21727285345 -0.0438911868638 0.3836188868 0.09845399906
#> [10416,] 0.21727285345 -0.0438911868638 0.3836188868 0.09845399906
#> [10417,] 0.21727285345 -0.0438911868638 0.3836188868 0.09845399906
#> [10418,] 0.19986739668 -0.0268379471977 0.3890113933 0.03075463059
#> [10419,] 0.21727285345 -0.0438911868638 0.3836188868 0.09845399906
#> [10420,] 0.21727285345 -0.0438911868638 0.3836188868 0.09845399906
#> [10421,] 0.21727285345 -0.0438911868638 0.3836188868 0.09845399906
#> [10422,] 0.21727285345 -0.0438911868638 0.3836188868 0.09845399906
#> [10423,] 0.19853740856 -0.0255348727336 0.3894234462 0.02558157726
#> [10424,] 0.21727285345 -0.0438911868638 0.3836188868 0.09845399906
#> [10425,] 0.21727285345 -0.0438911868638 0.3836188868 0.09845399906
#> [10426,] 0.21727285345 -0.0438911868638 0.3836188868 0.09845399906
#> [10427,] 0.21727285345 -0.0438911868638 0.3836188868 0.09845399906
#> [10428,] 0.21727285345 -0.0438911868638 0.3836188868 0.09845399906
#> [10429,] 0.21727285345 -0.0438911868638 0.3836188868 0.09845399906
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#> [10433,] 0.19993568770 -0.0268446191121 0.3826180696 0.02973842271
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#> [10440,] 0.21749693081 -0.0440304135649 0.3750532425 0.09761645332
#> [10441,] 0.38342145176 -0.1016421656448 -3.9105230394 -0.33431448892
#> [10442,] 0.36520643589 -0.0837957491293 -3.9048797178 -0.40516267679
#> [10443,] 0.36520643589 -0.0837957491293 -3.9048797178 -0.40516267679
#> [10444,] 0.36169964124 -0.0803599180376 -3.9037932532 -0.41880252468
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#> [10446,] 0.20203319878 -0.0290803964254 0.4010847230 0.04174228115
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#> [10448,] 0.19849764419 -0.0256967035956 0.4106763192 0.02969967553
#> [10449,] 0.19199229416 -0.0193229959305 0.4126917873 0.00439680100
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#> [10452,] 0.20100510058 -0.0280128656704 0.3950310793 0.03646161421
#> [10453,] 0.35533642851 -0.0741254713857 -3.9018218217 -0.44355254927
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#> [10456,] 0.22209051658 -0.0468845609371 0.1994575342 0.08044676575
#> [10457,] 0.20041981621 -0.0256523892067 0.2061714856 -0.00384247463
#> [10458,] 0.18502625371 -0.0121766555047 0.3808650997 -0.02953437317
#> [10459,] 0.18970585901 -0.0170627500617 0.4112761084 -0.00492367582
#> [10460,] 0.19338578926 -0.0206682131858 0.4101360035 0.00938959142
#> [10461,] 0.20310742389 -0.0301931206592 0.4071240758 0.04720236092
#> [10462,] 0.20308140883 -0.0301676320380 0.4071321357 0.04710117407
#> [10463,] 0.20245689400 -0.0295557549003 0.4073256210 0.04467209334
#> [10464,] 0.19890568464 -0.0260764078718 0.4084258460 0.03085949227
#> [10465,] 0.18962428460 -0.0170029054481 0.4134254369 -0.00481368707
#> [10466,] 0.19253873825 -0.0198583821664 0.4125224896 0.00652222178
#> [10467,] 0.19148980479 -0.0188306749485 0.4128474670 0.00244234423
#> [10468,] 0.20346125678 -0.0305598724394 0.4091385077 0.04900588749
#> [10469,] 0.19805745809 -0.0252654251073 0.4108126964 0.02798755034
#> [10470,] 0.20124491462 -0.0282076687127 0.3907086701 0.03653982979
#> [10471,] 0.19822295292 -0.0230783215237 0.1622469492 -0.02136008470
#> [10472,] 0.19962848184 -0.0244554081336 0.1618114924 -0.01589321180
#> [10473,] 0.19962848184 -0.0244554081336 0.1618114924 -0.01589321180
#> [10474,] 0.19913557562 -0.0239724763785 0.1619642032 -0.01781039443
#> [10475,] 0.20425207957 -0.0296078933754 0.2262247386 0.01533606331
#> [10476,] 0.20466842279 -0.0300158114672 0.2260957484 0.01695545046
#> [10477,] 0.20399187783 -0.0293529570870 0.2263053535 0.01432399604
#> [10478,] 0.20399187783 -0.0293529570870 0.2263053535 0.01432399604
#> [10479,] 0.22915326576 -0.1232731234926 0.3839421371 0.07500710704
#> [10480,] 0.22909724642 -0.1232383168173 0.3860835481 0.07521649347
#> [10481,] 0.34147203988 -0.1930605074111 -3.9095870733 -0.34481269282
#> [10482,] -5.16653184605 -0.0089124904755 0.2631312287 0.74873952909
#> [10483,] -5.16653184605 -0.0089124904755 0.2631312287 0.74873952909
#> [10484,] -0.01061249400 0.0587793018134 0.2777542502 -0.17690602441
#> [10485,] 0.04265406046 -0.0998641349007 0.3978515687 0.11366912921
#> [10486,] 0.19903210230 -0.1038941822823 0.1979842488 0.07461814632
#> [10487,] 0.19903210230 -0.1038941822823 0.1979842488 0.07461814632
#> [10488,] 0.18576231809 -0.0961379374855 0.3435150694 0.08731918124
#> [10489,] 0.18576234365 -0.0961379625235 0.3435150615 0.08731928064
#> [10490,] 0.18695180584 -0.0913305717921 0.2277926033 0.00759059372
#> [10491,] 0.09563929044 -0.1577381523689 0.2160491343 0.08011926605
#> [10492,] 0.04041608372 -0.0082633827637 0.2124167996 0.10028736722
#> [10493,] -0.00158690489 -0.0628401480504 0.2257064337 -0.01162306863
#> [10494,] 0.12306165525 -0.1034428234348 0.2200433602 0.08471199443
#> [10495,] -0.14903720180 -0.1153582161226 0.3384808431 0.22144532994
#> [10496,] 0.17438662304 -0.0804698316772 0.1838208672 -0.01843177114
#> [10497,] 0.07808433413 -0.1365195448919 0.2864079388 -0.06892544256
#> [10498,] 0.13294690762 -0.0634336377242 0.2683701235 0.09691200094
#> [10499,] -0.53516589481 -0.1348804894979 0.3506520859 0.06843930121
#> [10500,] 0.10071821670 -0.0358508541358 0.2076690707 -0.06069859323
#> [10501,] 0.07695638536 -0.0292687930983 0.2108777999 0.10426081259
#> [10502,] 0.14736944486 -0.0642628858743 0.2216514792 0.01860911166
#> [10503,] -0.26029445599 0.1162163092391 0.2469537807 -0.43256373847
#> [10504,] 0.24603568482 -0.0490428256072 0.3825791604 0.08856272257
#> [10505,] 0.24603568482 -0.0490428256072 0.3825791604 0.08856272257
#> [10506,] 0.12960532368 -0.0506109217840 0.2284551663 -0.03319181575
#> [10507,] 0.36430605055 -0.0882869334370 -3.9143190852 -0.31434369745
#> [10508,] 0.36734036494 -0.0904068261706 -3.9137163837 -0.31751505458
#> [10509,] 0.36274070768 -0.0859002476449 -3.9122913317 -0.33540564464
#> [10510,] 0.36733806499 -0.0904045727561 -3.9137156712 -0.31752400037
#> [10511,] -0.22633433661 0.2757664288190 0.4211454901 -0.89385995363
#> [10512,] -0.76110520815 -0.7352426833871 0.3702935318 -0.52168377684
#> [10513,] -0.59499724537 -0.8979892827357 0.3188304605 0.12440120246
#> [10514,] 0.22213525409 0.0110426061083 -3.9425521753 -0.16581093589
#> [10515,] 0.09106405726 -0.0350619719554 0.2098533564 0.12774246639
#> [10516,] 0.04774821158 0.0073773335670 0.2232733419 -0.04073661667
#> [10517,] -0.00567355733 0.0796768397119 0.3248818004 -0.48430902991
#> [10518,] 0.35355363737 -0.0807746153201 -3.9164543609 -0.30311012725
#> [10519,] 0.34080165685 -0.0682806840778 -3.9125035805 -0.35270957412
#> [10520,] -0.37106461729 0.3639138326521 0.3660939614 -0.99023344995
#> [10521,] 0.35646894590 -0.0790400741979 -3.9090544816 -0.37235645900
#> [10522,] -0.07029359791 0.1019239849861 0.2180968581 -0.34936433162
#> [10523,] 0.15973580193 -0.0749803846065 0.2231250046 0.03718508009
#> [10524,] -0.03099949662 -0.0830967594810 0.2927914461 0.09020095797
#> [10525,] -0.51925707035 0.4093566757209 0.4486027674 -0.84909176442
#> [10526,] 0.36430605055 -0.0882869334370 -3.9143190852 -0.31434369745
#> [10527,] 0.36462862295 -0.0885123029805 -3.9142550269 -0.31468070456
#> [10528,] 0.33429411255 -0.0604943223314 -3.9079363731 -0.40278026468
#> [10529,] 0.33451550653 -0.0604425687071 -3.9075190486 -0.40663519565
#> [10530,] 0.34608523280 -0.0717781698070 -3.9111035465 -0.36163418407
#> [10531,] 0.35952720025 -0.0849481253850 -3.9152680966 -0.30935099959
#> [10532,] 0.07052992419 0.1629383914909 -3.8895083150 -0.81443789095
#> [10533,] 0.36550076313 -0.0891216354500 -3.9140818323 -0.31559187192
#> [10534,] 0.04973152596 -0.0968791520020 0.2073239276 0.16441245565
#> [10535,] 0.36591891253 -0.0894137811545 -3.9139987938 -0.31602873298
#> [10536,] 0.35355363737 -0.0807746153201 -3.9164543609 -0.30311012725
#> [10537,] 0.37147432600 -0.0932951455149 -3.9128955680 -0.32183274426
#> [10538,] 0.29517122877 -0.0234628087534 -3.8981660576 -0.53213670981
#> [10539,] 0.36674503089 -0.0889134282510 -3.9118858983 -0.33580626677
#> [10540,] 0.35743645324 -0.0834873968623 -3.9156832891 -0.30716669427
#> [10541,] 0.35952720025 -0.0849481253850 -3.9152680966 -0.30935099959
#> [10542,] 0.35952720025 -0.0849481253850 -3.9152680966 -0.30935099959
#> [10543,] 0.21130778731 0.0602719171106 -3.8693472022 -0.88585759650
#> [10544,] 0.21795210582 0.0537620531367 -3.8714057251 -0.86001419733
#> [10545,] 0.34090419663 -0.0667288439120 -3.9095469650 -0.38131447024
#> [10546,] 0.34991859746 -0.0728472877179 -3.9074320271 -0.39388466216
#> [10547,] 0.35157807014 -0.0747250550443 -3.9084017063 -0.38300876240
#> [10548,] 0.32231644549 -0.0488933692636 -3.9044684462 -0.44700995500
#> [10549,] -0.31529100852 0.2429460783480 0.3270848118 -0.32637537601
#> [10550,] -0.06708218261 0.0776081656900 0.2148055806 -0.17168207482
#> [10551,] 0.15404488058 -0.0718231308316 0.2246702040 0.02338456610
#> [10552,] 0.10289789513 -0.0335450586294 0.2424920923 -0.05288829456
#> [10553,] 0.16299853662 -0.0827648548054 0.1860443800 0.07344010140
#> [10554,] 0.16299853662 -0.0827648548054 0.1860443800 0.07344010140
#> [10555,] -3.38801152585 0.1930624336293 0.1804347146 -0.24210614290
#> [10556,] 0.36430605055 -0.0882869334370 -3.9143190852 -0.31434369745
#> [10557,] 0.36430605055 -0.0882869334370 -3.9143190852 -0.31434369745
#> [10558,] 0.36430605055 -0.0882869334370 -3.9143190852 -0.31434369745
#> [10559,] 0.36430605055 -0.0882869334370 -3.9143190852 -0.31434369745
#> [10560,] 0.35832890387 -0.1188051715873 -3.9109421326 -0.33135647498
#> [10561,] 0.35832890387 -0.1188051715873 -3.9109421326 -0.33135647498
#> [10562,] 0.35439342291 -0.1149493290797 -3.9097228537 -0.34666371910
#> [10563,] 0.24606614909 -0.0490525943441 0.3804456667 0.08825393845
#> [10564,] 0.24551577410 -0.0486739891885 0.3976086249 0.08953143916
#> [10565,] 0.24195965097 -0.0450492744386 0.3838419850 0.07270879115
#> [10566,] 0.24603568482 -0.0490428256072 0.3825791604 0.08856272257
#> [10567,] 0.24603568482 -0.0490428256072 0.3825791604 0.08856272257
#> [10568,] 0.24603568482 -0.0490428256072 0.3825791604 0.08856272257
#> [10569,] 0.24603568482 -0.0490428256072 0.3825791604 0.08856272257
#> [10570,] 0.24603568482 -0.0490428256072 0.3825791604 0.08856272257
#> [10571,] 0.24603568482 -0.0490428256072 0.3825791604 0.08856272257
#> [10572,] 0.24603568482 -0.0490428256072 0.3825791604 0.08856272257
#> [10573,] 0.24603568482 -0.0490428256072 0.3825791604 0.08856272257
#> [10574,] 0.24581160747 -0.0489035989061 0.3911448047 0.08940026830
#> [10575,] 0.24514053130 -0.0482461026447 0.3913527155 0.08679008499
#> [10576,] 0.35835445894 -0.1188302095257 -3.9109500500 -0.33125707729
#> [10577,] 0.35835445894 -0.1188302095257 -3.9109500500 -0.33125707729
#> [10578,] 0.35835445894 -0.1188302095257 -3.9109500500 -0.33125707729
#> [10579,] -1.09188433096 1.2617628609584 0.8013376412 -5.11448753015
#> [10580,] 0.24592364615 -0.0489732122566 0.3868619825 0.08898149544
#> [10581,] 0.35809890823 -0.1185798301421 -3.9108708760 -0.33225105418
#> [10582,] 0.35815809377 -0.1186378180073 -3.9108892127 -0.33202084913
#> [10583,] 0.35809890823 -0.1185798301421 -3.9108708760 -0.33225105418
#> [10584,] 0.35818170666 -0.1186609530624 -3.9108965284 -0.33192900567
#> [10585,] 0.24593346454 -0.0489426738537 0.3826108299 0.08816513181
#> [10586,] 0.24383539319 -0.0468870591143 0.3832608481 0.08000458154
#> [10587,] 0.24603568482 -0.0490428256072 0.3825791604 0.08856272257
#> [10588,] 0.24603568482 -0.0490428256072 0.3825791604 0.08856272257
#> [10589,] 0.35835445894 -0.1188302095257 -3.9109500500 -0.33125707729
#> [10590,] 0.35835445894 -0.1188302095257 -3.9109500500 -0.33125707729
#> [10591,] 0.24447439775 -0.0475131327630 0.3830628736 0.08249002075
#> [10592,] 0.24603568482 -0.0490428256072 0.3825791604 0.08856272257
#> [10593,] 0.24586762681 -0.0489384055814 0.3890033936 0.08919088187
#> [10594,] 0.24586762681 -0.0489384055814 0.3890033936 0.08919088187
#> [10595,] 0.14190975422 0.0115817951262 0.2214178413 0.02470245768
#> [10596,] 0.17560672152 -0.0177696994288 0.2058982580 0.09850544602
#> [10597,] 0.15272414612 0.0043624433533 0.2127642507 0.01211438941
#> [10598,] 0.14037884202 0.0141982725012 0.1913578134 -0.00075729436
#> [10599,] 0.13317889609 0.0200549202754 0.2137077752 -0.01258679258
#> [10600,] 0.16398513625 -0.0100704482151 0.2042081618 0.10671320686
#> [10601,] 0.16869390919 -0.0133693350386 0.2051565426 0.10170912275
#> [10602,] 0.12304343592 -0.1029238955849 0.2192957434 0.08946859994
#> [10603,] 0.05841786368 -0.0357336177469 0.2447214036 -0.21673449572
#> [10604,] 0.02332705308 -0.0057303947486 0.2520618066 -0.31238564022
#> [10605,] 0.12786439980 -0.1067983255270 0.2209971167 0.07969433307
#> [10606,] 0.14163595510 0.0125163755003 0.2223669951 0.01473883070
#> [10607,] 0.16725700602 -0.0117417142332 0.2039544814 0.10904768966
#> [10608,] 0.13744382758 0.0176360814102 0.2134948085 -0.00985964763
#> [10609,] 0.14763800351 0.0017222439316 0.2111466057 0.12822623219
#> [10610,] 0.13660081929 0.0080098374120 0.2110472750 0.12643289848
#> [10611,] 0.16849381167 -0.0055002286466 0.2111838045 0.03119496043
#> [10612,] 0.17430759037 -0.0111963596238 0.2093825970 0.05380793471
#> [10613,] 0.15895336887 -0.0078059358218 0.2157784574 0.10121891173
#> [10614,] 0.15895336887 -0.0078059358218 0.2157784574 0.10121891173
#> [10615,] 0.15895336887 -0.0078059358218 0.2157784574 0.10121891173
#> [10616,] 0.13595380479 0.0147282087033 0.2229041134 0.01176099152
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#> [10669,] 0.14698150475 0.0087280779396 0.2128706209 0.00692249362
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#> [10672,] 0.08968427251 -0.0013057203749 0.2114306681 0.01801874473
#> [10673,] 0.07017908334 0.0144376182567 0.2242452733 -0.01527567801
#> [10674,] 0.06910476126 0.0155905956135 0.2139578399 -0.02159068770
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#> [10676,] 0.11885462886 -0.0281442590326 0.2043427593 0.11076083227
#> [10677,] 0.09992143398 -0.0086602101172 0.2109346945 0.02863080329
#> [10678,] 0.10017698469 -0.0089105895008 0.2108555205 0.02962478018
#> [10679,] 0.00050516747 -0.0591021677243 0.2173778128 -0.06295717027
#> [10680,] 0.08111069686 0.0075102174361 0.1915313582 -0.00938849583
#> [10681,] 0.08563394446 0.0030785023461 0.1901299792 0.00820489515
#> [10682,] 0.08990164135 -0.0011028333602 0.1888077742 0.02480430923
#> [10683,] 0.10916356845 -0.0216988827306 0.2028965380 0.11783997422
#> [10684,] 0.06605263935 0.0175028265804 0.2134869364 -0.01891600726
#> [10685,] 0.10131863760 -0.0170495283582 0.2025609305 0.11825280373
#> [10686,] 0.09993370045 -0.0169975320649 0.2250933282 0.11304446825
#> [10687,] 0.10394734378 -0.0119766954007 0.2437250631 0.03031445498
#> [10688,] 0.10368128908 -0.0107102268906 0.2004559117 0.02624462738
#> [10689,] 0.07516867435 0.0082593239096 0.2130174271 -0.00194521924
#> [10690,] 0.04579570606 -0.0915372608338 0.2260475212 0.00138930393
#> [10691,] 0.04669013356 -0.0924135886764 0.2257704124 0.00486822305
#> [10692,] 0.10862483901 -0.0212646751688 0.1919737327 0.11798690755
#> [10693,] 0.08622309170 0.0019642764441 0.1891836635 0.01821976023
#> [10694,] 0.12893577424 -0.0343162362979 0.1943331972 0.10742661789
#> [10695,] 0.05888690288 0.0217273495018 0.2244150166 -0.02165718592
#> [10696,] 0.11590050410 -0.0259121554686 0.2142397914 0.11637804100
#> [10697,] 0.11399004667 -0.0247852917110 0.2141659728 0.11642820097
#> [10698,] 0.09015889592 -0.0001231436028 0.2222204545 0.01467177656
#> [10699,] 0.10634755691 -0.0164461413245 0.2167176794 0.08288843439
#> [10700,] 0.11889173960 -0.0285136789009 0.2048549853 0.10750728063
#> [10701,] 0.08193958840 0.0066099107773 0.2258913528 -0.02295579379
#> [10702,] 0.10340839524 -0.0183694570901 0.2027699983 0.11738082399
#> [10703,] 0.11526029878 -0.0251720296055 0.2029514064 0.11883057761
#> [10704,] 0.08638386534 0.0027125682938 0.2219330399 0.01428455468
#> [10705,] 0.07914910417 -0.0037644010844 0.2979752301 0.12940087505
#> [10706,] 0.11233382417 -0.0242898921202 0.1933479974 0.11005117490
#> [10707,] 0.07589057453 0.0072090673358 0.1792789545 0.00977455380
#> [10708,] 0.10057314833 -0.0149703477700 0.1893916407 0.13265926283
#> [10709,] 0.10269245640 -0.0169481902703 0.1905432181 0.12579214698
#> [10710,] 0.09554138095 -0.0127058353768 0.2009619363 0.12716496770
#> [10711,] 0.09554138095 -0.0127058353768 0.2009619363 0.12716496770
#> [10712,] 0.09554138095 -0.0127058353768 0.2009619363 0.12716496770
#> [10713,] 0.09554138095 -0.0127058353768 0.2009619363 0.12716496770
#> [10714,] 0.06678541860 0.0143195046471 0.2188694064 0.03360508826
#> [10715,] 0.07662101232 0.0071614126776 0.2070506819 0.04811182824
#> [10716,] 0.11288764814 -0.0242971796890 0.1928999799 0.11302574616
#> [10717,] 0.10000887644 -0.0144946864336 0.1891601430 0.13400891953
#> [10718,] 0.07662538268 0.0091305650274 0.2037135608 -0.01887596168
#> [10719,] 0.08160259449 0.0034809845990 0.2003584386 0.01745931691
#> [10720,] 0.03046373279 0.0425364281355 0.2220831404 -0.02172860018
#> [10721,] 0.10523879570 -0.0189739277684 0.2128731700 0.12273697687
#> [10722,] 0.08718913696 0.0003951961655 0.2207862297 0.02891937335
#> [10723,] 0.09869549673 -0.0161207619012 0.2033685814 0.11253337886
#> [10724,] 0.09326917525 -0.0130968170505 0.2678037042 0.11676406707
#> [10725,] 0.08174760984 -0.0052233859854 0.2657747569 0.12715151825
#> [10726,] 0.07763643490 0.0085834470319 0.2221981320 0.00763837219
#> [10727,] 0.10046760637 -0.0164078712192 0.2237844281 0.12149651534
#> [10728,] 0.05811917042 0.0218358262295 0.2129831208 -0.01615057882
#> [10729,] 0.09261851654 -0.0119653905583 0.2022946368 0.11803630150
#> [10730,] 0.05878743462 0.0225175920196 0.2245134493 -0.02447410327
#> [10731,] 0.11054064541 -0.0160708874569 0.2311955320 0.04659662210
#> [10732,] 0.10977399327 -0.0153197493061 0.2314330538 0.04361469142
#> [10733,] 0.08053469862 0.0038031935424 0.1599921898 0.01097108320
#> [10734,] 0.10481201626 -0.0199828479009 0.1524706640 0.10539888787
#> [10735,] 0.09373996705 -0.0125897817509 0.2130143056 0.11931095859
#> [10736,] 0.06173024952 0.0190595670672 0.2231548786 -0.00780422103
#> [10737,] 0.06744067885 0.0040584541078 0.1888669595 0.12871815576
#> [10738,] 0.09021953685 -0.0112535261232 0.2890821605 0.11917459001
#> [10739,] 0.09659718604 -0.0046862641390 0.2221814004 0.01893743903
#> [10740,] -0.06123193472 0.0010581325662 0.2484304255 -0.29324008437
#> [10741,] 0.03983837186 -0.0979669136528 0.2171171260 0.09987777611
#> [10742,] 0.07715527168 0.0061004868175 0.2223602445 0.01365560327
#> [10743,] 0.09284536097 -0.0029425431316 0.2224199759 0.01715740081
#> [10744,] 0.09654306146 -0.0141866308887 0.2130395324 0.11976640842
#> [10745,] 0.09473941879 -0.0131976695386 0.2130799255 0.11911277743
#> [10746,] 0.09543235209 -0.0136817967061 0.2132175322 0.11838883624
#> [10747,] 0.03956626061 0.0377491932040 0.2224746604 -0.02386893953
#> [10748,] 0.09584228785 -0.0137874186043 0.2130332257 0.11965254596
#> [10749,] 0.09584228785 -0.0137874186043 0.2130332257 0.11965254596
#> [10750,] 0.04993569978 0.0275478220457 0.2230389405 -0.01442844372
#> [10751,] 0.09258443501 -0.0126152160459 0.2783938675 0.11846639865
#> [10752,] 0.09434516364 -0.0129222178743 0.2130016321 0.11952467500
#> [10753,] 0.09604094614 -0.0141702739589 0.2134313901 0.11716081201
#> [10754,] 0.05609204426 0.0220390130942 0.2405695369 0.02662880818
#> [10755,] 0.09765251267 -0.0151028106758 0.2027363175 0.11633021851
#> [10756,] 0.06352852064 0.0192896331039 0.2238000367 -0.01607051801
#> [10757,] 0.09303919345 -0.0121905694664 0.2130079989 0.11919709613
#> [10758,] 0.06786744832 0.0124717998195 0.2208066335 0.02129037234
#> [10759,] 0.06098814337 0.0198870512253 0.2127645191 -0.01282706077
#> [10760,] 0.09472083734 -0.0131630274117 0.2023135569 0.11837788887
#> [10761,] 0.06213812157 0.0187603439990 0.2124082363 -0.00835416476
#> [10762,] 0.10630165319 -0.0189897850728 0.2012852757 0.12747101579
#> [10763,] 0.10553080223 -0.0185506515599 0.2012783383 0.12734576708
#> [10764,] 0.02874659167 -0.0816861407785 0.2254547401 0.00185042240
#> [10765,] 0.04535923061 0.0304208243705 0.2086967715 0.01245888224
#> [10766,] 0.08539601040 0.0017197092417 0.2105359019 0.02277384952
#> [10767,] 0.09864538226 -0.0153842677422 0.2130584526 0.12010799579
#> [10768,] 0.09920557565 -0.0157323344949 0.1916443418 0.11801413145
#> [10769,] 0.09920557565 -0.0157323344949 0.1916443418 0.11801413145
#> [10770,] 0.00631992310 -0.0631996070542 0.2309427108 -0.06395695672
#> [10771,] 0.06919487924 0.0074551817213 0.1571876435 0.03891320326
#> [10772,] 0.09615236609 -0.0148185144936 0.1520529790 0.10615529748
#> [10773,] 0.05968781372 0.0206854060803 0.2224569948 -0.00380920022
#> [10774,] 0.06588188308 0.0049753983659 0.2102720832 0.13064976610
#> [10775,] 0.07056138673 0.0133891269369 0.2229968623 -0.00268877407
#> [10776,] 0.09023316980 -0.0098186292348 0.2139921565 0.12617112220
#> [10777,] 0.05781634191 0.0234690336774 0.2248143103 -0.02825121545
#> [10778,] 0.06121914810 0.0195603258344 0.2233132266 -0.00979217482
#> [10779,] 0.04349545683 0.0309820330424 0.1868942137 0.01425721538
#> [10780,] 0.09867881209 -0.0141630204154 0.1790432727 0.12885039768
#> [10781,] 0.10540899746 -0.0196632532302 0.2030145038 0.11626359135
#> [10782,] 0.04643243862 -0.1020315913856 0.2176294720 0.09806460192
#> [10783,] 0.04383991233 -0.1002202880175 0.2171146333 0.10077314052
#> [10784,] 0.12172440318 -0.0296249882695 0.2041420854 0.11266940900
#> [10785,] 0.10586824093 -0.0132152067726 0.1993824254 0.03898160644
#> [10786,] 0.09267861429 -0.0115228399360 0.2123252512 0.12346538684
#> [10787,] 0.07600705894 0.0077855709672 0.2211878618 0.02021815774
#> [10788,] 0.09446293136 -0.0102968281174 0.2154699187 0.09200316883
#> [10789,] 0.10479806807 -0.0190433966678 0.2133403254 0.11966539822
#> [10790,] 0.06180901808 0.0166103310609 0.2160917525 0.05670343038
#> [10791,] 0.06180901808 0.0166103310609 0.2160917525 0.05670343038
#> [10792,] 0.06434327980 0.0188797849954 0.2029723897 -0.02314382343
#> [10793,] 0.06093420997 0.0185029909688 0.2116641371 0.00002231497
#> [10794,] 0.05467321753 0.0246372858674 0.2136038991 -0.02433011886
#> [10795,] 0.08818708066 -0.0101101589608 0.2783542929 0.11775191173
#> [10796,] 0.08164393578 0.0048053491579 0.1907083942 0.00399167997
#> [10797,] 0.03727198598 -0.0870097738692 0.2262177632 -0.00113450903
#> [10798,] 0.05177339617 0.0267274981092 0.2236645005 -0.01974253757
#> [10799,] 0.05970051560 0.0225984102582 0.2239499621 -0.02125905973
#> [10800,] 0.11322168593 -0.0236735347966 0.2238992102 0.12356881208
#> [10801,] 0.10541713504 -0.0121371075814 0.2221059948 0.02820783540
#> [10802,] 0.10798945333 -0.0217860790313 0.2147280520 0.11153018197
#> [10803,] 0.10113383220 -0.0087230256999 0.2222844220 0.02309467312
#> [10804,] 0.04313540524 -0.0999992525192 0.2173732990 0.09897118902
#> [10805,] 0.10989279857 -0.0217916249079 0.2131596753 0.12193548825
#> [10806,] 0.09191774294 -0.0115661782738 0.2022883301 0.11792243904
#> [10807,] 0.08863311601 -0.0088880990588 0.1903419438 0.12398372661
#> [10808,] 0.02586611226 0.0514870638956 0.2077595291 -0.10046205565
#> [10809,] 0.09509651104 -0.0134038369491 0.1916254818 0.11723110275
#> [10810,] 0.09509651104 -0.0134038369491 0.1916254818 0.11723110275
#> [10811,] 0.08861797366 0.0018374657312 0.2219575098 0.01353563575
#> [10812,] 0.08030629921 0.0047514237939 0.2221569991 0.01486179589
#> [10813,] 0.10281698267 -0.0168977268788 0.2118275906 0.12886264091
#> [10814,] 0.05609720477 0.0244677960955 0.2246996513 -0.02776884973
#> [10815,] 0.07410986974 0.0107743426136 0.2239008257 -0.00766503946
#> [10816,] 0.10745414743 -0.0213578447916 0.2145420337 0.11259703902
#> [10817,] 0.05857541833 0.0216015186198 0.2024542549 -0.01872710740
#> [10818,] 0.08774813525 -0.0049949180515 0.2162111867 0.08033445538
#> [10819,] 0.03728662184 0.0359717399321 0.2217942248 -0.01049679693
#> [10820,] 0.09500093404 -0.0133370607880 0.1916065015 0.11733095671
#> [10821,] 0.09500093404 -0.0133370607880 0.1916065015 0.11733095671
#> [10822,] 0.06572408340 0.0172224031419 0.2108694608 0.00375892631
#> [10823,] 0.09305000571 -0.0122903926378 0.1916840742 0.11640820483
#> [10824,] 0.06810161295 0.0121800107952 0.1994621021 0.01889861553
#> [10825,] 0.09314558272 -0.0123571687989 0.1917030545 0.11630835087
#> [10826,] 0.05795094782 0.0238226828550 0.2038988689 -0.03578226630
#> [10827,] 0.05384601303 0.0256870618544 0.2136410490 -0.02639636951
#> [10828,] 0.12107179028 -0.0290202427144 0.1479934144 0.10976725563
#> [10829,] 0.04379528610 -0.0904269822754 0.2251305756 0.00852309289
#> [10830,] 0.13394856421 -0.0376557827307 0.1950895233 0.10371230249
#> [10831,] 0.07901160812 0.0064941052184 0.2111618123 0.01304848729
#> [10832,] 0.07508585568 0.0107250248226 0.2223641933 0.00380872483
#> [10833,] 0.10684443340 -0.0200550514705 0.2131322411 0.12144018655
#> [10834,] 0.06187998753 0.0191395480922 0.2031001437 -0.02167998408
#> [10835,] 0.05370068653 0.0244925562885 0.2020072790 -0.01651864881
#> [10836,] 0.08819977710 -0.0093084101199 0.1913188742 0.11766723753
#> [10837,] 0.07951383210 0.0072898758474 0.2113425041 0.00875588062
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#> [10854,] 0.06063669615 0.0185522148507 0.2098364278 0.01528130317
#> [10855,] 0.07742383730 -0.0007040544767 0.1875977991 0.13899398623
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#> [10871,] 0.07995949079 0.0050845974385 0.2217190627 0.01800787738
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#> [10873,] 0.09567569602 -0.0012642597170 0.1580957391 -0.01513038959
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#> [10876,] 0.11092697129 -0.0230789460545 0.2678493676 0.12035427135
#> [10877,] 0.10445350673 -0.0123165156376 0.2324856664 0.03379113843
#> [10878,] 0.07142306280 0.0027649429985 0.2089312365 0.14040578000
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#> [10880,] 0.07395477125 0.0087685676552 0.1996280289 0.01912849673
#> [10881,] 0.07099031842 0.0107192043322 0.3081734317 0.01713490125
#> [10882,] 0.09782314318 -0.0155706309472 0.2998601663 0.12150247483
#> [10883,] 0.07990464141 0.0053818245054 0.2211392330 0.02203493353
#> [10884,] 0.10084078218 -0.0145774784179 0.2147643120 0.10105503893
#> [10885,] 0.10595179642 -0.0195850660901 0.2131808329 0.12093457676
#> [10886,] 0.11081306287 -0.0235688359091 0.2686637456 0.11514350978
#> [10887,] 0.08593123376 -0.0001991047287 0.2315484374 0.03286942349
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#> [10889,] 0.00323054419 0.0647426546957 0.1773213131 -0.03501331098
#> [10890,] 0.05306293303 0.0159186748911 0.1618823917 0.15881218281
#> [10891,] 0.09696373836 -0.0144118097969 0.2237528945 0.12092720305
#> [10892,] 0.03333501311 0.0384129773298 0.2985262845 -0.01851335267
#> [10893,] 0.04114903655 0.0204520015580 0.2080109887 0.13961178026
#> [10894,] 0.11334357648 -0.0245279707488 0.2143232354 0.11528471106
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#> [10899,] 0.05860216570 0.0224584705716 0.1995240398 0.00297311127
#> [10900,] 0.07670864265 0.0096070408826 0.2011779990 0.00054046466
#> [10901,] 0.06086616389 0.0209690989549 0.2028522886 -0.02327337910
#> [10902,] 0.06693805575 0.0157541181157 0.2020023671 -0.01010873069
#> [10903,] 0.06894218846 0.0141098989450 0.1982844025 0.02224609008
#> [10904,] 0.04113820048 -0.0988614975085 0.2173553249 0.09864668101
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#> [10906,] 0.06127167666 0.0204473060618 0.2211417886 0.00556424957
#> [10907,] 0.09509357798 -0.0045315456941 0.2102312893 0.02953359387
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#> [10909,] 0.02842259913 -0.0177403327801 0.2001443993 0.13244274891
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#> [10911,] -0.01935517569 0.0264532342566 0.3559756733 -0.02859980896
#> [10912,] 0.01998497110 -0.0020113631696 0.2110982044 0.01096749435
#> [10913,] 0.03814393809 -0.0236373900866 0.2007596349 0.13066174074
#> [10914,] 0.04743515443 -0.0293840224758 0.1907792038 0.12696841100
#> [10915,] 0.03681565295 -0.0230492763381 0.1902646055 0.12791118427
#> [10916,] 0.03681565295 -0.0230492763381 0.1902646055 0.12791118427
#> [10917,] 0.03893793297 -0.0252118568929 0.1702235582 0.11741737346
#> [10918,] 0.01529941435 0.0011211218101 0.2556535876 -0.00096295743
#> [10919,] 0.00904742433 0.0047196524289 0.2538945008 0.01189985889
#> [10920,] 0.01916713196 -0.0006926011359 0.2224522109 0.00430741567
#> [10921,] 0.00034404035 0.0135716447548 0.1894778121 -0.00617824913
#> [10922,] -0.03035126342 0.0335606228389 0.2981304880 -0.02167146117
#> [10923,] 0.01181460406 -0.0077519754573 0.2850667853 0.14233472588
#> [10924,] 0.04157454403 -0.0254231406886 0.2112735844 0.13375388458
#> [10925,] 0.04803822661 -0.0282432796458 0.2207955766 0.14382916302
#> [10926,] 0.04226714129 -0.0262414857718 0.2119026949 0.12990011370
#> [10927,] -0.02659847785 0.0318614604875 0.1773606508 -0.01008355365
#> [10928,] 0.01363619035 -0.0073499159552 0.2078511370 0.14940652778
#> [10929,] 0.04297445424 -0.0269525299356 0.2123621437 0.12712950089
#> [10930,] 0.03155687898 -0.0198704461500 0.2114099299 0.13068391078
#> [10931,] 0.01289122214 0.0025826926347 0.2328608847 0.00723750579
#> [10932,] 0.00100762322 0.0007845622277 0.3630315735 0.09884178746
#> [10933,] 0.02119795737 -0.0145616070376 0.2014565055 0.12249974182
#> [10934,] -0.00234387525 0.0157627987563 0.2236200270 -0.02173365800
#> [10935,] 0.04635997649 -0.0290883794619 0.2019660807 0.12478522827
#> [10936,] 0.02825390168 -0.0174686311746 0.2535390063 0.13884388778
#> [10937,] 0.03522425838 -0.0230673348601 0.1916092888 0.11899885674
#> [10938,] 0.01279097996 0.0047377432423 0.3521725859 0.00161767421
#> [10939,] 0.02057055273 -0.0039783264973 0.2419286218 0.02957924377
#> [10940,] 0.04587007321 -0.0287658854750 0.2340904002 0.12798295600
#> [10941,] -0.00375841525 0.0162675047441 0.2128480233 -0.02187217346
#> [10942,] 0.03710933945 -0.0238474742320 0.1804636760 0.12109728951
#> [10943,] 0.04186147241 -0.0164653137775 0.2211377871 0.02815963604
#> [10944,] -0.03095837429 0.0401057565224 0.2053886407 -0.07869388471
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#> [10946,] -0.01867640578 0.0240996995955 0.1749062582 0.02072972998
#> [10947,] -0.00064509807 0.0140540795145 0.2011431474 -0.01290699241
#> [10948,] 0.00230095988 0.0117676494856 0.2120878173 -0.01136309225
#> [10949,] -0.03078574221 0.0339429554748 0.3775721656 -0.01533158170
#> [10950,] -0.00578808706 0.0022935087458 0.3642906015 0.14672216683
#> [10951,] 0.02072805597 -0.0032407742773 0.2081683392 0.03737628151
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#> [10953,] -0.00903916795 0.0211991266064 0.2125642061 -0.02599573463
#> [10954,] 0.02758094594 -0.0182747025375 0.2874736854 0.13047353161
#> [10955,] 0.01513399911 0.0004703154389 0.2423659735 0.02104606897
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#> [10960,] 0.04443255782 -0.0273312753234 0.3469194677 0.14365615634
#> [10961,] 0.01780216270 -0.0108233940514 0.1558515093 0.13500111449
#> [10962,] 0.00560453768 0.0085473596255 0.2002921873 0.00082371878
#> [10963,] 0.03879787138 -0.0237760187945 0.2218834262 0.13487112695
#> [10964,] 0.02050510634 -0.0019156664174 0.2204333040 0.02244431422
#> [10965,] 0.04292735454 -0.0264153726731 0.1901497330 0.12998593970
#> [10966,] 0.01633386315 -0.0006043766930 0.2190172052 0.03596549559
#> [10967,] 0.04495842929 -0.0282899548929 0.2019534673 0.12455750335
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#> [10975,] 0.03710322090 -0.0146334841208 0.2525067234 0.03904543956
#> [10976,] 0.05994963434 -0.0294835707919 0.2330057932 0.03140184945
#> [10977,] 0.08097096996 -0.0503481857929 0.2260071099 0.11788140770
#> [10978,] -0.02630734516 0.0297138653245 0.3183639268 -0.00454269476
#> [10979,] 0.00578710051 -0.0029074352943 0.1863613457 0.14594631395
#> [10980,] -0.03356770913 0.0356509897821 0.1985541349 -0.00712612730
#> [10981,] 0.03232735367 -0.0193623070184 0.3409411886 0.15134836122
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#> [10984,] -0.02491280561 0.0292131745518 0.3072138992 -0.00252396571
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#> [10986,] -0.01588176931 0.0125478028874 0.2030554685 0.17345627090
#> [10987,] -0.02654746285 0.0324272167309 0.2882698829 -0.03167040543
#> [10988,] 0.01817391175 -0.0113891754014 0.2744144406 0.14227555053
#> [10989,] -0.02341332222 0.0286241793606 0.1994113929 -0.00840164849
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#> [10991,] -0.05163111128 0.0433951358797 0.1929490831 0.04150757271
#> [10992,] 0.00245842591 -0.0010111769430 0.1863313889 0.14540546727
#> [10993,] 0.00652291280 -0.0033266081930 0.1863679678 0.14606586953
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#> [10998,] 0.07367837059 -0.0428879655257 0.3927759236 0.16295027074
#> [10999,] 0.21760896948 -0.0441000269154 0.3707704204 0.09719768046
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#> [11009,] 0.31214242314 -0.0965623896801 -3.9066283186 -0.38966260428
#> [11010,] 0.21727285345 -0.0438911868638 0.3836188868 0.09845399906
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#> [11504,] 0.29770380791 -0.0824159545059 -3.9021549901 -0.44582229863
#> [11505,] 0.21351827617 -0.0404133778159 0.4060226720 0.08812315226
#> [11506,] 0.21347355479 -0.0403695614238 0.4060365275 0.08794920630
#> [11507,] 0.21671266006 -0.0435431201111 0.4050329976 0.10054786340
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#> [11515,] 0.21347355479 -0.0403695614238 0.4060365275 0.08794920630
#> [11516,] 0.21428492830 -0.0411645159668 0.4057851502 0.09110508293
#> [11517,] 0.21428492830 -0.0411645159668 0.4057851502 0.09110508293
#> [11518,] 0.21347355479 -0.0403695614238 0.4060365275 0.08794920630
#> [11519,] 0.17007465513 0.0021511173983 0.4194822445 -0.08085291925
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#> [11521,] 0.19459443928 -0.0218724840041 0.4118855985 0.01451797069
#> [11522,] 0.15729711953 0.0146700865790 0.4234409423 -0.13055176381
#> [11523,] 0.15230958740 0.0195566909331 0.4249861646 -0.14995101200
#> [11524,] 0.16558051476 0.0065543142765 0.4208746056 -0.09833309626
#> [11525,] 0.13604616120 0.0354910101718 0.4300248506 -0.21320839714
#> [11526,] 0.16792245815 0.0042597624912 0.4201490318 -0.08922399383
#> [11527,] 0.18080305735 -0.0083601846948 0.4161584031 -0.03912427839
#> [11528,] 0.17898156854 -0.0065755555623 0.4167227313 -0.04620904748
#> [11529,] 0.17850782863 -0.0061114022609 0.4168695040 -0.04805168184
#> [11530,] 0.15699344862 0.0149676124005 0.4235350247 -0.13173290655
#> [11531,] 0.19498476744 -0.0222549134746 0.4117646682 0.01603617099
#> [11532,] 0.15439130350 0.0175171004742 0.4243412135 -0.14185407625
#> [11533,] 0.16573029303 0.0064075669197 0.4208282018 -0.09775052640
#> [11534,] 0.18483638868 -0.0123118974685 0.4149088085 -0.02343644051
#> [11535,] 0.16624139445 0.0059068081525 0.4206698539 -0.09576257262
#> [11536,] 0.17702995330 -0.0046634332475 0.4173273749 -0.05379994960
#> [11537,] 0.16479988400 0.0073191481796 0.4211164583 -0.10136939747
#> [11538,] 0.15751387765 0.0144577147858 0.4233737870 -0.12970867261
#> [11539,] 0.15439130350 0.0175171004742 0.4243412135 -0.14185407625
#> [11540,] 0.14905665683 0.0227437951450 0.4259939778 -0.16260344325
#> [11541,] 0.16987404782 0.0023476652145 0.4195443961 -0.08163319111
#> [11542,] 0.17377727829 -0.0014765794150 0.4183351089 -0.06645138687
#> [11543,] 0.16245794061 0.0096136999648 0.4218420322 -0.11047849989
#> [11544,] 0.11896451274 0.0522269941210 0.4353170357 -0.27964829750
#> [11545,] 0.15699344862 0.0149676124005 0.4235350247 -0.13173290655
#> [11546,] 0.16154718342 0.0105060270501 0.4221242003 -0.11402093413
#> [11547,] 0.12563758071 0.0456889624664 0.4332496058 -0.25369307592
#> [11548,] 0.09050863430 0.0801070389415 0.4441331507 -0.39032881711
#> [11549,] 0.29770380791 -0.0824159545059 -3.9021549901 -0.44582229863
#> [11550,] 0.21704877610 -0.0437519601627 0.3921845311 0.09929154480
#> [11551,] 0.18291257426 -0.0082986335380 0.1903549735 -0.07621050517
#> [11552,] 0.18907033733 -0.0142313927374 0.1778269171 -0.05439596885
#> [11553,] 0.22293080666 -0.0474066610662 0.1673363680 0.07730596924
#> [11554,] 0.19903681509 -0.0239961886983 0.1747391329 -0.01563087009
#> [11555,] -0.01774757923 -0.1081053810687 0.1815666053 0.10669899402
#> [11556,] -0.13066000378 -0.0569967766561 0.2026919137 -0.16032079326
#> [11557,] -0.55057563775 -0.0106670341173 0.2260970053 -0.90948219377
#> [11558,] -0.01506521035 -0.1097924442915 0.1496318928 0.10277578098
#> [11559,] -0.08917491682 -0.0371824230437 0.1725923400 -0.18547751747
#> [11560,] -0.03945170620 -0.0958711598668 0.1708315755 0.10099832174
#> [11561,] -0.26305857916 0.1232108007948 0.2401087868 -0.76873145808
#> [11562,] -0.03945170620 -0.0958711598668 0.1708315755 0.10099832174
#> [11563,] -0.03945170620 -0.0958711598668 0.1708315755 0.10099832174
#> [11564,] -0.02637537541 -0.1027906186836 0.1916322822 0.10999531455
#> [11565,] -0.04318434290 -0.0924271712871 0.1688614006 0.11272344117
#> [11566,] -0.23503798640 -0.0900279170654 0.2296932221 -0.07672596874
#> [11567,] -0.17881682977 -0.1451113814603 0.2122749518 0.14194894733
#> [11568,] -0.06470781099 -0.0538722289846 0.2380419542 -0.15743508700
#> [11569,] 0.00303345331 -0.1198068939047 0.1493598926 0.10848567349
#> [11570,] -0.35581812879 0.0623316336884 0.1913943357 -0.46642466092
#> [11571,] -0.11011721968 -0.0146489029241 0.1827249923 -0.30230402231
#> [11572,] -0.21355446182 -0.0476393962467 0.2393135944 -0.19578958177
#> [11573,] 0.30153706859 -0.0861716452601 -3.9033425995 -0.43091264527
#> [11574,] 0.18443949616 -0.0117021668681 0.3916671639 -0.02968021327
#> [11575,] 0.29962043825 -0.0842937998830 -3.9027487948 -0.43836747195
#> [11576,] 0.18217526609 0.0955315989506 -3.8481735492 -1.11707129077
#> [11577,] 0.19555561150 -0.0212881977314 0.2501596056 -0.01421650741
#> [11578,] 0.19144153913 -0.0187231488261 0.4064902546 0.00097278349
#> [11579,] 0.18554676477 -0.0110803090804 0.2107794098 -0.06169192970
#> [11580,] 0.18388568514 -0.0094528430869 0.2112940406 -0.06815277949
#> [11581,] 0.19346692021 -0.0188401921271 0.2083256110 -0.03088610089
#> [11582,] 0.19554863631 -0.0208797825860 0.2076806600 -0.02278916514
#> [11583,] 0.19666322074 -0.0219718122676 0.2073353428 -0.01845393493
#> [11584,] 0.18757046744 -0.0148500959806 0.3991933571 -0.01579304313
#> [11585,] 0.19836935054 -0.0254304527078 0.3958476795 0.02620973656
#> [11586,] 0.19832181811 -0.0253838821424 0.3958624058 0.02602485686
#> [11587,] 0.19745861891 -0.0245381506605 0.3961298396 0.02266740171
#> [11588,] 0.19706829075 -0.0241557211899 0.3962507699 0.02114920141
#> [11589,] 0.19631367506 -0.0234163759080 0.3964845627 0.01821408705
#> [11590,] 0.19576720541 -0.0228809646341 0.3966538683 0.01608856686
#> [11591,] 0.30153706859 -0.0861716452601 -3.9033425995 -0.43091264527
#> [11592,] 0.18743380368 -0.0125275807367 0.1677136664 -0.06289772770
#> [11593,] -0.14309640971 0.0562596251328 0.1884732915 -0.39567206290
#> [11594,] -0.43043717100 0.3635226905608 0.2249524945 -0.94626245475
#> [11595,] 0.15996864836 -0.0802393394102 0.2063037600 0.08234415037
#> [11596,] -1.21750564273 1.0423360894368 0.5164809524 -2.86686218971
#> [11597,] 0.07891072574 -0.0327583069121 0.3710581499 0.09631192380
#> [11598,] 0.06592287814 -0.2572782109086 0.2209358649 0.06100998677
#> [11599,] 0.00952980713 -0.0804286675566 0.1753016484 -0.21648877974
#> [11600,] -0.08288454378 0.0620614868571 0.1875761952 0.07893169275
#> [11601,] -0.16146388449 -0.4729507135270 0.1981363813 0.01782537427
#> [11602,] 0.11074049431 -0.0518205833623 0.2546717730 0.08225532749
#> [11603,] -0.10367887251 0.2026029486325 0.5104238015 -1.21485960078
#> [11604,] 0.22738707483 -0.1217635428384 0.4078539417 0.07283746180
#> [11605,] 0.10964121129 -0.1676381055004 0.2211483228 0.06458414358
#> [11606,] -0.82702515594 0.8735942855223 0.4697189677 -3.37308807261
#> [11607,] -0.19825283338 0.0154344827084 0.1834912760 0.08426844348
#> [11608,] 0.21425094006 -0.0411312155087 0.4057956803 0.09097288401
#> [11609,] 0.21425094006 -0.0411312155087 0.4057956803 0.09097288401
#> [11610,] 0.21428492830 -0.0411645159668 0.4057851502 0.09110508293
#> [11611,] 0.24490635250 -0.0479564255207 0.3850531021 0.08459740606
#> [11612,] 0.24346737132 -0.0467473541437 0.4067394762 0.08327318267
#> [11613,] 0.15221162454 0.0052962983204 0.1598842546 0.01692479763
#> [11614,] 0.15591710987 0.0016657972580 0.1587362323 0.03133746256
#> [11615,] 0.16041475718 -0.0042168232943 0.1959277722 0.07445869047
#> [11616,] 0.14492327302 0.0109611749404 0.2007272974 0.01420381133
#> [11617,] 0.16977411488 -0.0081016760524 0.1908366640 0.02550077625
#> [11618,] 0.05650647440 -0.0641702285776 0.2153024697 0.08641499188
#> [11619,] 0.15498594247 -0.0031788112924 0.2054993625 0.08920967019
#> [11620,] 0.17349336286 -0.0160842598991 0.2159025985 0.10362370212
#> [11621,] 0.11415514478 0.0358426867279 0.2045917011 -0.04469396528
#> [11622,] 0.14946907971 -0.0008686932780 0.2027071922 0.11308049282
#> [11623,] 0.13262044039 0.0223704004809 0.2152416918 -0.03071647929
#> [11624,] 0.12632388431 0.0266934498606 0.2047853562 -0.03740731036
#> [11625,] 0.14186944385 0.0150071088821 0.2043870621 -0.02280298379
#> [11626,] 0.15486117028 0.0025794690622 0.1685011743 0.02131982088
#> [11627,] -0.01742165598 0.1326540370338 0.3945209221 -0.21590137547
#> [11628,] 0.17340777098 -0.0159088978256 0.1942538286 0.10288257794
#> [11629,] 0.15816664504 0.0030053820929 0.2038061844 -0.00682745006
#> [11630,] 0.17256130554 -0.0110979878273 0.1993464738 0.04916128027
#> [11631,] 0.16865828056 -0.0133299455156 0.2158590031 0.10283904513
#> [11632,] 0.12468471474 0.0197209436479 0.2049138430 0.07159566516
#> [11633,] 0.10190514146 0.0438540953954 0.2273737351 -0.05930964980
#> [11634,] 0.15892545380 -0.0067704538203 0.2035488091 0.10979971728
#> [11635,] 0.18471937310 -0.0231104198101 0.2061999745 0.09858705569
#> [11636,] 0.18471937310 -0.0231104198101 0.2061999745 0.09858705569
#> [11637,] 0.12496015812 0.0259093925831 0.2357272695 -0.02036762278
#> [11638,] 0.12496015812 0.0259093925831 0.2357272695 -0.02036762278
#> [11639,] 0.14453418478 0.0011347319535 0.2253118320 0.10663190170
#> [11640,] 0.16009090375 -0.0032953549551 0.1984024966 0.05207234518
#> [11641,] 0.14510251791 0.0116025583702 0.2138995538 -0.00685078407
#> [11642,] 0.17366918901 -0.0162180907209 0.1944917422 0.10142506905
#> [11643,] 0.05315093282 0.0923279651131 0.1960959992 -0.22628373903
#> [11644,] 0.13687515437 0.0175007941264 0.2138114217 -0.01135025780
#> [11645,] 0.18174129804 -0.0213994191385 0.2168827490 0.09919561740
#> [11646,] 0.14829789077 0.0060363194275 0.2230996760 0.01756531750
#> [11647,] 0.17885941989 -0.0193868944113 0.2055809848 0.10124065578
#> [11648,] 0.12596966315 0.0111593787127 0.3418478196 0.10879377458
#> [11649,] 0.07580463242 0.0428224610454 0.3347153596 0.12932796228
#> [11650,] 0.17743589379 -0.0183977865861 0.1945754713 0.10171978296
#> [11651,] 0.16775895301 -0.0119476066473 0.2574955545 0.11466357411
#> [11652,] 0.12872653773 0.0099362333478 0.3692622617 0.11498107355
#> [11653,] 0.13822903570 0.0197295186206 0.2039822972 -0.02750878500
#> [11654,] 0.14773013300 0.0091723108790 0.2231998249 0.00899706133
#> [11655,] 0.11056293471 0.0399703673178 0.2134057606 -0.03448378436
#> [11656,] 0.16792990142 -0.0131798094880 0.2484341781 0.10311343972
#> [11657,] 0.16912307240 -0.0129912310396 0.2042453414 0.10760571603
#> [11658,] 0.15726353227 0.0029952339490 0.2140989114 -0.00106749586
#> [11659,] 0.15147785482 -0.0005123095708 0.1683270033 0.12458132556
#> [11660,] 0.16849009481 -0.0135278762407 0.2270200674 0.10101957538
#> [11661,] 0.17624372930 -0.0176801154202 0.1945081171 0.10188665194
#> [11662,] 0.15086978346 0.0062106417036 0.2123138333 0.01323062765
#> [11663,] 0.12318953394 0.0220838009960 0.2107572308 0.01918373234
#> [11664,] 0.17069009851 -0.0145163580657 0.1944581364 0.10098429196
#> [11665,] 0.12028537092 0.0324327939222 0.2048840349 -0.04586765420
#> [11666,] 0.12284087804 0.0299290000860 0.2040922953 -0.03592788529
#> [11667,] 0.16699485253 -0.0116453683715 0.1932991712 0.10755207893
#> [11668,] 0.14271753490 0.0121406730718 0.2008206970 0.01312427426
#> [11669,] 0.16699485253 -0.0116453683715 0.1932991712 0.10755207893
#> [11670,] 0.13627765696 0.0184502335388 0.2028158806 -0.01192394340
#> [11671,] 0.16161558300 -0.0049437308895 0.1985025877 0.05372153769
#> [11672,] 0.15282342104 0.0046326736061 0.1698795810 0.00710764162
#> [11673,] 0.14312688849 0.0125282712293 0.2244351973 -0.00421770322
#> [11674,] 0.17243032422 -0.0153416254869 0.2156913643 0.10473557137
#> [11675,] 0.16293079114 -0.0093012401964 0.2146817484 0.10907663097
#> [11676,] 0.15942692313 -0.0073051787741 0.2146502148 0.10850731868
#> [11677,] 0.13847828010 0.0145846043180 0.2222016975 0.01462036069
#> [11678,] 0.14814668054 0.0084970759059 0.2135638613 0.00033577348
#> [11679,] 0.12265132766 0.0290583408518 0.2031739258 -0.02578510461
#> [11680,] 0.14891086064 0.0054944271717 0.2098432931 0.03800708488
#> [11681,] 0.16630108658 -0.0115438898832 0.2044555054 0.10564721233
#> [11682,] 0.14100156610 0.0132436690945 0.2122937270 0.00724350010
#> [11683,] 0.14646673174 0.0065671465602 0.2095728017 0.04051494709
#> [11684,] 0.16307752802 -0.0097075133746 0.2044264946 0.10512344502
#> [11685,] 0.13903494370 0.0147349747054 0.2868466847 0.01709507141
#> [11686,] 0.15381175365 0.0044613833320 0.2031537731 0.00027263993
#> [11687,] 0.17296841541 -0.0158188784364 0.1944854354 0.10131120659
#> [11688,] 0.06366522957 -0.0680418814361 0.2150633847 0.08951082639
#> [11689,] 0.16928855130 -0.0137179334968 0.1944455230 0.10075656704
#> [11690,] 0.17168268443 -0.0162557527470 0.1747308185 0.08824444871
#> [11691,] 0.00341228969 -0.0065469375557 0.2367865468 -0.15878280247
#> [11692,] 0.06935305404 -0.0719630545436 0.3019621918 0.09171787790
#> [11693,] 0.15836246277 0.0018504853830 0.2036928967 -0.00302745851
#> [11694,] 0.18225015610 -0.0220279939417 0.1959234430 0.09419440378
#> [11695,] 0.18242534950 -0.0221277970128 0.1959250197 0.09422286939
#> [11696,] 0.13267550218 0.0207415757756 0.1725471767 -0.03208688316
#> [11697,] 0.13801231284 0.0153942505204 0.1718647720 -0.01897963301
#> [11698,] 0.16320098532 -0.0010744689718 0.1932533664 -0.00477602534
#> [11699,] 0.17011764985 -0.0065866937777 0.1920935066 0.01063462284
#> [11700,] 0.16602883846 -0.0025806236399 0.1933602899 -0.00526900742
#> [11701,] 0.14281153286 0.0079305306001 0.1946845619 0.07476802876
#> [11702,] 0.08765346228 0.0547818165910 0.2180382689 -0.08269204900
#> [11703,] -0.00312846414 0.1251615070018 0.1715945469 -0.12958989583
#> [11704,] 0.13018881131 0.0212806002565 0.2155604903 -0.02720980082
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#> [11910,] 0.09997198375 -0.0164124240202 0.1920091106 0.11585983586
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#> [11912,] 0.08881015748 -0.0001771270055 0.1890342253 0.02186484502
#> [11913,] 0.09174346666 -0.0052096757298 0.1771237896 0.04038217635
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#> [11915,] 0.07801582879 0.0086519000411 0.2027472838 -0.01146334695
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#> [11917,] 0.09832580261 -0.0134027804418 0.1543539225 0.08059785869
#> [11918,] 0.08409854629 0.0016943483939 0.1594332954 0.01661421303
#> [11919,] 0.10332192402 -0.0187998061721 0.2249358253 0.11479209342
#> [11920,] 0.05910725239 0.0192265588025 0.2441886885 0.00059443870
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#> [11922,] 0.05465879815 0.0253997261561 0.2248746021 -0.02984951058
#> [11923,] 0.10178000935 -0.0179358876088 0.2142123724 0.11344911886
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#> [11981,] 0.07632309612 -0.0028185314131 0.1916173434 0.11315675005
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#> [11995,] 0.09144927753 -0.0113076112852 0.1915654779 0.11681157139
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#> [12000,] 0.07523023851 0.0067627993242 0.1984580375 0.03249648561
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#> [12003,] -0.02044549654 -0.1063033155632 0.2154913375 0.11180450534
#> [12004,] 0.09626247590 -0.0135857056397 0.1909270273 0.12193492604
#> [12005,] 0.04133145087 -0.0987289342897 0.2792393099 0.10649980899
#> [12006,] 0.05914881212 0.0258431206725 0.2379465907 -0.05517248553
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#> [12317,] 0.19965114589 -0.0246984831646 0.1851690794 -0.01110501880
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#> [12324,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
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#> [12329,] 0.19452003078 -0.0217393440708 0.4055364855 0.01294672611
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#> [12336,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
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#> [12338,] 0.21688071808 -0.0436475401369 0.3986087644 0.09991970410
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#> [12344,] 0.21822518221 -0.0444829003434 0.3472148985 0.09489442968
#> [12345,] 0.21783304684 -0.0442392536165 0.3622047760 0.09636013472
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#> [12349,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
#> [12350,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
#> [12351,] 0.21861731758 -0.0447265470703 0.3322250210 0.09342872465
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#> [12353,] 0.20047096160 -0.0273891402546 0.3845762879 0.03224767287
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#> [12357,] 0.21716081477 -0.0438215735133 0.3879017090 0.09887277193
#> [12358,] 0.21828120155 -0.0445177070187 0.3450734874 0.09468504325
#> [12359,] 0.21828120155 -0.0445177070187 0.3450734874 0.09468504325
#> [12360,] 0.21811314353 -0.0444132869929 0.3514977207 0.09531320255
#> [12361,] 0.21828120155 -0.0445177070187 0.3450734874 0.09468504325
#> [12362,] 0.19241267837 -0.0195140036368 0.3891969364 0.00133186573
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#> [12681,] 0.21727285345 -0.0438911868638 0.3836188868 0.09845399906
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#> [12710,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
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#> [12716,] 0.21688071808 -0.0436475401369 0.3986087644 0.09991970410
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#> [12723,] 0.36169964124 -0.0803599180376 -3.9037932532 -0.41880252468
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#> [12750,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
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#> [12785,] 0.11549208936 -0.0989698420298 0.1961310432 0.08288157527
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#> [12788,] 0.10719479964 -0.0476381541697 0.3695006893 0.11244589228
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#> [12791,] 0.08444378276 -0.0332674669440 0.3500541584 0.12041469594
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#> [12793,] 0.11284297986 -0.0969542352703 0.2189706471 0.08929678017
#> [12794,] 0.09090575757 -0.0385670785395 0.2151361972 0.09406805775
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#> [12799,] 0.06527638986 -0.0213343886592 0.2088904619 0.11434848626
#> [12800,] 0.17198710368 0.0294186953595 0.2160837681 0.08362953569
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#> [12803,] 0.36048297031 -0.0856158869954 -3.9150782943 -0.31034953916
#> [12804,] 0.20992840694 -0.1111153578045 0.2854191723 0.07455612520
#> [12805,] 0.18701928066 0.0772414090346 -3.8741705528 -0.86048220959
#> [12806,] 0.09679795529 -0.0379100894439 0.2715289942 0.13814005847
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#> [12808,] 0.02018187534 0.0076583737370 0.2787449724 0.14463942015
#> [12809,] -0.39794971571 0.0842295563420 0.2541502747 -0.54817549335
#> [12810,] 0.12583239898 -0.0584580794126 0.2197343548 0.10017995353
#> [12811,] -0.08932027162 0.1058987908991 0.2321552917 -0.20135816638
#> [12812,] -0.05316669811 0.0498306029546 0.3225848997 0.14036758334
#> [12813,] -0.03189949535 0.0390971277122 0.2027059504 0.14622915985
#> [12814,] 0.37885764972 -0.0984536039552 -3.9114293454 -0.32954646246
#> [12815,] 0.37885764972 -0.0984536039552 -3.9114293454 -0.32954646246
#> [12816,] 0.37860209901 -0.0982032245715 -3.9113501714 -0.33054043935
#> [12817,] 0.37863065433 -0.0982950105727 -3.9114744234 -0.32930930931
#> [12818,] 0.24061839498 -0.0106041075942 0.4006304505 0.11901192940
#> [12819,] 0.37080999813 -0.0899575862743 -3.9078305869 -0.37157721564
#> [12820,] 0.12684749720 0.1228730070704 -3.8796236759 -0.86066597305
#> [12821,] 0.11800893331 -0.0453000732095 0.2025828165 0.17996134699
#> [12822,] -0.59681164088 0.2687975084783 0.1648357336 0.26789656240
#> [12823,] -0.67659053586 0.3724950268074 0.2580762383 -0.67402696784
#> [12824,] -0.02531496253 0.0670044353399 0.1834874247 -0.29660377116
#> [12825,] 0.05519955645 -0.0578806483045 0.1856790189 0.13618548305
#> [12826,] 0.04242202085 -0.0453616791238 0.1896377167 0.08648663848
#> [12827,] -0.24109692803 0.1600468667688 0.3720533739 0.14435902965
#> [12828,] -0.23606319536 0.1898314409243 0.3947013337 -0.32464495051
#> [12829,] -0.25763614829 0.2622958101568 0.2707581454 -0.72180565380
#> [12830,] -0.05256671111 0.0656061941790 0.2267579790 -0.09598132049
#> [12831,] 0.22813799029 -0.1224591046479 0.4033731847 0.07490363116
#> [12832,] 0.24609170416 -0.0490776322825 0.3804377493 0.08835333614
#> [12833,] 0.24592364615 -0.0489732122566 0.3868619825 0.08898149544
#> [12834,] 0.24592364615 -0.0489732122566 0.3868619825 0.08898149544
#> [12835,] 0.35840975804 -0.0771366089668 -3.9027739914 -0.43159868498
#> [12836,] 0.22046588604 -0.0240506948502 0.3968732848 -0.00961042112
#> [12837,] 0.24586762681 -0.0489384055814 0.3890033936 0.08919088187
#> [12838,] 0.24586762681 -0.0489384055814 0.3890033936 0.08919088187
#> [12839,] 0.24586762681 -0.0489384055814 0.3890033936 0.08919088187
#> [12840,] 0.24586762681 -0.0489384055814 0.3890033936 0.08919088187
#> [12841,] 0.24586762681 -0.0489384055814 0.3890033936 0.08919088187
#> [12842,] 0.21924951576 -0.0228589390601 0.3972501370 -0.01434155232
#> [12843,] 0.24592364615 -0.0489732122566 0.3868619825 0.08898149544
#> [12844,] 0.24592364615 -0.0489732122566 0.3868619825 0.08898149544
#> [12845,] 0.24592364615 -0.0489732122566 0.3868619825 0.08898149544
#> [12846,] 0.24592364615 -0.0489732122566 0.3868619825 0.08898149544
#> [12847,] 0.24592364615 -0.0489732122566 0.3868619825 0.08898149544
#> [12848,] 0.24592364615 -0.0489732122566 0.3868619825 0.08898149544
#> [12849,] 0.24592364615 -0.0489732122566 0.3868619825 0.08898149544
#> [12850,] 0.24592364615 -0.0489732122566 0.3868619825 0.08898149544
#> [12851,] 0.24490144330 -0.0479716947222 0.3871786783 0.08500558787
#> [12852,] 0.24547549144 -0.0486947588545 0.4039932711 0.09065658691
#> [12853,] 0.35835445894 -0.1188302095257 -3.9109500500 -0.33125707729
#> [12854,] 0.35835445894 -0.1188302095257 -3.9109500500 -0.33125707729
#> [12855,] 0.24547549144 -0.0486947588545 0.4039932711 0.09065658691
#> [12856,] 0.24547549144 -0.0486947588545 0.4039932711 0.09065658691
#> [12857,] 0.24547549144 -0.0486947588545 0.4039932711 0.09065658691
#> [12858,] 0.18623839063 -0.0236231214877 0.1735028093 0.09926323172
#> [12859,] 0.18047391335 -0.0203738352139 0.2164251363 0.10183100791
#> [12860,] 0.13470049674 0.0193457988255 0.1646787028 0.03364022183
#> [12861,] 0.17753944051 -0.0133542208153 0.1670647293 0.04663037312
#> [12862,] 0.18453681022 -0.0199423179514 0.1529595451 0.06425978046
#> [12863,] 0.17007331446 -0.0111844598437 0.2507912273 0.07556593936
#> [12864,] 0.16488457689 -0.0042267540653 0.2440231070 0.03002159459
#> [12865,] 0.19329377975 -0.0244454858729 0.2411420375 0.07130706004
#> [12866,] 0.17089002888 -0.0114792459022 0.2404059362 0.07150391426
#> [12867,] 0.18231428891 -0.0188634887570 0.1754991258 0.07511633447
#> [12868,] 0.17811113207 -0.0153508701071 0.1871674642 0.06435762985
#> [12869,] 0.17303900546 -0.0101764613534 0.1785669665 0.03852954615
#> [12870,] 0.15362957713 -0.0001261310643 0.1993318243 0.04430087638
#> [12871,] 0.15262707875 0.0035348479466 0.1969009093 0.05565703362
#> [12872,] 0.17028058339 -0.0110223575111 0.2170112402 0.08501717223
#> [12873,] 0.17666935119 -0.0172818421014 0.2150318913 0.10986659451
#> [12874,] 0.13847034987 0.0141650220379 0.2453464159 0.00386415504
#> [12875,] 0.03750459596 0.0842064924134 0.3883640486 0.00091554996
#> [12876,] 0.12040333844 -0.0293202598546 0.2155192751 0.10922032554
#> [12877,] 0.10532584643 -0.0145478762215 0.2201905385 0.05057568896
#> [12878,] 0.11029956471 -0.0222449203084 0.1920273098 0.11801382905
#> [12879,] 0.10435188806 -0.0133516523087 0.1965998700 0.06417259581
#> [12880,] 0.11574372607 -0.0258952728231 0.2143448359 0.11567468998
#> [12881,] 0.12603322252 -0.0277152806683 0.1761714584 0.06434713457
#> [12882,] 0.12018749227 -0.0235011441056 0.2434201934 0.04280698107
#> [12883,] 0.07762837404 0.0041377014347 0.1783690751 0.02328767161
#> [12884,] 0.10949153147 -0.0229248091324 0.2795426292 0.11486739437
#> [12885,] 0.10648767557 -0.0196110702770 0.1913135015 0.12172134715
#> [12886,] 0.10337543789 -0.0122615255328 0.2086568002 0.05256798627
#> [12887,] 0.10644204644 -0.0152660781362 0.2077067128 0.06449570897
#> [12888,] 0.10363098861 -0.0125119049164 0.2085776263 0.05356196316
#> [12889,] 0.10081993078 -0.0097577316967 0.2094485398 0.04262821736
#> [12890,] 0.11947513275 -0.0280354267005 0.2036688410 0.11518853042
#> [12891,] 0.08833360521 -0.0090620722348 0.2015765715 0.12166696244
#> [12892,] 0.06997579125 0.0057838788216 0.1502303340 0.06391121293
#> [12893,] 0.04331225408 -0.1005122491740 0.2093961319 0.09437600861
#> [12894,] 0.11027482618 -0.0233238589018 0.2687495020 0.11447913943
#> [12895,] 0.11679074332 -0.0214431285412 0.2206756421 0.05028841155
#> [12896,] 0.12852277706 -0.0337203553547 0.1937994683 0.11073447850
#> [12897,] 0.08691956189 -0.0003660890154 0.2418709381 0.03634031773
#> [12898,] 0.10736311211 -0.0207839068397 0.2352355639 0.11938246920
#> [12899,] 0.09196838969 -0.0050972133187 0.2404742891 0.05401910555
#> [12900,] 0.08921341685 -0.0019958237749 0.2430257122 0.02827698186
#> [12901,] 0.07377343856 -0.1175155884399 0.1941332629 0.10125745783
#> [12902,] 0.02163471126 -0.0778354949517 0.2109248251 0.01313332692
#> [12903,] 0.04722840991 -0.1031669707657 0.2100542533 0.09104600503
#> [12904,] 0.09491596453 -0.0064754313398 0.2216583794 0.03026787314
#> [12905,] 0.03792682510 -0.0241310702007 0.2123959107 0.12580550663
#> [12906,] 0.03854115895 -0.0186092633915 0.2155464769 0.08419598754
#> [12907,] 0.03949506767 -0.0198123364085 0.2136985525 0.10137653202
#> [12908,] 0.03687129715 -0.0180716254380 0.2042310378 0.08876275472
#> [12909,] 0.04837107919 -0.0293386977006 0.2006682098 0.13349171482
#> [12910,] 0.04723610224 -0.0285457307882 0.2004428196 0.13467748057
#> [12911,] 0.02139673024 -0.0081208975462 0.1955781574 0.06401746412
#> [12912,] 0.00747882904 0.0060290099045 0.2191927276 0.02813140619
#> [12913,] 0.04372141841 -0.0200190890935 0.2192154490 0.05113026474
#> [12914,] 0.04730319151 -0.0262804249678 0.1945695786 0.08762553929
#> [12915,] 0.01587316963 -0.0077570464017 0.2026954459 0.10086426742
#> [12916,] 0.04832214257 -0.0302061738584 0.2019837395 0.12510404315
#> [12917,] 0.04832214257 -0.0302061738584 0.2019837395 0.12510404315
#> [12918,] 0.03428851458 -0.0221585891169 0.2125103928 0.12427685974
#> [12919,] 0.05905597430 -0.0376838498484 0.1933526466 0.11313558440
#> [12920,] 0.03926836056 -0.0244465193337 0.1902866790 0.12830970287
#> [12921,] -0.01192681052 0.0204602520247 0.2437599417 -0.00917264251
#> [12922,] 0.31814786487 -0.1024463051950 -3.9084889066 -0.36630414734
#> [12923,] 0.31150354636 -0.0959364412211 -3.9064303837 -0.39214754651
#> [12924,] 0.20092850941 -0.0279579034547 0.3971788639 0.03659098551
#> [12925,] 0.33619547224 -0.0607452012395 -3.9056099500 -0.42368115549
#> [12926,] 0.36430605055 -0.0882869334370 -3.9143190852 -0.31434369745
#> [12927,] 0.18907719300 -0.0203142260433 0.2424484078 0.05490644134
#> [12928,] 0.36191662540 -0.0866175294110 -3.9147935909 -0.31184734852
#> [12929,] 0.35808336472 -0.0828618386568 -3.9136059816 -0.32675700189
#> [12930,] 0.36191662540 -0.0866175294110 -3.9147935909 -0.31184734852
#> [12931,] 0.35833891543 -0.0831122180404 -3.9136851555 -0.32576302500
#> [12932,] 0.35807058719 -0.0828493196876 -3.9136020229 -0.32680670073
#> [12933,] 0.35836447051 -0.0831372559788 -3.9136930729 -0.32566362731
#> [12934,] 0.36191662540 -0.0866175294110 -3.9147935909 -0.31184734852
#> [12935,] 0.35744448794 -0.0822358901978 -3.9134080467 -0.32924194412
#> [12936,] -0.06076237187 -0.0010723807000 0.2152776122 0.06589656869
#> [12937,] -0.02100548261 -0.0298620901032 0.2117094643 0.12120551401
#> [12938,] -0.01398124941 -0.0377860167355 0.2116495794 0.13397300500
#> [12939,] -0.01398124941 -0.0377860167355 0.2116495794 0.13397300500
#> [12940,] -0.01894488616 -0.0241783471095 0.2236035043 0.04111279061
#> [12941,] -0.00625167416 -0.0367770233891 0.2168613676 0.09617743672
#> [12942,] -0.05734628725 -0.0541689077077 0.2099827454 0.16373725018
#> [12943,] -0.05734628725 -0.0541689077077 0.2099827454 0.16373725018
#> [12944,] -0.00346736636 -0.0421575777375 0.2115123866 0.15101502785
#> [12945,] -0.12110524747 -0.0569886777514 0.2111342974 0.14247069202
#> [12946,] -0.12646750219 -0.0581164204549 0.2070800174 0.16799522877
#> [12947,] -0.43463145873 -0.1400989285450 0.2021053237 0.23474258277
#> [12948,] -0.04125950975 -0.0114923308962 0.2203527629 0.04478510883
#> [12949,] -0.08164136508 -0.0405212731553 0.2100472246 0.15798689363
#> [12950,] -0.14392394245 -0.0909283073724 0.3905245520 0.20261295719
#> [12951,] -0.94383871126 -0.2751693754403 0.3667143742 0.40077537001
#> [12952,] -3.45572717187 0.1257581947622 0.2709772249 0.69212209653
#> [12953,] 0.27090374660 -0.0301740261749 0.2258877084 0.05311310768
#> [12954,] 0.26885934091 -0.0281709911060 0.2265211001 0.04516129255
#> [12955,] 0.26885934091 -0.0281709911060 0.2265211001 0.04516129255
#> [12956,] 0.27075431628 -0.0299071453976 0.2131896725 0.04996823298
#> [12957,] 0.26706672207 -0.0270571774973 0.2950462546 0.05186165843
#> [12958,] 0.27339947053 -0.0332818554124 0.2952083167 0.07692046714
#> [12959,] 0.26586072452 -0.0258956635958 0.2975439484 0.04759814885
#> [12960,] 0.26675515202 -0.0267719914384 0.2972668396 0.05107706797
#> [12961,] 0.26837884000 -0.0282021900052 0.2797713508 0.05397427020
#> [12962,] 0.26592555317 -0.0257985479225 0.2805314207 0.04443209205
#> [12963,] 0.26957992835 -0.0293789731082 0.2793992332 0.05864596159
#> [12964,] 0.26715219658 -0.0270003689639 0.2801513858 0.04920318112
#> [12965,] 0.26765052047 -0.0274886087619 0.2799969965 0.05114143606
#> [12966,] 0.27126656305 -0.0310314770400 0.2788766851 0.06520620907
#> [12967,] 0.26771440815 -0.0275512036078 0.2799772031 0.05138993028
#> [12968,] 0.26434113875 -0.0242461957441 0.2810222993 0.03826943532
#> [12969,] 0.26880001313 -0.0286148402673 0.2796408642 0.05561244352
#> [12970,] 0.26873612545 -0.0285522454214 0.2796606577 0.05536394929
#> [12971,] 0.26426447354 -0.0241710819290 0.2810460515 0.03797124225
#> [12972,] 0.26425566424 -0.0243030042776 0.2959171681 0.04092791263
#> [12973,] 0.27345548987 -0.0333166620876 0.2930669057 0.07671108071
#> [12974,] 0.26400011352 -0.0240526248939 0.2959963420 0.03993393574
#> [12975,] 0.26923890312 -0.0291854022580 0.2943732759 0.06031046201
#> [12976,] 0.26693894671 -0.0269319878055 0.2950858415 0.05136466998
#> [12977,] 0.26412788888 -0.0241778145857 0.2959567550 0.04043092418
#> [12978,] 0.26515009173 -0.0251793321202 0.2956400592 0.04440683175
#> [12979,] 0.26361678746 -0.0236770558185 0.2961151030 0.03844297040
#> [12980,] 0.26681117136 -0.0268067981137 0.2951254285 0.05086768154
#> [12981,] 0.27345548987 -0.0333166620876 0.2930669057 0.07671108071
#> [12982,] 0.25658914288 -0.0167916227692 0.2982923867 0.01110860589
#> [12983,] 0.26739893799 -0.0273826706960 0.2949433284 0.05315382839
#> [12984,] 0.27345548987 -0.0333166620876 0.2930669057 0.07671108071
#> [12985,] 0.26689711306 -0.0268910007004 0.2950988023 0.05120195597
#> [12986,] 0.25888909928 -0.0190450372217 0.2975798211 0.02005439791
#> [12987,] 0.27345548987 -0.0333166620876 0.2930669057 0.07671108071
#> [12988,] 0.26476676566 -0.0248037630448 0.2957588202 0.04291586641
#> [12989,] 0.25441696183 -0.0146633980084 0.2989653654 0.00265980231
#> [12990,] 0.26784500640 -0.0271972617422 0.2289594135 0.04164326564
#> [12991,] 0.27011443041 -0.0291798129930 0.2027676433 0.04534298400
#> [12992,] 0.26937333335 -0.0284537127805 0.2029972478 0.04246045102
#> [12993,] 0.26668339600 -0.0266816084219 0.2951650155 0.05037069309
#> [12994,] 0.26988154375 -0.0291725086404 0.2262044043 0.04913720011
#> [12995,] 0.26652791114 -0.0258064239709 0.2187471953 0.03438397790
#> [12996,] 0.26959451968 -0.0288109765743 0.2177971079 0.04631170059
#> [12997,] 0.27010562111 -0.0293117353415 0.2176387599 0.04829965438
#> [12998,] 0.27547218606 -0.0345697023974 0.2159761069 0.06917316909
#> [12999,] 0.27547218606 -0.0345697023974 0.2159761069 0.06917316909
#> [13000,] 0.26946674433 -0.0286857868825 0.2178366948 0.04581471215
#> [13001,] 0.26952969104 -0.0289080922475 0.2348096355 0.04947775740
#> [13002,] 0.27127133599 -0.0304940189090 0.2215257123 0.05368831170
#> [13003,] 0.27530412804 -0.0344652823716 0.2224003401 0.06980132839
#> [13004,] 0.27536014738 -0.0345000890468 0.2202589290 0.06959194196
#> [13005,] 0.27050468386 -0.0297428807582 0.2217632342 0.05070638103
#> [13006,] 0.26577699568 -0.0251108621614 0.2232279524 0.03231780854
#> [13007,] 0.27024913314 -0.0294925013746 0.2218424081 0.04971240414
#> [13008,] 0.26922693030 -0.0284909838401 0.2221591040 0.04573649657
#> [13009,] 0.26804359681 -0.0275725449697 0.2480143848 0.04626117999
#> [13010,] 0.27003891054 -0.0297282720531 0.2686367560 0.05829481324
#> [13011,] 0.26733007299 -0.0270742505868 0.2694760000 0.04775865820
#> [13012,] 0.26876115698 -0.0284763751350 0.2690326258 0.05332492879
#> [13013,] 0.26812228020 -0.0278504266760 0.2692305607 0.05083998656
#> [13014,] 0.27412772193 -0.0337343421909 0.2673699727 0.07419844350
#> [13015,] 0.27502403135 -0.0342912489952 0.2331073955 0.07084826056
#> [13016,] 0.26952969104 -0.0289080922475 0.2348096355 0.04947775740
#> [13017,] 0.26607975643 -0.0255279705688 0.2358784839 0.03605906937
#> [13018,] 0.26993857218 -0.0293086992613 0.2346829572 0.05106812043
#> [13019,] 0.27351150921 -0.0333514687629 0.2909254946 0.07650169428
#> [13020,] 0.27351150921 -0.0333514687629 0.2909254946 0.07650169428
#> [13021,] 0.26622831391 -0.0262156563299 0.2931819523 0.04817335288
#> [13022,] 0.26049120043 -0.0205946391678 0.2949594076 0.02585857167
#> [13023,] 0.27351150921 -0.0333514687629 0.2909254946 0.07650169428
#> [13024,] 0.25779514042 -0.0179531366707 0.2957946929 0.01537211547
#> [13025,] 0.26482278500 -0.0248385697201 0.2936174091 0.04270647998
#> [13026,] 0.25716904118 -0.0173397071808 0.2959886691 0.01293687208
#> [13027,] 0.26558943713 -0.0255897078709 0.2933798872 0.04568841065
#> [13028,] 0.26431168357 -0.0243378109528 0.2937757570 0.04071852619
#> [13029,] 0.26098952432 -0.0210828789659 0.2948050184 0.02779682661
#> [13030,] 0.25690071293 -0.0170768088280 0.2960718017 0.01189319635
#> [13031,] 0.26303393001 -0.0230859140348 0.2941716268 0.03574864174
#> [13032,] 0.25506074780 -0.0152740772660 0.2966418542 0.00473656273
#> [13033,] 0.27351150921 -0.0333514687629 0.2909254946 0.07650169428
#> [13034,] 0.27367956722 -0.0334558887887 0.2845012614 0.07587353498
#> [13035,] 0.26090203162 -0.0209369196081 0.2884599591 0.02617469041
#> [13036,] 0.27367956722 -0.0334558887887 0.2845012614 0.07587353498
#> [13037,] 0.25502436525 -0.0151781937850 0.2902809601 0.00331322192
#> [13038,] 0.26384086481 -0.0238162825196 0.2875494587 0.03760542466
#> [13039,] 0.25706877094 -0.0171812288539 0.2896475685 0.01126503705
#> [13040,] 0.26384086481 -0.0238162825196 0.2875494587 0.03760542466
#> [13041,] 0.26281866196 -0.0228147649852 0.2878661545 0.03362951710
#> [13042,] 0.26690747335 -0.0268208351230 0.2865993712 0.04953314736
#> [13043,] 0.26460751695 -0.0245674206704 0.2873119368 0.04058735534
#> [13044,] 0.27367956722 -0.0334558887887 0.2845012614 0.07587353498
#> [13045,] 0.27367956722 -0.0334558887887 0.2845012614 0.07587353498
#> [13046,] 0.26154090840 -0.0215628680671 0.2882620243 0.02865963264
#> [13047,] 0.26524639373 -0.0251933691295 0.2871140019 0.04307229756
#> [13048,] 0.26281866196 -0.0228147649852 0.2878661545 0.03362951710
#> [13049,] 0.27367956722 -0.0334558887887 0.2845012614 0.07587353498
#> [13050,] 0.26281866196 -0.0228147649852 0.2878661545 0.03362951710
#> [13051,] 0.25655766952 -0.0166804700866 0.2898059164 0.00927708326
#> [13052,] 0.26026315484 -0.0203109711490 0.2886578940 0.02368974819
#> [13053,] 0.26096874219 -0.0205203828965 0.2374619631 0.01617953155
#> [13054,] 0.26582420572 -0.0252775911851 0.2359576579 0.03506509248
#> [13055,] 0.26702139396 -0.0265710274352 0.2483310806 0.04228527243
#> [13056,] 0.21727285345 -0.0438911868638 0.3836188868 0.09845399906
#> [13057,] 0.20653972355 -0.0333752527520 0.3869441930 0.05670696963
#> [13058,] 0.21727285345 -0.0438911868638 0.3836188868 0.09845399906
#> [13059,] 0.20122426874 -0.0281673615729 0.3885910112 0.03603225029
#> [13060,] 0.15849618970 0.0136960713672 0.4018288967 -0.13016068592
#> [13061,] 0.19337886188 -0.0204807144960 0.3910216517 0.00551715973
#> [13062,] 0.21727285345 -0.0438911868638 0.3836188868 0.09845399906
#> [13063,] 0.21727285345 -0.0438911868638 0.3836188868 0.09845399906
#> [13064,] 0.20509391197 -0.0320189358082 0.3937642960 0.05236524447
#> [13065,] 0.20149192469 -0.0284898383961 0.3948802529 0.03835514019
#> [13066,] 0.20087732523 -0.0278876759786 0.3950706663 0.03596462577
#> [13067,] 0.21704877610 -0.0437519601627 0.3921845311 0.09929154480
#> [13068,] 0.21704877610 -0.0437519601627 0.3921845311 0.09929154480
#> [13069,] 0.21704877610 -0.0437519601627 0.3921845311 0.09929154480
#> [13070,] 0.21704877610 -0.0437519601627 0.3921845311 0.09929154480
#> [13071,] 0.21704877610 -0.0437519601627 0.3921845311 0.09929154480
#> [13072,] 0.21704877610 -0.0437519601627 0.3921845311 0.09929154480
#> [13073,] 0.21704877610 -0.0437519601627 0.3921845311 0.09929154480
#> [13074,] 0.21704877610 -0.0437519601627 0.3921845311 0.09929154480
#> [13075,] 0.21704877610 -0.0437519601627 0.3921845311 0.09929154480
#> [13076,] 0.21704877610 -0.0437519601627 0.3921845311 0.09929154480
#> [13077,] 0.21704877610 -0.0437519601627 0.3921845311 0.09929154480
#> [13078,] 0.21704877610 -0.0437519601627 0.3921845311 0.09929154480
#> [13079,] 0.21704877610 -0.0437519601627 0.3921845311 0.09929154480
#> [13080,] 0.21704877610 -0.0437519601627 0.3921845311 0.09929154480
#> [13081,] 0.21704877610 -0.0437519601627 0.3921845311 0.09929154480
#> [13082,] 0.21704877610 -0.0437519601627 0.3921845311 0.09929154480
#> [13083,] 0.21704877610 -0.0437519601627 0.3921845311 0.09929154480
#> [13084,] 0.21704877610 -0.0437519601627 0.3921845311 0.09929154480
#> [13085,] 0.21704877610 -0.0437519601627 0.3921845311 0.09929154480
#> [13086,] 0.21704877610 -0.0437519601627 0.3921845311 0.09929154480
#> [13087,] 0.21704877610 -0.0437519601627 0.3921845311 0.09929154480
#> [13088,] 0.20119770458 -0.0280409396889 0.3779789646 0.03379254585
#> [13089,] 0.31431460419 -0.0986906144408 -3.9073012973 -0.38121380070
#> [13090,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
#> [13091,] 0.20378468506 -0.0306558862076 0.3856736954 0.04556383739
#> [13092,] 0.31367572741 -0.0980646659818 -3.9071033624 -0.38369874293
#> [13093,] 0.21716081477 -0.0438215735133 0.3879017090 0.09887277193
#> [13094,] 0.21716081477 -0.0438215735133 0.3879017090 0.09887277193
#> [13095,] 0.20219536145 -0.0291188032306 0.3882901502 0.03980936248
#> [13096,] 0.21727285345 -0.0438911868638 0.3836188868 0.09845399906
#> [13097,] 0.30984246673 -0.0943089752276 -3.9059157530 -0.39860839630
#> [13098,] 0.30562587998 -0.0901777153979 -3.9046093828 -0.41500901501
#> [13099,] 0.31303685063 -0.0974387175227 -3.9069054275 -0.38618368516
#> [13100,] 0.31738121273 -0.1016951670442 -3.9082513847 -0.36928607801
#> [13101,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
#> [13102,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
#> [13103,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
#> [13104,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
#> [13105,] 0.30920358995 -0.0936830267685 -3.9057178181 -0.40109333853
#> [13106,] 0.31687011131 -0.1011944082769 -3.9080930368 -0.37127403179
#> [13107,] 0.20151620201 -0.0285136244376 0.3948727314 0.03844956800
#> [13108,] 0.19793849204 -0.0250083130670 0.3959811667 0.02453389152
#> [13109,] 0.20232277116 -0.0293038718481 0.3946228425 0.04158675786
#> [13110,] 0.20586056411 -0.0327700739590 0.3935267741 0.05534717515
#> [13111,] 0.20049399916 -0.0275121069031 0.3951894272 0.03447366043
#> [13112,] 0.20189952807 -0.0288891935130 0.3947539704 0.03994053333
#> [13113,] 0.20087732523 -0.0278876759786 0.3950706663 0.03596462577
#> [13114,] 0.19985512238 -0.0268861584441 0.3953873621 0.03198871820
#> [13115,] 0.19896069489 -0.0260098306015 0.3956644709 0.02850979908
#> [13116,] 0.20177175272 -0.0287640038212 0.3947935574 0.03944354489
#> [13117,] 0.19017338641 -0.0175408956297 0.4132553158 -0.00267792893
#> [13118,] 0.18349106751 -0.0109938002414 0.4153256119 -0.02866913246
#> [13119,] 0.19342348037 -0.0207252206305 0.4122483815 0.00996346918
#> [13120,] 0.19217705732 -0.0195040202248 0.4126345445 0.00511544629
#> [13121,] 0.19255593681 -0.0198752326990 0.4125171612 0.00658911643
#> [13122,] 0.21671266006 -0.0435431201111 0.4050329976 0.10054786340
#> [13123,] 0.19764959916 -0.0248658196111 0.4109390580 0.02640116322
#> [13124,] 0.19777124129 -0.0249850001977 0.4109013712 0.02687429622
#> [13125,] 0.19303315221 -0.0203427911599 0.4123693118 0.00844526887
#> [13126,] 0.19394390939 -0.0212351182452 0.4120871437 0.01198770312
#> [13127,] 0.19278621356 -0.0201008495615 0.4124458176 0.00748478900
#> [13128,] 0.19719658441 -0.0244219720778 0.4110794097 0.02463914039
#> [13129,] 0.19743077108 -0.0246514197449 0.4110068547 0.02555002081
#> [13130,] 0.19303315221 -0.0203427911599 0.4123693118 0.00844526887
#> [13131,] 0.19199229416 -0.0193229959305 0.4126917873 0.00439680100
#> [13132,] 0.20292130368 -0.0300308458398 0.4093057943 0.04690571371
#> [13133,] 0.19589549907 -0.0231472155220 0.4114825080 0.01957850584
#> [13134,] 0.19719658441 -0.0244219720778 0.4110794097 0.02463914039
#> [13135,] 0.19251272318 -0.0198328935452 0.4125305495 0.00642103493
#> [13136,] 0.18879055040 -0.0161860427091 0.4136837419 -0.00805653668
#> [13137,] 0.19706648354 -0.0242945039336 0.4111197171 0.02413310675
#> [13138,] 0.19682542255 -0.0240583210610 0.4111944019 0.02319548835
#> [13139,] 0.19223169407 -0.0195575513370 0.4126176171 0.00532795855
#> [13140,] 0.19134176427 -0.0186856301715 0.4128933325 0.00186653342
#> [13141,] 0.19550519647 -0.0227648110894 0.4116034304 0.01806040493
#> [13142,] 0.19719658441 -0.0244219720778 0.4110794097 0.02463914039
#> [13143,] 0.19182651841 -0.0191605748243 0.4127431474 0.00375200819
#> [13144,] 0.18916429332 -0.0165522225576 0.4135679500 -0.00660284548
#> [13145,] 0.20240087466 -0.0295209482250 0.4094670321 0.04488147978
#> [13146,] 0.19648229461 -0.0237221366626 0.4113007088 0.02186087558
#> [13147,] 0.20266107639 -0.0297758845134 0.4093864171 0.04589354705
#> [13148,] 0.19188820835 -0.0192210164075 0.4127240348 0.00399195421
#> [13149,] 0.18067295648 -0.0082327165506 0.4161987106 -0.03963031203
#> [13150,] 0.19119604925 -0.0185428638470 0.4129384775 0.00129976780
#> [13151,] 0.17768048320 -0.0053007990065 0.4171258297 -0.05126968203
#> [13152,] 0.21760896948 -0.0441000269154 0.3707704204 0.09719768046
#> [13153,] 0.19895376751 -0.0258223319117 0.3765501191 0.02463736740
#> [13154,] 0.21760896948 -0.0441000269154 0.3707704204 0.09719768046
#> [13155,] 0.20738694101 -0.0340848515709 0.3739373786 0.05743860481
#> [13156,] 0.21760896948 -0.0441000269154 0.3707704204 0.09719768046
#> [13157,] 0.19096300341 -0.0179932690413 0.3790257937 -0.00644309722
#> [13158,] 0.30805361175 -0.0925563195423 -3.9053615353 -0.40556623454
#> [13159,] 0.32964739136 -0.1137131270782 -3.9120516554 -0.32157618121
#> [13160,] 0.18495449769 -0.0120862724882 0.3787632756 -0.03024074805
#> [13161,] 0.31239797385 -0.0968127690637 -3.9067074926 -0.38866862739
#> [13162,] 0.32078006276 -0.1050252378841 -3.9093044063 -0.35606608596
#> [13163,] 0.31338424627 -0.0977790832568 -3.9070130566 -0.38483247297
#> [13164,] 0.30991913194 -0.0943840890426 -3.9059395052 -0.39831020323
#> [13165,] 0.30894803924 -0.0934326473849 -3.9056386442 -0.40208731542
#> [13166,] 0.31546458239 -0.0998173216671 -3.9076575801 -0.37674090469
#> [13167,] 0.31175909707 -0.0961868206047 -3.9065095577 -0.39115356962
#> [13168,] 0.29770380791 -0.0824159545059 -3.9021549901 -0.44582229863
#> [13169,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
#> [13170,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
#> [13171,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
#> [13172,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
#> [13173,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
#> [13174,] 0.31252574921 -0.0969379587555 -3.9067470796 -0.38817163894
#> [13175,] 0.19341914454 -0.0204599448300 0.3846370054 0.00439201198
#> [13176,] 0.21744091147 -0.0439956068896 0.3771946536 0.09782583976
#> [13177,] 0.19955236163 -0.0264690500367 0.3827368305 0.02824745737
#> [13178,] 0.21744091147 -0.0439956068896 0.3771946536 0.09782583976
#> [13179,] 0.21749693081 -0.0440304135649 0.3750532425 0.09761645332
#> [13180,] 0.18044207757 -0.0077254029410 0.3865334661 -0.04651019590
#> [13181,] 0.21749693081 -0.0440304135649 0.3750532425 0.09761645332
#> [13182,] 0.21749693081 -0.0440304135649 0.3750532425 0.09761645332
#> [13183,] 0.21749693081 -0.0440304135649 0.3750532425 0.09761645332
#> [13184,] 0.30767028568 -0.0921807504669 -3.9052427744 -0.40705719988
#> [13185,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
#> [13186,] 0.29310389510 -0.0779091256009 -3.9007298589 -0.46371388268
#> [13187,] 0.29578717757 -0.0805381091288 -3.9015611855 -0.45327712532
#> [13188,] 0.19841812011 -0.0253979191517 0.3873363485 0.02469032268
#> [13189,] 0.18538503380 -0.0126285705874 0.3913742202 -0.02600249878
#> [13190,] 0.18870719305 -0.0158835025744 0.3903449588 -0.01308079919
#> [13191,] 0.19254045373 -0.0196391933286 0.3891573495 0.00182885418
#> [13192,] 0.16468542613 0.0076521594852 0.3977873106 -0.10651462697
#> [13193,] 0.19228490302 -0.0193888139450 0.3892365234 0.00083487729
#> [13194,] 0.21732887279 -0.0439259935391 0.3814774757 0.09824461263
#> [13195,] 0.18742943949 -0.0146316056563 0.3907408286 -0.01805068365
#> [13196,] 0.21732887279 -0.0439259935391 0.3814774757 0.09824461263
#> [13197,] 0.19688481583 -0.0238956428500 0.3878113922 0.01872646133
#> [13198,] 0.21732887279 -0.0439259935391 0.3814774757 0.09824461263
#> [13199,] 0.14577467344 0.0261802338726 0.4036461834 -0.18006891692
#> [13200,] 0.29591495293 -0.0806632988206 -3.9016007724 -0.45278013687
#> [13201,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
#> [13202,] 0.30728695961 -0.0918051813914 -3.9051240135 -0.40854816521
#> [13203,] 0.30562587998 -0.0901777153979 -3.9046093828 -0.41500901501
#> [13204,] 0.28748177943 -0.0724007791614 -3.8989880319 -0.48558137428
#> [13205,] 0.19541302719 -0.0226142697888 0.4052598200 0.01642007896
#> [13206,] 0.21688071808 -0.0436475401369 0.3986087644 0.09991970410
#> [13207,] 0.16321506857 0.0089321304219 0.4152352951 -0.10881544306
#> [13208,] 0.21732887279 -0.0439259935391 0.3814774757 0.09824461263
#> [13209,] 0.21732887279 -0.0439259935391 0.3814774757 0.09824461263
#> [13210,] -0.16781852657 -0.0920675069532 0.2221931956 -0.01251965720
#> [13211,] -0.15586555821 -0.1046407361985 0.2178197079 0.04180748445
#> [13212,] -0.15874224437 -0.1005638368369 0.2200979353 0.01582680367
#> [13213,] -0.34878187544 -0.2611519512105 0.2258823824 -0.04381114976
#> [13214,] 0.21704877610 -0.0437519601627 0.3921845311 0.09929154480
#> [13215,] 0.20510790042 -0.0321531155121 0.4065042941 0.05498331142
#> [13216,] 0.20219666671 -0.0293007935740 0.4074062438 0.04365992667
#> [13217,] 0.20128593508 -0.0284084915267 0.4076884040 0.04011759183
#> [13218,] 0.20115580866 -0.0282809983445 0.4077287194 0.03961145880
#> [13219,] 0.21732887279 -0.0439259935391 0.3814774757 0.09824461263
#> [13220,] 0.31771342866 -0.1020206602429 -3.9083543109 -0.36799390805
#> [13221,] 0.32108669806 -0.1053256681065 -3.9093994071 -0.35487341309
#> [13222,] 0.20805729114 -0.0348219527125 0.3822259141 0.06175506966
#> [13223,] 0.20438583468 -0.0313051081264 0.3918596150 0.04918386714
#> [13224,] 0.22887316907 -0.1230990901162 0.3946491924 0.07605403921
#> [13225,] 0.22859307237 -0.1229250567399 0.4053562478 0.07710097138
#> [13226,] 0.22859307237 -0.1229250567399 0.4053562478 0.07710097138
#> [13227,] 0.22859307237 -0.1229250567399 0.4053562478 0.07710097138
#> [13228,] 0.22859307237 -0.1229250567399 0.4053562478 0.07710097138
#> [13229,] 0.22898520774 -0.1231687034668 0.3903663703 0.07563526634
#> [13230,] 0.27030831600 -0.0303536488163 0.3067862856 0.06703365351
#> [13231,] 0.37664935789 -0.0950071119790 -3.9084249296 -0.36065487654
#> [13232,] 0.38342119621 -0.1016419152654 -3.9105229603 -0.33431548290
#> [13233,] 0.26181219579 -0.0218688237920 0.2924260855 0.03056937085
#> [13234,] 0.26590100718 -0.0258748939298 0.2911593022 0.04647300111
#> [13235,] 0.26321772471 -0.0232459104018 0.2919906287 0.03603624375
#> [13236,] -0.00258353252 -0.0837610119020 0.3691819969 -0.07352684973
#> [13237,] 0.10601672415 -0.0387325311000 0.2266224129 -0.03731105846
#> [13238,] 0.11103574013 -0.0436499821942 0.2250674364 -0.01778935231
#> [13239,] 0.04074416712 -0.1391657796738 0.2082777417 0.07108569977
#> [13240,] -0.62939106565 0.5210276860327 0.2807726354 -0.82305282403
#> [13241,] 0.05232598725 -0.1050923553322 0.2086618491 0.10103282339
#> [13242,] -0.07195307588 -0.1276219326026 0.2259958254 -0.12304538393
#> [13243,] -0.65718650753 -1.2070878001888 0.2289571019 -0.03429602274
#> [13244,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13245,] 0.24573003306 -0.0488437542925 0.3932941331 0.08951025705
#> [13246,] 0.24575558813 -0.0488687922308 0.3932862158 0.08960965474
#> [13247,] 0.21089746193 -0.0146156603604 0.3934655793 -0.04810909997
#> [13248,] 0.35835445894 -0.1188302095257 -3.9109500500 -0.33125707729
#> [13249,] 0.24558753012 -0.0487643722050 0.3997104490 0.09023781404
#> [13250,] 0.23672946630 -0.0390012913316 0.2877558397 0.03271102117
#> [13251,] 0.24597966549 -0.0490080189319 0.3847205714 0.08877210900
#> [13252,] 0.24597966549 -0.0490080189319 0.3847205714 0.08877210900
#> [13253,] 0.24597966549 -0.0490080189319 0.3847205714 0.08877210900
#> [13254,] 0.24597966549 -0.0490080189319 0.3847205714 0.08877210900
#> [13255,] 0.24597966549 -0.0490080189319 0.3847205714 0.08877210900
#> [13256,] 0.35835445894 -0.1188302095257 -3.9109500500 -0.33125707729
#> [13257,] 0.24581160747 -0.0489035989061 0.3911448047 0.08940026830
#> [13258,] 0.24581160747 -0.0489035989061 0.3911448047 0.08940026830
#> [13259,] 0.24581160747 -0.0489035989061 0.3911448047 0.08940026830
#> [13260,] 0.24575558813 -0.0488687922308 0.3932862158 0.08960965474
#> [13261,] 0.24575558813 -0.0488687922308 0.3932862158 0.08960965474
#> [13262,] 0.24575558813 -0.0488687922308 0.3932862158 0.08960965474
#> [13263,] 0.24575558813 -0.0488687922308 0.3932862158 0.08960965474
#> [13264,] 0.24575558813 -0.0488687922308 0.3932862158 0.08960965474
#> [13265,] 0.24575558813 -0.0488687922308 0.3932862158 0.08960965474
#> [13266,] 0.24575558813 -0.0488687922308 0.3932862158 0.08960965474
#> [13267,] 0.24575558813 -0.0488687922308 0.3932862158 0.08960965474
#> [13268,] 0.24575558813 -0.0488687922308 0.3932862158 0.08960965474
#> [13269,] 0.24575558813 -0.0488687922308 0.3932862158 0.08960965474
#> [13270,] 0.24575558813 -0.0488687922308 0.3932862158 0.08960965474
#> [13271,] 0.24575558813 -0.0488687922308 0.3932862158 0.08960965474
#> [13272,] 0.24575558813 -0.0488687922308 0.3932862158 0.08960965474
#> [13273,] 0.24575558813 -0.0488687922308 0.3932862158 0.08960965474
#> [13274,] 0.24575558813 -0.0488687922308 0.3932862158 0.08960965474
#> [13275,] 0.24575558813 -0.0488687922308 0.3932862158 0.08960965474
#> [13276,] 0.35835445894 -0.1188302095257 -3.9109500500 -0.33125707729
#> [13277,] 0.35835445894 -0.1188302095257 -3.9109500500 -0.33125707729
#> [13278,] 0.35835445894 -0.1188302095257 -3.9109500500 -0.33125707729
#> [13279,] 0.24597966549 -0.0490080189319 0.3847205714 0.08877210900
#> [13280,] 0.24597966549 -0.0490080189319 0.3847205714 0.08877210900
#> [13281,] 0.24597966549 -0.0490080189319 0.3847205714 0.08877210900
#> [13282,] 0.24581160747 -0.0489035989061 0.3911448047 0.08940026830
#> [13283,] 0.24581160747 -0.0489035989061 0.3911448047 0.08940026830
#> [13284,] 0.24581160747 -0.0489035989061 0.3911448047 0.08940026830
#> [13285,] 0.24581160747 -0.0489035989061 0.3911448047 0.08940026830
#> [13286,] 0.24581160747 -0.0489035989061 0.3911448047 0.08940026830
#> [13287,] 0.24581160747 -0.0489035989061 0.3911448047 0.08940026830
#> [13288,] 0.24581160747 -0.0489035989061 0.3911448047 0.08940026830
#> [13289,] 0.24581160747 -0.0489035989061 0.3911448047 0.08940026830
#> [13290,] 0.24581160747 -0.0489035989061 0.3911448047 0.08940026830
#> [13291,] 0.24581160747 -0.0489035989061 0.3911448047 0.08940026830
#> [13292,] 0.24581160747 -0.0489035989061 0.3911448047 0.08940026830
#> [13293,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13294,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13295,] 0.24260841427 -0.0459057789595 0.4070055957 0.07993222754
#> [13296,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13297,] 0.24350284176 -0.0467821068021 0.4067284869 0.08341114666
#> [13298,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13299,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13300,] 0.24363061712 -0.0469072964939 0.4066888999 0.08390813510
#> [13301,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13302,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13303,] 0.24439726925 -0.0476584346448 0.4064513780 0.08689006578
#> [13304,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13305,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13306,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13307,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13308,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13309,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13310,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13311,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13312,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13313,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13314,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13315,] 0.24503614603 -0.0482843831038 0.4062534432 0.08937500800
#> [13316,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13317,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13318,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13319,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13320,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13321,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13322,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13323,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13324,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13325,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13326,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13327,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13328,] 0.24490837068 -0.0481591934120 0.4062930301 0.08887801956
#> [13329,] 0.24414171854 -0.0474080552611 0.4065305520 0.08589608889
#> [13330,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13331,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13332,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13333,] 0.24350284176 -0.0467821068021 0.4067284869 0.08341114666
#> [13334,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13335,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13336,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13337,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13338,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13339,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13340,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13341,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13342,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13343,] 0.24541947210 -0.0486599521792 0.4061346822 0.09086597334
#> [13344,] 0.24631552597 -0.0492166086042 0.3718721842 0.08751479642
#> [13345,] 0.24631578152 -0.0492168589835 0.3718721050 0.08751579040
#> [13346,] 0.35835445894 -0.1188302095257 -3.9109500500 -0.33125707729
#> [13347,] 0.35835445894 -0.1188302095257 -3.9109500500 -0.33125707729
#> [13348,] 0.24307324662 -0.0460800981837 0.3771248081 0.07575834635
#> [13349,] 0.35835445894 -0.1188302095257 -3.9109500500 -0.33125707729
#> [13350,] 0.24301722728 -0.0460452915085 0.3792662192 0.07596773278
#> [13351,] 0.35682115467 -0.1173279332240 -3.9104750063 -0.33722093863
#> [13352,] 0.35705851017 -0.1175604855955 -3.9105485430 -0.33629773290
#> [13353,] 0.35835445894 -0.1188302095257 -3.9109500500 -0.33125707729
#> [13354,] 0.35835445894 -0.1188302095257 -3.9109500500 -0.33125707729
#> [13355,] 0.35835445894 -0.1188302095257 -3.9109500500 -0.33125707729
#> [13356,] 0.24620374284 -0.0491472456330 0.3761549271 0.08793456327
#> [13357,] 0.24620374284 -0.0491472456330 0.3761549271 0.08793456327
#> [13358,] 0.24620374284 -0.0491472456330 0.3761549271 0.08793456327
#> [13359,] 0.24620374284 -0.0491472456330 0.3761549271 0.08793456327
#> [13360,] 0.35579895182 -0.1163264156896 -3.9101583104 -0.34119684620
#> [13361,] 0.35835445894 -0.1188302095257 -3.9109500500 -0.33125707729
#> [13362,] 0.24603568482 -0.0490428256072 0.3825791604 0.08856272257
#> [13363,] 0.24437460520 -0.0474153596137 0.3830937911 0.08210187278
#> [13364,] 0.24603568482 -0.0490428256072 0.3825791604 0.08856272257
#> [13365,] 0.35507063229 -0.1156128344463 -3.9099326647 -0.34402968034
#> [13366,] 0.35835445894 -0.1188302095257 -3.9109500500 -0.33125707729
#> [13367,] 0.35820112851 -0.1186799818955 -3.9109025456 -0.33185346342
#> [13368,] 0.11714759768 0.0422929767809 0.0616372118 -0.19262439169
#> [13369,] 0.13308598383 0.0084330770744 -0.0034265133 0.09175132019
#> [13370,] 0.02892731639 0.1183815871803 0.1911691451 -0.38501423949
#> [13371,] 0.08651851282 0.0681124316404 0.1822343309 -0.26860823646
#> [13372,] -0.26231530196 0.3678919306490 0.1317512049 -1.20747443573
#> [13373,] -0.06676614759 0.2033428418634 0.0710290675 -0.67922099550
#> [13374,] 0.11877945748 0.0381407412724 0.3227132532 -0.13614574670
#> [13375,] 0.05655634149 0.0965750139298 0.1866224687 -0.36035884316
#> [13376,] 0.02489183386 0.1252503038657 0.2178384810 -0.45698136346
#> [13377,] -0.10002918048 0.2274994761197 0.2188531789 -0.73925156570
#> [13378,] 0.12356283012 -0.1032110532243 0.1549025303 0.08389255762
#> [13379,] 0.01574896205 0.0307913926761 0.1473218779 0.09089469071
#> [13380,] -0.05643427261 0.1310508103651 0.0919420820 -0.46864826443
#> [13381,] -0.03172301082 0.1117690621262 0.0512004074 -0.41703163824
#> [13382,] -0.03244047143 0.1123876945893 0.1897709989 -0.41550006946
#> [13383,] 0.06370115552 0.0036623697567 0.1818156933 0.10350874087
#> [13384,] -0.11901760353 0.1826836290401 0.2384250717 -0.60718473636
#> [13385,] 0.03879628113 0.0492483671808 0.2394644805 -0.19345625215
#> [13386,] 0.07496331701 -0.0025997292252 0.1516448443 0.10409707866
#> [13387,] -0.13961460556 0.1998049987982 0.2072863735 -0.65596619636
#> [13388,] -0.08731421556 0.1587888728363 0.0862469190 -0.56351270685
#> [13389,] 0.01902067923 -0.0866307114893 0.1726290571 0.08758015787
#> [13390,] -0.17290107270 0.2385061422885 0.2239519772 -0.81844532085
#> [13391,] -0.12783172664 0.1221966045717 0.1889595921 -0.37791877847
#> [13392,] 0.02055298873 -0.0143079540236 0.1458175302 0.11635367201
#> [13393,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
#> [13394,] 0.32964764691 -0.1137133774576 -3.9120517346 -0.32157518723
#> [13395,] -0.46950670158 0.0652665860470 0.0891492939 -0.37595088413
#> [13396,] -0.52960804862 0.0585020524930 0.0593080055 -0.35060691222
#> [13397,] -0.38640363839 -0.0808858724393 0.0074495625 0.19416610701
#> [13398,] -0.47305693768 0.1270285237011 0.0961582234 -0.52894899729
#> [13399,] -0.40245336628 0.1129709770483 0.0844696129 -0.38444085265
#> [13400,] -0.62484238799 0.1242102449578 0.1877045853 -0.46080763998
#> [13401,] -0.45617891810 -0.0410401482269 0.1354497745 0.19521710823
#> [13402,] -0.45617891810 -0.0410401482269 0.1354497745 0.19521710823
#> [13403,] -0.16414797122 -0.0369296171148 0.0998422010 0.14969364464
#> [13404,] -0.51105640993 0.0381414159352 0.1728574107 -0.25452571096
#> [13405,] -0.39350308243 -0.0770331005269 0.1364373910 0.20270365900
#> [13406,] -0.39350308243 -0.0770331005269 0.1364373910 0.20270365900
#> [13407,] -0.13780109968 0.0079598533178 0.1165481549 -0.04065341139
#> [13408,] -0.20201931862 -0.0582593556744 0.0343645109 0.15740926579
#> [13409,] -0.01331797081 -0.0379124682905 0.0331540467 0.12054714193
#> [13410,] -1.01888466474 0.1013959383943 0.2113362294 -0.79436738334
#> [13411,] -0.96570944374 0.0680441048675 0.0784863333 -0.43815952951
#> [13412,] -0.78426843825 -0.1097252574979 0.0222728247 0.26756406326
#> [13413,] -0.57416006809 -0.0591722980090 0.1815625363 0.22402569452
#> [13414,] -2.16147630222 -0.1736650652581 0.1202601000 0.53813524180
#> [13415,] -2.78656385580 0.7767605428012 0.5121447615 -2.46972718846
#> [13416,] 0.22919672507 0.0113114621060 0.1729635375 -0.12235394328
#> [13417,] 0.25692397732 -0.0158547010161 0.1643731633 -0.01450745058
#> [13418,] 0.24235758673 -0.0015830761501 0.1688860788 -0.07116413338
#> [13419,] 0.24184648531 -0.0010823173829 0.1690444267 -0.07315208717
#> [13420,] 0.26292941905 -0.0217386165310 0.1625125753 0.00885100636
#> [13421,] 0.27609028071 -0.0346331547871 0.1584351166 0.06004081626
#> [13422,] 0.26093410531 -0.0195828894476 0.1418902041 -0.00318262689
#> [13423,] 0.26817325409 -0.0273783136231 0.2139893294 0.03992906638
#> [13424,] 0.26584430659 -0.0232291426068 0.0171737309 -0.00886619026
#> [13425,] 0.22855784829 0.0119374105650 0.1731614724 -0.12483888551
#> [13426,] 0.23992985497 0.0007955279942 0.1696382314 -0.08060691385
#> [13427,] 0.27698470821 -0.0355094826297 0.1581580078 0.06351973538
#> [13428,] 0.26855153471 -0.0272469629705 0.1607707483 0.03071849797
#> [13429,] 0.24135676635 0.0003211281580 0.0714896046 -0.09471158582
#> [13430,] 0.18051431444 0.0590087346843 0.1880461761 -0.31170654106
#> [13431,] 0.24976855738 -0.0088440782749 0.1665900341 -0.04233880354
#> [13432,] 0.18754195902 0.0521233016349 0.1858688923 -0.28437217655
#> [13433,] 0.25278607396 -0.0120013228928 0.1868957095 -0.02632926272
#> [13434,] 0.23354108717 0.0070550125845 0.1716175803 -0.10545633613
#> [13435,] 0.22651344259 0.0139404456339 0.1737948641 -0.13279070064
#> [13436,] 0.26516078296 -0.0247279887334 0.2467834742 0.03462105931
#> [13437,] 0.26139611478 -0.0202363402293 0.1629876191 0.00288714501
#> [13438,] 0.24682972419 -0.0059647153634 0.1675005346 -0.05376953779
#> [13439,] 0.22292692332 0.0173138346560 0.1897744160 -0.14374970674
#> [13440,] 0.21986031478 0.0203183872593 0.1907245035 -0.15567742944
#> [13441,] 0.26408034279 -0.0228662501610 0.1621559996 0.01332758009
#> [13442,] 0.24787748211 -0.0069912708362 0.1671759213 -0.04969423253
#> [13443,] 0.25067743996 -0.0086302206541 0.0494854034 -0.06230386097
#> [13444,] 0.23737434785 0.0032993218303 0.1704299709 -0.09054668276
#> [13445,] 0.24870735347 -0.0090090922112 0.2943621331 -0.02082982549
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#> [13513,] 0.27547218606 -0.0345697023974 0.2159761069 0.06917316909
#> [13514,] 0.26351355808 -0.0234755201195 0.2855268085 0.03590507289
#> [13515,] 0.27698470821 -0.0355094826297 0.1581580078 0.06351973538
#> [13516,] 0.23219662304 0.0078903727910 0.2230114461 -0.10043106172
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#> [13524,] 0.25330222083 -0.0130090013881 0.2398371817 -0.01363977519
#> [13525,] 0.19998337859 0.0398131725059 0.1947586610 -0.23341701339
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#> [13527,] 0.26444826823 -0.0243310782961 0.2788650534 0.03825884426
#> [13528,] 0.25192628335 -0.0120624884991 0.2827445772 -0.01044602341
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#> [13533,] 0.26585561095 -0.0251276494029 0.2168314300 0.03134175733
#> [13534,] 0.26019516268 -0.0195817460559 0.2185851331 0.00932516918
#> [13535,] 0.24495667629 -0.0054146300162 0.3040203780 -0.03370916085
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#> [13537,] 0.26189968849 -0.0220147831498 0.2987711448 0.03219150704
#> [13538,] 0.25883307995 -0.0190102305464 0.2997212322 0.02026378434
#> [13539,] 0.25691644961 -0.0171323851693 0.3003150369 0.01280895766
#> [13540,] 0.25093656295 -0.0112735075928 0.3021677075 -0.01045010159
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#> [13544,] 0.25443458043 -0.0143995533114 0.2692231322 -0.00325353843
#> [13545,] 0.20524106838 0.0337984780341 0.2844641186 -0.19459409000
#> [13546,] 0.24932356619 -0.0093919656391 0.2708066113 -0.02313307626
#> [13547,] 0.26120667430 -0.0210346069772 0.2671250223 0.02308684918
#> [13548,] 0.23546969034 0.0044827487896 0.2432379476 -0.08342754401
#> [13549,] 0.23674744390 0.0032308518715 0.2428420778 -0.07845765956
#> [13550,] 0.22328442182 0.0180076813780 0.0792127796 -0.16457757021
#> [13551,] 0.24759637633 -0.0067158535142 0.1672630127 -0.05078760711
#> [13552,] 0.23406664368 0.0076444392808 0.0546317106 -0.12691235890
#> [13553,] 0.26034835686 -0.0192097847565 0.1633122323 -0.00118816024
#> [13554,] 0.26241831762 -0.0212378577638 0.1626709233 0.00686305258
#> [13555,] 0.26106995339 -0.0205191507043 0.2268103294 0.01443681555
#> [13556,] 0.26093350498 -0.0210480722906 0.2969464295 0.02800621304
#> [13557,] 0.24706830432 -0.0068008392382 0.2311482784 -0.04002327772
#> [13558,] 0.26099328817 -0.0204440368892 0.2268340816 0.01413862248
#> [13559,] 0.27530412804 -0.0344652823716 0.2224003401 0.06980132839
#> [13560,] 0.24399916583 -0.0037938078790 0.2320991497 -0.05196084078
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#> [13562,] 0.26022663604 -0.0196928987384 0.2270716035 0.01115669181
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#> [13564,] 0.25772223906 -0.0172391807790 0.2278475083 0.00141571828
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#> [13570,] 0.26680410773 -0.0260971104944 0.2207856803 0.03588553429
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#> [13575,] 0.25663318939 -0.0161320110265 0.2239368037 -0.00367474598
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#> [13579,] 0.26030720136 -0.0196513594064 0.2143023110 0.00890639632
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#> [13582,] 0.25513640393 -0.0152478071355 0.2859981380 0.00289444905
#> [13583,] 0.26690054598 -0.0266333364332 0.2674850194 0.04566071567
#> [13584,] 0.26907272703 -0.0287615611939 0.2668120408 0.05410951925
#> [13585,] 0.26460058957 -0.0243799219807 0.2681975850 0.03671492365
#> [13586,] 0.26575056777 -0.0255066292069 0.2678413022 0.04118781966
#> [13587,] 0.26651721991 -0.0262577673578 0.2676037803 0.04416975033
#> [13588,] 0.26677277062 -0.0265081467414 0.2675246064 0.04516372723
#> [13589,] 0.25160341149 -0.0106418022492 0.1660215651 -0.03520204946
#> [13590,] 0.25585080058 -0.0153252965344 0.2199310904 -0.00757243797
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#> [13597,] 0.15032682316 0.0215194109803 0.4234764033 -0.15809034607
#> [13598,] 0.21676867940 -0.0435779267864 0.4028915865 0.10033847696
#> [13599,] 0.14772467803 0.0240688990539 0.4242825921 -0.16821151577
#> [13600,] 0.14642359269 0.0253436556097 0.4246856905 -0.17327215032
#> [13601,] 0.14252038778 0.0291678752012 0.4258949697 -0.18845385516
#> [13602,] 0.11129464629 0.0597617320849 0.4355692354 -0.30990789150
#> [13603,] 0.12040214145 0.0508385363461 0.4327475785 -0.27448384727
#> [13604,] 0.14832325447 0.0234824354237 0.4240971430 -0.16588332370
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#> [13606,] 0.12040214145 0.0508385363461 0.4327475785 -0.27448384727
#> [13607,] 0.13863668139 0.0329729908457 0.4270982080 -0.20355971957
#> [13608,] 0.12300428657 0.0482890482725 0.4319413897 -0.26436267757
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#> [13610,] 0.10218712558 0.0686849528616 0.4383909002 -0.34533203513
#> [13611,] 0.12690751704 0.0444648036430 0.4307321026 -0.24918087333
#> [13612,] 0.11779999632 0.0533880244198 0.4335537674 -0.28460501696
#> [13613,] 0.11714946643 0.0540253901787 0.4337553126 -0.28713528453
#> [13614,] 0.02698514425 0.1423651456709 0.4616897527 -0.63783378962
#> [13615,] 0.15162788294 0.0202446794624 0.4230733129 -0.15302981093
#> [13616,] 0.12966577809 0.0417623588040 0.4298775464 -0.23845248315
#> [13617,] 0.16268701889 0.0094093363710 0.4196470045 -0.11001476517
#> [13618,] 0.11259570607 0.0584870005670 0.4351661450 -0.30484735635
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#> [13621,] 0.11389679141 0.0572122440113 0.4347630466 -0.29978672180
#> [13622,] 0.15497163623 0.0169685904175 0.4220373613 -0.14002412029
#> [13623,] 0.11519785120 0.0559375124934 0.4343599562 -0.29472618666
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#> [13625,] 0.10869250117 0.0623112201585 0.4363754242 -0.32002906119
#> [13626,] 0.16333754878 0.0087719706121 0.4194454593 -0.10748449760
#> [13627,] 0.12625698714 0.0451021694020 0.4309336478 -0.25171114090
#> [13628,] 0.08852587006 0.0820697589887 0.4426233894 -0.39846815118
#> [13629,] 0.11604354517 0.0551089319992 0.4340979458 -0.29143681893
#> [13630,] 0.16949179769 0.0027422591821 0.4175387683 -0.08354724791
#> [13631,] 0.10255143867 0.0683280120123 0.4382780298 -0.34391502167
#> [13632,] 0.10219233881 0.0686798451222 0.4383892850 -0.34531175800
#> [13633,] 0.14056877255 0.0310799975159 0.4264996133 -0.19604475728
#> [13634,] 0.11649893654 0.0546627559376 0.4339568578 -0.28966555211
#> [13635,] 0.08787534017 0.0827071247477 0.4428249347 -0.40099841875
#> [13636,] 0.18805791469 -0.0154481535686 0.4117866696 -0.01133343520
#> [13637,] 0.02021956693 0.1489938146623 0.4637858436 -0.66414883082
#> [13638,] 0.15423002807 0.0176951913888 0.4222671241 -0.14290864123
#> [13639,] 0.12560643170 0.0457395601988 0.4311352009 -0.25424150788
#> [13640,] 0.14915586424 0.0226666743539 0.4238391863 -0.16264484759
#> [13641,] 0.13682168357 0.0347512603420 0.4276605252 -0.21061924164
#> [13642,] 0.14512253291 0.0266183871276 0.4250887809 -0.17833268546
#> [13643,] 0.03843458280 0.1311473981469 0.4581425219 -0.59330064296
#> [13644,] 0.12820857682 0.0431900721252 0.4303290121 -0.24412033818
#> [13645,] 0.21676867940 -0.0435779267864 0.4028915865 0.10033847696
#> [13646,] 0.09145310125 0.0792017633012 0.4417164834 -0.38708254348
#> [13647,] 0.14317091768 0.0285305094423 0.4256934245 -0.18592358759
#> [13648,] 0.10348821092 0.0674101963058 0.4379878018 -0.34027140058
#> [13649,] 0.13276233718 0.0387284617368 0.4289181797 -0.22640826637
#> [13650,] 0.10075596492 0.0700871525237 0.4388342981 -0.35089860391
#> [13651,] 0.14525263378 0.0264909189834 0.4250484735 -0.17782665183
#> [13652,] 0.16281711976 0.0092818682268 0.4196066971 -0.10950873154
#> [13653,] 0.13052189853 0.0409235628309 0.4296123057 -0.23512256117
#> [13654,] 0.13081072195 0.0406405840516 0.4295228233 -0.23399916849
#> [13655,] 0.10622045691 0.0647332400880 0.4371413056 -0.32964419725
#> [13656,] 0.14395157399 0.0277656505012 0.4254515639 -0.18288718698
#> [13657,] 0.15618164330 0.0157830690741 0.4216624805 -0.13531773911
#> [13658,] 0.11259570607 0.0584870005670 0.4351661450 -0.30484735635
#> [13659,] 0.21676867940 -0.0435779267864 0.4028915865 0.10033847696
#> [13660,] 0.13212742143 0.0393505293154 0.4291148874 -0.22887780195
#> [13661,] 0.13731609753 0.0342668513485 0.4275073474 -0.20869619455
#> [13662,] 0.15026175995 0.0215831575713 0.4234965610 -0.15834341259
#> [13663,] 0.12479625927 0.0465333379587 0.4313862061 -0.25739271281
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#> [13665,] 0.07356352921 0.0967293216717 0.4472589770 -0.45666490177
#> [13666,] 0.07876781946 0.0916303455244 0.4456465994 -0.43642256238
#> [13667,] 0.03668615594 0.1328604438137 0.4586842143 -0.60010123405
#> [13668,] 0.05136074669 0.1184828083167 0.4541377766 -0.54302370144
#> [13669,] 0.06211409066 0.1079470691957 0.4508062078 -0.50119804843
#> [13670,] 0.04201252277 0.1276418614348 0.4570340153 -0.57938407190
#> [13671,] 0.15618164330 0.0157830690741 0.4216624805 -0.13531773911
#> [13672,] 0.10348821092 0.0674101963058 0.4379878018 -0.34027140058
#> [13673,] 0.17439665917 -0.0020633474414 0.4160191589 -0.06446955125
#> [13674,] 0.13887738461 0.0327371585043 0.4270236341 -0.20262349273
#> [13675,] 0.15423002807 0.0176951913888 0.4222671241 -0.14290864123
#> [13676,] 0.14382144757 0.0278931436833 0.4254918793 -0.18339332001
#> [13677,] 0.13731609753 0.0342668513485 0.4275073474 -0.20869619455
#> [13678,] 0.12170322679 0.0495637797903 0.4323444802 -0.26942321272
#> [13679,] -0.04512030353 0.2130114664510 0.4840292465 -0.91829142671
#> [13680,] 0.08397210970 0.0865313693771 0.4440342218 -0.41618022299
#> [13681,] 0.06575709383 0.1043777858926 0.4496775435 -0.48702841086
#> [13682,] 0.01770459015 0.1514578983282 0.4645650262 -0.67393095500
#> [13683,] 0.06055280358 0.1094767620399 0.4512899211 -0.50727075025
#> [13684,] 0.19739147214 -0.0224242990461 0.1794969988 -0.02117595857
#> [13685,] 0.18725693636 -0.0125550830594 0.1890090163 -0.05931289802
#> [13686,] 0.19581788521 -0.0209427924104 0.1863566887 -0.02601467217
#> [13687,] 0.20246220372 -0.0274526563844 0.1842981659 -0.00017127300
#> [13688,] 0.15432681299 0.0176606021731 0.4158649725 -0.14381402069
#> [13689,] 0.15179047217 0.0201456175554 0.4166507740 -0.15367924133
#> [13690,] 0.11220375435 0.0609190843779 0.2186339342 -0.34995406126
#> [13691,] 0.13303990277 0.0405045766006 0.2121785412 -0.26891085122
#> [13692,] 0.30713956424 -0.0269039196362 -3.8868896136 -0.63101659096
#> [13693,] 0.14294918042 0.0307355860889 0.2154806444 -0.22908640598
#> [13694,] 0.14034703529 0.0332850741625 0.2162868333 -0.23920757568
#> [13695,] 0.12603522433 0.0473072710865 0.2207208756 -0.29487405870
#> [13696,] 0.12213201942 0.0511314906780 0.2219301549 -0.31005576354
#> [13697,] 0.16637011077 0.0059413289799 0.4036375327 -0.09868013520
#> [13698,] 0.19773896067 -0.0247927403587 0.3939189296 0.02333052819
#> [13699,] 0.19428902605 -0.0214126186799 0.3949877780 0.00991184016
#> [13700,] 0.19825006209 -0.0252934991259 0.3937605817 0.02531848198
#> [13701,] 0.21716081477 -0.0438215735133 0.3879017090 0.09887277193
#> [13702,] 0.19173351893 -0.0189088248437 0.3957795176 -0.00002792875
#> [13703,] 0.19216795514 -0.0193344697959 0.3956449219 0.00166183197
#> [13704,] 0.18087261368 -0.0082677010402 0.3991444107 -0.04227194663
#> [13705,] 0.17933930940 -0.0067654247385 0.3996194544 -0.04823580797
#> [13706,] 0.21716081477 -0.0438215735133 0.3879017090 0.09887277193
#> [13707,] 0.19224462036 -0.0194095836110 0.3956211697 0.00196002503
#> [13708,] 0.16860617950 0.0037505093732 0.4029447606 -0.08998283741
#> [13709,] 0.16732842594 0.0050024062913 0.4033406304 -0.09495272186
#> [13710,] 0.18457809900 -0.0118982021026 0.3979963883 -0.02785928170
#> [13711,] 0.16860617950 0.0037505093732 0.4029447606 -0.08998283741
#> [13712,] 0.19163129865 -0.0188086730903 0.3958111872 -0.00042551951
#> [13713,] 0.18713360612 -0.0144019959387 0.3972046488 -0.01791951279
#> [13714,] 0.19173351893 -0.0189088248437 0.3957795176 -0.00002792875
#> [13715,] 0.21716081477 -0.0438215735133 0.3879017090 0.09887277193
#> [13716,] 0.18215036724 -0.0095195979583 0.3987485409 -0.03730206217
#> [13717,] 0.21716081477 -0.0438215735133 0.3879017090 0.09887277193
#> [13718,] 0.07251911181 0.0978931576118 0.4327141680 -0.46371814851
#> [13719,] 0.16783952737 0.0045016475241 0.4031822825 -0.09296476808
#> [13720,] 0.18572807720 -0.0130249093288 0.3976401055 -0.02338638569
#> [13721,] 0.18905026201 -0.0162798663537 0.3966108362 -0.01046458671
#> [13722,] 0.16413404204 0.0081321485865 0.4043303048 -0.10737743300
#> [13723,] 0.28722622872 -0.0721503997778 -3.8989088579 -0.48657535117
#> [13724,] 0.21749693081 -0.0440304135649 0.3750532425 0.09761645332
#> [13725,] 0.15360925282 0.0185644323384 0.3948467315 -0.15087776948
#> [13726,] 0.20366040105 -0.0288474765801 0.2072915527 0.00918921370
#> [13727,] 0.22203449724 -0.0468497542618 0.2015989452 0.08065615218
#> [13728,] 0.19775717961 -0.0230637128186 0.2091204710 -0.01377165248
#> [13729,] 0.20928251672 -0.0343558230195 0.2055497256 0.03105670531
#> [13730,] 0.19747607382 -0.0227882954966 0.2092075624 -0.01486502706
#> [13731,] -0.24867018986 -0.1045660547896 0.1440102298 0.13170087122
#> [13732,] -0.10092304625 -0.0244407196464 0.1789035887 -0.25643527270
#> [13733,] -0.25340294810 -0.0203144416892 0.1965089025 -0.24033531888
#> [13734,] -0.15884918467 -0.1129548136261 0.1672145388 0.12743613088
#> [13735,] -0.29118739703 -0.0416506412294 0.0794606833 -0.23679642913
#> [13736,] 0.22377109674 -0.0479287611952 0.1352152018 0.07416517273
#> [13737,] 0.17652380646 -0.0020391489476 0.1923343224 -0.10105992746
#> [13738,] 0.22321090336 -0.0475806944425 0.1566293126 0.07625903707
#> [13739,] 0.29131504011 -0.0761564699156 -3.9001756412 -0.47067172091
#> [13740,] 0.13156167687 0.0418123357079 0.2275049080 -0.27166954797
#> [13741,] 0.12865713993 0.0450596774943 0.1859236763 -0.29151241268
#> [13742,] 0.19599475253 -0.0209152900877 0.1650613389 -0.02959950184
#> [13743,] 0.26101278871 -0.0198607711539 0.1631063800 0.00139617968
#> [13744,] 0.26126833942 -0.0201111505375 0.1630272061 0.00239015657
#> [13745,] -0.81352016338 0.7877053087880 0.4234683595 -1.68998193160
#> [13746,] -0.42102758926 0.2612343991045 0.1405794735 0.08215203762
#> [13747,] -0.01650227901 0.0228164727027 0.2067387968 -0.33959028255
#> [13748,] 0.12721276931 -0.1776583216470 0.3372145039 0.07767989331
#> [13749,] -4.07463701829 3.2768219959548 0.9154519826 -8.67347120200
#> [13750,] 0.22859307237 -0.1229250567399 0.4053562478 0.07710097138
#> [13751,] 0.22859307237 -0.1229250567399 0.4053562478 0.07710097138
#> [13752,] 0.11556403879 -0.0434576230975 0.1353686881 0.17783897818
#> [13753,] 0.07718228960 -0.0058525676000 0.1472600066 0.02855130274
#> [13754,] -0.16809725148 0.2344634927132 0.2232517790 -0.92547537109
#> [13755,] 0.04913772003 0.0216244916026 0.1559486911 -0.08052941107
#> [13756,] 0.35375673851 -0.0809165146623 -3.9164140279 -0.30332231691
#> [13757,] -1.93408434899 1.6931518177274 0.6340458294 -4.87162178996
#> [13758,] -0.60522067236 0.3911790479767 0.2223412670 0.29705794504
#> [13759,] -0.60522067236 0.3911790479767 0.2223412670 0.29705794504
#> [13760,] 0.14133601313 0.0556263635773 0.1941151442 -0.36310847201
#> [13761,] 0.24586762681 -0.0489384055814 0.3890033936 0.08919088187
#> [13762,] 0.24586762681 -0.0489384055814 0.3890033936 0.08919088187
#> [13763,] 0.24242650150 -0.0454263615541 0.3752011254 0.07281552347
#> [13764,] 0.24625976218 -0.0491820523083 0.3740135161 0.08772517683
#> [13765,] 0.24547549144 -0.0486947588545 0.4039932711 0.09065658691
#> [13766,] 0.24547549144 -0.0486947588545 0.4039932711 0.09065658691
#> [13767,] 0.24547549144 -0.0486947588545 0.4039932711 0.09065658691
#> [13768,] 0.24547549144 -0.0486947588545 0.4039932711 0.09065658691
#> [13769,] 0.25074130928 -0.0519665863300 0.2027006299 0.07097426213
#> [13770,] 0.24564354945 -0.0487991788803 0.3975690379 0.09002842761
#> [13771,] 0.24564354945 -0.0487991788803 0.3975690379 0.09002842761
#> [13772,] 0.09261703565 -0.0853316900886 0.2164949500 0.08675829429
#> [13773,] 0.17728081104 -0.0183898547234 0.3384855677 0.11376603464
#> [13774,] 0.16661156882 -0.0079365154576 0.3417910804 0.07226749943
#> [13775,] 0.16580658407 -0.0071478203992 0.3420404783 0.06913647222
#> [13776,] 0.15853339442 -0.0044581637198 0.3401522663 0.08685216124
#> [13777,] 0.15483488563 -0.0008344980146 0.3412981272 0.07246663189
#> [13778,] 0.15395591896 0.0000266818753 0.3415704461 0.06904784837
#> [13779,] 0.17728081104 -0.0183898547234 0.3384855677 0.11376603464
#> [13780,] 0.16515362861 -0.0071125799638 0.3411494638 0.07720789084
#> [13781,] 0.15724513895 -0.0030522871785 0.3406630989 0.08053551385
#> [13782,] 0.15813956644 -0.0039286150211 0.3403859901 0.08401443297
#> [13783,] 0.16319299413 -0.0053220310554 0.1768320196 0.05248689144
#> [13784,] 0.16825289822 -0.0102795428509 0.1752643752 0.07216763389
#> [13785,] 0.16163035272 -0.0058306609607 0.2185237749 0.06984188290
#> [13786,] 0.15976244349 -0.0036556942358 0.2193705869 0.05944236280
#> [13787,] 0.16642640766 -0.0079649265348 0.3395456565 0.07320949414
#> [13788,] 0.17204852333 -0.0134732729743 0.3378038294 0.09507698575
#> [13789,] 0.17733683038 -0.0184246613987 0.3363441566 0.11355664820
#> [13790,] 0.17733683038 -0.0184246613987 0.3363441566 0.11355664820
#> [13791,] 0.17733683038 -0.0184246613987 0.3363441566 0.11355664820
#> [13792,] 0.16666733652 -0.0076753446368 0.2172953764 0.06053355766
#> [13793,] 0.16813700475 -0.0094110035886 0.3391944190 0.07777348012
#> [13794,] 0.16936855736 -0.0105975554285 0.3366888078 0.08213638738
#> [13795,] 0.17739284972 -0.0184594680740 0.3342027455 0.11334726177
#> [13796,] 0.16563751697 -0.0069420164278 0.3378447475 0.06762432477
#> [13797,] 0.12086639698 -0.0960305590344 0.2205963742 0.04516783731
#> [13798,] 0.16253428542 -0.0050692108915 0.2191779122 0.06123120980
#> [13799,] 0.17380634622 -0.0161131700853 0.2156856361 0.10507443709
#> [13800,] 0.17484559513 -0.0169490309016 0.1495221095 0.09702795394
#> [13801,] 0.10382666915 -0.0920380632173 0.2170669545 0.08557967901
#> [13802,] 0.11657487013 -0.0949449872876 0.2230264786 0.02788309653
#> [13803,] 0.17733683038 -0.0184246613987 0.3363441566 0.11355664820
#> [13804,] 0.17733683038 -0.0184246613987 0.3363441566 0.11355664820
#> [13805,] 0.17733683038 -0.0184246613987 0.3363441566 0.11355664820
#> [13806,] 0.17542020004 -0.0165468160216 0.3369379613 0.10610182152
#> [13807,] 0.13183890848 -0.1082917819223 0.2177539363 0.08736193625
#> [13808,] 0.17237368343 -0.0138119321876 0.3398271446 0.09676898811
#> [13809,] 0.17276738183 -0.0139276012306 0.3356357941 0.09535628004
#> [13810,] 0.16768192266 -0.0089450514967 0.3372113559 0.07557613990
#> [13811,] 0.16678749517 -0.0080687236540 0.3374884647 0.07209722078
#> [13812,] 0.16816847811 -0.0095221562712 0.3476808894 0.07960500274
#> [13813,] 0.17711275303 -0.0182854346976 0.3449098009 0.11439419394
#> [13814,] 0.17711249748 -0.0182851843182 0.3449098801 0.11439319996
#> [13815,] 0.16752960133 -0.0088962078121 0.3478788243 0.07712006052
#> [13816,] 0.17711275303 -0.0182854346976 0.3449098009 0.11439419394
#> [13817,] 0.17711275303 -0.0182854346976 0.3449098009 0.11439419394
#> [13818,] 0.16678749517 -0.0080687236540 0.3374884647 0.07209722078
#> [13819,] 0.16730185010 -0.0088092911357 0.3371382263 0.07630519494
#> [13820,] 0.16583870916 -0.0071659330342 0.3398943222 0.06895204928
#> [13821,] 0.17731293613 -0.0184079673585 0.3363394116 0.11358161169
#> [13822,] 0.16147241706 -0.0052959295052 0.3368920506 0.09423677463
#> [13823,] 0.16874659141 -0.0124229035460 0.3346383877 0.12253002864
#> [13824,] 0.17709571802 -0.0181951448824 0.3364067094 0.11273673133
#> [13825,] 0.17736895547 -0.0184427740337 0.3341980005 0.11337222526
#> [13826,] 0.17736895547 -0.0184427740337 0.3341980005 0.11337222526
#> [13827,] 0.17733683038 -0.0184246613987 0.3363441566 0.11355664820
#> [13828,] 0.15995465844 -0.0063526872283 0.3329985910 0.13103985473
#> [13829,] 0.17731268058 -0.0184077169791 0.3363394907 0.11358061772
#> [13830,] 0.16936096656 -0.0128793346290 0.3348001210 0.12163562350
#> [13831,] 0.17697128567 -0.0181963864517 0.3363114217 0.11368475215
#> [13832,] 0.17019919180 -0.0115613327859 0.3384095316 0.08734436453
#> [13833,] 0.17697128567 -0.0181963864517 0.3363114217 0.11368475215
#> [13834,] 0.16647592512 -0.0077835375952 0.3397090497 0.07131263033
#> [13835,] 0.17186472863 -0.0133132766072 0.3399848275 0.09478938374
#> [13836,] 0.17733657483 -0.0184244110193 0.3363442358 0.11355565423
#> [13837,] 0.16839255546 -0.0096613829723 0.3391152451 0.07876745701
#> [13838,] 0.17733683038 -0.0184246613987 0.3363441566 0.11355664820
#> [13839,] 0.16679945378 -0.0082298405262 0.3395082768 0.07374633445
#> [13840,] 0.00857754629 -0.0681556822861 0.2247200502 -0.02021802188
#> [13841,] 0.07511261370 0.0033932256069 0.3708712671 0.06898291039
#> [13842,] 0.09079629243 -0.0109417870812 0.1915686613 0.11664778196
#> [13843,] 0.02871595511 -0.0851625949341 0.2438998739 0.02016682721
#> [13844,] 0.09935166870 -0.0117004672511 0.3784727055 0.06921830806
#> [13845,] 0.07905953610 0.0023385957514 0.2173629146 0.06237450899
#> [13846,] 0.08735163348 -0.0045489638028 0.2163787133 0.07826987640
#> [13847,] 0.11240296151 -0.0220114285773 0.2158546254 0.09713048446
#> [13848,] 0.10192538232 -0.0117458738492 0.2191007576 0.05637743192
#> [13849,] 0.09626383758 -0.0095736125807 0.2164996569 0.07924171366
#> [13850,] 0.09175667057 -0.0084916416666 0.1939074556 0.08956361987
#> [13851,] 0.09612557576 -0.0137462250421 0.3629698414 0.13499277108
#> [13852,] 0.08279169094 0.0007445466997 0.1970368425 0.05058026373
#> [13853,] 0.07466198112 0.0048603771626 0.3655965172 0.07328236107
#> [13854,] 0.07056874100 0.0008563929073 0.3755528253 0.13239638958
#> [13855,] 0.06969332213 0.0089534111422 0.2171648729 0.05832460237
#> [13856,] 0.13363590030 -0.0379326188764 0.2172170745 0.10131758671
#> [13857,] 0.08513153772 -0.0016660364472 0.2169241543 0.06888805399
#> [13858,] 0.10875824371 -0.0187278457936 0.2167604027 0.08556600822
#> [13859,] 0.10975489149 -0.0197043253897 0.2164516242 0.08944251809
#> [13860,] 0.09078208562 -0.0038042322099 0.3756805221 0.04633697409
#> [13861,] 0.11653209637 -0.0263443866431 0.2143519309 0.11580278525
#> [13862,] 0.10713982729 -0.0175231250273 0.2183508864 0.07136181387
#> [13863,] 0.11096051665 -0.0192959388178 0.2169676084 0.08252765855
#> [13864,] 0.09238040811 -0.0086713108027 0.2154462847 0.09051641397
#> [13865,] 0.08989418200 -0.0060917057868 0.2163282689 0.07954020171
#> [13866,] 0.08859145884 -0.0054840137921 0.3591441686 0.08263426217
#> [13867,] 0.05977595543 0.0131009039520 0.3798457658 0.06029610297
#> [13868,] 0.09244376751 -0.0070466846748 0.1564191892 0.05412016475
#> [13869,] 0.11218942709 -0.0251944942205 0.3772214996 0.11706089571
#> [13870,] 0.09236550962 -0.0067401060434 0.1566221695 0.05172631249
#> [13871,] 0.08936751733 -0.0055439400689 0.1546389858 0.06868274187
#> [13872,] 0.08270746214 0.0010215002463 0.1524542734 0.04192358139
#> [13873,] 0.09676019579 -0.0127468620586 0.1481004976 0.09658237064
#> [13874,] 0.08104332409 0.0015352089980 0.3783075881 0.05865250971
#> [13875,] 0.08850284937 -0.0057733652097 0.3759965003 0.08766669516
#> [13876,] 0.04958135225 -0.0995414928661 0.1581627740 0.04109735240
#> [13877,] 0.11364765261 -0.0224590127488 0.2195321856 0.06652757514
#> [13878,] 0.11514318648 -0.0239242829775 0.2190688438 0.07234452670
#> [13879,] 0.10593489031 -0.0181381855474 0.1538927053 0.08726699591
#> [13880,] 0.08958946905 -0.0069187761525 0.1517657520 0.09570050917
#> [13881,] 0.03809709754 -0.0913987686307 0.2220673453 0.02592846445
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#> [14051,] -21.06310333165 12.2222232541511 -0.3073677331 -1.38061203392
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#> [14101,] 0.09146730656 -0.0075141058156 0.3692347902 0.09058701895
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#> [14110,] 0.10828946808 -0.0225570608222 0.2048818792 0.10500577397
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#> [14114,] 0.09580286324 -0.0081691064276 0.3894232849 0.04563733496
#> [14115,] 0.11348741783 -0.0217476200421 0.1957210536 0.08218419542
#> [14116,] 0.08431549154 -0.0002137600284 0.3874324295 0.03763625757
#> [14117,] 0.10550064557 -0.0209702109300 0.3808689085 0.12003694185
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#> [14122,] 0.02626568012 -0.0902889876421 0.1483970641 0.09104141099
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#> [14124,] 0.03275784954 -0.0854708651031 0.2253639147 0.00760269489
#> [14125,] 0.06001117712 -0.1101370375292 0.1496180899 0.09068313080
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#> [14130,] 0.06658433143 0.0115783683515 0.3799972660 0.03647580570
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#> [14132,] 0.08363462519 0.0023089205114 0.1896671500 0.01669704089
#> [14133,] 0.09247895818 -0.0094954390193 0.1429795708 0.13540960715
#> [14134,] 0.12973292591 -0.0351407016346 0.1841540936 0.10313104886
#> [14135,] 0.10020317765 -0.0170855354232 0.1820763295 0.10987136454
#> [14136,] 0.03925792244 0.0319891241531 0.2230271300 0.00539690634
#> [14137,] 0.07594945901 0.0064647667989 0.3657015089 0.04858815310
#> [14138,] 0.07936918438 0.0092207276666 0.2234765703 -0.00684313715
#> [14139,] 0.07352838757 0.0033354097153 0.1634255786 0.15348367616
#> [14140,] 0.07612433928 0.0097016061321 0.1632185785 -0.02572082803
#> [14141,] 0.09280119987 -0.0051203959230 0.1589440299 0.02771359549
#> [14142,] 0.03829143675 -0.0903661675457 0.2237123751 0.02718542642
#> [14143,] 0.11316746973 -0.0240901428004 0.1945726121 0.09836934925
#> [14144,] 0.08234258509 0.0061109689822 0.2041226854 -0.02152553494
#> [14145,] 0.09396676090 -0.0135184480083 0.1927296987 0.10995145979
#> [14146,] 0.05166085304 0.0219865893570 0.1977520725 0.02785772288
#> [14147,] 0.11073980777 -0.0209667070292 0.1956718250 0.08406160735
#> [14148,] 0.11073980777 -0.0209667070292 0.1956718250 0.08406160735
#> [14149,] 0.08522944974 0.0008865715829 0.2006729857 0.01716418191
#> [14150,] 0.08775779485 -0.0018424856477 0.1994341151 0.03141960310
#> [14151,] 0.09255682827 -0.0114919880686 0.2123807804 0.12308502574
#> [14152,] 0.07339052488 0.0072864657024 0.2183188271 0.04853675890
#> [14153,] 0.07495676661 0.0115734765807 0.1643782491 -0.03878255676
#> [14154,] 0.08461702781 0.0050580255888 0.1629856161 -0.02232743202
#> [14155,] 0.09503112833 -0.0141797748384 0.1520428883 0.10597311755
#> [14156,] 0.09503112833 -0.0141797748384 0.1520428883 0.10597311755
#> [14157,] 0.13437230140 -0.0378608606433 0.1499704213 0.10010153730
#> [14158,] 0.00229674462 0.0595911055798 0.1581082147 -0.02241551508
#> [14159,] 0.07320501154 0.0111334768210 0.1623545848 -0.01869253385
#> [14160,] 0.09728246297 -0.0124567429063 0.1548949810 0.07495788149
#> [14161,] 0.10514859499 -0.0201636957513 0.1524579195 0.10555358358
#> [14162,] 0.06052090066 0.0205011626181 0.1772303404 0.01068168171
#> [14163,] 0.08130293570 0.0044810559849 0.1613857936 -0.00330657512
#> [14164,] 0.10011236358 -0.0109791210186 0.1572601728 0.04784857236
#> [14165,] 0.11809303870 -0.0279601591719 0.1531949458 0.10370588144
#> [14166,] 0.06680848440 0.0102818322083 0.1583068002 0.02519109296
#> [14167,] 0.11227143542 -0.0239143062610 0.2164555017 0.11532899693
#> [14168,] 0.09095245150 -0.0024243619940 0.1593388254 0.01958948371
#> [14169,] 0.08267856824 0.0049748303708 0.2031592154 -0.01098006061
#> [14170,] 0.06076587339 0.0193327199937 0.1958608769 -0.03255859841
#> [14171,] 0.09564887951 -0.0134862394587 0.3543978904 0.13404136289
#> [14172,] 0.08670019037 -0.0001935101104 0.2015368195 0.01107611650
#> [14173,] 0.07554147767 0.0070674550327 0.3622743111 0.04000479844
#> [14174,] 0.09879659246 -0.0157170688761 0.3550694812 0.13045669554
#> [14175,] 0.08687763569 -0.0087591775722 0.3547153289 0.13009218947
#> [14176,] 0.11366189656 -0.0248923543313 0.1931334487 0.11170925422
#> [14177,] 0.04509411809 0.0317687545177 0.1996191816 -0.00537181508
#> [14178,] 0.10237604412 -0.0183089954219 0.1928053792 0.11131780929
#> [14179,] 0.06281132284 -0.1112851579705 0.2176636256 0.10144700721
#> [14180,] 0.10303037086 -0.0112853855353 0.1769639125 0.04340393827
#> [14181,] 0.11826716273 -0.0279038588863 0.1722834892 0.10691209580
#> [14182,] 0.07174766705 0.0134785129400 0.1834341129 -0.03589501465
#> [14183,] 0.09351488600 -0.0051156545199 0.1776614377 0.03340168431
#> [14184,] 0.05047377253 0.0208268932937 0.2233134627 0.01861466463
#> [14185,] 0.11240075587 -0.0252305873495 0.1538979652 0.09797815854
#> [14186,] 0.10189744734 -0.0176172399081 0.3510015530 0.12932644587
#> [14187,] 0.09274072642 -0.0120639496332 0.1808765843 0.11587127313
#> [14188,] 0.10389551425 -0.0106022686112 0.1799533851 0.01588492582
#> [14189,] 0.09289438211 -0.0052244868520 0.1783353560 0.02897398616
#> [14190,] 0.09059442571 -0.0029710723995 0.1790479216 0.02002819414
#> [14191,] 0.07681783021 0.0054195541328 0.1784798957 0.01996680746
#> [14192,] 0.09213664560 -0.0107977244620 0.3490631971 0.13952403126
#> [14193,] 0.09542418347 -0.0052067484397 0.1694866038 0.00921627265
#> [14194,] 0.09976854557 -0.0094631979612 0.1681406466 0.02611387980
#> [14195,] 0.10109698992 -0.0170579895594 0.3508425936 0.13016272276
#> [14196,] 0.07681967228 0.0067280518838 0.3583641194 0.03573491810
#> [14197,] 0.11089000417 -0.0163798347630 0.1672106887 0.03794917313
#> [14198,] 0.09712024210 -0.0153149032884 0.1927580789 0.11046384085
#> [14199,] 0.09077039754 -0.0030604930394 0.1803288695 0.00952507111
#> [14200,] 0.09137037989 -0.0118020556468 0.3683433812 0.12744565537
#> [14201,] 0.09774256107 -0.0108496824801 0.2613690266 0.06861815939
#> [14202,] 0.08815829237 -0.0006256188699 0.1902333434 0.01408593227
#> [14203,] 0.11025159795 -0.0238795917275 0.3962094958 0.12044318298
#> [14204,] 0.07286868023 0.0081705124505 0.1803924103 0.00197684431
#> [14205,] 0.03130614693 -0.0853996156144 0.1794840283 0.01193764273
#> [14206,] 0.03258390049 -0.0866515125325 0.1790881585 0.01690752718
#> [14207,] 0.09423258116 -0.0096624488920 0.3854783533 0.08411309600
#> [14208,] 0.10362406982 -0.0188638912398 0.3825687104 0.12064174676
#> [14209,] 0.10437082591 -0.0203373013138 0.1726725842 0.10138019950
#> [14210,] 0.09164622871 -0.0121326217643 0.3428467318 0.12357054998
#> [14211,] 0.09164622871 -0.0121326217643 0.3428467318 0.12357054998
#> [14212,] 0.07819879577 0.0017882409345 0.3483613923 0.05817905852
#> [14213,] 0.09164622871 -0.0121326217643 0.3428467318 0.12357054998
#> [14214,] 0.09164622871 -0.0121326217643 0.3428467318 0.12357054998
#> [14215,] 0.06928554141 0.0097755743018 0.3497744529 0.03659757200
#> [14216,] 0.10437325094 -0.0190436152000 0.3574858202 0.13015341586
#> [14217,] 0.10537680951 -0.0197447648909 0.3576851126 0.12910494931
#> [14218,] 0.10537680951 -0.0197447648909 0.3576851126 0.12910494931
#> [14219,] 0.02252202566 -0.0735989821054 0.1859008949 -0.06120946652
#> [14220,] 0.07602540778 0.0074614170551 0.1788434528 0.01249065128
#> [14221,] 0.06916063740 0.0145561890591 0.1828154658 -0.03035598146
#> [14222,] 0.08278532687 0.0059561709893 0.1822862925 -0.02052258921
#> [14223,] 0.07813080603 0.0034910528053 0.1774007758 0.03233074433
#> [14224,] 0.07209470027 0.0107107551869 0.1806322958 -0.00585697660
#> [14225,] 0.02013512209 -0.0869573688857 0.1721860849 0.09064581910
#> [14226,] 0.08836354404 -0.0105094877870 0.1714866204 0.10541386517
#> [14227,] 0.08977532632 -0.0111856827049 0.1519955879 0.10511914911
#> [14228,] 0.06230362478 0.0157301010336 0.1605067882 -0.00173336670
#> [14229,] 0.09406253046 -0.0114899554332 0.3763323643 0.11093282563
#> [14230,] 0.08310838677 -0.0070867337353 0.3746947719 0.12675870328
#> [14231,] 0.10394161146 -0.0196109187685 0.3672853786 0.12304476494
#> [14232,] 0.07254729163 0.0090619743860 0.1685103668 0.00847701239
#> [14233,] 0.09796053219 -0.0158370034174 0.1606369128 0.10732304434
#> [14234,] 0.10979033353 -0.0227687621296 0.1610265028 0.10744229752
#> [14235,] 0.08512968983 0.0013928483890 0.1686667895 0.01152352751
#> [14236,] 0.07171299546 0.0130137059432 0.1711778555 -0.02302655275
#> [14237,] 0.06633613158 0.0151474453047 0.1704346898 -0.01568159595
#> [14238,] 0.10508017915 -0.0202010903636 0.1611539888 0.10559526700
#> [14239,] 0.06992924345 0.0095520065402 0.1591496241 0.01617360996
#> [14240,] 0.08043742193 0.0026372522576 0.1674273021 0.02445606215
#> [14241,] 0.08307981629 0.0000483294310 0.1666086434 0.03473378320
#> [14242,] 0.10152035567 -0.0180190468905 0.1608954508 0.10645915567
#> [14243,] 0.04613403547 -0.1017537961770 0.1831296419 0.09596259345
#> [14244,] 0.08977532632 -0.0111856827049 0.1519955879 0.10511914911
#> [14245,] 0.06462913626 0.0134516486427 0.1597863052 0.00731182301
#> [14246,] 0.08977532632 -0.0111856827049 0.1519955879 0.10511914911
#> [14247,] 0.08977532632 -0.0111856827049 0.1519955879 0.10511914911
#> [14248,] 0.07778785674 0.0042979402928 0.1999623709 0.02347945616
#> [14249,] 0.07991734087 0.0052263722714 0.3656214805 0.02960750563
#> [14250,] 0.10039485807 -0.0162640574968 0.3566957682 0.13430983684
#> [14251,] 0.09611135825 -0.0115141579444 0.1745529586 0.07284698487
#> [14252,] 0.06343664009 0.0178878673631 0.1819532782 -0.02482292691
#> [14253,] 0.06241443724 0.0188893848975 0.1822699740 -0.02879883448
#> [14254,] 0.10657722541 -0.0206478522951 0.3451411406 0.12609965970
#> [14255,] 0.10657722541 -0.0206478522951 0.3451411406 0.12609965970
#> [14256,] 0.08919977700 -0.0036220542094 0.3505249696 0.05850923109
#> [14257,] 0.10352428677 -0.0184787185927 0.3444817279 0.12962761144
#> [14258,] 0.07560461335 0.0064528344808 0.1789081229 0.01523871740
#> [14259,] 0.09768043549 -0.0156629700411 0.1713439681 0.10836997651
#> [14260,] 0.09768043549 -0.0156629700411 0.1713439681 0.10836997651
#> [14261,] 0.09768043549 -0.0156629700411 0.1713439681 0.10836997651
#> [14262,] 0.10124025897 -0.0178450135142 0.1716025061 0.10750608784
#> [14263,] 0.10619845590 -0.0202869941360 0.3599476728 0.12873579349
#> [14264,] 0.06776398977 0.0114927326111 0.1789369546 0.01159723807
#> [14265,] 0.03667061988 -0.0961796922821 0.2042371260 0.09805214521
#> [14266,] 0.08053399181 0.0010361026537 0.1872765046 0.04381443386
#> [14267,] 0.06516692425 0.0117814952095 0.1886862091 0.02322093605
#> [14268,] 0.10966387683 -0.0224751516430 0.1821613910 0.11140950170
#> [14269,] 0.10616000882 -0.0204790902206 0.1821298574 0.11084018941
#> [14270,] 0.09242463348 -0.0126688779076 0.1712966678 0.10751600808
#> [14271,] 0.09572717719 -0.0073767426527 0.1782885213 0.03148538259
#> [14272,] 0.05462616227 0.0238871198364 0.4086860858 -0.02083105895
#> [14273,] 0.08613688913 -0.0091639682191 0.1713533308 0.10577322219
#> [14274,] 0.07056853106 0.0087449440657 0.1780680600 0.02250563746
#> [14275,] 0.09242463348 -0.0126688779076 0.1712966678 0.10751600808
#> [14276,] 0.08418287776 0.0006070659614 0.1787003907 0.02156689996
#> [14277,] 0.09842152743 -0.0111390377257 0.1516595766 0.06084541643
#> [14278,] 0.07606084013 0.0107691583405 0.1585872977 -0.02612756156
#> [14279,] 0.07519197284 0.0063704157169 0.1783112763 0.02090001008
#> [14280,] 0.08362514633 -0.0018921039424 0.1756985357 0.05370124749
#> [14281,] 0.11212423027 -0.0244271161204 0.3611244469 0.12254484814
#> [14282,] 0.11211228314 -0.0244187691002 0.3611220744 0.12255732988
#> [14283,] 0.04241632518 -0.0994962784025 0.1721601068 0.09570838591
#> [14284,] 0.10433778471 -0.0194554867436 0.1714038819 0.10945166987
#> [14285,] 0.09740033880 -0.0154889366647 0.1820510235 0.10941690868
#> PC5 PC6 PC7
#> [1,] 0.073172981750 -0.1514114414273 -0.000540799026
#> [2,] 0.312356092109 -0.1395631373021 -0.000527813533
#> [3,] 0.100597042688 -0.2821035827357 -0.000525070468
#> [4,] 0.255659016406 -0.1397555792214 -0.000532291375
#> [5,] 0.702605162336 -0.5597453635509 -0.000394994608
#> [6,] 0.175687239307 -0.2496183121635 -0.000399722407
#> [7,] 0.765367007478 -0.4403709398539 -0.000415632829
#> [8,] 0.018143024115 -0.0735659540972 -0.000557831513
#> [9,] -0.004587533126 -0.1857978835593 -0.000538034299
#> [10,] 0.086651172610 -0.1579162073508 -0.000540739290
#> [11,] -0.117153785011 -0.0239096164859 -0.000576880434
#> [12,] -0.108273897690 -0.1862010510834 -0.000546220596
#> [13,] -0.034852775402 0.1485857606831 -0.000598905092
#> [14,] -0.034852775402 0.1485857606831 -0.000598905092
#> [15,] -0.034852775402 0.1485857606831 -0.000598905092
#> [16,] -0.097268771010 -0.1872896646929 -0.000523004056
#> [17,] -0.035728262130 -0.2656141282221 -0.000532116774
#> [18,] 0.023014869589 -0.5932354551808 -0.000470940261
#> [19,] 0.047491296067 -0.2127624076383 -0.000535894817
#> [20,] 0.929173954891 -0.5843370183694 -0.000463675016
#> [21,] 0.025934503196 -0.2854303142865 -0.000531506110
#> [22,] 0.670139268453 -0.5661362519883 -0.000430887074
#> [23,] 0.309449247511 -0.0357023095492 -0.000558934535
#> [24,] 0.321483957421 0.0082189500655 -0.000566713061
#> [25,] 0.319281503934 0.0001809888569 -0.000565289525
#> [26,] -0.002063742784 -1.0282333534002 -0.000357321773
#> [27,] 0.163623376335 -0.1780899525690 -0.000511430521
#> [28,] 0.512243375750 -0.2970221583271 -0.000509347110
#> [29,] 0.194727045432 -0.1899424272924 -0.000515696647
#> [30,] 0.248730907556 -0.1574933290426 -0.000538930809
#> [31,] 0.011732456560 0.2662323362464 -0.000456225416
#> [32,] 0.578213444898 1.4511577578294 -0.000422239667
#> [33,] 0.908366163526 -0.1346246123520 -0.000559457926
#> [34,] -0.030588858453 -0.3188194851389 -0.000506688395
#> [35,] 0.060158346364 0.0552977174553 -0.000580466935
#> [36,] -0.034194996622 -0.2605158462652 -0.000519702828
#> [37,] -0.302403952984 -0.5222260168794 -0.000484043374
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#> [1909,] 0.009674270600 0.0118796605299 -0.000566147542
#> [1910,] 0.005596335980 0.0216133115054 -0.000570397511
#> [1911,] 0.009205563064 0.0347853614305 -0.000572730303
#> [1912,] 0.005555322462 0.0026909573896 -0.000568535299
#> [1913,] 0.009030428360 -0.0052908379926 -0.000527315712
#> [1914,] 0.013324790320 0.0047353638806 -0.000530676992
#> [1915,] -0.002033165669 0.0062521464031 -0.000490551060
#> [1916,] 0.013331149311 -0.0225774428342 -0.000559358084
#> [1917,] 0.007484037601 -0.0092038357547 -0.000563451873
#> [1918,] 0.005800024975 -0.0044017440505 -0.000532083925
#> [1919,] 0.011567243542 -0.0180999644434 -0.000536892427
#> [1920,] -0.047398909829 -0.0373240624006 -0.000523209015
#> [1921,] 0.029017689781 0.0133647617892 -0.000543696429
#> [1922,] 0.018898257730 -0.0133367390768 -0.000541922230
#> [1923,] -0.008619760263 -0.0334650102991 -0.000539287318
#> [1924,] 0.016748823166 -0.0008409603299 -0.000551809071
#> [1925,] 0.006101222054 -0.0342902915064 -0.000535433688
#> [1926,] 0.006771507084 -0.0318440536632 -0.000535866921
#> [1927,] 0.016623147219 0.0083974069932 -0.000556739363
#> [1928,] 0.020054607180 0.0018194015130 -0.000570525159
#> [1929,] 0.011470373346 0.0264867228657 -0.000561495270
#> [1930,] -0.000532143814 -0.0112632666554 -0.000561059524
#> [1931,] 0.048940168208 -0.0000590695381 -0.000572740875
#> [1932,] -0.019586953357 -0.0275750618954 -0.000556241370
#> [1933,] -0.034566286911 -0.0306906041806 -0.000560704377
#> [1934,] 0.032583344079 0.0142558760231 -0.000492357282
#> [1935,] 0.025190148896 0.0096178747614 -0.000491794615
#> [1936,] 0.022505319875 0.0055540180941 -0.000544859116
#> [1937,] 0.016418065683 -0.0026597063819 -0.000533052267
#> [1938,] 0.006973055819 0.0047206471419 -0.000543979357
#> [1939,] 0.025912668201 0.0078489345940 -0.000549695080
#> [1940,] 0.017040005387 0.0054025231185 -0.000546887518
#> [1941,] -0.010473702858 -0.0219661916557 -0.000548263355
#> [1942,] 0.004027645184 -0.0009739357192 -0.000541659682
#> [1943,] 0.020713444333 0.0451059931238 -0.000537419062
#> [1944,] 0.008407713330 0.0253041030272 -0.000529416097
#> [1945,] 0.016984128726 0.0139106101960 -0.000535832029
#> [1946,] 0.030359908178 0.0228577757768 -0.000536954930
#> [1947,] 0.014149271555 0.0091157044296 -0.000541747531
#> [1948,] 0.016417928579 0.0173952786683 -0.000543213857
#> [1949,] 0.016356056115 0.0171694720981 -0.000543173866
#> [1950,] 0.011835840574 -0.0056089108237 -0.000560584527
#> [1951,] 0.019696667248 0.0296071417889 -0.000544111215
#> [1952,] 0.021243478856 0.0352523060425 -0.000545110983
#> [1953,] 0.020914248458 0.0076075387682 -0.000542722014
#> [1954,] -0.012514015294 0.0052512413652 -0.000479591713
#> [1955,] 0.009687762679 0.0201850536323 -0.000481471193
#> [1956,] 0.009763082092 0.0204599354971 -0.000481519875
#> [1957,] 0.009624766198 0.0199551449095 -0.000481430476
#> [1958,] -0.061577943241 -0.0567592466147 -0.000562608671
#> [1959,] -0.012462814285 0.0051628252848 -0.000483804559
#> [1960,] -0.019813005242 -0.0216620543877 -0.000479053829
#> [1961,] 0.015647342059 -0.0008870653823 -0.000544201104
#> [1962,] -0.026405244091 -0.0412753361726 -0.000487382030
#> [1963,] -0.031135816214 -0.0018789334209 -0.000543551175
#> [1964,] -0.020560803514 -0.0245964639363 -0.000566971465
#> [1965,] 0.008104874145 0.0165681330641 -0.000544566648
#> [1966,] 0.015167303612 -0.0015602686916 -0.000553243615
#> [1967,] 0.002481116401 0.0088101889355 -0.000562114030
#> [1968,] 0.024948083672 0.0307593714555 -0.000541561240
#> [1969,] 0.012161858553 -0.0070485652147 -0.000565016700
#> [1970,] -0.061377777793 0.0613535752379 -0.000508210423
#> [1971,] 0.005292579490 -0.0034124215752 -0.000532033778
#> [1972,] 0.017771547069 -0.0012743095474 -0.000537443703
#> [1973,] 0.019132741283 0.0036934349958 -0.000538323499
#> [1974,] 0.013873094135 -0.0073537035409 -0.000541524852
#> [1975,] 0.012353412148 0.0116597822093 -0.000540030082
#> [1976,] -0.023749571671 -0.0325325605912 -0.000575145462
#> [1977,] -0.002004415460 0.0130664847407 -0.000534764259
#> [1978,] 0.006742884315 0.0149300102376 -0.000569364750
#> [1979,] 0.012552782588 0.0072730382657 -0.000574776356
#> [1980,] 0.006112511607 0.0186724969330 -0.000550922805
#> [1981,] -0.031116759328 -0.0469520125027 -0.000541396303
#> [1982,] 0.021129207053 -0.0055495833163 -0.000547000242
#> [1983,] 0.021737619619 -0.0033291520432 -0.000547393484
#> [1984,] 0.025408719167 0.0100687044521 -0.000549766266
#> [1985,] 0.007047132633 0.0000416690744 -0.000555272324
#> [1986,] 0.030835211745 0.0004212191382 -0.000542643953
#> [1987,] 0.010980439115 0.0124471109354 -0.000546960125
#> [1988,] 0.013110261922 0.0017429026092 -0.000542051335
#> [1989,] 0.005860258407 0.0121987941094 -0.000561537947
#> [1990,] 0.045755900234 0.0157335947007 -0.000561894727
#> [1991,] -0.009321075695 -0.0233742969633 -0.000556349905
#> [1992,] 0.043053280707 0.0118572138534 -0.000560733353
#> [1993,] 0.049835203003 0.0285876422658 -0.000564793296
#> [1994,] 0.049835203003 0.0285876422658 -0.000564793296
#> [1995,] 0.001686570445 -0.0170429054389 -0.000560155369
#> [1996,] 0.038438114877 0.0252251624776 -0.000496697201
#> [1997,] 0.052926906203 -0.0150223332751 -0.000560962993
#> [1998,] 0.058940542536 0.0007517078501 -0.000547397123
#> [1999,] 0.003540115034 0.0004748032497 -0.000502803499
#> [2000,] 0.012296554823 0.0034251776764 -0.000547548416
#> [2001,] 0.047461362938 0.0163039137846 -0.000505203099
#> [2002,] 0.054882360988 -0.0241989146841 -0.000547195951
#> [2003,] 0.034507310630 -0.0148188486434 -0.000556411958
#> [2004,] 0.055173308245 -0.0221642375902 -0.000551957713
#> [2005,] -0.060968812316 0.1022199644457 -0.000481073410
#> [2006,] 0.049339251665 0.0118543151367 -0.000487155187
#> [2007,] 0.056712386994 0.0387629314124 -0.000491920747
#> [2008,] 0.049240362198 0.0492380368285 -0.000524734619
#> [2009,] 0.053778077667 0.0261995434458 -0.000586737484
#> [2010,] 0.029887766068 -0.0235563224476 -0.000570494867
#> [2011,] 0.046933052913 -0.0041849503644 -0.000486754251
#> [2012,] -0.000009234463 -0.0069275679393 -0.000569610789
#> [2013,] 0.036392104435 0.0347877020719 -0.000487912204
#> [2014,] -0.005201365423 -0.0312215804218 -0.000556775068
#> [2015,] 0.042488061902 0.0137359306386 -0.000518243223
#> [2016,] 0.034764353238 0.0010614005505 -0.000489923830
#> [2017,] 0.064254576993 0.0076847289911 -0.000577053683
#> [2018,] 0.046441846137 0.0154630245839 -0.000574791451
#> [2019,] 0.062511094798 0.0198495687679 -0.000506863210
#> [2020,] 0.035136135493 0.0341267446437 -0.002330094864
#> [2021,] 0.038735050500 0.0472611601405 -0.002332420990
#> [2022,] 0.038735050500 0.0472611601405 -0.002332420990
#> [2023,] 0.085083725592 0.0781565805645 -0.002336291675
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#> [2027,] 0.038735050500 0.0472611601405 -0.002332420990
#> [2028,] 0.087030643499 0.0795664675753 -0.002336475417
#> [2029,] 0.087030643499 0.0795664675753 -0.002336475417
#> [2030,] 0.040689525959 0.0465706455274 -0.002332208107
#> [2031,] 0.187575994117 -0.0555363547816 -0.000547541727
#> [2032,] 0.076112863537 0.0017310854760 -0.000555007288
#> [2033,] 0.504564485533 -0.4040857752856 -0.000405474963
#> [2034,] 25.534479424385 -9.8211863066289 0.002504325495
#> [2035,] 26.062973390280 -7.8924218533043 0.002162738190
#> [2036,] 24.626663213250 -7.5765334605387 0.002042655750
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#> [2038,] 0.091016076146 -0.0036714432592 -0.000558593283
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#> [2040,] 0.044844919096 -0.0260140240775 -0.000551322620
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#> [10309,] 0.013718476697 0.0786482661248 -0.000560157250
#> [10310,] 0.049346949584 -0.0169337852963 -0.000583489203
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#> [10312,] 0.073051607213 0.0636434459255 -0.000558022908
#> [10313,] 0.073051607213 0.0636434459255 -0.000558022908
#> [10314,] 0.070933203639 -0.0217185655583 -0.000545891209
#> [10315,] 0.087948131321 0.0403782412317 -0.000556888654
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#> [10320,] 0.045474548608 0.0758706526491 -0.000580583429
#> [10321,] 0.029669576222 0.0019575935767 -0.000553369568
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#> [10324,] 0.000701487982 0.1849694555730 -0.000558572759
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#> [10326,] -0.027397647404 0.1002615410764 -0.000564202899
#> [10327,] 0.047869690617 -0.0037478662032 -0.000539483401
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#> [10329,] 0.165339434225 0.0576966287368 -0.000570328847
#> [10330,] 0.060434223937 0.0032194004993 -0.000546428476
#> [10331,] 0.031657414165 0.0190013080523 -0.000551660948
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#> [10333,] 0.018001391887 0.0447828068849 -0.000553284010
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#> [10336,] 0.046384099918 0.0669798972672 -0.000580204879
#> [10337,] 0.035704421812 0.0228385700975 -0.000577979661
#> [10338,] 0.009948790081 0.0237814278443 -0.000567806161
#> [10339,] 0.092953153805 0.0308566424303 -0.000565490180
#> [10340,] 0.038332338277 0.0617760191764 -0.000584119449
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#> [10344,] 0.125878603541 -0.0444391543838 -0.000533393847
#> [10345,] 0.153927454024 0.0579264907488 -0.000551522969
#> [10346,] 0.025964415863 -0.0081869721995 -0.000549029483
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#> [10349,] 0.024617958868 -0.0207489780076 -0.000591423012
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#> [10380,] 0.022166092883 -0.0100625548071 -0.000488750919
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#> [10384,] 0.017976481459 -0.0253527456291 -0.000486043002
#> [10385,] 0.017451472976 -0.0272687896456 -0.000485703667
#> [10386,] 0.027887190871 0.0109876066715 -0.000491569679
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#> [10388,] 0.077684913531 0.0329412224499 -0.002328073063
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#> [10390,] 0.079679960206 0.0402222424009 -0.002329362544
#> [10391,] 0.077590413654 0.0325963405484 -0.002328011984
#> [10392,] 0.077841388993 0.0335122872658 -0.002328174200
#> [10393,] 0.080928494975 0.0447788308143 -0.002330169523
#> [10394,] 0.079679960206 0.0402222424009 -0.002329362544
#> [10395,] 0.077590413654 0.0325963405484 -0.002328011984
#> [10396,] 0.018447453362 -0.0234631748536 -0.000485468390
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#> [10399,] 0.029849110529 0.0038059131195 -0.000566675465
#> [10400,] 0.025043682468 -0.0137317304951 -0.000563569520
#> [10401,] 0.024924834683 -0.0194582838906 -0.000590742338
#> [10402,] 0.127974853891 0.0322295844474 -0.002327486627
#> [10403,] 0.033562114625 0.0137712485932 -0.000587534761
#> [10404,] 0.031087216053 0.0047389857874 -0.000585935133
#> [10405,] 0.033562114625 0.0137712485932 -0.000587534761
#> [10406,] 0.033562114625 0.0137712485932 -0.000587534761
#> [10407,] 0.022888319847 -0.0074267523483 -0.000489217724
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#> [10409,] 0.028589800479 0.0113322480523 -0.000503451070
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#> [10412,] 0.022777517870 -0.0080018654445 -0.000490025129
#> [10413,] 0.028373612908 0.0112262045505 -0.000499795257
#> [10414,] 0.028373612908 0.0112262045505 -0.000499795257
#> [10415,] 0.028373612908 0.0112262045505 -0.000499795257
#> [10416,] 0.028373612908 0.0112262045505 -0.000499795257
#> [10417,] 0.028373612908 0.0112262045505 -0.000499795257
#> [10418,] 0.021350098250 -0.0144064540661 -0.000495255672
#> [10419,] 0.028373612908 0.0112262045505 -0.000499795257
#> [10420,] 0.028373612908 0.0112262045505 -0.000499795257
#> [10421,] 0.028373612908 0.0112262045505 -0.000499795257
#> [10422,] 0.028373612908 0.0112262045505 -0.000499795257
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#> [10424,] 0.028373612908 0.0112262045505 -0.000499795257
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#> [10428,] 0.028373612908 0.0112262045505 -0.000499795257
#> [10429,] 0.028373612908 0.0112262045505 -0.000499795257
#> [10430,] 0.026011781133 0.0019236409629 -0.000501784790
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#> [10432,] 0.017732281155 -0.0262439665270 -0.000485885165
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#> [10439,] 0.028589800479 0.0113322480523 -0.000503451070
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#> [10441,] 0.091230260281 0.0823756247435 -0.002336827976
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#> [10471,] 0.024050794612 -0.0228188715673 -0.000591056430
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#> [14281,] 0.030897295530 0.0265240115087 -0.000502572755
#> [14282,] 0.030876297446 0.0265099657229 -0.000502570992
#> [14283,] -0.004097556862 0.0646289986520 -0.000582711917
#> [14284,] 0.022512844600 0.0320843987443 -0.000582430894
#> [14285,] 0.019848852226 0.0424957511928 -0.000578199262
#> [ reached getOption("max.print") -- omitted 33958 rows ]Reduce Dimension
pca#> Standard deviations (1, .., p=7):
#> [1] 1.705249835 1.085811853 0.999591384 0.987849523 0.840500004 0.481289277
#> [7] 0.005136074
#>
#> Rotation (n x k) = (7 x 7):
#> PC1 PC2 PC3 PC4 PC5
#> RESIDENTIAL.UNITS -0.50138338 0.08936884 -0.019241647 0.16910059 0.56011546
#> COMMERCIAL.UNITS -0.18548792 -0.81557172 0.014975088 -0.14893618 -0.36170475
#> TOTAL.UNITS -0.52014300 -0.35665390 -0.008860518 0.06344165 0.27995828
#> LAND.SQUARE.FEET -0.37554855 0.26238205 -0.074578580 0.39235388 -0.66005834
#> GROSS.SQUARE.FEET -0.50070661 0.28523938 -0.004506179 -0.08135536 -0.18003718
#> YEAR.BUILT -0.02601345 0.01616302 0.994397509 0.09723184 -0.02509751
#> SALE.PRICE -0.22636182 0.22178116 0.070130740 -0.88044527 -0.09134236
#> PC6 PC7
#> RESIDENTIAL.UNITS -0.20433374 -0.59680907352
#> COMMERCIAL.UNITS 0.07891239 -0.37546407004
#> TOTAL.UNITS -0.13009145 0.70911598103
#> LAND.SQUARE.FEET -0.44151829 0.00005541206
#> GROSS.SQUARE.FEET 0.79301891 -0.00002543141
#> YEAR.BUILT -0.01231074 0.00042440835
#> SALE.PRICE -0.33335840 0.00005903831Misal kita hanya ingin mereduksi 7 dimensi menjadi 5 dimensi, maka
kita gunakan kolom PC1 sampai PC5 pada pca$x. Namun
bagaimana cara kita memilih sebaiknya berapa dimensi yang kita
pertahankan? Untuk itu, Kita melihat cumulative
variance dengan fungsi summary().
# Please type your code down here
summary(pca)#> Importance of components:
#> PC1 PC2 PC3 PC4 PC5 PC6 PC7
#> Standard deviation 1.7052 1.0858 0.9996 0.9878 0.8405 0.48129 0.005136
#> Proportion of Variance 0.4154 0.1684 0.1427 0.1394 0.1009 0.03309 0.000000
#> Cumulative Proportion 0.4154 0.5838 0.7266 0.8660 0.9669 1.00000 1.000000Keterangan:
- Standard deviation: standar deviasi (akar variance)
yang ditangkap oleh masing-masing PC, sama seperti
pca$sdev - Proportion of Variance: persentase informasi yang ditangkap oleh tiap PC
- Cumulative Proportion: jumlah persentase informasi yang ditangkap secara kumulatif dari PC1 hingga PC terakhir
Pemilihan banyaknya PC disesuaikan dengan kebutuhan. Misal, kita ingin merangkum minimal 75% informasi, maka jumlah PC yang kita gunakan adalah PC 1 - 4
# subsetting base R: [baris, kolom]
pc_keep <- data.frame(pca$x[ , 1:4])
head(pc_keep)Setelah dipilih PC yang merangkum informasi yang dibutuhkan, PC dapat digabung dengan data awal dan digunakan untuk analisis lebih lanjut (misal: supervised learning).
# Please run the code down below
property_clean %>%
select_if(~!is.integer(.)) %>% # ambil kolom selain integer
cbind(pc_keep) # gabungkan dengan kolom PCPros and Cons of PCA
Kelebihan melakukan PCA sebelum modeling:
- Beban komputasi relatif lebih rendah, karena menggunakan fitur yang lebih sedikit
- Bisa jadi salah satu teknik yang digunakan untuk improve performa model, namun belum tentu menjadi lebih baik
- Mengurangi resiko terjadinya multikolinearitas, karena nilai antar PC tidak saling berkorelasi
library(GGally)
# korelasi sebelum PCA
ggcorr(property_num, label = T, hjust = 1, layout.exp = 2)
# korelasi setelah PCA
ggcorr(pca$x, label = T)
Kekurangan melakukan PCA sebelum modeling:
- Apabila menggunakan model yang highly interpretable, maka model menjadi tidak dapat diinterpretasikan karena nilai PC merupakan nilai campuran dari beberapa variable.
Visualizing PCA
PCA tidak hanya berguna untuk dimensionality reduction namun baik untuk visualisasi high-dimensional data. Visualisasi dapat menggunakan biplot yang menampilkan:
- Individual factor map, yaitu sebaran data secara keseluruhan menggunakan 2 PC. Tujuannya untuk mengetahui observasi yang serupa dan outlier.
- Variables factor map, yaitu plot yang menunjukkan korelasi antar variable dan kontribusinya terhadap PC.
Biplot
Mari kita buat biplot dari 100 observasi pertama dari
property_num
Parameter fungsi biplot():
x: objek hasil PCAcex: ukuran font di biplot
# ambil 100 data pertama agar tidak terlalu menumpuk
property_num_100 <- head(property_num, 100)
# melakukan PCA
property_num_100_pca <- prcomp(property_num_100, scale. = T)
# membuat biplot
biplot(x = property_num_100_pca,
cex = 0.5)
Biplot menggunakan PC1 dan PC2 secara default, karena PC tersebut yang merangkum informasi terbanyak dari data sehingga mampu mewakili data kita.
- Titik-titik = index angka dari observasi. Semakin berdekatan maka karakteristiknya semakin mirip, sedangkan yang jauh dari gerombolan data dianggap sebagai outlier
- Panah merah = loading score, menunjukkan kontribusi variabel tersebut terhadap PC, atau banyaknya informasi variabel tersebut yang dirangkum oleh PC.
Variables Factor Map
- Variable Contribution
Loading score dilihat dari jarak titik nol (pusat) ke ujung panah, secara horizontal (PC1) / vertikal (PC2). Semakin jauh panah, semakin banyak informasi yang dirangkum. Bila panah kearah negatif, maka bila nilai variabel awal tinggi, nilai di PC akan rendah, dan sebaliknya.
Berdasarkan penjelasan tersebut, maka:
Variable yang paling berkontribusi ke PC1 adalah: Gross Square Feet
Variable yang paling berkontribusi ke PC2 adalah: Residential Units
Dari panah merah tersebut, kita tahu variable mana yang paling banyak
berkontribusi untuk tiap PC. Mari kita gunakan fungsi
fviz_contrib() untuk melihat urutan kontribusi
variabel ke tiap PC
Parameter:
X: objek PCAchoice = "var": VARiable contributionaxes: PC keberapa yang ingin kita lihat variable contributionnya
# install.packages("factoextra")
library(factoextra)# Please type your code down here
fviz_contrib(X = property_num_100_pca,
choice = "var",
axes = 1)
# Please type your code down here
fviz_contrib(X = property_num_100_pca,
choice = "var",
axes = 2)
Catatan: garis horizontal putus-putus merah adalah batas nilai kontribusi yang diharapkan apabila PC menangkap informasi dari tiap variable dengan sama rata. Cara menghitungnya adalah 100% dibagi dengan jumlah variable. Pada kasus ini 100% / 7 = 14.28%. Bila melebihi batas tersebut, maka dapat dikatakan variable tersebut berkontribusi terhadap PC tersebut.
- Korelasi antar variabel dapat dilihat dari sudut antar dua panah
- Panah saling berdekatan (sudut antar panah < 90), maka korelasi positif
- Panah saling tegak lurus (sudut antar panah = 90), maka berkorelasi = 0
- Panah saling bertolak belakang (sudut antar panah mendekati 180), maka korelasi negatif
Panah yang berhimpit pada biplot adalah: Gross Square Feet & Land Square Feet (Korelasi Positif Kuat), Land Square Feet & Total Units (Korealasi Positif tapi lemah)
Panah yang (hampir) tegak lurus adalah: Sale Price & Total Units korelasinya = 0
Individual Factor Map
- Outlier detection: observasi yang jauh dari kumpulan observasi lainnya mengindikasikan outlier dari keseluruhan data. Observasi ini dapat ditandai untuk nantinya dicek karakteristik datanya untuk keperluan bisnis, atau apakah mempengaruhi performa model/clustering, dll.
Dari biplot di atas, outlier terluar adalah observasi 32, 96, 51 & 39
- Observasi searah panah mengindikasikan observasi tersebut nilainya tinggi pada variabel tersebut. Bila bertolak belakang, maka nilainya rendah pada variable tersebut.
Tiga outlier tersebut tinggi di nilai apa saja?
Observasi 39 ekstrim di nilai Sale.price Observasi 96 ekstrim di nilai Total Units Observasi 51 ekstrim di nilai Gross Square Feet
property_num_100[c(39, 96, 6, 51), ]Additional Notes: ketika kita sudah mengetahui observasi mana saja yang dirasa sebagai outlier, kita bisa mengeluar observasi tersebut sebelum kita melakukan modeling.
Dsini kita bisa melihat infromasi outlier dari PC1 & PC2 saja, kenapa? karena pada 2 PC tersebut, informasi paling banyak ditangkap.
Dive Deeper
Buatlah biplot dengan menggunakan 300 data pertama dari
property_num:
# Bu Lia
# your code here
property_num_300 <- head(property_num, 300)
# melakukan PCA
property_num_300_pca <- prcomp(property_num_300, scale = T)
# membuat biplot
biplot(x = property_num_300_pca,
cex = 0.75)
Insight: Outlier
Dari biplot, identifikasilah:
- Tiga observasi yang memiliki nilai
TOTAL.UNITSyang sangat tinggi: 110, 114 & 115 - Tiga observasi yang memiliki nilai
SALE.PRICEyang sangat tinggi: 103, 116 & 118
Insight: Variable Contribution
- Tiga variabel yang berkontribusi tinggi ke PC1: Gross Square Feet, Land Square Feet & Sale
# Bu Aureli
fviz_contrib(X = property_num_300_pca,
choice = "var",
axes = 1)
- Dua variabel yang berkontribusi tinggi ke PC2: Residential Units & Total Units
# Bu Aureli
fviz_contrib(X = property_num_300_pca,
choice = "var",
axes = 2)
- Variabel yang berkontribusi rendah pada PC1 maupun PC2: Commercial units
Insight: Variable Correlation
Gunakan biplot, identifikasilah:
- Pasangan variabel yang berkorelasi tinggi positif:
- Residental Units - Total Units
- Gross Square Feet - Land Square Feet
- Pasangan variabel yang tidak berkorelasi:
- Resindential Units - Year Built
[Additional] - Fancy Biplot
Lakukan PCA untuk built-in dataset USArrests dan
visualisasikan menggunakan fancy_biplot()!
# load custom function
source("R/biplot.R")
# built-in dataset
head(USArrests)Dataset USArrests merupakan data tentang jumlah tiga
tindak kejahatan (Murder, Assault, dan
Rape) per 100 ribu penduduk yang berhasil dicatat di 50
negara bagian US pada tahun 1973.
Deskripsi data:
Murder: murder arrests per 100,000Assault: assault arrests per 100,000UrbanPop: percent of population in urban areasRape: rape arrests per 100,000
# biplot visualization
fancy_biplot(prcomp(USArrests, scale = T))
Insight dari biplot:
- Perhatikan cluster di mana Arizona, Colorado, Illinois, dan Texas berada. Negara bagian mana lagi yang ada dalam cluster tersebut? Apa insight yang dapat diperoleh?
New York, dan kelima negara bagian tersebut tingkat Rapenya cukup tinggi
- Di antara Ohio, Louisiana, North Dakota, dan Colorado, manakah yang memiliki:
- Tingkat
Murdertertinggi: Louisiana - Tingkat
Assaulttertinggi: Louisiana - Tingkat
Rapetertinggi: Colorado - Tingkat kriminalitas terendah, meliputi ketiga tipe kejahatan: North Dakota
Principal Component Analysis using FactoMiner
FactoMineR menyediakan dua fungsi utama dalam PCA:
PCA()untuk melakukan analisis PCAplot.PCA()untuk visualisasi
Kelebihan FactoMineR dari fungsi base
biplot() adalah:
- Memisahkan dua grafik yang terdapat pada biplot yaitu individual factor map dan variables factor map
- Dapat melibatkan variable kategorik untuk mewarnai plot sehingga plot lebih informatif
# install.packages("FactoMineR")
library(FactoMineR)Read Data
Mari kita lakukan analisis PCA untuk data loan dari sebuah platform di quarter ke-4 tahun 2017.
# Please run the code down below
loan <- read.csv("data_input/loan2017Q4.csv", stringsAsFactors = T)
glimpse(loan)#> Rows: 1,556
#> Columns: 16
#> $ initial_list_status <fct> w, f, w, w, w, w, w, w, w, w, w, w, w, f, w, w, w,…
#> $ purpose <fct> debt_consolidation, debt_consolidation, debt_conso…
#> $ int_rate <dbl> 14.08, 9.44, 28.72, 13.59, 15.05, 10.91, 15.05, 10…
#> $ installment <dbl> 675.99, 480.08, 1010.30, 484.19, 476.33, 130.79, 3…
#> $ annual_inc <dbl> 156700, 50000, 25000, 175000, 109992, 49000, 65000…
#> $ dti <dbl> 19.11, 19.35, 65.58, 12.60, 10.00, 5.12, 22.38, 33…
#> $ verification_status <fct> Source Verified, Not Verified, Verified, Not Verif…
#> $ grade <fct> C, B, F, C, C, B, C, B, D, D, F, C, C, E, B, C, C,…
#> $ revol_bal <int> 21936, 5457, 23453, 31740, 2284, 2016, 14330, 2758…
#> $ inq_last_12m <int> 3, 1, 0, 0, 3, 5, 0, 1, 8, 1, 0, 12, 4, 8, 1, 3, 0…
#> $ delinq_2yrs <int> 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,…
#> $ home_ownership <fct> MORTGAGE, RENT, OWN, MORTGAGE, MORTGAGE, MORTGAGE,…
#> $ not_paid <int> 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1,…
#> $ log_inc <dbl> 11.962088, 10.819778, 10.126631, 12.072541, 11.608…
#> $ verified <int> 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,…
#> $ grdCtoA <int> 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0,…initial_list_status: Either w (whole) or f (fractional). This variable indicates if the loan was a whole loan or fractional loan. For background: Some institutional investors have a preference to purchase loans in their entirety to obtain legal and accounting treatment specific to their situation - with the added benefit of “instant funding” to borrowerspurpose: Simplified from the original data; One of: credit_card, debt_consolidation, home_improvement, major_purchase and small_businessint_rate: Interest rate in percentagesinstallment: Monthly payment owed by the borrowerannual_inc: Self-reported annual income provided by the borrower / co-borrowers during applicationdti: A ratio of the borrower’s total monthly debt payments on his/her total obligations to the self-reported monthly income (debt to income ratio)verification_status: is the reported income verified, not verified, or if the income source was verifiedgrade: software-assigned loan graderevol_bal: total credit revolving balance (in the case of credit card, it refers to the portion of credit card spending that goes unpaid at the end of a billing cycle)inq_last_12m: number of credit inquiries in the last 12 monthsdelinq_2yrs: number of 30+ days past-due incidences of delinquency in the borrower’s credit file for the past 2 yearshome_ownership: one of MORTGAGE, OWN and RENTnot_paid: 1 for charged-off, past-due / grace period or defaulted, 0 for fully-paid loanslog_inc: log of annual_incverified: 0 for “Not verified” under verification_status, 1 otherwisegrdCtoA: 0 for a grade of A, B or C, 1 otherwise
Data Cleansing
Adakah tipe data yang belum tepat?
Ubah
not_paid,verifieddangrdCtoAke tipe data factor
# Please run the code down below
loan_clean <- loan %>%
mutate_at(vars(not_paid, verified, grdCtoA), as.factor)
glimpse(loan_clean)#> Rows: 1,556
#> Columns: 16
#> $ initial_list_status <fct> w, f, w, w, w, w, w, w, w, w, w, w, w, f, w, w, w,…
#> $ purpose <fct> debt_consolidation, debt_consolidation, debt_conso…
#> $ int_rate <dbl> 14.08, 9.44, 28.72, 13.59, 15.05, 10.91, 15.05, 10…
#> $ installment <dbl> 675.99, 480.08, 1010.30, 484.19, 476.33, 130.79, 3…
#> $ annual_inc <dbl> 156700, 50000, 25000, 175000, 109992, 49000, 65000…
#> $ dti <dbl> 19.11, 19.35, 65.58, 12.60, 10.00, 5.12, 22.38, 33…
#> $ verification_status <fct> Source Verified, Not Verified, Verified, Not Verif…
#> $ grade <fct> C, B, F, C, C, B, C, B, D, D, F, C, C, E, B, C, C,…
#> $ revol_bal <int> 21936, 5457, 23453, 31740, 2284, 2016, 14330, 2758…
#> $ inq_last_12m <int> 3, 1, 0, 0, 3, 5, 0, 1, 8, 1, 0, 12, 4, 8, 1, 3, 0…
#> $ delinq_2yrs <int> 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,…
#> $ home_ownership <fct> MORTGAGE, RENT, OWN, MORTGAGE, MORTGAGE, MORTGAGE,…
#> $ not_paid <fct> 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1,…
#> $ log_inc <dbl> 11.962088, 10.819778, 10.126631, 12.072541, 11.608…
#> $ verified <fct> 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,…
#> $ grdCtoA <fct> 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0,…Data Pre-Processing
PCA dengan FactoMineR dapat melibatkan variable kategorik untuk visualisasi data. Mari kita pisahkan dulu variabel numerik dan kategorik:
# nama kolom numerik (quantitative)
quanti <- loan_clean %>%
select_if(is.numeric) %>%
colnames()
# indeks kolom numerik
quantivar <- which(colnames(loan_clean) %in% quanti)# nama kolom kategorik (qualitative)
quali <- loan_clean %>%
select_if(is.factor) %>%
colnames()
# indeks kolom kategorik
qualivar <- which(colnames(loan_clean) %in% quali)PCA with FactoMineR
Parameter fungsi PCA(): untuk variable numerik saja
X: dataframe awalscale.unit = T: untuk melakukan scaling dengan fungsiscale()quali.sup: untuk tidak mengikut sertakan index kolom variable kategorikal (qualitative)graph = F: untuk tidak menampilkan plot secara langsungncp: banyaknya PC yang digunakan, default = 5 (disesuaikan saja dengan jumlah variable numeriknya)
# melakukan PCA dengan FactoMineR
loan_pca <- PCA(X = loan_clean,
scale.unit = T,
quali.sup = qualivar, # untuk menghilangkan variable yang kategorik
graph = F,
ncp = 8)Untuk melihat hasil dari PCA yang sudah dilakukan, kita dapa melakukan beberapa hal berikut ini:
- Melihat nilai cumulative variance
Sebernya sama dengan hasil dari summary(object_pca)
# Please run the code down below
loan_pca$eig#> eigenvalue percentage of variance cumulative percentage of variance
#> comp 1 2.3492124 29.365155 29.36515
#> comp 2 1.4050728 17.563410 46.92857
#> comp 3 1.0985925 13.732406 60.66097
#> comp 4 1.0131555 12.664444 73.32542
#> comp 5 0.8294041 10.367552 83.69297
#> comp 6 0.6467516 8.084395 91.77736
#> comp 7 0.4922722 6.153403 97.93076
#> comp 8 0.1655389 2.069236 100.00000- Melihat nilai pada setiap PC
Sebernya sama dengan hasil dari object_pca$x
# Please run the code down below
head(loan_pca$ind$coord)#> Dim.1 Dim.2 Dim.3 Dim.4 Dim.5 Dim.6
#> 1 1.8726407 -0.02630256 -0.2620212 -0.3818516 -0.1440523 0.29379806
#> 2 -0.7953612 -0.59637757 0.1002547 0.9009347 0.4275856 0.77186601
#> 3 -1.3593014 4.73853507 -0.5401945 0.8218723 -0.5799966 0.74642058
#> 4 2.0152497 -0.64397562 -0.9941929 0.4797471 -0.3253111 -0.52434576
#> 5 0.6545361 -0.71599161 0.3267262 -0.5351297 -0.6294665 -0.01941924
#> 6 -0.9730541 -1.37420746 0.4126093 -1.2286800 0.1841724 -0.34258151
#> Dim.7 Dim.8
#> 1 0.4142317 0.2487058
#> 2 -0.1167101 -0.1040927
#> 3 0.8142216 -0.2268024
#> 4 0.5452035 0.2257019
#> 5 0.3436425 0.2451064
#> 6 -0.5383739 -0.1755210Visualisasi PCA
Biplot dapat divisualisasikan menggunakan plot.PCA()
Kelebihan plot.PCA() dari fungsi base
biplot() adalah:
- memisahkan grafik observasi dan variable agar bisa dilihat lebih mudah
- bisa melibatkan variable kategorik untuk mewarnai plot sehingga plot lebih informatif
Individual Factor Map
Plot sebaran observasi untuk mengetahui index yang dianggap sebagai outlier
Parameter fungsi plot.PCA():
x: object PCA (FactoMineR)choix = "ind": plot INDividual factor mapinvisible = "quali": menghilangkan label kolom kategorik, agar tidak mengganggu visualisasiselect = "contrib n": hanya menampilkan indeks dari n outlier terluarhabillage: mewarnai titik berdasarkan index kolom (bisa kategorikal maupun numerik)axes= untuk menentukan dim/PC yang ingin ditampilkan
glimpse(loan_clean)#> Rows: 1,556
#> Columns: 16
#> $ initial_list_status <fct> w, f, w, w, w, w, w, w, w, w, w, w, w, f, w, w, w,…
#> $ purpose <fct> debt_consolidation, debt_consolidation, debt_conso…
#> $ int_rate <dbl> 14.08, 9.44, 28.72, 13.59, 15.05, 10.91, 15.05, 10…
#> $ installment <dbl> 675.99, 480.08, 1010.30, 484.19, 476.33, 130.79, 3…
#> $ annual_inc <dbl> 156700, 50000, 25000, 175000, 109992, 49000, 65000…
#> $ dti <dbl> 19.11, 19.35, 65.58, 12.60, 10.00, 5.12, 22.38, 33…
#> $ verification_status <fct> Source Verified, Not Verified, Verified, Not Verif…
#> $ grade <fct> C, B, F, C, C, B, C, B, D, D, F, C, C, E, B, C, C,…
#> $ revol_bal <int> 21936, 5457, 23453, 31740, 2284, 2016, 14330, 2758…
#> $ inq_last_12m <int> 3, 1, 0, 0, 3, 5, 0, 1, 8, 1, 0, 12, 4, 8, 1, 3, 0…
#> $ delinq_2yrs <int> 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0,…
#> $ home_ownership <fct> MORTGAGE, RENT, OWN, MORTGAGE, MORTGAGE, MORTGAGE,…
#> $ not_paid <fct> 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1,…
#> $ log_inc <dbl> 11.962088, 10.819778, 10.126631, 12.072541, 11.608…
#> $ verified <fct> 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1,…
#> $ grdCtoA <fct> 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0,…# Please type your code down here
plot.PCA(x = loan_pca,
choix = "ind",
invisible = "quali",
select = "contrib 15",
habillage = 13,
axes = c(3, 4))
Note: persentase yang tampil pada sumbu Dim 1 (29.37%) dan Dim 2 (17.56%) menunjukkan seberapa besar sumbu merangkum informasi. Secara kolektif, biplot di atas menjelaskan 29.37% + 17.56% = 46.93% informasi data asli.
Tindak lanjut terhadap outlier ini:
- Identifikasi nilai apa yang menyebabkan observasi tersebut disebut outlier, lihat dari variable factor map (panah searah dengan observasi)
- Apabila masuk ke ranah supervised learning, outlier ini bisa dicoba untuk dihandle (misal remove/transformasi nilai) sebagai salah satu strategi model improvement
Variables Factor Map
- Mengetahui variable contribution ke tiap PC, serta besar informasi yang dirangkum dari tiap variable ke tiap PC (loading)
- Mengetahui correlation antar variable awal
Parameter fungsi plot.PCA():
x: object PCA (FactoMineR)choix = "var": plot VARiable factor map
# Please type your code down here
plot.PCA(x = loan_pca,
choix = "var")
[Additional] Dimension Description
Untuk lebih jelas dan objektif, kontribusi/korelasi tiap variable ke
tiap PC dapat dilihat menggunakan dimdesc(). Semakin tinggi
nilai korelasi, semakin banyak informasi yang dirangkum pada PC
tersebut.
# Please run the code down below
# dimension description
loan_dim <- dimdesc(loan_pca)
# variable yang berkontribusi untuk PC1
as.data.frame(loan_dim$Dim.1$quanti) %>%
arrange(desc(abs(correlation)))fviz_contrib(X = loan_pca,
choice = "var",
axes = 1)
Reduce Dimension
Menampilkan cumulative proportion dari PCA:
# summary PCA untuk FactoMineR
loan_pca$eig#> eigenvalue percentage of variance cumulative percentage of variance
#> comp 1 2.3492124 29.365155 29.36515
#> comp 2 1.4050728 17.563410 46.92857
#> comp 3 1.0985925 13.732406 60.66097
#> comp 4 1.0131555 12.664444 73.32542
#> comp 5 0.8294041 10.367552 83.69297
#> comp 6 0.6467516 8.084395 91.77736
#> comp 7 0.4922722 6.153403 97.93076
#> comp 8 0.1655389 2.069236 100.00000Misalkan kita ingin mempertahankan informasi sebesar 80%, maka berapa PC yang kita gunakan? PC 1 -5
Subsetting base di R: df[baris,kolom]
# Please type your code down here
loan_keep <- data.frame(loan_pca$ind$coord[ , 1:5])
loan_keeploan_keep kemudian dapat dikembalikan ke data frame awal
(menggantikan variable numerik awal) dan digunakan untuk supervised
learning.
loan_clean %>%
head()[Additional] Reconstruction
Fungsi reconst() memungkinkan kita untuk melakukan
rekonstruksi data hasil PCA ke data semula. Umumnya rekonstruksi ini
digunakan pada data gambar untuk kasus image compression.
Misalnya gambar asli adalah 40x40 pixel (1600 kolom), lalu direduksi dengan menggunakan 50 PC saja. Untuk menampilkan data berupa gambar, tetap diperlukan struktur data yang 1600 kolom yang mewakili tiap pixel. Kita bisa melakukan rekonstruksi gambar dari 50 PC ke 1600 kolom kembali. Namun, nilai hasil rekonstruksi tersebut menjadi sedikit berbeda dari nilai awal.
Catatan: rekonstruksi data jarang dilakukan pada data tabular, karena nilai hasil rekonstruksi tidak merepresentasikan nilai asli, sehingga kurang ada manfaatnya.
Berikut contoh rekonstruksi data dengan menggunakan data
loan:
# reconstruct data menggunakan PC1 - PC5
loan_reconst <- reconst(res = loan_pca,
ncp = 5) # jumlah PC yang ingin di reconstruct
data.frame(loan_reconst)Bandingkan dengan nilai asli sebelum dilakukan PCA:
# data awal (coba bandingkan dengan hasil reconstruct di atas)
loan_clean %>%
select_if(is.numeric)Kita juga dapat rekonstruksi data hingga 100% sama persis bila
menggunakan seluruh PC, dengan menggunakan parameter
ncp = 8 di fungsi reconst().
— End of PCA —
Clustering
Clustering adalah pengelompokkan data berdasarkan karakteristiknya. Tujuan clustering:
- Observasi di cluster yang sama memiliki karakteristik semirip mungkin
- observasi dari cluster berbeda memiliki karakteristik yang sebeda mungkin
K-means Clustering
K-means adalah salah satu algoritma centroid-based clustering, artinya tiap cluster memiliki satu centroid yang mewakili cluster tersebut.
Banyaknya cluster/centroid/ \(k\) ditentukan oleh user.
Algoritma
- Random initialization: meletakkan \(k\) centroid secara random
- Cluster assignment: assign masing-masing observasi ke cluster terdekat, berdasarkan perhitungan jarak (jarak Euclidean)
- Centroid update: menggeser centroid ke rata-rata (means) dari cluster yang terbentuk
- Ulangi langkah 2 dan 3 sampai tidak ada observasi yang clusternya berubah lagi
Kebaikan hasil clustering dapat dilihat dari 3 nilai:
- Within Sum of Squares (
$withinss): jumlah jarak kuadrat dari tiap observasi ke centroid tiap cluster.- Harapannya nilai WSS nya rendah karena akan mengindikasikan bahwa jarak observasi setiap cluster itu semakin merapat
- Between Sum of Squares (
$betweenss): jumlah jarak kuadrat terbobot dari tiap centroid ke rata-rata global. Bobotnya berdasarkan banyaknya observasi pada cluster.- Harapannya nilai dari BSS nya tinggi karena akan mengindikasikan bahwa jarak antar tiap centroid saling berjauhan, intuisinya untuk jarak antara setiap cluster harus saling berjauhan karena agar posisi antar setiap cluster tidak berdekatan.
- Total Sum of Squares (
$totss): jumlah jarak kuadrat dari tiap observasi per cluster ke rata-rata global.- TSS tidak bisa berdiri secara sendiri, melainkan harus dibandingkan dengan nilai BSS.
- Harapannya perbandingan antara nilai BSS/TSS = 1 atau mendekati 1
- Perbadingan nilai BSS/TSS bisa dibilang tidak mungkin satu karena BSS hanya terdiri dari jarak antara setiap centroid dan TSS merupakan jarak dari keseluruhan data kita.
- Agar kita mendapatkan nilai mendekati 1, nilai TSS tidak boleh
terlalu lebih tinggi dibandingkan nilai BSS karena jika perbedaanya
terlalu jauh.
- hal tersebut dapat mengindikasikan bahwa terdapat beberapa observasi yang nilai nya sangat jauh. Hal tersebut akan menjadi indikasi bahwa pada data kita terdapat outlier
Study Case: Credit Card Marketing
Berdasarkan data transaksi di bawah ini, tim marketing ingin melakukan pengelompokan customer berdasarkan transaksi yang mereka lakukan agar ketika tim marketing ingin menawarkan kartu kredit nantinya, mereka bisa memberikan penawaran yang tepat sasaran.
Read Data
library(dplyr)
# read data
credit <- read.csv("cc_marketing.csv")
# cek data
glimpse(credit)#> Rows: 8,950
#> Columns: 18
#> $ CUST_ID <chr> "C10001", "C10002", "C10003", "C10004…
#> $ BALANCE <dbl> 40.90075, 3202.46742, 2495.14886, 166…
#> $ BALANCE_FREQUENCY <dbl> 0.818182, 0.909091, 1.000000, 0.63636…
#> $ PURCHASES <dbl> 95.40, 0.00, 773.17, 1499.00, 16.00, …
#> $ ONEOFF_PURCHASES <dbl> 0.00, 0.00, 773.17, 1499.00, 16.00, 0…
#> $ INSTALLMENTS_PURCHASES <dbl> 95.40, 0.00, 0.00, 0.00, 0.00, 1333.2…
#> $ CASH_ADVANCE <dbl> 0.0000, 6442.9455, 0.0000, 205.7880, …
#> $ PURCHASES_FREQUENCY <dbl> 0.166667, 0.000000, 1.000000, 0.08333…
#> $ ONEOFF_PURCHASES_FREQUENCY <dbl> 0.000000, 0.000000, 1.000000, 0.08333…
#> $ PURCHASES_INSTALLMENTS_FREQUENCY <dbl> 0.083333, 0.000000, 0.000000, 0.00000…
#> $ CASH_ADVANCE_FREQUENCY <dbl> 0.000000, 0.250000, 0.000000, 0.08333…
#> $ CASH_ADVANCE_TRX <int> 0, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0…
#> $ PURCHASES_TRX <int> 2, 0, 12, 1, 1, 8, 64, 12, 5, 3, 12, …
#> $ CREDIT_LIMIT <dbl> 1000, 7000, 7500, 7500, 1200, 1800, 1…
#> $ PAYMENTS <dbl> 201.8021, 4103.0326, 622.0667, 0.0000…
#> $ MINIMUM_PAYMENTS <dbl> 139.50979, 1072.34022, 627.28479, NA,…
#> $ PRC_FULL_PAYMENT <dbl> 0.000000, 0.222222, 0.000000, 0.00000…
#> $ TENURE <int> 12, 12, 12, 12, 12, 12, 12, 12, 12, 1…Deskripsi data:
CUST_ID: Identitas Pemegang Kartu KreditBALANCE: Sisa saldo di akun mereka untuk melakukan pembelianBALANCE_FREQUENCY: Seberapa sering Saldo diperbarui, skor antara 0 - 1 (~1 = sering diperbarui, ~0 = tidak sering diperbarui)PURCHASES: Jumlah pembelian yang dilakukan dari akunONEOFF_PURCHASES: Jumlah pembelian maksimum yang dilakukan dalam sekali jalanINSTALLMENTS_PURCHASES: Jumlah pembelian yang dilakukan secara cicilanCASH_ADVANCE: Uang tunai di muka yang diberikan oleh penggunaPURCHASES_FREQUENCY: Seberapa sering Pembelian dilakukan, skor antara 0 dan 1 (~1 = sering dibeli, ~0 = tidak sering dibeli)ONEOFF_PURCHASES_FREQUENCY: Seberapa sering Pembelian terjadi dalam sekali jalan (~1 = sering dibeli, ~0 = tidak sering dibeli)PURCHASES_INSTALLMENTS_FREQUENCY: Seberapa sering pembelian secara mencicil dilakukan (~1 = sering dilakukan, ~0 = tidak sering dilakukan)CASH_ADVANCE_FREQUENCY: Seberapa sering pembayaran tunai di mukaCASH_ADVANCE_TRX: Jumlah Transaksi yang dilakukan dengan “Cash in Advanced”PURCHASES_TRX: Jumlah transaksi pembelian yang dilakukanCREDIT_LIMIT: Batas Kartu Kredit untuk penggunaPAYMENTS: Jumlah Pembayaran yang dilakukan oleh penggunaMINIMUM_PAYMENTS: Jumlah pembayaran minimum yang dilakukan oleh penggunaPRC_FULL_PAYMENT: Persentase pembayaran penuh yang dibayarkan oleh penggunaTENURE: Jangka waktu layanan kartu kredit untuk pengguna
Data Wrangling & Preparation
- Cek NA/missing value:
# Please type your code down here
anyNA(credit)#> [1] TRUEcolSums(is.na(credit))#> CUST_ID BALANCE
#> 0 0
#> BALANCE_FREQUENCY PURCHASES
#> 0 0
#> ONEOFF_PURCHASES INSTALLMENTS_PURCHASES
#> 0 0
#> CASH_ADVANCE PURCHASES_FREQUENCY
#> 0 0
#> ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY
#> 0 0
#> CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX
#> 0 0
#> PURCHASES_TRX CREDIT_LIMIT
#> 0 1
#> PAYMENTS MINIMUM_PAYMENTS
#> 0 313
#> PRC_FULL_PAYMENT TENURE
#> 0 0# handling NA
credit <- credit %>% na.omit()
# cek NA
anyNA(credit)#> [1] FALSE- Mari kita siapkan kolom yang ingin dipertimbangkan untuk pembuatan
cluster. Terdapat kolom
CUST_IDyang menjelaskan customer ID. Apakah kolom tersebut kita gunakan?
# Please type your code down here
# preparasi data
rownames(credit) <- credit$CUST_ID
credit <- credit %>% select(-CUST_ID)
# cek data
head(credit)EDA
- Cek outlier yang dapat mengganggu clustering dengan menggunakan
bantuan
library(FactoMiner)
# Please type your code down here
library(FactoMineR)
# buat PCA
credit_pca <- PCA(credit, scale.unit = T, graph = F)
# buat biplot
plot.PCA(credit_pca,
choix = "ind",
invisible = "quali",
select = "contrib6")
Dari beberapa outlier yang muncul, kita bisa melakukan takeout terlebih dahulu, agar hasil dari pembuatan cluster lebih baik lagi.
# customer id outlier
outlier <- c("C12226", "C10523", "C10574", "C11657", "C14048","C11300")
# pisahkan customer id outlier
credit_clean <- credit[!(rownames(credit) %in% outlier),]- Cek range antar data
Sebelum melakukan clustering, kita perlu memastikan range nilai antar variable sama. Hal ini karena algoritma k-means berdasarkan perhitungan jarak.
# cek range data
summary(credit_clean)#> BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES
#> Min. : 0.0 Min. :0.0000 Min. : 0.00 Min. : 0.0
#> 1st Qu.: 147.8 1st Qu.:0.9091 1st Qu.: 43.26 1st Qu.: 0.0
#> Median : 916.6 Median :1.0000 Median : 374.98 Median : 44.8
#> Mean : 1597.0 Mean :0.8950 Mean : 1002.44 Mean : 585.2
#> 3rd Qu.: 2097.2 3rd Qu.:1.0000 3rd Qu.: 1142.14 3rd Qu.: 597.9
#> Max. :19043.1 Max. :1.0000 Max. :32539.78 Max. :26547.4
#> INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY
#> Min. : 0.00 Min. : 0.0 Min. :0.00000
#> 1st Qu.: 0.00 1st Qu.: 0.0 1st Qu.:0.08333
#> Median : 94.39 Median : 0.0 Median :0.50000
#> Mean : 417.58 Mean : 989.3 Mean :0.49572
#> 3rd Qu.: 483.14 3rd Qu.: 1133.2 3rd Qu.:0.91667
#> Max. :22500.00 Max. :29282.1 Max. :1.00000
#> ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY
#> Min. :0.00000 Min. :0.0000
#> 1st Qu.:0.00000 1st Qu.:0.0000
#> Median :0.08333 Median :0.1667
#> Mean :0.20548 Mean :0.3685
#> 3rd Qu.:0.33333 3rd Qu.:0.7500
#> Max. :1.00000 Max. :1.0000
#> CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_TRX CREDIT_LIMIT
#> Min. :0.0000 Min. : 0.000 Min. : 0.00 Min. : 50
#> 1st Qu.:0.0000 1st Qu.: 0.000 1st Qu.: 1.00 1st Qu.: 1600
#> Median :0.0000 Median : 0.000 Median : 7.00 Median : 3000
#> Mean :0.1376 Mean : 3.302 Mean : 14.91 Mean : 4513
#> 3rd Qu.:0.2500 3rd Qu.: 4.000 3rd Qu.: 18.00 3rd Qu.: 6500
#> Max. :1.5000 Max. :123.000 Max. :347.00 Max. :30000
#> PAYMENTS MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE
#> Min. : 0.05 Min. : 0.02 Min. :0.0000 Min. : 6.00
#> 1st Qu.: 418.03 1st Qu.: 169.09 1st Qu.:0.0000 1st Qu.:12.00
#> Median : 894.93 Median : 311.99 Median :0.0000 Median :12.00
#> Mean : 1760.14 Mean : 861.84 Mean :0.1591 Mean :11.53
#> 3rd Qu.: 1943.79 3rd Qu.: 824.93 3rd Qu.:0.1667 3rd Qu.:12.00
#> Max. :50721.48 Max. :76406.21 Max. :1.0000 Max. :12.00Apakah skala nilai antar variable berbeda pada data credit card? berbeda
Apakah kita perlu melakukan scaling untuk data credit card? scaling
credit_scaled <- scale(credit_clean)
head(credit_scaled)#> BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES
#> C10001 -0.7456205 -0.36957836 -0.4672254 -0.3998317
#> C10002 0.7693055 0.06800878 -0.5163669 -0.3998317
#> C10003 0.4303801 0.50559591 -0.1180990 0.1284600
#> C10005 -0.3733952 0.50559591 -0.5081251 -0.3888992
#> C10006 0.1019957 0.50559591 0.1704195 -0.3998317
#> C10007 -0.4646547 0.50559591 3.1362863 3.9749581
#> INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY
#> C10001 -0.3589079 -0.4795359 -0.8200673
#> C10002 -0.4651815 2.6433777 -1.2354390
#> C10003 -0.4651815 -0.4795359 1.2567865
#> C10005 -0.4651815 -0.4795359 -1.0277544
#> C10006 1.0200647 -0.4795359 0.4260455
#> C10007 0.3016595 -0.4795359 1.2567865
#> ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY
#> C10001 -0.6857890 -0.7165233
#> C10002 -0.6857890 -0.9258830
#> C10003 2.6516732 -0.9258830
#> C10005 -0.4076683 -0.9258830
#> C10006 -0.6857890 0.5396403
#> C10007 2.6516732 1.5864441
#> CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_TRX CREDIT_LIMIT
#> C10001 -0.6823266 -0.4860398 -0.5263475 -0.9643620
#> C10002 0.5575968 0.1027685 -0.6079049 0.6827944
#> C10003 -0.6823266 -0.4860398 -0.1185606 0.8200575
#> C10005 -0.6823266 -0.4860398 -0.5671262 -0.9094568
#> C10006 -0.6823266 -0.4860398 -0.2816754 -0.7447411
#> C10007 -0.6823266 -0.4860398 2.0019312 2.4672139
#> PAYMENTS MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE
#> C10001 -0.5653001 -0.30513539 -0.5373164 0.3552991
#> C10002 0.8499077 0.08892272 0.2133796 0.3552991
#> C10003 -0.4128452 -0.09908326 -0.5373164 0.3552991
#> C10005 -0.3924334 -0.26066106 -0.5373164 0.3552991
#> C10006 -0.1306217 0.65283063 -0.5373164 0.3552991
#> C10007 1.6665812 -0.28039937 2.8408188 0.3552991Determine Optimum k
Semakin tinggi k, maka:
- WSS semakin mendekati 0
- Rasio BSS/TSS mendekati 1 (BSS semakin mendekati nilai TSS)
Kalau begitu apakah kita selalu memilih k = banyak observasi? Bagaimana menentukan k optimum?
- Kebutuhan dari segi bisnis, data dibutuhkan menjadi berapa kelompok; atau
- Secara statistik: Elbow method, visualisasi dengan
fviz_nbclust()dari packagefactoextra
# Please type your code down here
RNGkind(sample.kind = "Rounding")
set.seed(100)
nbclust_plot <-
fviz_nbclust(x = credit_scaled,
FUNcluster = kmeans,
method = "wss",
k.max = 9)
nbclust_plot$datanbclust_plot
Pilih nilai k di mana ketika k ditambah, penurunan Total WSS tidak terlalu drastis (atau dapat dikatakan sudah melandai)
K-means
Kita bisa melakukan K-means Clustering menggunakan fungsi
k-means().
Parameter:
x: datasetcenters: banyaknya centroid (nilai k)
Penting: perlu dilakukan set.seed() karena terdapat
random initialization pada tahap awal k-means
# Please type your code down here
RNGkind(sample.kind = "Rounding")
set.seed(100)
credit_kmeans <- kmeans(credit_scaled, 4)Hasil dari kmeans():
- Banyaknya pengulangan (iterasi) algoritma k-means sampai dihasilkan cluster yang stabil
# Please run the code down below
credit_kmeans$iter#> [1] 5- Banyaknya observasi pada tiap cluster
# Please run the code down below
credit_kmeans$size#> [1] 3429 587 1346 3268- Letak pusat cluster/centroid, biasa digunakan untuk profiling cluster (akan dibahas lebih dalam di bagian akhir)
# Please run the code down below
credit_kmeans$centers#> BALANCE BALANCE_FREQUENCY PURCHASES ONEOFF_PURCHASES
#> 1 -0.3215580 0.3533348 0.05376027 -0.03840054
#> 2 0.8514343 0.4325922 2.62864377 2.31555604
#> 3 -0.6901778 -2.0067317 -0.32572188 -0.24211454
#> 4 0.4687300 0.3780735 -0.39441133 -0.27590875
#> INSTALLMENTS_PURCHASES CASH_ADVANCE PURCHASES_FREQUENCY
#> 1 0.1790632 -0.3761079 0.8510283
#> 2 1.9103593 0.1128109 1.1218226
#> 3 -0.3097790 -0.3269420 -0.5451675
#> 4 -0.4034351 0.5090324 -0.8699175
#> ONEOFF_PURCHASES_FREQUENCY PURCHASES_INSTALLMENTS_FREQUENCY
#> 1 0.2529212 0.7282956
#> 2 1.7069389 1.0241117
#> 3 -0.4023106 -0.4721402
#> 4 -0.4062820 -0.7536653
#> CASH_ADVANCE_FREQUENCY CASH_ADVANCE_TRX PURCHASES_TRX CREDIT_LIMIT
#> 1 -0.4705025 -0.368243791 0.2094171 -0.14525374
#> 2 -0.1365965 0.008729737 2.4733523 1.31817965
#> 3 -0.4899493 -0.377989535 -0.4294299 -0.24478359
#> 4 0.7200143 0.540501077 -0.4871286 0.01645726
#> PAYMENTS MINIMUM_PAYMENTS PRC_FULL_PAYMENT TENURE
#> 1 -0.18785344 -0.07580383 0.2391267 0.07309393
#> 2 1.70438362 0.40595230 0.3837314 0.30463535
#> 3 -0.20128287 -0.29431873 0.3418977 -0.16364580
#> 4 -0.02613128 0.12784282 -0.4606517 -0.06401248- Label cluster untuk tiap observasi
# Please run the code down below
head(credit_kmeans$cluster)#> C10001 C10002 C10003 C10005 C10006 C10007
#> 3 4 1 4 1 2- Withinss, Betweenss, Totss
# Please run the code down below
credit_kmeans$withinss#> [1] 28009.586 25117.283 9306.142 35965.440credit_kmeans$betweenss#> [1] 48294.55credit_kmeans$totss#> [1] 146693Note: nilai diatas menunjukkan rata-rata nilai tiap variable untuk masing-masing cluster, namun karena berupa hasil scaling, tidak bisa diinterpretasikan. Untuk interpretasi cluster, akan dilakukan di bawah.
Interpretasi/Cluster Profiling
Statistik
Dalam melakukan interpretasi dari setiap cluster, kita akan membuat sebuh kolom baru pada data asli kita dan menempelkan setiap hasil cluster pada setiap observasi datanya.
# Please type your code down here
credit_clean_w_cluster <- credit_clean
credit_clean_w_cluster$cluster <- credit_kmeans$cluster
credit_clean_w_cluster$cluster <- as.factor(credit_clean_w_cluster$cluster)
# cek data
head(credit_clean_w_cluster)Setelah itu, kita akan mencoba melihat hasil rangkuman untuk setiap
clusternya dengan menggunakan fungsi summarise_all()
# Please type your code down here
credit_clusteragg <- credit_clean_w_cluster %>%
group_by(cluster) %>%
summarise_all(mean)
credit_clusteraggCluster Characteristic:
- Cluster 1: BALANCE peringkat ketiga, Banyak di transaksi installment
- Cluster 2: BALANCE paling tinggi, secara umum tinggi di tiap transaksi kecuali Cash Advanced
- Cluster 3: BALANCE paling rendah, lebih sering transaksi full payment / transaksi keseharian
- Cluster 4: BALANCE kedua paling tinggi, lebih sering CASH ADVANCE
Visualization
Selain melihat hasil dari rangkuman statistik, kita juga bisa memanfaatkan sebuah visualisasi.
# Please type your code down here
library(tidyr)
library(ggplot2)
# prepare data structure
plot_data <- credit_clusteragg %>%
pivot_longer(-cluster,
names_to = "variable",
values_to = "values") %>%
mutate(values = round(values, 2))
head(plot_data)ggplot(plot_data, aes(x = cluster, y = values)) +
geom_col(aes(fill = cluster)) +
facet_wrap(~variable, scales = "free_y", ncol = 4)
Dive Deeper!
Berapa banyak nasabah yang memiliki karakteristik mirip dengan
nasabah ID C14447? (penghitungan jumlah termasuk nasabah
tersebut)
# Please type your code down here
credit_clean_w_cluster["C14447", ]credit_clean_w_cluster %>%
filter(cluster == 2)Combining PCA with K-means
Untuk visualisasi clustering kita dapat menggunakan biplot. Hal ini akan membantu dalam mengetahui pola data yang ada pada data, sehingga kita bisa lebih yakin tentang hasil clustering yang di dapat (bentuk persebaran cluster nya seperti apa).
Dalam melakukan hal tersebut, kita akan menggunakan fungsi
fviz_cluster() dari package factoextra.
Berikut beberapa parameter yang kita akan digunakan
object: object kmeansdata: data variable numerik
# Please type your code down here
fviz_cluster(object = credit_kmeans,
data = credit_scaled,
geom = "point")