Çok Değişkenli İstatistiğin İncelenmesi

1 Çok Değişkenli İstatistiğe Giriş

• Çok değişkenli istatistikler karmaşık veri setlerini analiz etmede kullanım yaygınlığı gittikçe artan tekniklerdir.

• Bu ders kapsamında kullanılacak paketlerin yüklenmesi

library(tidyverse)

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## ✔ lubridate 1.9.3     ✔ tibble    3.2.1
## ✔ purrr     1.0.4     ✔ tidyr     1.3.1
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library(dplyr)
library(stevemisc)

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library(knitr)
library(haven)
library(summarytools)

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library(outliers)
library(ggplot2)
library(plotly)

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library(ggpmisc)

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library(psych)

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library(sur)

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library(moments)
library(corrplot)

## corrplot 0.95 loaded

library(olsrr)

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• Veri setinin yüklenmesi

library(readr)
scr_canada <- read_csv("D:/OLC_733/scr_canada.csv")

## Rows: 13879 Columns: 29
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr  (1): idbid
## dbl (28): IDCNTRY, IDPOP, IDGRADER, IDGRADE, IDSCHOOL, IDCLASS, IDSTUD, ITSE...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

head(scr_canada) # ilk satırların gözlemlenmesi

#Kullanılacak verinin seçilmesi

#scr <-select(scr_canada, starts_with("ASBR08"))

# Geçerli olmayan yanıtların çıkarılması, 9 'u kayıp veri olarak atanması
#scr %>%  filter_all(all_vars(!is.na(.))) %>%
#mutate_all(~na_if(., 9)) %>%
  #as.data.frame()

2 Eksik Verileirn Düzenlenmesi

scr_canada <- scr_canada %>% 
mutate(IDGRADE = ifelse(is.na(IDGRADE), mean(IDGRADE, na.rm = TRUE),IDGRADE)) %>% na.omit()

summary(scr_canada)

##     IDCNTRY         IDPOP      IDGRADER    IDGRADE         IDSCHOOL   
##  Min.   :9130   Min.   :1   Min.   :2   Min.   :4.000   Min.   :5001  
##  1st Qu.:9133   1st Qu.:1   1st Qu.:2   1st Qu.:4.000   1st Qu.:5163  
##  Median :9134   Median :1   Median :2   Median :4.000   Median :5331  
##  Mean   :9133   Mean   :1   Mean   :2   Mean   :4.272   Mean   :5328  
##  3rd Qu.:9135   3rd Qu.:1   3rd Qu.:2   3rd Qu.:5.000   3rd Qu.:5493  
##  Max.   :9135   Max.   :1   Max.   :2   Max.   :5.000   Max.   :5661  
##     IDCLASS           IDSTUD             ITSEX          ITADMINI    
##  Min.   :500101   Min.   :50010101   Min.   :1.000   Min.   :2.000  
##  1st Qu.:516303   1st Qu.:51630302   1st Qu.:1.000   1st Qu.:2.000  
##  Median :533101   Median :53310112   Median :2.000   Median :3.000  
##  Mean   :532834   Mean   :53283439   Mean   :1.501   Mean   :3.208  
##  3rd Qu.:549302   3rd Qu.:54930208   3rd Qu.:2.000   3rd Qu.:3.000  
##  Max.   :566101   Max.   :56610107   Max.   :2.000   Max.   :9.000  
##    ITLANG_SA      ITLANG_SQ        IDBOOK         ASBR08A         ASBR08B     
##  Min.   :1.00   Min.   :1.00   Min.   : 1.00   Min.   :1.000   Min.   :1.000  
##  1st Qu.:1.00   1st Qu.:1.00   1st Qu.: 7.00   1st Qu.:1.000   1st Qu.:1.000  
##  Median :1.00   Median :1.00   Median :14.00   Median :1.000   Median :1.000  
##  Mean   :1.59   Mean   :1.59   Mean   :19.15   Mean   :1.661   Mean   :1.779  
##  3rd Qu.:3.00   3rd Qu.:3.00   3rd Qu.:26.00   3rd Qu.:2.000   3rd Qu.:2.000  
##  Max.   :3.00   Max.   :3.00   Max.   :83.00   Max.   :9.000   Max.   :9.000  
##     ASBR08C         ASBR08D         ASBR08E         ASBR08F    
##  Min.   :1.000   Min.   :1.000   Min.   :1.000   Min.   :1.00  
##  1st Qu.:2.000   1st Qu.:2.000   1st Qu.:3.000   1st Qu.:3.00  
##  Median :3.000   Median :4.000   Median :4.000   Median :4.00  
##  Mean   :2.807   Mean   :3.352   Mean   :3.554   Mean   :3.67  
##  3rd Qu.:4.000   3rd Qu.:4.000   3rd Qu.:4.000   3rd Qu.:4.00  
##  Max.   :9.000   Max.   :9.000   Max.   :9.000   Max.   :9.00  
##      HOUWGT           TOTWGT            SENWGT            JKREP       
##  Min.   :0.1141   Min.   :  1.052   Min.   :0.01220   Min.   :0.0000  
##  1st Qu.:0.6444   1st Qu.:  5.420   1st Qu.:0.08509   1st Qu.:0.0000  
##  Median :0.8461   Median : 10.040   Median :0.12338   Median :1.0000  
##  Mean   :0.9992   Mean   : 12.576   Mean   :0.14390   Mean   :0.5041  
##  3rd Qu.:1.2028   3rd Qu.: 17.635   3rd Qu.:0.17512   3rd Qu.:1.0000  
##  Max.   :5.9587   Max.   :129.220   Max.   :0.79683   Max.   :1.0000  
##      JKZONE          ASRREA01        ASRREA02        ASRREA03    
##  Min.   :  1.00   Min.   :181.7   Min.   :238.8   Min.   :222.6  
##  1st Qu.: 31.00   1st Qu.:494.3   1st Qu.:493.0   1st Qu.:491.9  
##  Median : 62.00   Median :546.2   Median :544.4   Median :544.9  
##  Mean   : 62.61   Mean   :540.1   Mean   :539.2   Mean   :538.0  
##  3rd Qu.: 93.00   3rd Qu.:591.2   3rd Qu.:591.5   3rd Qu.:589.1  
##  Max.   :125.00   Max.   :784.4   Max.   :809.1   Max.   :794.9  
##     ASRREA04        ASRREA05        idbid          
##  Min.   :221.2   Min.   :223.1   Length:13685      
##  1st Qu.:492.8   1st Qu.:492.9   Class :character  
##  Median :545.2   Median :544.9   Mode  :character  
##  Mean   :538.8   Mean   :539.0                     
##  3rd Qu.:590.6   3rd Qu.:590.5                     
##  Max.   :795.4   Max.   :787.3

library(skimr)
skim(scr_canada)

Table 2.1: Data summary

Name	scr_canada
Number of rows	13685
Number of columns	29
_______________________
Column type frequency:
character	1
numeric	28
________________________
Group variables	None

Variable type: character

skim_variable	n_missing	complete_rate	min	max	empty	n_unique	whitespace
idbid	0	1	3	3	0	1	0

Variable type: numeric

skim_variable	n_missing	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
IDCNTRY	0	1	9133.36	1.74	9130.00	9133.00	9134.00	9135.00	9135.00	▅▁▆▅▇
IDPOP	0	1	1.00	0.00	1.00	1.00	1.00	1.00	1.00	▁▁▇▁▁
IDGRADER	0	1	2.00	0.00	2.00	2.00	2.00	2.00	2.00	▁▁▇▁▁
IDGRADE	0	1	4.27	0.45	4.00	4.00	4.00	5.00	5.00	▇▁▁▁▃
IDSCHOOL	0	1	5328.32	192.91	5001.00	5163.00	5331.00	5493.00	5661.00	▇▇▇▇▇
IDCLASS	0	1	532834.28	19290.59	500101.00	516303.00	533101.00	549302.00	566101.00	▇▇▇▇▇
IDSTUD	0	1	53283438.61	1929059.15	50010101.00	51630302.00	53310112.00	54930208.00	56610107.00	▇▇▇▇▇
ITSEX	0	1	1.50	0.50	1.00	1.00	2.00	2.00	2.00	▇▁▁▁▇
ITADMINI	0	1	3.21	1.81	2.00	2.00	3.00	3.00	9.00	▇▁▁▁▁
ITLANG_SA	0	1	1.59	0.91	1.00	1.00	1.00	3.00	3.00	▇▁▁▁▃
ITLANG_SQ	0	1	1.59	0.91	1.00	1.00	1.00	3.00	3.00	▇▁▁▁▃
IDBOOK	0	1	19.15	17.44	1.00	7.00	14.00	26.00	83.00	▇▂▁▁▁
ASBR08A	0	1	1.66	1.31	1.00	1.00	1.00	2.00	9.00	▇▁▁▁▁
ASBR08B	0	1	1.78	1.51	1.00	1.00	1.00	2.00	9.00	▇▁▁▁▁
ASBR08C	0	1	2.81	1.58	1.00	2.00	3.00	4.00	9.00	▇▇▁▁▁
ASBR08D	0	1	3.35	1.50	1.00	2.00	4.00	4.00	9.00	▃▇▁▁▁
ASBR08E	0	1	3.55	1.51	1.00	3.00	4.00	4.00	9.00	▂▇▁▁▁
ASBR08F	0	1	3.67	1.52	1.00	3.00	4.00	4.00	9.00	▂▇▁▁▁
HOUWGT	0	1	1.00	0.62	0.11	0.64	0.85	1.20	5.96	▇▂▁▁▁
TOTWGT	0	1	12.58	11.22	1.05	5.42	10.04	17.64	129.22	▇▁▁▁▁
SENWGT	0	1	0.14	0.09	0.01	0.09	0.12	0.18	0.80	▇▂▁▁▁
JKREP	0	1	0.50	0.50	0.00	0.00	1.00	1.00	1.00	▇▁▁▁▇
JKZONE	0	1	62.61	36.16	1.00	31.00	62.00	93.00	125.00	▇▇▇▆▇
ASRREA01	0	1	540.12	74.34	181.71	494.28	546.24	591.19	784.44	▁▁▇▇▁
ASRREA02	0	1	539.19	75.18	238.85	493.03	544.40	591.46	809.14	▁▂▇▅▁
ASRREA03	0	1	537.96	74.47	222.57	491.90	544.89	589.13	794.87	▁▂▇▆▁
ASRREA04	0	1	538.82	74.59	221.16	492.81	545.23	590.58	795.42	▁▂▇▆▁
ASRREA05	0	1	539.04	74.59	223.06	492.92	544.85	590.52	787.30	▁▂▇▆▁

#Aletrnatif paketlerle betimsel istatistik özetleri elde edilebilir.
library(psych)
describe(scr_canada)

• Summary ile veri setindeki değişkenler ile ilgili betimsel istatistikler ile ilgili bilgi edinilebilir.
• Veri setinde 13685 kişinin olduğu, “ASBR” kodu ile başlayan değişkenlerin ortalamalarının 1.66 ile 3.67 arasında değiştiği gözlemlenmiştir.

3 Kategorik Değişkenler İçin Uç Değerlerin İncelenmesi

library(summarytools)
freq(scr_canada$ITSEX, 
     round.digits = 2,report.nas = FALSE,
 style = "rmarkdown") 

## setting plain.ascii to FALSE

## ### Frequencies  
## #### scr_canada$ITSEX  
## **Type:** Numeric  
## 
## |      |  Freq |      % | % Cum. |
## |----------:|------:|-------:|-------:|
## |     **1** |  6829 |  49.90 |  49.90 |
## |     **2** |  6856 |  50.10 | 100.00 |
## | **Total** | 13685 | 100.00 | 100.00 |

#Farklı bir şekilde de özet frekans tablosu alınabilir.
library(knitr)
freq(scr_canada$ITSEX,report.nas = FALSE) %>%
  kable(format='markdown', 
      caption="Frekans Tablosu",digits = 2)

Table 3.1: Frekans Tablosu

	Freq	% Valid	% Valid Cum.	% Total	% Total Cum.
1	6829	49.9	49.9	49.9	49.9
2	6856	50.1	100.0	50.1	100.0
	0	NA	NA	0.0	100.0
Total	13685	100.0	100.0	100.0	100.0

library(janitor)

## 
## Attaching package: 'janitor'

## The following objects are masked from 'package:stats':
## 
##     chisq.test, fisher.test

scr_canada %>% 
  tabyl(ITSEX) %>% 
  adorn_percentages("row") %>% 
  adorn_pct_formatting(digits = 2) %>% 
  adorn_ns()

## Warning in adorn_ns(.): adorn_ns() is meant to be called on a two_way tabyl;
## consider combining columns of a one_way tabyl with tidyr::unite()

• Veri setinde cinsiyet değişkenin benzer oranlarda dağıldığı gözlemlenmiştir.
• Özet tablolar, üç farklı paket kullanılarak ele alınmıştır.

4 Sürekli Değişkenlerde Uç Değerler

library(outliers)
z.scores <- scr_canada %>%  
 select(ASBR08A:ASBR08F) %>% 
 scores(type = "z") %>%
 round(2)
head(z.scores)

library(rstatix)

## 
## Attaching package: 'rstatix'

## The following object is masked from 'package:janitor':
## 
##     make_clean_names

## The following object is masked from 'package:stats':
## 
##     filter

library(tidyr)
scr_canada %>%
  select(ASBR08A:ASBR08F) %>%
  pivot_longer(cols = everything(), names_to = "Degisken", values_to = "Deger") %>%
  group_by(Degisken) %>%
  identify_outliers(Deger)

• ASBR08A: ASBR08F’ye kadar olan değişkenlerin uç değer tablosu incelendiğinde değerlerin -3 ile +3 arasında dağıldığı gözlenmiştir.

library(DT)

DT::datatable(z.scores)

## Warning in instance$preRenderHook(instance): It seems your data is too big for
## client-side DataTables. You may consider server-side processing:
## https://rstudio.github.io/DT/server.html

• Data table paketi kullanılarakta bu uç değerler incelenebilir.

library(ggplot2)

scr_canada %>%
  mutate(ITSEX = factor(ITSEX, levels = c(1,2), labels = c("Erkek", "Kadın"))) %>%
  ggplot(aes(x = ITSEX, fill = ITSEX)) +
  geom_bar() +
  scale_fill_manual(values = c("Erkek" = "blue", "Kadın" = "red")) +
  labs(x = "Cinsiyet", y = "Frekans", title = "Cinsiyete Göre Dağılım") +
  theme_minimal()

* Cinsiyete göre dağılım, grafiktede incelenmiş olup, dağılımın dengeli olduğu grafiktede görülmektedir.

library(plotly)

cinsiyet_oran <- scr_canada %>%
  count(ITSEX) %>%
  mutate(oran = n / sum(n) * 100)

# Şimdi yüzdelik grafiği çizelim
plot_ly(
  data = cinsiyet_oran,
  x = ~ITSEX,
  y = ~oran,
  type = "bar",
  color = ~ITSEX,
  colors = c("purple", "yellow"),
  text = ~paste0(round(oran, 1), "%"),  # Çubuk üstüne % yazalım
  textposition = 'outside'              # Yazı çubuğun üstünde gözüksün
) %>%
  layout(
    title = "Cinsiyete Göre Yüzdelik Dağılım",
    xaxis = list(title = "Cinsiyet"),
    yaxis = list(title = "Yüzde (%)"),
    yaxis = list(range = c(0, 100)),     # Y ekseni 0-100 arası ayarla
    showlegend = FALSE
  )

## Warning: textfont.color doesn't (yet) support data arrays
## Warning: textfont.color doesn't (yet) support data arrays

scr_canada %>%
  select(ASBR08A:ASBR08F) %>%
  pivot_longer(cols = everything(), names_to = "Degisken", values_to = "Deger") %>%
  ggplot(aes(x = Degisken, y = Deger)) +
  geom_boxplot(fill = "#0c4c8a", color = "black") +
  labs(title = "ASBR08A-F Değişkenlerinin Boxplot Grafiği",
       x = "Değişkenler", y = "Değerler") +
  theme_minimal()

* Box plot grafiği incelendiğinde ASBR08A, ASBR08B, ASBR08E ve ASBR08F değişkenlerinde ikişer tane uç değer olduğu görülmektedir. * ASBR08C ve ASBR08D değişkenlerinde ise bir tane uç değerin olduğu söylenebilir.

5 Uç değerlerin Hangi Değerler Olduğunun İncelenmesi

degiskenler <- c("ASBR08A", "ASBR08B", "ASBR08C", "ASBR08D", "ASBR08E", "ASBR08F")

outlier_listesi <- lapply(degiskenler, function(var) {
  which(scr_canada[[var]] %in% boxplot.stats(scr_canada[[var]])$out)
})

names(outlier_listesi) <- degiskenler

outlier_listesi

## $ASBR08A
##   [1]    29    36    38   180   208   265   285   292   304   315   352   365
##  [13]   368   374   391   433   434   435   532   569   594   599   632   637
##  [25]   665   684   695   696   728   750   778   781   783   795   808   809
##  [37]   835   869   895   914   917   918   925   952   985   996  1010  1023
##  [49]  1028  1029  1042  1053  1070  1135  1160  1188  1380  1432  1490  1581
##  [61]  1587  1589  1593  1595  1636  1652  1731  1757  1773  1796  1841  1877
##  [73]  1915  1939  2058  2067  2098  2100  2107  2112  2117  2123  2199  2224
##  [85]  2246  2254  2255  2256  2258  2284  2290  2335  2350  2365  2393  2394
##  [97]  2400  2451  2454  2456  2480  2513  2514  2544  2582  2590  2607  2617
## [109]  2631  2688  2695  2735  2769  2789  2816  2836  2872  2905  2912  2974
## [121]  2989  3006  3018  3058  3060  3153  3157  3170  3177  3228  3336  3341
## [133]  3359  3361  3366  3395  3396  3397  3401  3421  3447  3510  3513  3516
## [145]  3522  3567  3608  3615  3617  3645  3654  3664  3666  3697  3720  3721
## [157]  3730  3737  3743  3844  3879  3895  3944  3978  4000  4017  4064  4065
## [169]  4103  4119  4128  4137  4189  4202  4231  4299  4300  4303  4312  4349
## [181]  4355  4357  4358  4363  4375  4410  4413  4419  4432  4440  4449  4475
## [193]  4482  4490  4514  4526  4543  4553  4562  4584  4587  4589  4595  4596
## [205]  4599  4605  4638  4667  4692  4747  4785  4789  4845  4849  4928  4965
## [217]  4980  4989  4990  5066  5079  5093  5148  5219  5226  5240  5256  5301
## [229]  5320  5343  5383  5425  5442  5445  5450  5468  5479  5525  5534  5587
## [241]  5589  5638  5644  5651  5669  5673  5719  5723  5726  5737  5739  5773
## [253]  5836  5837  5846  5851  5858  5860  5871  5900  6003  6006  6011  6019
## [265]  6071  6116  6132  6142  6148  6160  6196  6212  6253  6267  6279  6292
## [277]  6320  6363  6389  6398  6424  6431  6469  6507  6509  6526  6551  6559
## [289]  6570  6673  6690  6699  6784  6791  6799  6826  6869  6875  6881  6888
## [301]  6953  6962  6965  6972  6975  6982  7020  7064  7069  7070  7078  7094
## [313]  7129  7159  7185  7220  7226  7230  7232  7238  7280  7284  7320  7338
## [325]  7349  7357  7375  7397  7447  7493  7517  7537  7542  7551  7597  7617
## [337]  7627  7628  7631  7690  7764  7770  7772  7778  7843  7845  7846  7848
## [349]  7851  7852  7857  7871  7880  7920  7937  7988  7995  8042  8066  8068
## [361]  8161  8191  8195  8205  8232  8234  8270  8276  8293  8309  8348  8356
## [373]  8364  8373  8384  8390  8473  8512  8522  8524  8577  8603  8616  8622
## [385]  8630  8632  8692  8698  8699  8716  8723  8725  8759  8777  8784  8787
## [397]  8790  8794  8795  8839  8888  8909  8930  8939  8940  8941  8954  8975
## [409]  9023  9041  9043  9045  9095  9118  9123  9126  9145  9156  9170  9172
## [421]  9233  9237  9252  9262  9324  9338  9343  9409  9425  9506  9509  9511
## [433]  9528  9561  9578  9641  9643  9690  9711  9764  9811  9853  9887  9916
## [445]  9921  9922 10027 10030 10040 10046 10067 10124 10167 10178 10291 10306
## [457] 10311 10326 10352 10357 10400 10483 10553 10556 10580 10584 10598 10642
## [469] 10648 10662 10716 10757 10759 10789 10812 10844 10846 10880 10920 10928
## [481] 10972 10983 10986 11056 11099 11187 11244 11288 11290 11304 11307 11309
## [493] 11409 11420 11432 11433 11434 11441 11443 11527 11541 11556 11636 11667
## [505] 11673 11675 11681 11735 11745 11787 11790 11791 11800 11806 11818 11823
## [517] 11859 11885 11963 12014 12062 12072 12091 12092 12125 12128 12155 12180
## [529] 12300 12345 12393 12431 12432 12449 12471 12482 12495 12546 12613 12620
## [541] 12667 12753 12794 12811 12822 12879 12903 12908 12909 13001 13068 13074
## [553] 13086 13128 13198 13208 13218 13219 13295 13303 13350 13354 13374 13391
## [565] 13412 13414 13456 13577 13578 13605 13633 13648 13658 13663
## 
## $ASBR08B
##   [1]    19    29    36    38    54    60    63   111   142   155   170   171
##  [13]   180   192   252   262   269   285   292   304   336   344   347   352
##  [25]   365   368   374   375   391   433   496   511   512   514   532   555
##  [37]   569   594   599   615   637   656   684   691   696   750   781   783
##  [49]   785   809   819   823   840   893   894   898   904   911   917   925
##  [61]   952   980   982   985   996  1023  1027  1029  1045  1053  1068  1160
##  [73]  1188  1218  1249  1318  1342  1351  1359  1432  1446  1453  1469  1476
##  [85]  1490  1579  1581  1587  1589  1593  1595  1626  1629  1673  1677  1731
##  [97]  1767  1773  1789  1795  1796  1812  1841  1866  1876  1915  1927  1933
## [109]  1937  1998  2067  2095  2098  2100  2107  2112  2116  2117  2123  2124
## [121]  2186  2195  2199  2224  2246  2250  2254  2284  2290  2329  2335  2350
## [133]  2351  2353  2365  2392  2451  2454  2459  2460  2480  2517  2544  2565
## [145]  2569  2582  2607  2615  2636  2674  2688  2695  2725  2769  2789  2816
## [157]  2835  2836  2854  2856  2865  2872  2905  2912  2974  2995  3006  3018
## [169]  3031  3058  3060  3089  3115  3153  3157  3158  3170  3177  3186  3195
## [181]  3228  3249  3290  3336  3362  3380  3395  3396  3397  3398  3401  3430
## [193]  3495  3516  3522  3540  3541  3542  3567  3588  3608  3614  3615  3617
## [205]  3645  3654  3664  3666  3678  3683  3697  3711  3720  3721  3730  3737
## [217]  3769  3869  3879  3895  3908  3970  3978  4017  4065  4079  4103  4119
## [229]  4120  4135  4137  4181  4194  4201  4202  4255  4261  4277  4295  4299
## [241]  4303  4345  4349  4355  4357  4358  4363  4368  4410  4413  4432  4438
## [253]  4440  4449  4462  4475  4482  4490  4496  4514  4526  4543  4553  4562
## [265]  4567  4584  4588  4589  4595  4599  4605  4629  4635  4638  4667  4673
## [277]  4692  4723  4739  4747  4767  4785  4789  4806  4813  4829  4845  4849
## [289]  4850  4905  4928  4970  4989  4990  4997  5000  5037  5071  5072  5075
## [301]  5079  5219  5224  5228  5240  5253  5256  5277  5305  5331  5343  5364
## [313]  5379  5383  5399  5425  5445  5450  5453  5478  5479  5490  5525  5534
## [325]  5550  5556  5575  5587  5632  5638  5639  5658  5673  5719  5737  5739
## [337]  5773  5779  5836  5837  5846  5871  5895  5900  5945  6003  6006  6011
## [349]  6019  6071  6094  6116  6145  6148  6154  6160  6179  6198  6212  6253
## [361]  6267  6279  6285  6292  6304  6320  6325  6363  6389  6398  6415  6420
## [373]  6426  6456  6469  6481  6526  6551  6559  6567  6570  6625  6655  6663
## [385]  6686  6699  6701  6702  6708  6728  6774  6784  6789  6791  6799  6826
## [397]  6854  6865  6869  6875  6881  6888  6895  6953  6959  6962  6965  6975
## [409]  6982  6993  7020  7040  7069  7070  7078  7085  7086  7094  7123  7128
## [421]  7159  7161  7184  7185  7194  7195  7207  7220  7226  7238  7246  7261
## [433]  7284  7348  7375  7397  7481  7493  7517  7532  7536  7537  7542  7551
## [445]  7589  7603  7617  7627  7639  7764  7770  7772  7778  7780  7788  7789
## [457]  7825  7836  7842  7843  7845  7846  7851  7852  7857  7871  7877  7878
## [469]  7880  7899  7920  7937  7995  7996  7998  8012  8020  8026  8034  8035
## [481]  8042  8056  8064  8075  8129  8154  8156  8161  8200  8205  8234  8236
## [493]  8263  8268  8270  8276  8323  8348  8356  8364  8373  8384  8390  8431
## [505]  8442  8473  8509  8512  8522  8524  8548  8565  8573  8577  8615  8616
## [517]  8622  8630  8632  8667  8692  8698  8699  8702  8723  8749  8759  8777
## [529]  8794  8858  8888  8909  8917  8922  8924  8930  8939  8940  8941  8944
## [541]  8954  8955  8981  8990  9007  9023  9036  9041  9043  9045  9100  9118
## [553]  9123  9145  9149  9155  9156  9158  9168  9170  9172  9237  9242  9243
## [565]  9252  9262  9264  9277  9281  9285  9299  9324  9328  9338  9343  9409
## [577]  9496  9507  9511  9528  9554  9561  9578  9605  9641  9643  9651  9678
## [589]  9682  9690  9699  9711  9764  9767  9779  9805  9808  9811  9814  9817
## [601]  9853  9859  9870  9887  9907  9916  9921 10009 10019 10098 10124 10129
## [613] 10172 10178 10191 10214 10236 10311 10325 10337 10352 10357 10413 10442
## [625] 10456 10460 10466 10469 10471 10483 10520 10553 10566 10584 10642 10648
## [637] 10656 10657 10677 10693 10702 10715 10722 10736 10757 10783 10789 10812
## [649] 10880 10901 10910 10920 10928 10976 10983 10986 11013 11017 11045 11056
## [661] 11058 11099 11151 11153 11187 11207 11288 11302 11304 11307 11311 11352
## [673] 11379 11409 11420 11432 11433 11434 11443 11490 11527 11541 11550 11556
## [685] 11563 11566 11598 11608 11624 11634 11667 11670 11673 11680 11735 11748
## [697] 11778 11787 11790 11791 11800 11806 11818 11823 11856 11859 11885 11886
## [709] 12014 12024 12043 12062 12072 12091 12092 12098 12130 12149 12155 12180
## [721] 12201 12247 12294 12300 12321 12393 12415 12432 12442 12449 12468 12471
## [733] 12490 12495 12497 12613 12624 12667 12677 12678 12681 12720 12753 12794
## [745] 12822 12879 12889 12908 12909 12929 13016 13049 13057 13062 13074 13111
## [757] 13128 13131 13160 13198 13208 13218 13225 13268 13272 13295 13303 13350
## [769] 13354 13356 13377 13386 13391 13404 13456 13557 13578 13605 13614 13648
## [781] 13679
## 
## $ASBR08C
##   [1]    19    26    29    38    52    63   155   192   202   263   278   292
##  [13]   315   344   352   360   365   375   433   496   500   505   511   512
##  [25]   532   538   555   569   599   637   695   696   703   750   809   835
##  [37]   893   904   911   914   917  1015  1019  1023  1026  1027  1029  1042
##  [49]  1053  1068  1127  1128  1142  1144  1160  1188  1242  1249  1380  1432
##  [61]  1476  1581  1587  1589  1593  1595  1652  1812  1902  1917  1937  1963
##  [73]  2063  2079  2098  2107  2112  2116  2123  2199  2224  2246  2254  2258
##  [85]  2284  2290  2335  2350  2351  2353  2365  2392  2393  2400  2404  2451
##  [97]  2454  2456  2480  2507  2544  2615  2688  2695  2721  2733  2769  2789
## [109]  2836  2856  2905  2924  2974  2989  3018  3023  3061  3153  3177  3228
## [121]  3336  3351  3361  3396  3421  3516  3522  3553  3588  3616  3631  3637
## [133]  3654  3657  3664  3666  3720  3721  3730  3737  3819  3879  3912  3945
## [145]  4002  4017  4064  4103  4106  4119  4120  4137  4171  4181  4189  4194
## [157]  4201  4202  4209  4255  4277  4295  4299  4300  4303  4349  4355  4357
## [169]  4358  4363  4413  4438  4440  4462  4475  4482  4490  4513  4514  4521
## [181]  4526  4543  4553  4556  4560  4562  4587  4589  4595  4596  4599  4659
## [193]  4667  4680  4723  4785  4789  4806  4813  4845  4849  4850  4912  4928
## [205]  4955  4970  5066  5072  5079  5084  5145  5219  5224  5226  5240  5253
## [217]  5280  5301  5305  5332  5425  5445  5449  5450  5479  5525  5527  5534
## [229]  5550  5651  5658  5673  5719  5737  5740  5773  5779  5836  5837  5860
## [241]  5871  5976  5989  6003  6006  6116  6148  6154  6174  6212  6253  6279
## [253]  6285  6292  6363  6389  6398  6431  6456  6467  6469  6481  6488  6503
## [265]  6509  6559  6617  6630  6693  6708  6711  6728  6731  6826  6869  6875
## [277]  6881  6882  6888  6953  6965  6972  6982  7020  7064  7069  7070  7078
## [289]  7086  7094  7123  7128  7129  7139  7185  7207  7220  7246  7284  7303
## [301]  7308  7375  7397  7493  7517  7537  7551  7565  7589  7597  7603  7639
## [313]  7690  7764  7770  7772  7778  7788  7825  7836  7842  7843  7846  7852
## [325]  7857  7920  7937  7995  8020  8026  8034  8035  8064  8129  8148  8154
## [337]  8161  8205  8270  8276  8287  8323  8348  8353  8356  8364  8384  8390
## [349]  8431  8442  8473  8488  8570  8573  8615  8630  8667  8712  8748  8759
## [361]  8777  8794  8839  8909  8922  8924  8955  8989  9007  9023  9036  9045
## [373]  9093  9095  9100  9123  9158  9168  9174  9252  9253  9262  9264  9277
## [385]  9285  9324  9326  9331  9336  9347  9409  9436  9547  9578  9580  9682
## [397]  9699  9711  9764  9769  9781  9808  9811  9814  9824  9853  9870  9916
## [409]  9921  9922  9976 10014 10015 10027 10126 10483 10556 10563 10591 10745
## [421] 10757 10789 10812 10903 11011 11056 11064 11107 11230 11290 11311 11384
## [433] 11409 11420 11433 11442 11443 11591 11616 11629 11667 11680 11699 11729
## [445] 11735 11787 11791 11800 11806 11859 11882 12009 12014 12062 12092 12109
## [457] 12134 12155 12300 12393 12449 12471 12667 12669 12716 12794 12808 12822
## [469] 12909 12931 12971 13000 13001 13057 13062 13102 13128 13208 13218 13295
## [481] 13350 13354 13391 13522 13557 13578 13587 13610 13648 13679
## 
## $ASBR08D
##   [1]     3    16    19    29    38    52    63   155   188   189   192   292
##  [13]   316   344   352   365   375   380   428   433   453   496   503   511
##  [25]   512   532   538   555   599   637   657   696   750   784   809   822
##  [37]   835   893   898   904   911   914   930   996  1019  1023  1027  1029
##  [49]  1042  1046  1053  1068  1089  1096  1160  1188  1249  1258  1270  1358
##  [61]  1381  1432  1447  1476  1490  1581  1587  1589  1593  1595  1626  1652
##  [73]  1761  1812  1877  1937  1939  2050  2098  2107  2112  2116  2123  2199
##  [85]  2224  2246  2254  2258  2276  2284  2290  2292  2335  2350  2351  2353
##  [97]  2365  2392  2393  2394  2400  2448  2451  2453  2454  2456  2480  2517
## [109]  2544  2615  2688  2695  2733  2769  2789  2795  2836  2854  2856  2874
## [121]  2905  2912  2954  2974  2989  3018  3075  3079  3153  3177  3185  3186
## [133]  3228  3336  3351  3355  3361  3371  3396  3421  3442  3464  3516  3522
## [145]  3528  3541  3565  3629  3654  3664  3666  3693  3697  3720  3721  3727
## [157]  3730  3737  3879  3965  3990  4017  4052  4064  4103  4119  4120  4137
## [169]  4181  4189  4194  4201  4202  4255  4277  4295  4299  4300  4303  4339
## [181]  4349  4355  4357  4358  4363  4377  4413  4419  4438  4440  4462  4475
## [193]  4490  4519  4526  4543  4553  4562  4587  4589  4595  4596  4599  4605
## [205]  4667  4680  4687  4723  4785  4789  4806  4813  4845  4849  4850  4928
## [217]  4970  5005  5037  5066  5079  5219  5224  5226  5240  5253  5301  5305
## [229]  5332  5366  5373  5403  5425  5445  5450  5473  5479  5515  5525  5534
## [241]  5550  5651  5658  5668  5673  5688  5719  5737  5773  5779  5836  5837
## [253]  5871  5874  5884  5885  6006  6116  6148  6154  6160  6196  6212  6227
## [265]  6253  6266  6279  6285  6292  6320  6325  6330  6363  6376  6389  6398
## [277]  6431  6456  6469  6481  6509  6554  6559  6570  6594  6679  6708  6711
## [289]  6728  6814  6826  6869  6875  6881  6888  6953  6962  6965  6972  6975
## [301]  6982  7020  7035  7038  7064  7069  7070  7071  7078  7086  7094  7123
## [313]  7128  7129  7139  7181  7185  7197  7207  7220  7246  7257  7274  7284
## [325]  7375  7397  7493  7517  7537  7551  7589  7597  7603  7607  7633  7639
## [337]  7690  7703  7714  7764  7770  7772  7778  7788  7825  7836  7842  7843
## [349]  7846  7852  7857  7899  7920  7937  7995  8020  8026  8034  8035  8053
## [361]  8056  8064  8129  8154  8161  8202  8205  8256  8270  8276  8323  8348
## [373]  8356  8364  8373  8384  8390  8397  8415  8431  8442  8465  8473  8506
## [385]  8573  8577  8615  8616  8622  8630  8667  8686  8759  8777  8794  8839
## [397]  8885  8909  8954  8955  9007  9023  9036  9040  9045  9093  9095  9100
## [409]  9123  9158  9168  9252  9262  9264  9277  9285  9324  9347  9409  9411
## [421]  9578  9682  9699  9711  9749  9764  9779  9808  9811  9853  9865  9870
## [433]  9916  9921  9922 10014 10027 10195 10483 10556 10606 10702 10757 10789
## [445] 10812 10979 11056 11191 11290 11311 11345 11351 11359 11384 11409 11420
## [457] 11433 11503 11600 11667 11680 11699 11735 11737 11787 11791 11800 11806
## [469] 11859 11991 12014 12062 12092 12112 12120 12140 12155 12201 12210 12289
## [481] 12300 12365 12393 12432 12449 12471 12667 12690 12750 12794 12822 12860
## [493] 12867 12882 12909 13057 13062 13128 13198 13208 13218 13295 13350 13354
## [505] 13369 13391 13410 13449 13557 13578 13648 13679 13681
## 
## $ASBR08E
##    [1]    19    22    27    28    29    36    37    38    41    42    52    53
##   [13]    63    71    77    79   103   108   112   128   139   141   143   155
##   [25]   173   183   189   192   199   216   217   260   262   279   292   303
##   [37]   305   317   328   336   344   345   347   352   354   365   370   374
##   [49]   375   378   382   394   413   415   424   433   434   441   448   449
##   [61]   476   478   491   493   496   503   507   510   511   512   513   515
##   [73]   522   532   538   542   547   548   555   562   569   570   571   573
##   [85]   599   617   632   637   638   647   653   655   660   662   674   675
##   [97]   678   681   695   696   699   702   704   709   714   721   741   750
##  [109]   770   785   809   813   835   848   861   879   882   893   894   898
##  [121]   900   903   904   911   913   914   917   918   920   934   957   958
##  [133]   969   970   972   979   982   985   996  1003  1018  1019  1023  1027
##  [145]  1029  1032  1042  1053  1062  1068  1078  1085  1108  1118  1120  1121
##  [157]  1144  1158  1160  1164  1188  1233  1249  1272  1273  1277  1279  1285
##  [169]  1292  1302  1306  1333  1346  1366  1383  1389  1401  1406  1417  1420
##  [181]  1423  1429  1430  1432  1453  1462  1471  1476  1479  1485  1490  1495
##  [193]  1510  1523  1557  1581  1587  1589  1591  1593  1595  1609  1621  1623
##  [205]  1647  1652  1677  1688  1715  1742  1743  1761  1769  1773  1785  1787
##  [217]  1796  1806  1809  1812  1830  1834  1836  1841  1850  1851  1855  1879
##  [229]  1887  1889  1915  1927  1928  1929  1930  1934  1937  1940  1978  1986
##  [241]  1993  1995  2004  2005  2011  2029  2039  2044  2050  2052  2067  2094
##  [253]  2098  2101  2106  2107  2112  2113  2116  2122  2123  2168  2172  2188
##  [265]  2195  2199  2224  2227  2233  2238  2246  2251  2254  2258  2261  2262
##  [277]  2263  2268  2284  2290  2314  2326  2335  2336  2339  2347  2350  2351
##  [289]  2353  2360  2363  2365  2380  2384  2392  2393  2394  2397  2400  2432
##  [301]  2438  2450  2451  2454  2456  2480  2504  2513  2514  2530  2543  2544
##  [313]  2561  2569  2573  2575  2586  2598  2601  2613  2615  2626  2636  2661
##  [325]  2675  2688  2689  2690  2693  2695  2696  2704  2717  2722  2725  2729
##  [337]  2733  2742  2769  2776  2780  2789  2795  2803  2804  2818  2836  2838
##  [349]  2839  2852  2855  2856  2863  2900  2905  2912  2920  2932  2948  2952
##  [361]  2968  2974  2979  2982  2986  2989  2997  3000  3018  3031  3046  3054
##  [373]  3058  3060  3085  3090  3091  3093  3094  3116  3141  3144  3145  3153
##  [385]  3160  3170  3177  3192  3194  3228  3276  3278  3284  3299  3329  3332
##  [397]  3334  3336  3337  3342  3351  3353  3357  3361  3362  3365  3368  3380
##  [409]  3389  3396  3398  3403  3407  3421  3427  3430  3432  3433  3435  3440
##  [421]  3451  3501  3516  3522  3523  3533  3536  3537  3541  3542  3559  3561
##  [433]  3568  3570  3571  3573  3574  3575  3580  3587  3605  3614  3637  3654
##  [445]  3664  3666  3669  3693  3697  3706  3708  3711  3720  3721  3730  3731
##  [457]  3734  3737  3740  3743  3749  3756  3757  3776  3796  3810  3819  3838
##  [469]  3879  3893  3908  3931  3953  3960  3965  3968  3971  3990  3993  3999
##  [481]  4015  4017  4019  4021  4029  4041  4053  4056  4057  4064  4066  4078
##  [493]  4079  4080  4103  4119  4120  4123  4133  4137  4140  4147  4154  4181
##  [505]  4189  4193  4194  4201  4202  4208  4218  4222  4227  4241  4244  4255
##  [517]  4268  4272  4277  4283  4291  4295  4297  4299  4300  4303  4308  4326
##  [529]  4346  4349  4355  4357  4358  4363  4364  4368  4375  4382  4391  4403
##  [541]  4407  4408  4413  4418  4430  4432  4437  4438  4440  4444  4455  4462
##  [553]  4463  4468  4469  4475  4479  4481  4482  4486  4490  4511  4514  4521
##  [565]  4526  4530  4537  4543  4553  4562  4575  4584  4585  4587  4588  4589
##  [577]  4595  4596  4597  4599  4605  4616  4624  4627  4629  4635  4638  4667
##  [589]  4674  4680  4686  4692  4709  4716  4719  4723  4740  4756  4760  4767
##  [601]  4770  4775  4785  4786  4789  4795  4799  4805  4806  4813  4816  4826
##  [613]  4836  4837  4849  4850  4863  4868  4877  4894  4907  4911  4928  4934
##  [625]  4947  4949  4954  4967  4970  4989  4997  5002  5024  5031  5032  5037
##  [637]  5047  5066  5067  5069  5072  5075  5077  5079  5084  5093  5138  5141
##  [649]  5162  5168  5187  5195  5211  5212  5213  5219  5224  5226  5227  5232
##  [661]  5236  5240  5253  5274  5278  5288  5290  5301  5305  5306  5324  5330
##  [673]  5331  5332  5344  5348  5365  5366  5379  5383  5385  5390  5402  5419
##  [685]  5425  5431  5432  5433  5434  5445  5447  5450  5461  5468  5474  5479
##  [697]  5484  5490  5525  5528  5534  5537  5550  5564  5575  5582  5587  5638
##  [709]  5639  5650  5651  5652  5658  5673  5692  5719  5737  5739  5740  5760
##  [721]  5762  5766  5773  5779  5780  5803  5827  5832  5836  5837  5840  5842
##  [733]  5858  5861  5871  5873  5875  5884  5888  5900  5909  5932  5945  5952
##  [745]  5962  5969  5976  5980  5989  6001  6003  6006  6019  6021  6036  6044
##  [757]  6059  6116  6117  6118  6142  6145  6148  6154  6160  6183  6196  6198
##  [769]  6212  6214  6227  6253  6267  6273  6278  6279  6281  6283  6285  6289
##  [781]  6291  6292  6295  6299  6302  6304  6320  6325  6363  6389  6398  6419
##  [793]  6422  6424  6428  6430  6431  6443  6456  6469  6481  6495  6509  6517
##  [805]  6520  6526  6559  6565  6570  6573  6576  6588  6596  6599  6604  6620
##  [817]  6625  6631  6657  6680  6686  6690  6699  6708  6711  6716  6719  6722
##  [829]  6724  6728  6739  6775  6781  6799  6808  6812  6817  6822  6826  6866
##  [841]  6868  6869  6881  6888  6922  6953  6962  6965  6972  6975  6982  6983
##  [853]  6989  6998  7003  7017  7020  7028  7042  7046  7063  7064  7069  7070
##  [865]  7078  7086  7088  7094  7106  7107  7116  7123  7128  7129  7136  7159
##  [877]  7161  7176  7184  7185  7191  7194  7195  7207  7220  7226  7230  7232
##  [889]  7235  7246  7253  7284  7285  7311  7375  7380  7393  7397  7464  7469
##  [901]  7471  7481  7484  7493  7495  7496  7502  7517  7534  7536  7537  7549
##  [913]  7551  7569  7589  7597  7603  7607  7610  7624  7629  7638  7639  7662
##  [925]  7676  7689  7690  7705  7730  7737  7738  7739  7754  7764  7770  7772
##  [937]  7776  7778  7780  7788  7799  7808  7811  7825  7836  7839  7842  7843
##  [949]  7846  7848  7852  7857  7868  7878  7881  7893  7904  7920  7928  7937
##  [961]  7967  7979  7995  8001  8005  8006  8011  8012  8018  8020  8026  8033
##  [973]  8034  8035  8038  8042  8043  8047  8056  8064  8065  8075  8095  8097
##  [985]  8098  8100  8106  8114  8116  8129  8138  8147  8148  8152  8154  8157
##  [997]  8161  8193  8205  8214  8225  8244  8263  8266  8268  8270  8272  8276
## [1009]  8279  8283  8291  8323  8324  8326  8327  8336  8348  8351  8356  8364
## [1021]  8368  8373  8384  8390  8397  8399  8405  8431  8439  8442  8453  8466
## [1033]  8470  8473  8494  8498  8512  8522  8524  8525  8547  8563  8569  8573
## [1045]  8577  8583  8588  8590  8598  8605  8610  8612  8615  8616  8622  8630
## [1057]  8637  8640  8642  8659  8667  8686  8689  8692  8695  8696  8698  8702
## [1069]  8705  8719  8724  8731  8741  8759  8766  8777  8781  8782  8790  8794
## [1081]  8795  8801  8802  8823  8832  8839  8850  8865  8878  8909  8912  8913
## [1093]  8919  8922  8925  8929  8930  8935  8939  8940  8950  8952  8954  8955
## [1105]  8967  8969  8970  8974  8980  8981  9007  9010  9018  9023  9028  9029
## [1117]  9036  9043  9045  9064  9077  9093  9095  9100  9120  9121  9123  9135
## [1129]  9141  9145  9155  9156  9158  9168  9176  9191  9195  9205  9208  9209
## [1141]  9220  9235  9237  9252  9262  9264  9273  9277  9281  9282  9285  9303
## [1153]  9324  9335  9343  9347  9359  9364  9373  9374  9379  9391  9408  9409
## [1165]  9411  9422  9424  9436  9482  9486  9490  9500  9508  9511  9519  9520
## [1177]  9540  9554  9576  9578  9582  9583  9598  9636  9641  9643  9650  9654
## [1189]  9659  9670  9678  9682  9690  9699  9711  9712  9723  9738  9750  9762
## [1201]  9763  9764  9765  9767  9770  9771  9779  9785  9789  9792  9805  9808
## [1213]  9811  9812  9814  9816  9817  9818  9839  9852  9853  9868  9870  9873
## [1225]  9879  9882  9884  9888  9905  9907  9913  9915  9916  9921  9922  9925
## [1237]  9946  9955  9959  9964  9972  9981 10007 10009 10014 10025 10027 10036
## [1249] 10040 10060 10065 10078 10089 10090 10092 10095 10097 10099 10102 10115
## [1261] 10124 10154 10156 10167 10172 10185 10191 10205 10206 10209 10213 10218
## [1273] 10219 10221 10223 10236 10245 10249 10251 10269 10271 10272 10292 10302
## [1285] 10303 10311 10319 10326 10333 10337 10365 10385 10387 10396 10400 10408
## [1297] 10412 10418 10436 10439 10441 10454 10456 10462 10467 10468 10471 10473
## [1309] 10483 10492 10498 10507 10545 10554 10556 10569 10576 10584 10587 10602
## [1321] 10615 10621 10626 10627 10631 10636 10638 10643 10651 10653 10656 10674
## [1333] 10693 10700 10702 10704 10708 10716 10721 10726 10743 10744 10748 10757
## [1345] 10776 10789 10812 10828 10832 10837 10862 10865 10867 10874 10875 10882
## [1357] 10886 10887 10890 10891 10910 10916 10920 10921 10923 10928 10948 10972
## [1369] 10983 10985 10986 10987 10991 10997 11002 11009 11017 11032 11038 11046
## [1381] 11050 11054 11056 11061 11081 11099 11100 11108 11117 11124 11135 11138
## [1393] 11149 11151 11153 11155 11189 11191 11194 11198 11200 11207 11221 11248
## [1405] 11252 11273 11282 11284 11288 11289 11290 11298 11301 11302 11304 11307
## [1417] 11309 11311 11312 11315 11330 11336 11338 11343 11345 11362 11384 11385
## [1429] 11389 11391 11393 11409 11414 11426 11427 11433 11438 11439 11443 11445
## [1441] 11447 11462 11465 11472 11487 11492 11497 11498 11510 11520 11527 11541
## [1453] 11542 11552 11555 11566 11568 11571 11575 11594 11599 11600 11608 11609
## [1465] 11610 11621 11624 11629 11634 11636 11656 11667 11669 11670 11673 11676
## [1477] 11678 11680 11681 11696 11699 11707 11712 11718 11728 11735 11736 11738
## [1489] 11740 11741 11742 11748 11754 11767 11778 11783 11784 11787 11791 11800
## [1501] 11806 11823 11824 11826 11834 11844 11859 11872 11874 11877 11885 11886
## [1513] 11893 11903 11906 11911 11925 11931 11932 11946 11947 11950 11957 11962
## [1525] 11976 11984 11993 11997 12005 12014 12030 12033 12034 12042 12044 12046
## [1537] 12049 12061 12062 12076 12078 12088 12090 12091 12092 12093 12097 12102
## [1549] 12114 12116 12120 12130 12153 12159 12178 12180 12188 12193 12207 12210
## [1561] 12218 12221 12231 12236 12244 12250 12256 12259 12264 12273 12283 12284
## [1573] 12297 12300 12308 12312 12322 12340 12355 12362 12391 12393 12396 12399
## [1585] 12413 12415 12421 12422 12424 12428 12431 12432 12444 12445 12449 12453
## [1597] 12456 12459 12471 12472 12474 12480 12481 12482 12490 12495 12504 12505
## [1609] 12514 12519 12528 12533 12544 12551 12578 12584 12598 12599 12602 12603
## [1621] 12609 12620 12624 12630 12667 12678 12686 12695 12699 12706 12709 12722
## [1633] 12727 12731 12750 12753 12763 12767 12780 12794 12798 12814 12822 12835
## [1645] 12858 12862 12870 12876 12882 12888 12900 12908 12909 12933 12936 12937
## [1657] 12962 12967 12971 12993 13003 13013 13015 13031 13057 13062 13064 13070
## [1669] 13076 13079 13086 13089 13091 13105 13109 13127 13128 13130 13145 13146
## [1681] 13167 13168 13180 13188 13192 13198 13199 13208 13209 13212 13214 13215
## [1693] 13218 13225 13226 13235 13236 13243 13253 13255 13269 13282 13295 13297
## [1705] 13303 13306 13308 13312 13318 13319 13330 13331 13339 13341 13350 13354
## [1717] 13360 13366 13374 13381 13391 13396 13400 13404 13406 13423 13430 13442
## [1729] 13456 13492 13536 13537 13553 13557 13564 13578 13582 13589 13605 13606
## [1741] 13607 13621 13622 13636 13648 13663 13677 13679 13680 13682 13685
## 
## $ASBR08F
##    [1]     3    19    22    27    28    29    30    36    38    42    52    54
##   [13]    55    60    63    71    77    81    90    94    97   103   108   112
##   [25]   126   130   141   148   155   163   178   183   189   192   199   232
##   [37]   241   249   260   270   292   300   304   310   312   315   317   330
##   [49]   336   339   343   344   351   352   353   365   375   378   380   382
##   [61]   385   389   394   433   434   449   451   474   478   491   496   510
##   [73]   511   512   515   517   522   529   530   532   535   538   547   548
##   [85]   555   561   569   570   573   599   610   612   615   617   621   629
##   [97]   632   637   644   649   655   657   660   661   673   674   680   684
##  [109]   686   695   696   704   714   721   750   758   770   782   783   789
##  [121]   808   809   820   824   835   836   843   861   888   893   894   898
##  [133]   903   904   905   911   913   914   917   918   920   925   933   934
##  [145]   940   958   970   974   979   980   982   985   994   996  1000  1003
##  [157]  1010  1019  1023  1027  1029  1032  1036  1042  1045  1053  1068  1078
##  [169]  1087  1104  1125  1127  1158  1160  1164  1188  1208  1228  1232  1249
##  [181]  1256  1277  1284  1294  1302  1303  1306  1318  1320  1334  1344  1346
##  [193]  1362  1380  1395  1419  1423  1430  1432  1448  1451  1453  1454  1459
##  [205]  1476  1477  1490  1510  1564  1565  1581  1587  1589  1591  1593  1595
##  [217]  1602  1629  1635  1636  1645  1647  1648  1652  1678  1687  1690  1731
##  [229]  1737  1742  1755  1761  1762  1773  1787  1796  1800  1809  1812  1831
##  [241]  1841  1851  1879  1891  1913  1915  1928  1930  1934  1937  1950  1960
##  [253]  1993  1995  2002  2004  2005  2011  2029  2062  2067  2098  2100  2106
##  [265]  2107  2112  2113  2116  2123  2130  2159  2168  2195  2199  2219  2224
##  [277]  2227  2238  2246  2250  2251  2254  2258  2261  2262  2268  2284  2290
##  [289]  2302  2326  2335  2336  2339  2350  2351  2353  2360  2365  2374  2384
##  [301]  2392  2393  2394  2400  2424  2427  2451  2454  2456  2459  2466  2480
##  [313]  2482  2496  2513  2530  2536  2540  2543  2544  2569  2573  2575  2582
##  [325]  2584  2586  2591  2604  2607  2615  2631  2636  2641  2675  2688  2690
##  [337]  2693  2695  2696  2704  2717  2733  2769  2776  2789  2818  2820  2824
##  [349]  2825  2835  2836  2843  2850  2852  2854  2855  2856  2861  2900  2905
##  [361]  2912  2914  2928  2932  2940  2948  2952  2968  2970  2973  2974  2979
##  [373]  2980  2982  2986  2989  2996  3006  3018  3037  3040  3051  3058  3060
##  [385]  3068  3075  3090  3091  3094  3138  3141  3144  3153  3157  3158  3170
##  [397]  3177  3186  3188  3190  3192  3196  3228  3243  3252  3276  3278  3296
##  [409]  3304  3305  3307  3329  3334  3336  3337  3342  3351  3353  3357  3360
##  [421]  3361  3365  3383  3392  3396  3402  3413  3419  3421  3430  3435  3440
##  [433]  3445  3451  3469  3483  3495  3501  3516  3522  3523  3526  3541  3559
##  [445]  3567  3568  3570  3574  3575  3579  3580  3601  3617  3622  3631  3639
##  [457]  3654  3664  3666  3693  3697  3706  3711  3720  3721  3730  3731  3737
##  [469]  3740  3776  3796  3832  3833  3834  3838  3840  3844  3848  3850  3879
##  [481]  3880  3883  3886  3887  3893  3908  3926  3956  3958  3968  3971  3978
##  [493]  3999  4000  4011  4014  4019  4021  4038  4050  4053  4056  4057  4064
##  [505]  4067  4078  4079  4080  4095  4103  4119  4120  4123  4133  4137  4140
##  [517]  4163  4166  4167  4170  4180  4181  4186  4189  4193  4194  4201  4202
##  [529]  4206  4208  4218  4222  4227  4231  4239  4241  4249  4255  4272  4277
##  [541]  4283  4291  4292  4295  4299  4300  4301  4303  4308  4349  4351  4355
##  [553]  4357  4358  4363  4374  4375  4380  4382  4413  4430  4432  4437  4438
##  [565]  4440  4462  4474  4475  4480  4482  4490  4498  4514  4526  4543  4547
##  [577]  4553  4562  4566  4577  4584  4587  4588  4589  4593  4595  4596  4597
##  [589]  4599  4605  4614  4616  4624  4632  4638  4643  4647  4653  4667  4671
##  [601]  4674  4680  4692  4708  4716  4719  4723  4739  4756  4767  4770  4785
##  [613]  4786  4789  4795  4796  4799  4806  4809  4813  4822  4826  4832  4835
##  [625]  4840  4845  4849  4850  4894  4907  4928  4931  4947  4952  4953  4954
##  [637]  4970  4989  5013  5022  5024  5037  5044  5055  5065  5066  5071  5075
##  [649]  5079  5084  5142  5151  5155  5156  5175  5182  5184  5187  5212  5213
##  [661]  5221  5224  5226  5227  5228  5240  5253  5256  5261  5274  5278  5284
##  [673]  5288  5301  5305  5306  5318  5324  5329  5332  5365  5379  5383  5385
##  [685]  5390  5414  5419  5425  5431  5434  5445  5447  5450  5453  5461  5468
##  [697]  5474  5477  5479  5481  5490  5498  5500  5525  5528  5534  5537  5550
##  [709]  5569  5570  5587  5592  5618  5622  5632  5638  5639  5642  5647  5651
##  [721]  5656  5658  5667  5673  5676  5719  5720  5726  5737  5738  5739  5756
##  [733]  5762  5765  5766  5773  5774  5779  5781  5791  5795  5804  5827  5836
##  [745]  5837  5838  5840  5852  5858  5871  5900  5904  5931  5933  5945  5946
##  [757]  5950  5952  5962  5988  5991  5994  6003  6006  6017  6019  6024  6029
##  [769]  6035  6051  6075  6079  6116  6117  6118  6128  6133  6134  6137  6145
##  [781]  6148  6149  6154  6159  6160  6161  6183  6196  6198  6203  6204  6212
##  [793]  6214  6220  6253  6277  6279  6285  6286  6292  6295  6302  6304  6320
##  [805]  6322  6323  6325  6330  6331  6353  6363  6389  6398  6400  6415  6419
##  [817]  6422  6424  6428  6430  6431  6432  6437  6442  6449  6454  6456  6467
##  [829]  6469  6470  6477  6481  6496  6507  6509  6516  6540  6544  6546  6548
##  [841]  6559  6570  6591  6599  6601  6604  6620  6631  6642  6655  6662  6686
##  [853]  6699  6708  6711  6722  6724  6728  6732  6739  6750  6775  6784  6791
##  [865]  6799  6808  6812  6826  6842  6866  6868  6870  6881  6888  6949  6953
##  [877]  6954  6962  6965  6972  6975  6977  6982  6998  7017  7019  7020  7028
##  [889]  7033  7035  7038  7046  7064  7065  7069  7070  7078  7079  7086  7089
##  [901]  7094  7102  7106  7111  7115  7123  7128  7129  7159  7161  7169  7176
##  [913]  7185  7191  7194  7195  7203  7207  7208  7213  7220  7226  7230  7235
##  [925]  7246  7284  7285  7292  7296  7319  7335  7341  7356  7375  7379  7380
##  [937]  7393  7397  7450  7452  7469  7471  7475  7483  7485  7493  7495  7517
##  [949]  7528  7537  7539  7540  7542  7546  7551  7561  7564  7589  7597  7603
##  [961]  7631  7632  7639  7675  7690  7705  7709  7717  7724  7764  7770  7772
##  [973]  7773  7776  7778  7780  7788  7799  7825  7836  7839  7840  7842  7843
##  [985]  7845  7846  7847  7851  7852  7857  7862  7863  7876  7878  7893  7899
##  [997]  7904  7906  7920  7930  7933  7937  7988  7995  8001  8011  8012  8013
## [1009]  8020  8026  8034  8035  8038  8042  8043  8047  8056  8064  8066  8069
## [1021]  8095  8106  8110  8124  8128  8129  8149  8152  8154  8161  8193  8195
## [1033]  8205  8217  8232  8234  8244  8265  8268  8270  8272  8276  8283  8287
## [1045]  8323  8327  8344  8348  8356  8359  8364  8370  8373  8384  8386  8390
## [1057]  8396  8397  8404  8427  8431  8434  8439  8442  8453  8455  8466  8469
## [1069]  8473  8498  8508  8512  8524  8525  8526  8527  8537  8540  8573  8577
## [1081]  8590  8599  8603  8615  8616  8621  8622  8630  8631  8667  8669  8673
## [1093]  8674  8679  8687  8689  8692  8698  8701  8702  8713  8719  8720  8723
## [1105]  8738  8741  8759  8763  8770  8771  8777  8782  8790  8794  8799  8802
## [1117]  8837  8839  8851  8853  8909  8925  8930  8939  8945  8947  8954  8955
## [1129]  8960  8967  8969  8974  9007  9010  9017  9018  9021  9023  9024  9028
## [1141]  9030  9036  9039  9043  9045  9077  9093  9095  9100  9111  9120  9123
## [1153]  9135  9141  9145  9155  9156  9158  9168  9174  9185  9191  9195  9204
## [1165]  9205  9231  9233  9237  9252  9262  9264  9273  9277  9279  9281  9285
## [1177]  9290  9298  9302  9309  9322  9323  9324  9326  9343  9347  9348  9359
## [1189]  9362  9373  9374  9376  9391  9408  9409  9424  9448  9462  9480  9482
## [1201]  9486  9502  9507  9511  9519  9520  9528  9537  9548  9550  9554  9561
## [1213]  9572  9578  9582  9588  9602  9641  9643  9644  9650  9654  9657  9659
## [1225]  9662  9682  9698  9699  9700  9711  9715  9720  9723  9730  9735  9762
## [1237]  9764  9767  9771  9773  9774  9779  9792  9808  9834  9853  9870  9879
## [1249]  9882  9883  9888  9907  9912  9913  9916  9921  9922  9971  9981  9989
## [1261] 10002 10004 10007 10009 10014 10019 10024 10027 10036 10060 10065 10067
## [1273] 10080 10089 10092 10097 10101 10102 10124 10130 10137 10149 10154 10156
## [1285] 10185 10212 10235 10236 10242 10245 10261 10265 10269 10272 10280 10293
## [1297] 10301 10311 10319 10326 10339 10346 10357 10360 10385 10387 10395 10408
## [1309] 10436 10439 10456 10466 10467 10470 10476 10482 10483 10503 10509 10524
## [1321] 10551 10556 10565 10569 10598 10609 10615 10621 10631 10635 10636 10638
## [1333] 10648 10651 10653 10656 10665 10669 10670 10693 10702 10704 10716 10721
## [1345] 10726 10728 10729 10748 10757 10789 10792 10812 10828 10869 10880 10887
## [1357] 10910 10920 10922 10928 10948 10972 10983 11017 11018 11026 11032 11046
## [1369] 11050 11054 11056 11073 11092 11099 11108 11109 11113 11121 11135 11149
## [1381] 11151 11153 11155 11160 11167 11184 11191 11194 11198 11205 11221 11231
## [1393] 11238 11272 11278 11285 11288 11289 11290 11296 11300 11302 11304 11307
## [1405] 11309 11311 11312 11343 11345 11354 11362 11384 11386 11387 11393 11409
## [1417] 11420 11430 11432 11433 11437 11443 11467 11478 11524 11527 11532 11541
## [1429] 11542 11552 11555 11556 11571 11600 11601 11610 11614 11621 11629 11640
## [1441] 11641 11667 11670 11673 11675 11676 11678 11685 11699 11709 11714 11728
## [1453] 11734 11735 11738 11748 11758 11764 11767 11775 11787 11791 11800 11806
## [1465] 11807 11823 11824 11834 11839 11844 11859 11884 11886 11889 11893 11911
## [1477] 11916 11931 11950 11957 11962 11969 11976 11984 11997 12014 12025 12030
## [1489] 12034 12044 12046 12049 12062 12078 12087 12091 12092 12098 12101 12108
## [1501] 12114 12123 12136 12153 12155 12157 12166 12178 12195 12201 12218 12221
## [1513] 12230 12243 12251 12256 12273 12279 12300 12322 12327 12355 12364 12393
## [1525] 12399 12413 12414 12415 12421 12422 12424 12428 12431 12449 12471 12472
## [1537] 12481 12495 12507 12508 12519 12528 12529 12539 12546 12548 12563 12578
## [1549] 12584 12587 12609 12614 12620 12639 12643 12667 12669 12687 12688 12695
## [1561] 12699 12706 12710 12731 12753 12768 12771 12775 12794 12798 12822 12846
## [1573] 12870 12876 12882 12888 12890 12900 12909 12911 12920 12933 12936 12980
## [1585] 12996 13042 13057 13062 13076 13079 13109 13128 13130 13141 13142 13145
## [1597] 13146 13157 13180 13188 13198 13199 13206 13208 13209 13212 13214 13218
## [1609] 13219 13222 13225 13226 13295 13302 13303 13308 13312 13318 13319 13322
## [1621] 13330 13331 13333 13340 13350 13354 13360 13361 13374 13381 13382 13391
## [1633] 13401 13404 13430 13456 13466 13472 13504 13514 13531 13536 13557 13563
## [1645] 13578 13605 13607 13610 13614 13631 13648 13653 13658 13663 13679

6 Mahalanobis Uzaklığının İncelenmesi

library(psych)
veri <- scr_canada[,13:18]
md <- mahalanobis(veri, center = colMeans(veri), cov = cov(veri))
head(md,20)

##  [1]  1.2901572  1.1857361 51.9217371  0.9579200  1.3105692  2.8212676
##  [7]  1.4731264  1.4731264  1.4281701  1.1733226  0.9056886  0.7783855
## [13]  1.4731264  3.6865307  1.4852135 34.5645940  1.0821552  1.8221609
## [19] 46.7636688  0.7783855

#Mahalonobis uzaklığı için Kritik değerin belirlenmesi 
alpha <- .001
cutoff <- (qchisq(p = 1 - alpha, df = ncol(veri)))
cutoff

## [1] 22.45774

ucdegerler <- which(md > cutoff)
veri[ucdegerler, ]

data_temiz <- veri[-ucdegerler, ]

veri[ucdegerler, ]

7 Alternatif Maholonobis İnceleme

library(rrcov)

## Loading required package: robustbase

## Scalable Robust Estimators with High Breakdown Point (version 1.7-7)

result <- CovMcd(veri)

## Warning in covMcd(x = x, raw.only = raw.only, alpha = alpha, nsamp = nsamp, : The 6846-th order statistic of the absolute deviation of variable 1 is
## zero.
## There are 8150 observations (in the entire dataset of 13685 obs.) lying
## on the hyperplane with equation a_1*(x_i1 - m_1) + ... + a_p*(x_ip -
## m_p) = 0 with (m_1, ..., m_p) the mean of these observations and
## coefficients a_i from the vector a <- c(1, 0, 0, 0, 0, 0)

# Robust Mahalanobis
md_rrcov <- result@mah

head(md_rrcov, 20)

## NULL

# 1. Varyansı sıfır olan değişkenleri tespit et ve çıkar
veri <- scr_canada[, 13:18]   # İlk seçim (ASBR08A - ASBR08F arası)

# Varyansları kontrol et
varyanslar <- apply(veri, 2, var)

# Varyansı sıfır olanları çıkar
veri_temiz <- veri[, varyanslar != 0]

# 2. CovMcd ile robust kovaryans ve ortalama hesapla
result <- CovMcd(veri_temiz)

## Warning in covMcd(x = x, raw.only = raw.only, alpha = alpha, nsamp = nsamp, : The 6846-th order statistic of the absolute deviation of variable 1 is
## zero.
## There are 8150 observations (in the entire dataset of 13685 obs.) lying
## on the hyperplane with equation a_1*(x_i1 - m_1) + ... + a_p*(x_ip -
## m_p) = 0 with (m_1, ..., m_p) the mean of these observations and
## coefficients a_i from the vector a <- c(1, 0, 0, 0, 0, 0)

# 3. Robust Mahalanobis mesafeleri doğrudan al
md_rrcov <- result@mah

# 4. Kritik değeri belirle (khi-kare tablosundan)
alpha <- 0.001
cutoff <- qchisq(p = 1 - alpha, df = ncol(veri_temiz))

# 5. Uç değerleri seçelim
uc_degerler <- which(md_rrcov > cutoff)

# 6. Uç değerli gözlemleri listele
veri_temiz[uc_degerler, ]

# 7. (İsteğe bağlı) Uç değerler temizlenmiş veri seti
veri_final <- veri_temiz[-uc_degerler, ]

# Sonuçları görelim
cat("Uç değer sayısı:", length(uc_degerler), "\n")

## Uç değer sayısı: 0

cat("Temiz kalan gözlem sayısı:", nrow(veri_final), "\n")

## Temiz kalan gözlem sayısı: 0

• Bu veri setinde 9 , kayıp veri olarak kodlanmış olduğu düşünülebilir. Tüm değişkenlerde 9 değerinin yer aldığı görülmüştür.

8 Çok Değişkenli Normallik Sayıltısı

library(moments)

veri <- scr_canada[, 13:18]  
sonuclar <- lapply(names(veri), function(degisken) {
  degisken_veri <- veri[[degisken]] 
  jb_test <- jarque.test(degisken_veri)
  data.frame(
    Degisken = degisken,
    JB_Statistic = jb_test$statistic,
    p_value = jb_test$p.value
  )
})

sonuclar_df <- do.call(rbind, sonuclar)
print(sonuclar_df)

##     Degisken JB_Statistic p_value
## JB   ASBR08A    250549.66       0
## JB1  ASBR08B    142184.60       0
## JB2  ASBR08C     28355.46       0
## JB3  ASBR08D     21523.92       0
## JB4  ASBR08E     19962.51       0
## JB5  ASBR08F     21311.35       0

#Değerlerin grafik olarak gösterilmesi

veri <- scr_canada[, 13:18]
veri_long <- veri %>%
  pivot_longer(cols = everything(), names_to = "Degisken", values_to = "Deger")

ggplot(veri_long, aes(x = Deger)) +
  geom_histogram(aes(y = ..density..), bins = 30, fill = "lightblue", color = "black") +
  stat_function(fun = dnorm, 
                args = list(mean = mean(veri_long$Deger, na.rm = TRUE),
                            sd = sd(veri_long$Deger, na.rm = TRUE)),
                color = "red", size = 1) +
  facet_wrap(~Degisken, scales = "free") +
  labs(title = "Değişkenlerin Dağılımı",
       x = "Değerler", y = "Yoğunluk") +
  theme_minimal()

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

## Warning: The dot-dot notation (`..density..`) was deprecated in ggplot2 3.4.0.
## ℹ Please use `after_stat(density)` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

9 Veri Dönüştürme

# Dönüştürülmüş veri çerçevesi oluşturulması
veri_donusmus <- veri %>% 
  mutate(
    ASBR08A = 1 / (ASBR08A + 1),  # Ters çevirme (+1 sıfır değerler varsa hata almamak için)
    ASBR08B = 1 / (ASBR08B + 1),  # Ters çevirme
    ASBR08C = log(ASBR08C + 1),   # Log dönüşümü (+1 negatif değerlerden kaçınmak için)
    ASBR08D = log(ASBR08D + 1),   # Log dönüşümü
    ASBR08E = 1 / (ASBR08E + 1),  # Ters çevirme
    ASBR08F = 1 / (ASBR08F + 1)   # Ters çevirme
  )

# Sonuçları kontrol edilmesi
summary(veri_donusmus)

##     ASBR08A          ASBR08B          ASBR08C          ASBR08D      
##  Min.   :0.1000   Min.   :0.1000   Min.   :0.6931   Min.   :0.6931  
##  1st Qu.:0.3333   1st Qu.:0.3333   1st Qu.:1.0986   1st Qu.:1.0986  
##  Median :0.5000   Median :0.5000   Median :1.3863   Median :1.6094  
##  Mean   :0.4197   Mean   :0.4115   Mean   :1.2654   Mean   :1.4152  
##  3rd Qu.:0.5000   3rd Qu.:0.5000   3rd Qu.:1.6094   3rd Qu.:1.6094  
##  Max.   :0.5000   Max.   :0.5000   Max.   :2.3026   Max.   :2.3026  
##     ASBR08E          ASBR08F      
##  Min.   :0.1000   Min.   :0.1000  
##  1st Qu.:0.2000   1st Qu.:0.2000  
##  Median :0.2000   Median :0.2000  
##  Mean   :0.2454   Mean   :0.2378  
##  3rd Qu.:0.2500   3rd Qu.:0.2500  
##  Max.   :0.5000   Max.   :0.5000

10 Çoklu Bağlantı ve Tekillik

cor(scr_canada[, 13:18] ) %>% kable(digit=2)

	ASBR08A	ASBR08B	ASBR08C	ASBR08D	ASBR08E	ASBR08F
ASBR08A	1.00	0.62	0.35	0.29	0.27	0.25
ASBR08B	0.62	1.00	0.36	0.31	0.31	0.28
ASBR08C	0.35	0.36	1.00	0.60	0.54	0.50
ASBR08D	0.29	0.31	0.60	1.00	0.66	0.58
ASBR08E	0.27	0.31	0.54	0.66	1.00	0.60
ASBR08F	0.25	0.28	0.50	0.58	0.60	1.00

library(corrplot)
library(ggcorrplot)

## 
## Attaching package: 'ggcorrplot'

## The following object is masked from 'package:rstatix':
## 
##     cor_pmat

# Korelasyon matrisi oluşturma
cor_mat <- cor(scr_canada[, 13:18])

# Korelasyon matrisini tablo şeklinde görüntüleme (kable ile)
cor_mat %>% kable(digits = 2)

	ASBR08A	ASBR08B	ASBR08C	ASBR08D	ASBR08E	ASBR08F
ASBR08A	1.00	0.62	0.35	0.29	0.27	0.25
ASBR08B	0.62	1.00	0.36	0.31	0.31	0.28
ASBR08C	0.35	0.36	1.00	0.60	0.54	0.50
ASBR08D	0.29	0.31	0.60	1.00	0.66	0.58
ASBR08E	0.27	0.31	0.54	0.66	1.00	0.60
ASBR08F	0.25	0.28	0.50	0.58	0.60	1.00

# corrplot ile korelasyon grafiği çizimi
corrplot(cor_mat, method = "circle")

# ggcorrplot için p-değer matrisinin hesaplanması
cor_pmat <- ggcorrplot::cor_pmat(scr_canada[, 13:18])

# ggcorrplot ile korelasyon grafiği (p-değerlerini de gösteren)
ggcorrplot(
  cor_mat,
  lab = TRUE,
  lab_size = 6,
  p.mat = cor_pmat,
  insig = "blank" # anlamsız korelasyonları boş bırakır, istersen değiştirebilirsin
)

*Korelasyon matrisi incelendiğinde değişkenler arasında çok yüksek değerlerin olmadığı söylenebilir.

library(PerformanceAnalytics)

## Loading required package: xts

## Loading required package: zoo

## 
## Attaching package: 'zoo'

## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric

## 
## ######################### Warning from 'xts' package ##########################
## #                                                                             #
## # The dplyr lag() function breaks how base R's lag() function is supposed to  #
## # work, which breaks lag(my_xts). Calls to lag(my_xts) that you type or       #
## # source() into this session won't work correctly.                            #
## #                                                                             #
## # Use stats::lag() to make sure you're not using dplyr::lag(), or you can add #
## # conflictRules('dplyr', exclude = 'lag') to your .Rprofile to stop           #
## # dplyr from breaking base R's lag() function.                                #
## #                                                                             #
## # Code in packages is not affected. It's protected by R's namespace mechanism #
## # Set `options(xts.warn_dplyr_breaks_lag = FALSE)` to suppress this warning.  #
## #                                                                             #
## ###############################################################################

## 
## Attaching package: 'xts'

## The following objects are masked from 'package:dplyr':
## 
##     first, last

## 
## Attaching package: 'PerformanceAnalytics'

## The following objects are masked from 'package:moments':
## 
##     kurtosis, skewness

## The following object is masked from 'package:graphics':
## 
##     legend

chart.Correlation(scr_canada[, 13:18], histogram=TRUE, pch=19)

#Bu çıktı biraz görüntü olarak karmaşık geldi.


library(pheatmap)
pheatmap(cor(scr_canada[, 13:18]))

#Bu da okunaklı geldi :)

DeBruine, L., & Barr, D. (2022). Data skills for reproducible research. Zenodo. https://doi.org/10.5281/zenodo.6527194

R Core Team. (2022). R: A language and environment for statistical computing. R Foundation for Statistical Computing. https://www.R-project.org/

Xie, Y. (2016). Bookdown: Authoring books and technical documents with R markdown. Chapman; Hall/CRC. https://bookdown.org/yihui/bookdown

Xie, Y. (2022). Bookdown: Authoring books and technical documents with r markdown. https://github.com/rstudio/bookdown