WQD_7006_EDA
Nasir
2022-12-30
In this file I have done the Exploratory Data Analysis of Our WQD-7006 Project
I have formatted our data set and named “myr3.csv” to do EDA in R. The data set is available in this link
https://drive.google.com/file/d/1rXhO170CY82E7ujXhN1EXsCmuloVLfTg/view?usp=sharing
Loading necessary library
library("readxl")## Warning: package 'readxl' was built under R version 4.2.2library("ggplot2")## Warning: package 'ggplot2' was built under R version 4.2.2library("dplyr")## Warning: package 'dplyr' was built under R version 4.2.2##
## Attaching package: 'dplyr'## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary("corrplot")## Warning: package 'corrplot' was built under R version 4.2.2## corrplot 0.92 loadedlibrary("gridExtra")## Warning: package 'gridExtra' was built under R version 4.2.2##
## Attaching package: 'gridExtra'## The following object is masked from 'package:dplyr':
##
## combineReading the data set into a dataframe
Attribute meaning in the data frame moed = Month Ende Date, mpr = Malaysian Policy Rate, upr = US Policy Rate, mcpi = Malaysia CPI, mnbfbf = Malaysia Net foreign bond flow, mfr = Malaysia Foreign Reserve, bco = Brent Crude Oil Price, metb = Malaysia External trade Balance, uscpi = US CPI, mgdpqa = Malaysia GDP- QA, myrer = MYR exchange rate
df <- read.csv("myr3.csv")
View(df)Exploring the structure of the data set
str(df)## 'data.frame': 205 obs. of 11 variables:
## $ moed : chr "2005-10-31'T'00:00:00" "2005-11-30'T'00:00:00" "2005-12-31'T'00:00:00" "2006-01-31'T'00:00:00" ...
## $ mpr : num 2.7 3 3 3 3.25 3.25 3.5 3.5 3.5 3.5 ...
## $ upr : num 3.75 4 4.25 4.5 4.5 4.75 4.75 5 5.25 5.25 ...
## $ mcpi : num 3.3 3.5 3.5 3.2 3.2 4.8 4.6 3.9 3.9 4.1 ...
## $ mnfbf : num -1510.7 -1104.9 70.6 -84.6 1398.1 ...
## $ mfr : num 77.1 73.1 70.5 71.3 72.2 ...
## $ bco : num 58.1 55 59 66 61.8 ...
## $ metb : num 10.62 9.1 9.77 9.03 7.68 ...
## $ uscpi : num 4.3 3.5 3.4 4 3.6 3.4 3.5 4.2 4.3 4.1 ...
## $ mgdpqa: num 4.7 4.7 4.7 4.7 4.6 5.7 5.7 5.7 5.6 5.6 ...
## $ myrer : num 3.77 3.78 3.78 3.75 3.71 ...Checking for missing values
sum(is.na(df))## [1] 0Finding out the correlation
correlations <- cor(select_if(df, is.numeric))
corrplot(correlations,method = 'color', order = 'alphabet')
Visualizing the distribution of each variable
p1 <- ggplot(df, aes(x=df$mpr)) + geom_histogram(bins=30)
p2 <- ggplot(df, aes(x=df$upr)) + geom_histogram(bins=30)
p3 <- ggplot(df, aes(x=df$mcpi)) + geom_histogram(bins=30)
p4 <- ggplot(df, aes(x=df$mnfbf)) + geom_histogram(bins=30)
p5 <- ggplot(df, aes(x=df$mfr)) + geom_histogram(bins=30)
p6 <- ggplot(df, aes(x=df$bco)) + geom_histogram(bins=30)
p7 <- ggplot(df, aes(x=df$metb)) + geom_histogram(bins=30)
p8 <- ggplot(df, aes(x=df$uscpi)) + geom_histogram(bins=30)
p9 <- ggplot(df, aes(x=df$mgdpqa)) + geom_histogram(bins=30)
p10 <- ggplot(df, aes(x=df$myrer)) + geom_histogram(bins=30)
grid.arrange(p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, nrow = 2, ncol = 5)## Warning: Use of `df$mpr` is discouraged.
## ℹ Use `mpr` instead.## Warning: Use of `df$upr` is discouraged.
## ℹ Use `upr` instead.## Warning: Use of `df$mcpi` is discouraged.
## ℹ Use `mcpi` instead.## Warning: Use of `df$mnfbf` is discouraged.
## ℹ Use `mnfbf` instead.## Warning: Use of `df$mfr` is discouraged.
## ℹ Use `mfr` instead.## Warning: Use of `df$bco` is discouraged.
## ℹ Use `bco` instead.## Warning: Use of `df$metb` is discouraged.
## ℹ Use `metb` instead.## Warning: Use of `df$uscpi` is discouraged.
## ℹ Use `uscpi` instead.## Warning: Use of `df$mgdpqa` is discouraged.
## ℹ Use `mgdpqa` instead.## Warning: Use of `df$myrer` is discouraged.
## ℹ Use `myrer` instead.
Exploring the relationship between between the target variable and each predictor variable
p11 <- ggplot(df, aes(x=df$mpr, y=df$myrer)) + geom_point() + geom_smooth(method=lm) + xlab("Malaysian Policy Rate") +
ylab("Malaysian Exchange Rate")
p11## Warning: Use of `df$mpr` is discouraged.
## ℹ Use `mpr` instead.## Warning: Use of `df$myrer` is discouraged.
## ℹ Use `myrer` instead.## Warning: Use of `df$mpr` is discouraged.
## ℹ Use `mpr` instead.## Warning: Use of `df$myrer` is discouraged.
## ℹ Use `myrer` instead.## `geom_smooth()` using formula = 'y ~ x'
p12 <- ggplot(df, aes(x=df$upr, y=df$myrer)) + geom_point() + geom_smooth(method=lm) + xlab("US Policy Rate") +
ylab("Malaysian Exchange Rate")
p12## Warning: Use of `df$upr` is discouraged.
## ℹ Use `upr` instead.
## Use of `df$myrer` is discouraged.
## ℹ Use `myrer` instead.## Warning: Use of `df$upr` is discouraged.
## ℹ Use `upr` instead.## Warning: Use of `df$myrer` is discouraged.
## ℹ Use `myrer` instead.## `geom_smooth()` using formula = 'y ~ x'
p13 <- ggplot(df, aes(x=df$mcpi, y=df$myrer)) + geom_point() + geom_smooth(method=lm)+ xlab("Malaysian CPI") +
ylab("Malaysian Exchange Rate")
p13## Warning: Use of `df$mcpi` is discouraged.
## ℹ Use `mcpi` instead.
## Use of `df$myrer` is discouraged.
## ℹ Use `myrer` instead.## Warning: Use of `df$mcpi` is discouraged.
## ℹ Use `mcpi` instead.## Warning: Use of `df$myrer` is discouraged.
## ℹ Use `myrer` instead.## `geom_smooth()` using formula = 'y ~ x'
p14 <- ggplot(df, aes(x=df$mnfbf, y=df$myrer)) + geom_point() + geom_smooth(method=lm) + xlab("Malaysia Net Foreign Bond Flow") +
ylab("Malaysian Exchange Rate")
p14## Warning: Use of `df$mnfbf` is discouraged.
## ℹ Use `mnfbf` instead.
## Use of `df$myrer` is discouraged.
## ℹ Use `myrer` instead.## Warning: Use of `df$mnfbf` is discouraged.
## ℹ Use `mnfbf` instead.## Warning: Use of `df$myrer` is discouraged.
## ℹ Use `myrer` instead.## `geom_smooth()` using formula = 'y ~ x'
p15 <- ggplot(df, aes(x=df$mfr, y=df$myrer)) + geom_point() + geom_smooth(method=lm) + xlab("Malaysia Foreign Reserve") +
ylab("Malaysian Exchange Rate")
p15## Warning: Use of `df$mfr` is discouraged.
## ℹ Use `mfr` instead.
## Use of `df$myrer` is discouraged.
## ℹ Use `myrer` instead.## Warning: Use of `df$mfr` is discouraged.
## ℹ Use `mfr` instead.## Warning: Use of `df$myrer` is discouraged.
## ℹ Use `myrer` instead.## `geom_smooth()` using formula = 'y ~ x'
p16 <- ggplot(df, aes(x=df$bco, y=df$myrer)) + geom_point() + geom_smooth(method=lm) + xlab("Brent Crude Oil Price") +
ylab("Malaysian Exchange Rate")
p16## Warning: Use of `df$bco` is discouraged.
## ℹ Use `bco` instead.
## Use of `df$myrer` is discouraged.
## ℹ Use `myrer` instead.## Warning: Use of `df$bco` is discouraged.
## ℹ Use `bco` instead.## Warning: Use of `df$myrer` is discouraged.
## ℹ Use `myrer` instead.## `geom_smooth()` using formula = 'y ~ x'
p17 <- ggplot(df, aes(x=df$metb, y=df$myrer)) + geom_point() + geom_smooth(method=lm) + xlab("Malaysian External Trade Balance") +
ylab("Malaysian Exchange Rate")
p17## Warning: Use of `df$metb` is discouraged.
## ℹ Use `metb` instead.
## Use of `df$myrer` is discouraged.
## ℹ Use `myrer` instead.## Warning: Use of `df$metb` is discouraged.
## ℹ Use `metb` instead.## Warning: Use of `df$myrer` is discouraged.
## ℹ Use `myrer` instead.## `geom_smooth()` using formula = 'y ~ x'
p18 <- ggplot(df, aes(x=df$uscpi, y=df$myrer)) + geom_point() + geom_smooth(method=lm) + xlab("US CPI") +
ylab("Malaysian Exchange Rate")
p18## Warning: Use of `df$uscpi` is discouraged.
## ℹ Use `uscpi` instead.
## Use of `df$myrer` is discouraged.
## ℹ Use `myrer` instead.## Warning: Use of `df$uscpi` is discouraged.
## ℹ Use `uscpi` instead.## Warning: Use of `df$myrer` is discouraged.
## ℹ Use `myrer` instead.## `geom_smooth()` using formula = 'y ~ x'
p19 <- ggplot(df, aes(x=df$mgdpqa, y=df$myrer)) + geom_point() + geom_smooth(method=lm) + xlab("Malaysian GDP QA") +
ylab("Malaysian Exchange Rate")
p19## Warning: Use of `df$mgdpqa` is discouraged.
## ℹ Use `mgdpqa` instead.
## Use of `df$myrer` is discouraged.
## ℹ Use `myrer` instead.## Warning: Use of `df$mgdpqa` is discouraged.
## ℹ Use `mgdpqa` instead.## Warning: Use of `df$myrer` is discouraged.
## ℹ Use `myrer` instead.## `geom_smooth()` using formula = 'y ~ x'
Here we are trying to find out if there is any outliers Drawing boxplot of each variable
ggplot(df, aes(x=df$mpr)) + geom_boxplot() + xlab("Malaysian Policy Rate")## Warning: Use of `df$mpr` is discouraged.
## ℹ Use `mpr` instead.
ggplot(df, aes(x=df$upr)) + geom_boxplot() + xlab("US Policy Rate")## Warning: Use of `df$upr` is discouraged.
## ℹ Use `upr` instead.
ggplot(df, aes(x=df$mcpi)) + geom_boxplot() + xlab("Malaysian CPI")## Warning: Use of `df$mcpi` is discouraged.
## ℹ Use `mcpi` instead.
ggplot(df, aes(x=df$mnfbf)) + geom_boxplot() + xlab("Malaysia Net Foreign Bond Flow")## Warning: Use of `df$mnfbf` is discouraged.
## ℹ Use `mnfbf` instead.
ggplot(df, aes(x=df$mfr)) + geom_boxplot() + xlab("Malaysia Foreign Reserve")## Warning: Use of `df$mfr` is discouraged.
## ℹ Use `mfr` instead.
ggplot(df, aes(x=df$bco)) + geom_boxplot() + xlab("Brent Crude Oil Price")## Warning: Use of `df$bco` is discouraged.
## ℹ Use `bco` instead.
ggplot(df, aes(x=df$metb)) + geom_boxplot() + xlab("Malaysian External Trade Balance")## Warning: Use of `df$metb` is discouraged.
## ℹ Use `metb` instead.
ggplot(df, aes(x=df$uscpi)) + geom_boxplot() + xlab("US CPI")## Warning: Use of `df$uscpi` is discouraged.
## ℹ Use `uscpi` instead.
ggplot(df, aes(x=df$mgdpqa)) + geom_boxplot() + xlab("Malaysian GDP QA")## Warning: Use of `df$mgdpqa` is discouraged.
## ℹ Use `mgdpqa` instead.
Calculating the Z-score of each value in the data The Z-score, also known as the standard score, is a measure of how many standard deviations a value is from the mean of a distribution. It is commonly used to identify outliers in a dataset, as values with a Z-score greater than 3 or less than -3 are considered to be unusual or extreme.
The Z-score is useful for identifying outliers because it standardizes the data, making it easier to compare values from different distributions. For example, if you have two datasets with different means and standard deviations, the Z-score allows you to compare the values in the two datasets on a common scale.
In addition to identifying outliers, the Z-score is also useful for identifying trends or patterns in the data. For example, if the Z-score of a series of values is consistently positive or negative, it may indicate that the values are increasing or decreasing over time.
Overall, the Z-score is an important tool for data analysis because it helps you to understand the distribution of your data and identify unusual or interesting values.
data_z <- df %>% mutate_if(is.numeric, scale)
data_z## moed mpr upr mcpi mnfbf
## 1 2005-10-31'T'00:00:00 -0.2959445 1.54197189 0.58070253 -0.556877853
## 2 2005-11-30'T'00:00:00 0.2441323 1.69427458 0.68941853 -0.460995610
## 3 2005-12-31'T'00:00:00 0.2441323 1.84657727 0.68941853 -0.183248996
## 4 2006-01-31'T'00:00:00 0.2441323 1.99887997 0.52634453 -0.219919582
## 5 2006-02-28'T'00:00:00 0.6941963 1.99887997 0.52634453 0.130412111
## 6 2006-03-31'T'00:00:00 0.6941963 2.15118266 1.39607252 -0.240215996
## 7 2006-04-30'T'00:00:00 1.1442604 2.15118266 1.28735652 0.113612635
## 8 2006-05-31'T'00:00:00 1.1442604 2.30348535 0.90685053 -0.070874440
## 9 2006-06-30'T'00:00:00 1.1442604 2.45578804 0.90685053 -0.111372756
## 10 2006-07-31'T'00:00:00 1.1442604 2.45578804 1.01556653 0.035215079
## 11 2006-08-31'T'00:00:00 1.1442604 2.45578804 0.58070253 0.246850675
## 12 2006-09-30'T'00:00:00 1.1442604 2.45578804 0.58070253 -0.173726930
## 13 2006-10-31'T'00:00:00 1.1442604 2.45578804 0.47198653 -0.225897455
## 14 2006-11-30'T'00:00:00 1.1442604 2.45578804 0.41762853 -0.233174865
## 15 2006-12-31'T'00:00:00 1.1442604 2.45578804 0.47198653 -0.072292117
## 16 2007-01-31'T'00:00:00 1.1442604 2.45578804 0.52634453 0.085448112
## 17 2007-02-28'T'00:00:00 1.1442604 2.45578804 0.47198653 -0.485096125
## 18 2007-03-31'T'00:00:00 1.1442604 2.45578804 -0.39774146 0.492935830
## 19 2007-04-30'T'00:00:00 1.1442604 2.45578804 -0.39774146 0.133341978
## 20 2007-05-31'T'00:00:00 1.1442604 2.45578804 -0.45209946 0.394241860
## 21 2007-06-30'T'00:00:00 1.1442604 2.45578804 -0.45209946 0.148298473
## 22 2007-07-31'T'00:00:00 1.1442604 2.45578804 -0.34338346 0.084195831
## 23 2007-08-31'T'00:00:00 1.1442604 2.45578804 -0.18030946 0.341409752
## 24 2007-09-30'T'00:00:00 1.1442604 2.15118266 -0.23466746 -0.666984125
## 25 2007-10-31'T'00:00:00 1.1442604 1.99887997 -0.18030946 0.267123461
## 26 2007-11-30'T'00:00:00 1.1442604 1.99887997 0.03712254 0.483248368
## 27 2007-12-31'T'00:00:00 1.1442604 1.84657727 0.09148054 -0.259709059
## 28 2008-01-31'T'00:00:00 1.1442604 1.08506381 0.03712254 0.926721461
## 29 2008-02-29'T'00:00:00 1.1442604 1.08506381 0.25455453 1.104710849
## 30 2008-03-31'T'00:00:00 1.1442604 0.62815574 0.30891253 0.534473775
## 31 2008-04-30'T'00:00:00 1.1442604 0.47585305 0.41762853 1.581333964
## 32 2008-05-31'T'00:00:00 1.1442604 0.47585305 0.85249253 -0.834529956
## 33 2008-06-30'T'00:00:00 1.1442604 0.47585305 2.97245451 -0.989812878
## 34 2008-07-31'T'00:00:00 1.1442604 0.47585305 3.40731850 -0.472289773
## 35 2008-08-31'T'00:00:00 1.1442604 0.47585305 3.40731850 -0.605953116
## 36 2008-09-30'T'00:00:00 1.1442604 0.47585305 3.24424450 -0.862198292
## 37 2008-10-31'T'00:00:00 1.1442604 -0.13335772 2.91809651 -1.482172211
## 38 2008-11-30'T'00:00:00 0.6941963 -0.13335772 1.88529452 -0.971713865
## 39 2008-12-31'T'00:00:00 0.6941963 -0.66641715 1.17864052 -0.360080613
## 40 2009-01-31'T'00:00:00 -0.6559958 -0.66641715 0.90685053 -0.207254998
## 41 2009-02-28'T'00:00:00 -1.5561238 -0.66641715 0.79813453 -0.423072742
## 42 2009-03-31'T'00:00:00 -1.5561238 -0.66641715 0.68941853 -0.496886475
## 43 2009-04-30'T'00:00:00 -1.5561238 -0.66641715 0.41762853 -0.016412003
## 44 2009-05-31'T'00:00:00 -1.5561238 -0.66641715 0.09148054 0.163774784
## 45 2009-06-30'T'00:00:00 -1.5561238 -0.66641715 -1.97412344 -0.374966225
## 46 2009-07-31'T'00:00:00 -1.5561238 -0.66641715 -2.51770344 0.445798059
## 47 2009-08-31'T'00:00:00 -1.5561238 -0.66641715 -2.51770344 0.427202858
## 48 2009-09-30'T'00:00:00 -1.5561238 -0.66641715 -2.30027144 0.157962307
## 49 2009-10-31'T'00:00:00 -1.5561238 -0.66641715 -2.02848144 -0.382361775
## 50 2009-11-30'T'00:00:00 -1.5561238 -0.66641715 -1.26746945 0.212991815
## 51 2009-12-31'T'00:00:00 -1.5561238 -0.66641715 -0.61517346 0.937613949
## 52 2010-01-31'T'00:00:00 -1.5561238 -0.66641715 -0.50645746 0.758325024
## 53 2010-02-28'T'00:00:00 -1.5561238 -0.66641715 -0.56081546 0.280733163
## 54 2010-03-31'T'00:00:00 -1.1060598 -0.66641715 -0.50645746 1.770712026
## 55 2010-04-30'T'00:00:00 -1.1060598 -0.66641715 -0.39774146 0.059764525
## 56 2010-05-31'T'00:00:00 -0.6559958 -0.66641715 -0.34338346 0.134121700
## 57 2010-06-30'T'00:00:00 -0.6559958 -0.66641715 -0.28902546 0.062812531
## 58 2010-07-31'T'00:00:00 -0.2059317 -0.66641715 -0.18030946 0.498913702
## 59 2010-08-31'T'00:00:00 -0.2059317 -0.66641715 -0.07159346 0.047974175
## 60 2010-09-30'T'00:00:00 -0.2059317 -0.66641715 -0.23466746 0.964786097
## 61 2010-10-31'T'00:00:00 -0.2059317 -0.66641715 -0.12595146 0.719338898
## 62 2010-11-30'T'00:00:00 -0.2059317 -0.66641715 -0.12595146 0.151299224
## 63 2010-12-31'T'00:00:00 -0.2059317 -0.66641715 -0.01723546 -0.103433763
## 64 2011-01-31'T'00:00:00 -0.2059317 -0.66641715 0.09148054 0.138374732
## 65 2011-02-28'T'00:00:00 -0.2059317 -0.66641715 0.36327053 0.793885097
## 66 2011-03-31'T'00:00:00 -0.2059317 -0.66641715 0.41762853 0.138964013
## 67 2011-04-30'T'00:00:00 -0.2059317 -0.66641715 0.52634453 0.330767721
## 68 2011-05-31'T'00:00:00 0.2441323 -0.66641715 0.58070253 0.929844605
## 69 2011-06-30'T'00:00:00 0.2441323 -0.66641715 0.68941853 0.684795299
## 70 2011-07-31'T'00:00:00 0.2441323 -0.66641715 0.63506053 0.686301582
## 71 2011-08-31'T'00:00:00 0.2441323 -0.66641715 0.58070253 0.600546281
## 72 2011-09-30'T'00:00:00 0.2441323 -0.66641715 0.63506053 -1.628060895
## 73 2011-10-31'T'00:00:00 0.2441323 -0.66641715 0.63506053 0.272287823
## 74 2011-11-30'T'00:00:00 0.2441323 -0.66641715 0.58070253 0.238665243
## 75 2011-12-31'T'00:00:00 0.2441323 -0.66641715 0.41762853 1.212317519
## 76 2012-01-31'T'00:00:00 0.2441323 -0.66641715 0.25455453 1.238566051
## 77 2012-02-29'T'00:00:00 0.2441323 -0.66641715 -0.01723546 -0.216435404
## 78 2012-03-31'T'00:00:00 0.2441323 -0.66641715 -0.07159346 0.169712489
## 79 2012-04-30'T'00:00:00 0.2441323 -0.66641715 -0.18030946 0.271386180
## 80 2012-05-31'T'00:00:00 0.2441323 -0.66641715 -0.28902546 0.493720278
## 81 2012-06-30'T'00:00:00 0.2441323 -0.66641715 -0.34338346 -0.975457005
## 82 2012-07-31'T'00:00:00 0.2441323 -0.66641715 -0.45209946 1.977007231
## 83 2012-08-31'T'00:00:00 0.2441323 -0.66641715 -0.45209946 -1.281704605
## 84 2012-09-30'T'00:00:00 0.2441323 -0.66641715 -0.50645746 0.607297260
## 85 2012-10-31'T'00:00:00 0.2441323 -0.66641715 -0.50645746 1.096759569
## 86 2012-11-30'T'00:00:00 0.2441323 -0.66641715 -0.50645746 0.461319263
## 87 2012-12-31'T'00:00:00 0.2441323 -0.66641715 -0.56081546 0.176953985
## 88 2013-01-31'T'00:00:00 0.2441323 -0.66641715 -0.50645746 0.394226030
## 89 2013-02-28'T'00:00:00 0.2441323 -0.66641715 -0.39774146 -0.574200689
## 90 2013-03-31'T'00:00:00 0.2441323 -0.66641715 -0.34338346 1.555530346
## 91 2013-04-30'T'00:00:00 0.2441323 -0.66641715 -0.28902546 1.434794330
## 92 2013-05-31'T'00:00:00 0.2441323 -0.66641715 -0.23466746 -0.309202537
## 93 2013-06-30'T'00:00:00 0.2441323 -0.66641715 -0.23466746 -1.767359033
## 94 2013-07-31'T'00:00:00 0.2441323 -0.66641715 -0.12595146 -3.115306003
## 95 2013-08-31'T'00:00:00 0.2441323 -0.66641715 -0.18030946 -0.208107259
## 96 2013-09-30'T'00:00:00 0.2441323 -0.66641715 0.20019653 0.417006686
## 97 2013-10-31'T'00:00:00 0.2441323 -0.66641715 0.30891253 2.224052862
## 98 2013-11-30'T'00:00:00 0.2441323 -0.66641715 0.36327053 -0.767345283
## 99 2013-12-31'T'00:00:00 0.2441323 -0.66641715 0.52634453 0.066853148
## 100 2014-01-31'T'00:00:00 0.2441323 -0.66641715 0.63506053 -0.005555194
## 101 2014-02-28'T'00:00:00 0.2441323 -0.66641715 0.68941853 0.149779237
## 102 2014-03-31'T'00:00:00 0.2441323 -0.66641715 0.68941853 0.129359958
## 103 2014-04-30'T'00:00:00 0.2441323 -0.66641715 0.63506053 -1.442095182
## 104 2014-05-31'T'00:00:00 0.2441323 -0.66641715 0.52634453 1.971095280
## 105 2014-06-30'T'00:00:00 0.2441323 -0.66641715 0.58070253 0.403389423
## 106 2014-07-31'T'00:00:00 0.6941963 -0.66641715 0.52634453 1.390059286
## 107 2014-08-31'T'00:00:00 0.6941963 -0.66641715 0.58070253 -1.542792094
## 108 2014-09-30'T'00:00:00 0.6941963 -0.66641715 0.20019653 0.150721284
## 109 2014-10-31'T'00:00:00 0.6941963 -0.66641715 0.30891253 -0.926083321
## 110 2014-11-30'T'00:00:00 0.6941963 -0.66641715 0.41762853 -0.548830172
## 111 2014-12-31'T'00:00:00 0.6941963 -0.66641715 0.25455453 -0.188979720
## 112 2015-01-31'T'00:00:00 0.6941963 -0.66641715 -0.66953146 0.126651958
## 113 2015-02-28'T'00:00:00 0.6941963 -0.66641715 -1.15875345 -0.435980694
## 114 2015-03-31'T'00:00:00 0.6941963 -0.66641715 -0.72388946 1.154184479
## 115 2015-04-30'T'00:00:00 0.6941963 -0.66641715 -0.23466746 1.250073338
## 116 2015-05-31'T'00:00:00 0.6941963 -0.66641715 -0.07159346 -0.058903573
## 117 2015-06-30'T'00:00:00 0.6941963 -0.66641715 0.14583854 1.842324814
## 118 2015-07-31'T'00:00:00 0.6941963 -0.66641715 0.58070253 -0.522100102
## 119 2015-08-31'T'00:00:00 0.6941963 -0.66641715 0.47198653 -2.092402907
## 120 2015-09-30'T'00:00:00 0.6941963 -0.66641715 0.20019653 -1.062121510
## 121 2015-10-31'T'00:00:00 0.6941963 -0.66641715 0.14583854 -0.168612895
## 122 2015-11-30'T'00:00:00 0.6941963 -0.66641715 0.20019653 0.990550729
## 123 2015-12-31'T'00:00:00 0.6941963 -0.51411445 0.25455453 0.554653467
## 124 2016-01-31'T'00:00:00 0.6941963 -0.51411445 0.68941853 0.332397341
## 125 2016-02-29'T'00:00:00 0.6941963 -0.51411445 1.06992453 -0.063436124
## 126 2016-03-31'T'00:00:00 0.6941963 -0.51411445 0.20019653 1.349118891
## 127 2016-04-30'T'00:00:00 0.6941963 -0.51411445 -0.07159346 0.722707299
## 128 2016-05-31'T'00:00:00 0.6941963 -0.51411445 -0.12595146 0.183697876
## 129 2016-06-30'T'00:00:00 0.6941963 -0.51411445 -0.34338346 0.982701049
## 130 2016-07-31'T'00:00:00 0.2441323 -0.51411445 -0.61517346 0.565706388
## 131 2016-08-31'T'00:00:00 0.2441323 -0.51411445 -0.39774146 0.186023576
## 132 2016-09-30'T'00:00:00 0.2441323 -0.51411445 -0.39774146 -1.506002422
## 133 2016-10-31'T'00:00:00 0.2441323 -0.51411445 -0.45209946 0.545930262
## 134 2016-11-30'T'00:00:00 0.2441323 -0.51411445 -0.28902546 -2.927990425
## 135 2016-12-31'T'00:00:00 0.2441323 -0.36181176 -0.28902546 -1.273418281
## 136 2017-01-31'T'00:00:00 0.2441323 -0.36181176 0.47198653 -0.695023183
## 137 2017-02-28'T'00:00:00 0.2441323 -0.36181176 1.23299852 -1.959283480
## 138 2017-03-31'T'00:00:00 0.2441323 -0.20950907 1.45043052 -5.644462424
## 139 2017-04-30'T'00:00:00 0.2441323 -0.20950907 1.12428253 1.151532950
## 140 2017-05-31'T'00:00:00 0.2441323 -0.20950907 0.85249253 1.905604022
## 141 2017-06-30'T'00:00:00 0.2441323 -0.05720638 0.63506053 -0.413334953
## 142 2017-07-31'T'00:00:00 0.2441323 -0.05720638 0.47198653 -0.376057837
## 143 2017-08-31'T'00:00:00 0.2441323 -0.05720638 0.74377653 0.292191540
## 144 2017-09-30'T'00:00:00 0.2441323 -0.05720638 1.06992453 1.159095786
## 145 2017-10-31'T'00:00:00 0.2441323 -0.05720638 0.79813453 -1.025482349
## 146 2017-11-30'T'00:00:00 0.2441323 -0.05720638 0.63506053 1.476469790
## 147 2017-12-31'T'00:00:00 0.2441323 0.09509632 0.68941853 0.774778114
## 148 2018-01-31'T'00:00:00 0.6941963 0.09509632 0.25455453 0.786075585
## 149 2018-02-28'T'00:00:00 0.6941963 0.09509632 -0.45209946 -0.940045080
## 150 2018-03-31'T'00:00:00 0.6941963 0.24739901 -0.50645746 -0.095497841
## 151 2018-04-30'T'00:00:00 0.6941963 0.24739901 -0.45209946 -0.937707094
## 152 2018-05-31'T'00:00:00 0.6941963 0.24739901 -0.23466746 -1.583064762
## 153 2018-06-30'T'00:00:00 0.6941963 0.39970170 -0.77824746 -1.619272950
## 154 2018-07-31'T'00:00:00 0.6941963 0.39970170 -0.72388946 0.628538792
## 155 2018-08-31'T'00:00:00 0.6941963 0.39970170 -1.10439545 -0.331551039
## 156 2018-09-30'T'00:00:00 0.6941963 0.55200439 -1.05003745 -1.526002069
## 157 2018-10-31'T'00:00:00 0.6941963 0.55200439 -0.88696345 0.913065448
## 158 2018-11-30'T'00:00:00 0.6941963 0.55200439 -1.10439545 -1.467854852
## 159 2018-12-31'T'00:00:00 0.6941963 0.70430708 -1.10439545 -0.546706018
## 160 2019-01-31'T'00:00:00 0.6941963 0.70430708 -1.59361745 -0.610706825
## 161 2019-02-28'T'00:00:00 0.6941963 0.70430708 -1.43054345 0.947783657
## 162 2019-03-31'T'00:00:00 0.6941963 0.70430708 -1.10439545 0.128165329
## 163 2019-04-30'T'00:00:00 0.6941963 0.70430708 -1.10439545 -1.037539931
## 164 2019-05-31'T'00:00:00 0.2441323 0.70430708 -1.10439545 -1.089133934
## 165 2019-06-30'T'00:00:00 0.2441323 0.70430708 -0.39774146 1.164851320
## 166 2019-07-31'T'00:00:00 0.2441323 0.55200439 -0.45209946 1.117312110
## 167 2019-08-31'T'00:00:00 0.2441323 0.55200439 -0.39774146 -0.427681139
## 168 2019-09-30'T'00:00:00 0.2441323 0.39970170 -0.61517346 -0.090673013
## 169 2019-10-31'T'00:00:00 0.2441323 0.24739901 -0.61517346 -0.305399145
## 170 2019-11-30'T'00:00:00 0.2441323 0.24739901 -0.72388946 0.902733416
## 171 2019-12-31'T'00:00:00 0.2441323 0.24739901 -0.66953146 1.091568271
## 172 2020-01-31'T'00:00:00 -0.2059317 0.24739901 -0.34338346 0.590563706
## 173 2020-02-29'T'00:00:00 -0.2059317 0.24739901 -0.50645746 -1.882020066
## 174 2020-03-31'T'00:00:00 -0.6559958 -0.66641715 -1.32182745 -3.145285862
## 175 2020-04-30'T'00:00:00 -0.6559958 -0.66641715 -2.78949344 -0.304330925
## 176 2020-05-31'T'00:00:00 -1.5561238 -0.66641715 -2.78949344 0.248537475
## 177 2020-06-30'T'00:00:00 -1.5561238 -0.66641715 -2.24591344 1.644272930
## 178 2020-07-31'T'00:00:00 -2.0061879 -0.66641715 -1.91976544 1.613812242
## 179 2020-08-31'T'00:00:00 -2.0061879 -0.66641715 -1.97412344 0.559941876
## 180 2020-09-30'T'00:00:00 -2.0061879 -0.66641715 -1.97412344 0.136886644
## 181 2020-10-31'T'00:00:00 -2.0061879 -0.66641715 -2.02848144 0.732547397
## 182 2020-11-30'T'00:00:00 -2.0061879 -0.66641715 -2.13719744 0.224184378
## 183 2020-12-31'T'00:00:00 -2.0061879 -0.66641715 -1.97412344 0.357819840
## 184 2021-01-31'T'00:00:00 -2.0061879 -0.66641715 -1.32182745 0.332006771
## 185 2021-02-28'T'00:00:00 -2.0061879 -0.66641715 -1.15875345 0.630543624
## 186 2021-03-31'T'00:00:00 -2.0061879 -0.66641715 -0.28902546 0.155984884
## 187 2021-04-30'T'00:00:00 -2.0061879 -0.66641715 1.34171452 0.918493971
## 188 2021-05-31'T'00:00:00 -2.0061879 -0.66641715 1.17864052 0.357659170
## 189 2021-06-30'T'00:00:00 -2.0061879 -0.66641715 0.63506053 -0.095975598
## 190 2021-07-31'T'00:00:00 -2.0061879 -0.66641715 -0.01723546 -1.045728435
## 191 2021-08-31'T'00:00:00 -2.0061879 -0.66641715 -0.12595146 0.540506465
## 192 2021-09-30'T'00:00:00 -2.0061879 -0.66641715 -0.01723546 -0.764365798
## 193 2021-10-31'T'00:00:00 -2.0061879 -0.66641715 0.36327053 0.428190034
## 194 2021-11-30'T'00:00:00 -2.0061879 -0.66641715 0.58070253 -1.351534428
## 195 2021-12-31'T'00:00:00 -2.0061879 -0.66641715 0.52634453 0.364322489
## 196 2022-01-31'T'00:00:00 -2.0061879 -0.66641715 0.03712254 0.886263077
## 197 2022-02-28'T'00:00:00 -2.0061879 -0.66641715 -0.01723546 -0.083081823
## 198 2022-03-31'T'00:00:00 -2.0061879 -0.51411445 -0.01723546 -0.954116472
## 199 2022-04-30'T'00:00:00 -2.0061879 -0.51411445 0.03712254 -0.700446508
## 200 2022-05-31'T'00:00:00 -1.5561238 -0.20950907 0.30891253 -0.073537074
## 201 2022-06-30'T'00:00:00 -1.5561238 0.24739901 0.63506053 -0.404043259
## 202 2022-07-31'T'00:00:00 -1.1060598 0.70430708 1.17864052 -0.972350402
## 203 2022-08-31'T'00:00:00 -1.1060598 0.70430708 1.34171452 0.615444415
## 204 2022-09-30'T'00:00:00 -0.6559958 1.16121516 1.23299852 -0.808601819
## 205 2022-10-31'T'00:00:00 -0.6559958 1.16121516 1.23299852 -0.808601819
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## 105 1.401778135 1.403008445 -1.175150639 -0.155059204 0.517165931
## 106 1.395977514 1.149579798 -1.257828695 -0.205196644 0.517165931
## 107 1.407578756 1.036456285 -1.218287016 -0.355608964 0.517165931
## 108 1.134949557 0.695886558 -0.235137092 -0.355608964 0.303322107
## 109 1.181354527 0.343724668 -1.705368606 -0.355608964 0.303322107
## 110 1.042139616 -0.284250734 0.088385735 -0.556158724 0.303322107
## 111 0.479479354 -0.796704245 -0.260299979 -0.806845923 0.327082532
## 112 0.166245805 -0.970186946 -0.292652261 -1.258082883 0.327082532
## 113 0.160445184 -0.586846138 -1.092472583 -1.207945443 0.327082532
## 114 -0.152788364 -0.885444244 -0.506536797 -1.258082883 0.374603382
## 115 -0.112184015 -0.418959652 -0.673690257 -1.308220323 0.374603382
## 116 -0.077380288 -0.467726679 -0.921724425 -1.207945443 0.374603382
## 117 -0.129585879 -0.546473435 -0.477779212 -1.157808003 0.160759558
## 118 -0.640040550 -1.001365865 -1.484294674 -1.107670563 0.160759558
## 119 -0.756052976 -0.923818298 -0.080565075 -1.107670563 0.160759558
## 120 -0.837261673 -1.154862080 -0.170432527 -1.207945443 0.113238708
## 121 -0.796657325 -1.107294243 0.273512686 -1.107670563 0.113238708
## 122 -0.761853597 -1.305160458 -0.071578330 -0.957258243 0.113238708
## 123 -0.721249248 -1.598162348 -0.475981863 -0.856983363 0.089478283
## 124 -0.709648006 -1.699693699 -0.943292613 -0.506021284 0.089478283
## 125 -0.703847384 -1.650526942 -0.591012202 -0.706571044 0.089478283
## 126 -0.622638687 -1.505425051 0.099169829 -0.756708483 -0.005563417
## 127 -0.622638687 -1.164455594 -0.283665516 -0.656433604 -0.005563417
## 128 -0.605236823 -1.102097756 -1.322533260 -0.706571044 -0.005563417
## 129 -0.611037444 -1.102497486 -0.919927076 -0.706571044 -0.029323841
## 130 -0.605236823 -1.391102349 -1.568770079 -0.806845923 -0.029323841
## 131 -0.593635580 -1.208026134 -0.382519713 -0.656433604 -0.029323841
## 132 -0.582034338 -1.127280729 -0.553267872 -0.455883844 0.041957433
## 133 -0.576233716 -1.157660188 -0.157851083 -0.405746404 0.041957433
## 134 -0.657442414 -1.070918838 -0.289057563 -0.355608964 0.041957433
## 135 -0.761853597 -0.817090461 -0.344775383 -0.155059204 0.113238708
## 136 -0.738651112 -0.861860190 -1.065512348 0.045490555 0.113238708
## 137 -0.738651112 -0.866257217 -0.346572732 0.145765435 0.113238708
## 138 -0.715448627 -0.976582622 -0.939697915 -0.004646885 0.303322107
## 139 -0.674844278 -1.020552892 -0.355559478 -0.104921765 0.303322107
## 140 -0.564632474 -1.077314513 -0.919927076 -0.255334084 0.303322107
## 141 -0.512426883 -1.172849918 -0.134485546 -0.405746404 0.327082532
## 142 -0.483423776 -0.983777757 -0.466995118 -0.355608964 0.327082532
## 143 -0.419616942 -0.994570460 -0.112917357 -0.255334084 0.327082532
## 144 -0.379012593 -0.788309920 -0.366343572 -0.104921765 0.422124231
## 145 -0.361610730 -0.635213435 -0.035631349 -0.205196644 0.422124231
## 146 -0.338408245 -0.547272895 -0.123701452 -0.104921765 0.422124231
## 147 -0.309405138 -0.415362085 -0.608985692 -0.155059204 0.350842957
## 148 -0.233997062 -0.328221004 -0.174027225 -0.155059204 0.350842957
## 149 -0.233997062 -0.458932625 -0.290854912 -0.104921765 0.350842957
## 150 0.003828410 -0.279453977 0.728241993 -0.004646885 0.232040832
## 151 0.102438972 -0.083586411 0.437071448 0.045490555 0.232040832
## 152 0.044432759 0.013148183 -0.452616326 0.195902875 0.232040832
## 153 -0.175990849 0.087098183 -0.833654322 0.246040315 0.113238708
## 154 -0.187592092 -0.120361546 -0.414871996 0.246040315 0.113238708
## 155 -0.193392713 0.006352778 -1.622690550 0.145765435 0.113238708
## 156 -0.274601411 0.218209533 0.825298841 -0.054784325 0.041957433
## 157 -0.350009487 -0.071594519 1.019412537 0.045490555 0.041957433
## 158 -0.332607623 -0.741541542 -0.502942099 -0.104921765 0.041957433
## 159 -0.367411351 -0.937808838 0.007505028 -0.255334084 0.113238708
## 160 -0.326807002 -0.614427489 0.156684998 -0.405746404 0.113238708
## 161 -0.309405138 -0.448939382 0.075804292 -0.455883844 0.113238708
## 162 -0.274601411 -0.354603166 0.672524172 -0.255334084 0.089478283
## 163 -0.251398926 -0.178322356 0.030870566 -0.205196644 0.089478283
## 164 -0.315205760 -0.510497760 -0.280070818 -0.305471524 0.089478283
## 165 -0.292003274 -0.428153436 -0.023049905 -0.405746404 0.136999133
## 166 -0.222395819 -0.483316138 0.654550682 -0.305471524 0.136999133
## 167 -0.245598304 -0.672788029 0.047046707 -0.355608964 0.136999133
## 168 -0.274601411 -0.658797489 -0.411277298 -0.355608964 0.041957433
## 169 -0.263000168 -0.680782624 1.202742139 -0.305471524 0.041957433
## 170 -0.263000168 -0.592842084 -0.724016031 -0.155059204 0.041957433
## 171 -0.239797683 -0.450138571 0.334622553 -0.054784325 -0.171886391
## 172 -0.204993956 -0.763526677 0.250147148 0.045490555 -0.171886391
## 173 -0.251398926 -1.068920189 0.356190742 -0.054784325 -0.171886391
## 174 -0.350009487 -2.179369372 0.300472921 -0.455883844 -0.860938713
## 175 -0.303604517 -2.078237751 -2.564501446 -1.057533123 -0.860938713
## 176 -0.280402032 -1.676109645 -0.044618094 -1.157808003 -0.860938713
## 177 -0.251398926 -1.443466943 1.835409000 -0.907120803 -5.090294343
## 178 -0.204993956 -1.357525052 2.613661134 -0.706571044 -5.090294343
## 179 -0.193392713 -1.278378566 0.464031684 -0.556158724 -5.090294343
## 180 -0.158588985 -1.451461538 2.033117395 -0.506021284 -1.621272309
## 181 -0.181791470 -1.590967213 2.065469677 -0.606296164 -1.621272309
## 182 -0.141187122 -1.186040999 1.152416366 -0.606296164 -1.621272309
## 183 -0.007772832 -1.017754784 1.806651416 -0.506021284 -1.811355708
## 184 0.050233380 -0.854665055 1.071535659 -0.506021284 -1.811355708
## 185 0.073435865 -0.444942084 1.305191034 -0.355608964 -1.811355708
## 186 0.050233380 -0.548472084 2.428534183 0.095627995 -1.146063811
## 187 0.177847048 -0.400172355 1.747338898 0.897827034 -1.146063811
## 188 0.183647669 -0.317428301 0.559291183 1.298926553 -1.146063811
## 189 0.195248912 -0.085185330 2.088835215 1.499476313 2.750645870
## 190 0.195248912 -0.037217762 0.561088532 1.499476313 2.750645870
## 191 0.496881218 -0.170727491 2.784409293 1.449338873 2.750645870
## 192 0.433074384 0.050323048 2.779017246 1.499476313 -2.096480807
## 193 0.485279975 0.284564668 2.814964226 1.900575832 -2.096480807
## 194 0.520083703 -0.267462085 1.492115334 2.201400472 -2.096480807
## 195 0.531684945 0.020743048 3.657920926 2.301675352 -0.171886391
## 196 0.485279975 0.557580072 1.431005467 2.552362551 -0.171886391
## 197 0.467878111 0.948515745 1.648484700 2.752912311 -0.171886391
## 198 0.456276869 1.225128717 2.868884698 3.053736951 0.160759558
## 199 0.276457609 1.282290068 2.308111798 2.953462071 0.160759558
## 200 0.293859473 1.821925200 0.370569534 3.103874390 0.160759558
## 201 0.073435865 1.500942229 2.016941253 3.354561590 1.087416128
## 202 0.085037108 1.309071959 0.890003406 3.053736951 1.087416128
## 203 0.027030895 0.768637368 1.150619017 2.953462071 1.087416128
## 204 -0.094782151 0.427667911 3.787330056 2.903324631 1.087416128
## 205 -0.187592092 0.702282233 3.787330056 2.903324631 1.087416128
## myrer
## 1 0.158220697
## 2 0.163543850
## 3 0.167802371
## 4 0.106053807
## 5 0.030465048
## 6 -0.037458372
## 7 -0.161168425
## 8 -0.148392860
## 9 -0.055770015
## 10 -0.092393301
## 11 -0.041929820
## 12 -0.027024994
## 13 -0.099206936
## 14 -0.180331773
## 15 -0.369835986
## 16 -0.428603584
## 17 -0.422002876
## 18 -0.516542056
## 19 -0.593195446
## 20 -0.645362336
## 21 -0.524207395
## 22 -0.524207395
## 23 -0.424132137
## 24 -0.621088762
## 25 -0.769285315
## 26 -0.728616434
## 27 -0.828691692
## 28 -0.990515515
## 29 -1.078028134
## 30 -1.080157395
## 31 -1.151913485
## 32 -0.978804580
## 33 -0.924508429
## 34 -0.948994929
## 35 -0.653027675
## 36 -0.560404829
## 37 -0.324056878
## 38 -0.164362317
## 39 -0.496527004
## 40 -0.199495120
## 41 0.007894884
## 42 -0.113260057
## 43 -0.301486713
## 44 -0.439036962
## 45 -0.386657146
## 46 -0.379417659
## 47 -0.381546920
## 48 -0.509302569
## 49 -0.613636350
## 50 -0.656221566
## 51 -0.583826698
## 52 -0.619385354
## 53 -0.634290179
## 54 -0.930257433
## 55 -1.100598299
## 56 -0.935154733
## 57 -0.988386254
## 58 -1.104430968
## 59 -1.173631945
## 60 -1.306071968
## 61 -1.254543856
## 62 -1.136369881
## 63 -1.314163159
## 64 -1.362071527
## 65 -1.389751918
## 66 -1.437660287
## 67 -1.574997609
## 68 -1.462146786
## 69 -1.450435851
## 70 -1.560092784
## 71 -1.552001593
## 72 -1.089526143
## 73 -1.352489854
## 74 -1.109754120
## 75 -1.133814768
## 76 -1.406360153
## 77 -1.503667372
## 78 -1.356748375
## 79 -1.432337135
## 80 -1.117206533
## 81 -1.110818751
## 82 -1.214087901
## 83 -1.226863465
## 84 -1.367394680
## 85 -1.386558027
## 86 -1.407637709
## 87 -1.367394680
## 88 -1.266680643
## 89 -1.299258333
## 90 -1.292231773
## 91 -1.401462853
## 92 -1.288612029
## 93 -1.150210076
## 94 -0.972416798
## 95 -0.885755882
## 96 -0.939413255
## 97 -1.160430528
## 98 -1.017131275
## 99 -0.905345082
## 100 -0.753102933
## 101 -0.902151191
## 102 -0.926637690
## 103 -0.926637690
## 104 -1.038423883
## 105 -1.042682405
## 106 -1.075260095
## 107 -1.168308793
## 108 -0.894698778
## 109 -0.875535430
## 110 -0.676875396
## 111 -0.434778441
## 112 -0.152012604
## 113 -0.205457050
## 114 0.005978549
## 115 -0.296376487
## 116 -0.070674841
## 117 0.153962176
## 118 0.264683738
## 119 1.052510242
## 120 1.479427036
## 121 1.273314589
## 122 1.199429238
## 123 1.260113171
## 124 0.964571770
## 125 1.069544328
## 126 0.423313670
## 127 0.433959974
## 128 0.910914397
## 129 0.704376098
## 130 0.788056048
## 131 0.744832053
## 132 0.926245075
## 133 1.050380981
## 134 1.629965776
## 135 1.672550992
## 136 1.549692643
## 137 1.575243773
## 138 1.543304860
## 139 1.363382321
## 140 1.236265450
## 141 1.261816580
## 142 1.236265450
## 143 1.214334064
## 144 1.106806392
## 145 1.131292892
## 146 0.831067116
## 147 0.736315010
## 148 0.421184409
## 149 0.460575734
## 150 0.346660280
## 151 0.474415929
## 152 0.594293313
## 153 0.719280923
## 154 0.776132187
## 155 0.869393811
## 156 0.931781153
## 157 1.029514225
## 158 1.029514225
## 159 0.921560701
## 160 0.840222938
## 161 0.777409744
## 162 0.811903769
## 163 0.924115814
## 164 1.041863938
## 165 0.918366810
## 166 0.906655875
## 167 1.074867480
## 168 1.036966638
## 169 1.016738660
## 170 1.015886956
## 171 0.831067116
## 172 0.845971942
## 173 1.095095458
## 174 1.321222957
## 175 1.280767001
## 176 1.375093256
## 177 1.246911754
## 178 1.146836496
## 179 0.986503156
## 180 0.970533700
## 181 0.969043217
## 182 0.794443830
## 183 0.680528376
## 184 0.722474815
## 185 0.743341571
## 186 0.946047201
## 187 0.824679334
## 188 0.903887836
## 189 0.954564244
## 190 1.106806392
## 191 0.967765661
## 192 1.033772746
## 193 0.936039675
## 194 1.071247737
## 195 0.990761678
## 196 1.032282264
## 197 1.061666063
## 198 1.070608959
## 199 1.390636860
## 200 1.440035711
## 201 1.507107427
## 202 1.597175159
## 203 1.650832532
## 204 1.994708154
## 205 2.184638219Finding out outliers using the Z-score
outliers_z <- data_z %>%
mutate(outlier=ifelse(abs(mpr)>3 | abs(upr)>3 | abs(mcpi)>3 | abs(mnfbf)>3 | abs(mfr)>3 | abs(bco)>3 | abs(metb)>3 | abs(uscpi)>3 | abs(mgdpqa)>3 | abs(myrer)>3, 1, 0))
outliers_z## moed mpr upr mcpi mnfbf
## 1 2005-10-31'T'00:00:00 -0.2959445 1.54197189 0.58070253 -0.556877853
## 2 2005-11-30'T'00:00:00 0.2441323 1.69427458 0.68941853 -0.460995610
## 3 2005-12-31'T'00:00:00 0.2441323 1.84657727 0.68941853 -0.183248996
## 4 2006-01-31'T'00:00:00 0.2441323 1.99887997 0.52634453 -0.219919582
## 5 2006-02-28'T'00:00:00 0.6941963 1.99887997 0.52634453 0.130412111
## 6 2006-03-31'T'00:00:00 0.6941963 2.15118266 1.39607252 -0.240215996
## 7 2006-04-30'T'00:00:00 1.1442604 2.15118266 1.28735652 0.113612635
## 8 2006-05-31'T'00:00:00 1.1442604 2.30348535 0.90685053 -0.070874440
## 9 2006-06-30'T'00:00:00 1.1442604 2.45578804 0.90685053 -0.111372756
## 10 2006-07-31'T'00:00:00 1.1442604 2.45578804 1.01556653 0.035215079
## 11 2006-08-31'T'00:00:00 1.1442604 2.45578804 0.58070253 0.246850675
## 12 2006-09-30'T'00:00:00 1.1442604 2.45578804 0.58070253 -0.173726930
## 13 2006-10-31'T'00:00:00 1.1442604 2.45578804 0.47198653 -0.225897455
## 14 2006-11-30'T'00:00:00 1.1442604 2.45578804 0.41762853 -0.233174865
## 15 2006-12-31'T'00:00:00 1.1442604 2.45578804 0.47198653 -0.072292117
## 16 2007-01-31'T'00:00:00 1.1442604 2.45578804 0.52634453 0.085448112
## 17 2007-02-28'T'00:00:00 1.1442604 2.45578804 0.47198653 -0.485096125
## 18 2007-03-31'T'00:00:00 1.1442604 2.45578804 -0.39774146 0.492935830
## 19 2007-04-30'T'00:00:00 1.1442604 2.45578804 -0.39774146 0.133341978
## 20 2007-05-31'T'00:00:00 1.1442604 2.45578804 -0.45209946 0.394241860
## 21 2007-06-30'T'00:00:00 1.1442604 2.45578804 -0.45209946 0.148298473
## 22 2007-07-31'T'00:00:00 1.1442604 2.45578804 -0.34338346 0.084195831
## 23 2007-08-31'T'00:00:00 1.1442604 2.45578804 -0.18030946 0.341409752
## 24 2007-09-30'T'00:00:00 1.1442604 2.15118266 -0.23466746 -0.666984125
## 25 2007-10-31'T'00:00:00 1.1442604 1.99887997 -0.18030946 0.267123461
## 26 2007-11-30'T'00:00:00 1.1442604 1.99887997 0.03712254 0.483248368
## 27 2007-12-31'T'00:00:00 1.1442604 1.84657727 0.09148054 -0.259709059
## 28 2008-01-31'T'00:00:00 1.1442604 1.08506381 0.03712254 0.926721461
## 29 2008-02-29'T'00:00:00 1.1442604 1.08506381 0.25455453 1.104710849
## 30 2008-03-31'T'00:00:00 1.1442604 0.62815574 0.30891253 0.534473775
## 31 2008-04-30'T'00:00:00 1.1442604 0.47585305 0.41762853 1.581333964
## 32 2008-05-31'T'00:00:00 1.1442604 0.47585305 0.85249253 -0.834529956
## 33 2008-06-30'T'00:00:00 1.1442604 0.47585305 2.97245451 -0.989812878
## 34 2008-07-31'T'00:00:00 1.1442604 0.47585305 3.40731850 -0.472289773
## 35 2008-08-31'T'00:00:00 1.1442604 0.47585305 3.40731850 -0.605953116
## 36 2008-09-30'T'00:00:00 1.1442604 0.47585305 3.24424450 -0.862198292
## 37 2008-10-31'T'00:00:00 1.1442604 -0.13335772 2.91809651 -1.482172211
## 38 2008-11-30'T'00:00:00 0.6941963 -0.13335772 1.88529452 -0.971713865
## 39 2008-12-31'T'00:00:00 0.6941963 -0.66641715 1.17864052 -0.360080613
## 40 2009-01-31'T'00:00:00 -0.6559958 -0.66641715 0.90685053 -0.207254998
## 41 2009-02-28'T'00:00:00 -1.5561238 -0.66641715 0.79813453 -0.423072742
## 42 2009-03-31'T'00:00:00 -1.5561238 -0.66641715 0.68941853 -0.496886475
## 43 2009-04-30'T'00:00:00 -1.5561238 -0.66641715 0.41762853 -0.016412003
## 44 2009-05-31'T'00:00:00 -1.5561238 -0.66641715 0.09148054 0.163774784
## 45 2009-06-30'T'00:00:00 -1.5561238 -0.66641715 -1.97412344 -0.374966225
## 46 2009-07-31'T'00:00:00 -1.5561238 -0.66641715 -2.51770344 0.445798059
## 47 2009-08-31'T'00:00:00 -1.5561238 -0.66641715 -2.51770344 0.427202858
## 48 2009-09-30'T'00:00:00 -1.5561238 -0.66641715 -2.30027144 0.157962307
## 49 2009-10-31'T'00:00:00 -1.5561238 -0.66641715 -2.02848144 -0.382361775
## 50 2009-11-30'T'00:00:00 -1.5561238 -0.66641715 -1.26746945 0.212991815
## 51 2009-12-31'T'00:00:00 -1.5561238 -0.66641715 -0.61517346 0.937613949
## 52 2010-01-31'T'00:00:00 -1.5561238 -0.66641715 -0.50645746 0.758325024
## 53 2010-02-28'T'00:00:00 -1.5561238 -0.66641715 -0.56081546 0.280733163
## 54 2010-03-31'T'00:00:00 -1.1060598 -0.66641715 -0.50645746 1.770712026
## 55 2010-04-30'T'00:00:00 -1.1060598 -0.66641715 -0.39774146 0.059764525
## 56 2010-05-31'T'00:00:00 -0.6559958 -0.66641715 -0.34338346 0.134121700
## 57 2010-06-30'T'00:00:00 -0.6559958 -0.66641715 -0.28902546 0.062812531
## 58 2010-07-31'T'00:00:00 -0.2059317 -0.66641715 -0.18030946 0.498913702
## 59 2010-08-31'T'00:00:00 -0.2059317 -0.66641715 -0.07159346 0.047974175
## 60 2010-09-30'T'00:00:00 -0.2059317 -0.66641715 -0.23466746 0.964786097
## 61 2010-10-31'T'00:00:00 -0.2059317 -0.66641715 -0.12595146 0.719338898
## 62 2010-11-30'T'00:00:00 -0.2059317 -0.66641715 -0.12595146 0.151299224
## 63 2010-12-31'T'00:00:00 -0.2059317 -0.66641715 -0.01723546 -0.103433763
## 64 2011-01-31'T'00:00:00 -0.2059317 -0.66641715 0.09148054 0.138374732
## 65 2011-02-28'T'00:00:00 -0.2059317 -0.66641715 0.36327053 0.793885097
## 66 2011-03-31'T'00:00:00 -0.2059317 -0.66641715 0.41762853 0.138964013
## 67 2011-04-30'T'00:00:00 -0.2059317 -0.66641715 0.52634453 0.330767721
## 68 2011-05-31'T'00:00:00 0.2441323 -0.66641715 0.58070253 0.929844605
## 69 2011-06-30'T'00:00:00 0.2441323 -0.66641715 0.68941853 0.684795299
## 70 2011-07-31'T'00:00:00 0.2441323 -0.66641715 0.63506053 0.686301582
## 71 2011-08-31'T'00:00:00 0.2441323 -0.66641715 0.58070253 0.600546281
## 72 2011-09-30'T'00:00:00 0.2441323 -0.66641715 0.63506053 -1.628060895
## 73 2011-10-31'T'00:00:00 0.2441323 -0.66641715 0.63506053 0.272287823
## 74 2011-11-30'T'00:00:00 0.2441323 -0.66641715 0.58070253 0.238665243
## 75 2011-12-31'T'00:00:00 0.2441323 -0.66641715 0.41762853 1.212317519
## 76 2012-01-31'T'00:00:00 0.2441323 -0.66641715 0.25455453 1.238566051
## 77 2012-02-29'T'00:00:00 0.2441323 -0.66641715 -0.01723546 -0.216435404
## 78 2012-03-31'T'00:00:00 0.2441323 -0.66641715 -0.07159346 0.169712489
## 79 2012-04-30'T'00:00:00 0.2441323 -0.66641715 -0.18030946 0.271386180
## 80 2012-05-31'T'00:00:00 0.2441323 -0.66641715 -0.28902546 0.493720278
## 81 2012-06-30'T'00:00:00 0.2441323 -0.66641715 -0.34338346 -0.975457005
## 82 2012-07-31'T'00:00:00 0.2441323 -0.66641715 -0.45209946 1.977007231
## 83 2012-08-31'T'00:00:00 0.2441323 -0.66641715 -0.45209946 -1.281704605
## 84 2012-09-30'T'00:00:00 0.2441323 -0.66641715 -0.50645746 0.607297260
## 85 2012-10-31'T'00:00:00 0.2441323 -0.66641715 -0.50645746 1.096759569
## 86 2012-11-30'T'00:00:00 0.2441323 -0.66641715 -0.50645746 0.461319263
## 87 2012-12-31'T'00:00:00 0.2441323 -0.66641715 -0.56081546 0.176953985
## 88 2013-01-31'T'00:00:00 0.2441323 -0.66641715 -0.50645746 0.394226030
## 89 2013-02-28'T'00:00:00 0.2441323 -0.66641715 -0.39774146 -0.574200689
## 90 2013-03-31'T'00:00:00 0.2441323 -0.66641715 -0.34338346 1.555530346
## 91 2013-04-30'T'00:00:00 0.2441323 -0.66641715 -0.28902546 1.434794330
## 92 2013-05-31'T'00:00:00 0.2441323 -0.66641715 -0.23466746 -0.309202537
## 93 2013-06-30'T'00:00:00 0.2441323 -0.66641715 -0.23466746 -1.767359033
## 94 2013-07-31'T'00:00:00 0.2441323 -0.66641715 -0.12595146 -3.115306003
## 95 2013-08-31'T'00:00:00 0.2441323 -0.66641715 -0.18030946 -0.208107259
## 96 2013-09-30'T'00:00:00 0.2441323 -0.66641715 0.20019653 0.417006686
## 97 2013-10-31'T'00:00:00 0.2441323 -0.66641715 0.30891253 2.224052862
## 98 2013-11-30'T'00:00:00 0.2441323 -0.66641715 0.36327053 -0.767345283
## 99 2013-12-31'T'00:00:00 0.2441323 -0.66641715 0.52634453 0.066853148
## 100 2014-01-31'T'00:00:00 0.2441323 -0.66641715 0.63506053 -0.005555194
## 101 2014-02-28'T'00:00:00 0.2441323 -0.66641715 0.68941853 0.149779237
## 102 2014-03-31'T'00:00:00 0.2441323 -0.66641715 0.68941853 0.129359958
## 103 2014-04-30'T'00:00:00 0.2441323 -0.66641715 0.63506053 -1.442095182
## 104 2014-05-31'T'00:00:00 0.2441323 -0.66641715 0.52634453 1.971095280
## 105 2014-06-30'T'00:00:00 0.2441323 -0.66641715 0.58070253 0.403389423
## 106 2014-07-31'T'00:00:00 0.6941963 -0.66641715 0.52634453 1.390059286
## 107 2014-08-31'T'00:00:00 0.6941963 -0.66641715 0.58070253 -1.542792094
## 108 2014-09-30'T'00:00:00 0.6941963 -0.66641715 0.20019653 0.150721284
## 109 2014-10-31'T'00:00:00 0.6941963 -0.66641715 0.30891253 -0.926083321
## 110 2014-11-30'T'00:00:00 0.6941963 -0.66641715 0.41762853 -0.548830172
## 111 2014-12-31'T'00:00:00 0.6941963 -0.66641715 0.25455453 -0.188979720
## 112 2015-01-31'T'00:00:00 0.6941963 -0.66641715 -0.66953146 0.126651958
## 113 2015-02-28'T'00:00:00 0.6941963 -0.66641715 -1.15875345 -0.435980694
## 114 2015-03-31'T'00:00:00 0.6941963 -0.66641715 -0.72388946 1.154184479
## 115 2015-04-30'T'00:00:00 0.6941963 -0.66641715 -0.23466746 1.250073338
## 116 2015-05-31'T'00:00:00 0.6941963 -0.66641715 -0.07159346 -0.058903573
## 117 2015-06-30'T'00:00:00 0.6941963 -0.66641715 0.14583854 1.842324814
## 118 2015-07-31'T'00:00:00 0.6941963 -0.66641715 0.58070253 -0.522100102
## 119 2015-08-31'T'00:00:00 0.6941963 -0.66641715 0.47198653 -2.092402907
## 120 2015-09-30'T'00:00:00 0.6941963 -0.66641715 0.20019653 -1.062121510
## 121 2015-10-31'T'00:00:00 0.6941963 -0.66641715 0.14583854 -0.168612895
## 122 2015-11-30'T'00:00:00 0.6941963 -0.66641715 0.20019653 0.990550729
## 123 2015-12-31'T'00:00:00 0.6941963 -0.51411445 0.25455453 0.554653467
## 124 2016-01-31'T'00:00:00 0.6941963 -0.51411445 0.68941853 0.332397341
## 125 2016-02-29'T'00:00:00 0.6941963 -0.51411445 1.06992453 -0.063436124
## 126 2016-03-31'T'00:00:00 0.6941963 -0.51411445 0.20019653 1.349118891
## 127 2016-04-30'T'00:00:00 0.6941963 -0.51411445 -0.07159346 0.722707299
## 128 2016-05-31'T'00:00:00 0.6941963 -0.51411445 -0.12595146 0.183697876
## 129 2016-06-30'T'00:00:00 0.6941963 -0.51411445 -0.34338346 0.982701049
## 130 2016-07-31'T'00:00:00 0.2441323 -0.51411445 -0.61517346 0.565706388
## 131 2016-08-31'T'00:00:00 0.2441323 -0.51411445 -0.39774146 0.186023576
## 132 2016-09-30'T'00:00:00 0.2441323 -0.51411445 -0.39774146 -1.506002422
## 133 2016-10-31'T'00:00:00 0.2441323 -0.51411445 -0.45209946 0.545930262
## 134 2016-11-30'T'00:00:00 0.2441323 -0.51411445 -0.28902546 -2.927990425
## 135 2016-12-31'T'00:00:00 0.2441323 -0.36181176 -0.28902546 -1.273418281
## 136 2017-01-31'T'00:00:00 0.2441323 -0.36181176 0.47198653 -0.695023183
## 137 2017-02-28'T'00:00:00 0.2441323 -0.36181176 1.23299852 -1.959283480
## 138 2017-03-31'T'00:00:00 0.2441323 -0.20950907 1.45043052 -5.644462424
## 139 2017-04-30'T'00:00:00 0.2441323 -0.20950907 1.12428253 1.151532950
## 140 2017-05-31'T'00:00:00 0.2441323 -0.20950907 0.85249253 1.905604022
## 141 2017-06-30'T'00:00:00 0.2441323 -0.05720638 0.63506053 -0.413334953
## 142 2017-07-31'T'00:00:00 0.2441323 -0.05720638 0.47198653 -0.376057837
## 143 2017-08-31'T'00:00:00 0.2441323 -0.05720638 0.74377653 0.292191540
## 144 2017-09-30'T'00:00:00 0.2441323 -0.05720638 1.06992453 1.159095786
## 145 2017-10-31'T'00:00:00 0.2441323 -0.05720638 0.79813453 -1.025482349
## 146 2017-11-30'T'00:00:00 0.2441323 -0.05720638 0.63506053 1.476469790
## 147 2017-12-31'T'00:00:00 0.2441323 0.09509632 0.68941853 0.774778114
## 148 2018-01-31'T'00:00:00 0.6941963 0.09509632 0.25455453 0.786075585
## 149 2018-02-28'T'00:00:00 0.6941963 0.09509632 -0.45209946 -0.940045080
## 150 2018-03-31'T'00:00:00 0.6941963 0.24739901 -0.50645746 -0.095497841
## 151 2018-04-30'T'00:00:00 0.6941963 0.24739901 -0.45209946 -0.937707094
## 152 2018-05-31'T'00:00:00 0.6941963 0.24739901 -0.23466746 -1.583064762
## 153 2018-06-30'T'00:00:00 0.6941963 0.39970170 -0.77824746 -1.619272950
## 154 2018-07-31'T'00:00:00 0.6941963 0.39970170 -0.72388946 0.628538792
## 155 2018-08-31'T'00:00:00 0.6941963 0.39970170 -1.10439545 -0.331551039
## 156 2018-09-30'T'00:00:00 0.6941963 0.55200439 -1.05003745 -1.526002069
## 157 2018-10-31'T'00:00:00 0.6941963 0.55200439 -0.88696345 0.913065448
## 158 2018-11-30'T'00:00:00 0.6941963 0.55200439 -1.10439545 -1.467854852
## 159 2018-12-31'T'00:00:00 0.6941963 0.70430708 -1.10439545 -0.546706018
## 160 2019-01-31'T'00:00:00 0.6941963 0.70430708 -1.59361745 -0.610706825
## 161 2019-02-28'T'00:00:00 0.6941963 0.70430708 -1.43054345 0.947783657
## 162 2019-03-31'T'00:00:00 0.6941963 0.70430708 -1.10439545 0.128165329
## 163 2019-04-30'T'00:00:00 0.6941963 0.70430708 -1.10439545 -1.037539931
## 164 2019-05-31'T'00:00:00 0.2441323 0.70430708 -1.10439545 -1.089133934
## 165 2019-06-30'T'00:00:00 0.2441323 0.70430708 -0.39774146 1.164851320
## 166 2019-07-31'T'00:00:00 0.2441323 0.55200439 -0.45209946 1.117312110
## 167 2019-08-31'T'00:00:00 0.2441323 0.55200439 -0.39774146 -0.427681139
## 168 2019-09-30'T'00:00:00 0.2441323 0.39970170 -0.61517346 -0.090673013
## 169 2019-10-31'T'00:00:00 0.2441323 0.24739901 -0.61517346 -0.305399145
## 170 2019-11-30'T'00:00:00 0.2441323 0.24739901 -0.72388946 0.902733416
## 171 2019-12-31'T'00:00:00 0.2441323 0.24739901 -0.66953146 1.091568271
## 172 2020-01-31'T'00:00:00 -0.2059317 0.24739901 -0.34338346 0.590563706
## 173 2020-02-29'T'00:00:00 -0.2059317 0.24739901 -0.50645746 -1.882020066
## 174 2020-03-31'T'00:00:00 -0.6559958 -0.66641715 -1.32182745 -3.145285862
## 175 2020-04-30'T'00:00:00 -0.6559958 -0.66641715 -2.78949344 -0.304330925
## 176 2020-05-31'T'00:00:00 -1.5561238 -0.66641715 -2.78949344 0.248537475
## 177 2020-06-30'T'00:00:00 -1.5561238 -0.66641715 -2.24591344 1.644272930
## 178 2020-07-31'T'00:00:00 -2.0061879 -0.66641715 -1.91976544 1.613812242
## 179 2020-08-31'T'00:00:00 -2.0061879 -0.66641715 -1.97412344 0.559941876
## 180 2020-09-30'T'00:00:00 -2.0061879 -0.66641715 -1.97412344 0.136886644
## 181 2020-10-31'T'00:00:00 -2.0061879 -0.66641715 -2.02848144 0.732547397
## 182 2020-11-30'T'00:00:00 -2.0061879 -0.66641715 -2.13719744 0.224184378
## 183 2020-12-31'T'00:00:00 -2.0061879 -0.66641715 -1.97412344 0.357819840
## 184 2021-01-31'T'00:00:00 -2.0061879 -0.66641715 -1.32182745 0.332006771
## 185 2021-02-28'T'00:00:00 -2.0061879 -0.66641715 -1.15875345 0.630543624
## 186 2021-03-31'T'00:00:00 -2.0061879 -0.66641715 -0.28902546 0.155984884
## 187 2021-04-30'T'00:00:00 -2.0061879 -0.66641715 1.34171452 0.918493971
## 188 2021-05-31'T'00:00:00 -2.0061879 -0.66641715 1.17864052 0.357659170
## 189 2021-06-30'T'00:00:00 -2.0061879 -0.66641715 0.63506053 -0.095975598
## 190 2021-07-31'T'00:00:00 -2.0061879 -0.66641715 -0.01723546 -1.045728435
## 191 2021-08-31'T'00:00:00 -2.0061879 -0.66641715 -0.12595146 0.540506465
## 192 2021-09-30'T'00:00:00 -2.0061879 -0.66641715 -0.01723546 -0.764365798
## 193 2021-10-31'T'00:00:00 -2.0061879 -0.66641715 0.36327053 0.428190034
## 194 2021-11-30'T'00:00:00 -2.0061879 -0.66641715 0.58070253 -1.351534428
## 195 2021-12-31'T'00:00:00 -2.0061879 -0.66641715 0.52634453 0.364322489
## 196 2022-01-31'T'00:00:00 -2.0061879 -0.66641715 0.03712254 0.886263077
## 197 2022-02-28'T'00:00:00 -2.0061879 -0.66641715 -0.01723546 -0.083081823
## 198 2022-03-31'T'00:00:00 -2.0061879 -0.51411445 -0.01723546 -0.954116472
## 199 2022-04-30'T'00:00:00 -2.0061879 -0.51411445 0.03712254 -0.700446508
## 200 2022-05-31'T'00:00:00 -1.5561238 -0.20950907 0.30891253 -0.073537074
## 201 2022-06-30'T'00:00:00 -1.5561238 0.24739901 0.63506053 -0.404043259
## 202 2022-07-31'T'00:00:00 -1.1060598 0.70430708 1.17864052 -0.972350402
## 203 2022-08-31'T'00:00:00 -1.1060598 0.70430708 1.34171452 0.615444415
## 204 2022-09-30'T'00:00:00 -0.6559958 1.16121516 1.23299852 -0.808601819
## 205 2022-10-31'T'00:00:00 -0.6559958 1.16121516 1.23299852 -0.808601819
## mfr bco metb uscpi mgdpqa
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## 31 0.948749614 1.363035473 0.336419902 0.747414714 0.778530605
## 32 1.012556448 2.019391685 0.922355689 0.897827034 0.778530605
## 33 1.046780113 2.501066007 0.485599872 1.298926553 0.540926356
## 34 1.005595703 1.867494389 0.737228738 1.599751193 0.540926356
## 35 0.861160233 1.470562769 0.446058194 1.499476313 0.540926356
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## 43 -1.160356278 -1.057727757 -0.569444013 -1.558907522 -2.405366330
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## 48 -0.683545210 -0.327421545 -0.147066989 -1.859732162 -1.288626361
## 49 -0.678324651 -0.082387222 0.223186913 -1.308220323 -1.288626361
## 50 -0.673104092 0.048324399 -0.299841657 -0.305471524 -1.288626361
## 51 -0.639460488 0.026738994 0.284296780 0.145765435 0.041957433
## 52 -0.624958935 -0.231886140 0.438868797 0.095627995 0.041957433
## 53 -0.631339618 0.013148183 0.162077045 -0.155059204 0.041957433
## 54 -0.721829310 0.217410074 0.670726823 -0.054784325 1.420062077
## 55 -0.680644899 0.406881965 -0.260299979 -0.104921765 1.420062077
## 56 -0.711388192 -0.104372357 -0.438237533 -0.205196644 1.420062077
## 57 -0.751992541 -0.089982086 -0.826464926 -0.656433604 1.206218253
## 58 -0.737490988 0.036732237 -0.664703512 -0.606296164 1.206218253
## 59 -0.724149559 -0.104772086 -0.425656090 -0.656433604 1.206218253
## 60 -0.406855576 0.201820615 -0.679082305 -0.656433604 0.279561682
## 61 -0.141187122 0.235397912 -0.693461097 -0.606296164 0.279561682
## 62 -0.112184015 0.346123046 -0.305233705 -0.656433604 0.279561682
## 63 -0.071579666 0.699084395 -0.152459036 -0.455883844 0.160759558
## 64 0.022390398 0.949315205 -0.116512055 -0.405746404 0.160759558
## 65 0.119840835 1.380623581 -0.035631349 -0.155059204 0.160759558
## 66 0.354185934 1.602873309 0.126130065 0.145765435 0.160759558
## 67 1.290986269 1.943842767 0.066817546 0.396452635 0.160759558
## 68 1.451083416 1.577690336 -0.386114411 0.597002394 0.160759558
## 69 1.542733232 1.407805202 -0.493955354 0.597002394 0.065717858
## 70 1.556654723 1.578090066 -0.213568904 0.597002394 0.065717858
## 71 1.655845346 1.502541147 0.061425499 0.697277274 0.065717858
## 72 1.348412419 1.019267907 -0.181216621 0.747414714 0.398363807
## 73 1.568836027 1.291084122 0.478410476 0.546864954 0.398363807
## 74 1.568836027 1.329458176 -0.206379507 0.496727515 0.398363807
## 75 1.502708945 1.203943041 -0.418466694 0.296177755 0.279561682
## 76 1.528231678 1.347845743 -0.339383336 0.246040315 0.279561682
## 77 1.564195530 1.814730065 -0.010468462 0.246040315 0.279561682
## 78 1.622201743 1.823524119 -0.033834000 0.145765435 0.184519983
## 79 1.633802986 1.687216282 -0.562254617 -0.054784325 0.184519983
## 80 1.639603607 0.983691961 -1.085283187 -0.355608964 0.184519983
## 81 1.535192424 0.821001962 -0.258502630 -0.355608964 0.208280407
## 82 1.552594288 1.105609528 -1.263220742 -0.506021284 0.208280407
## 83 1.575796773 1.491348715 -0.637743277 -0.355608964 0.208280407
## 84 1.726612926 1.404207635 -0.749178917 -0.205196644 0.160759558
## 85 1.773017896 1.256707365 -0.190203366 -0.104921765 0.160759558
## 86 1.819422866 1.357838986 -0.341180685 -0.305471524 0.160759558
## 87 1.854226594 1.353042229 -0.431048137 -0.355608964 0.517165931
## 88 1.883229700 1.530522228 -1.324330609 -0.405746404 0.517165931
## 89 1.889030321 1.363834932 -0.436440184 -0.205196644 0.517165931
## 90 1.854226594 1.309471689 -1.034957414 -0.455883844 -0.005563417
## 91 1.889030321 1.003678448 -1.725139445 -0.656433604 -0.005563417
## 92 1.952837155 0.924531962 -1.394427222 -0.506021284 -0.005563417
## 93 1.645404228 0.995284123 -1.135608960 -0.305471524 0.065717858
## 94 1.744014790 1.216734392 -1.398021920 -0.205196644 0.065717858
## 95 1.569996152 1.468963850 -0.634148579 -0.455883844 0.065717858
## 96 1.668606713 1.243516284 -0.355559478 -0.606296164 0.136999133
## 97 1.703410441 1.262303581 -0.432845486 -0.706571044 0.136999133
## 98 1.657005471 1.296280608 -0.165040480 -0.606296164 0.136999133
## 99 1.575796773 1.340650608 -0.188406017 -0.455883844 0.160759558
## 100 1.471385590 1.164769528 -0.768949756 -0.405746404 0.160759558
## 101 1.326370058 1.271497365 -0.035631349 -0.656433604 0.160759558
## 102 1.303167573 1.219132771 -0.199190111 -0.455883844 0.469645081
## 103 1.361173786 1.231524392 -0.341180685 -0.205196644 0.469645081
## 104 1.343771922 1.285088176 -0.896561538 -0.155059204 0.469645081
## 105 1.401778135 1.403008445 -1.175150639 -0.155059204 0.517165931
## 106 1.395977514 1.149579798 -1.257828695 -0.205196644 0.517165931
## 107 1.407578756 1.036456285 -1.218287016 -0.355608964 0.517165931
## 108 1.134949557 0.695886558 -0.235137092 -0.355608964 0.303322107
## 109 1.181354527 0.343724668 -1.705368606 -0.355608964 0.303322107
## 110 1.042139616 -0.284250734 0.088385735 -0.556158724 0.303322107
## 111 0.479479354 -0.796704245 -0.260299979 -0.806845923 0.327082532
## 112 0.166245805 -0.970186946 -0.292652261 -1.258082883 0.327082532
## 113 0.160445184 -0.586846138 -1.092472583 -1.207945443 0.327082532
## 114 -0.152788364 -0.885444244 -0.506536797 -1.258082883 0.374603382
## 115 -0.112184015 -0.418959652 -0.673690257 -1.308220323 0.374603382
## 116 -0.077380288 -0.467726679 -0.921724425 -1.207945443 0.374603382
## 117 -0.129585879 -0.546473435 -0.477779212 -1.157808003 0.160759558
## 118 -0.640040550 -1.001365865 -1.484294674 -1.107670563 0.160759558
## 119 -0.756052976 -0.923818298 -0.080565075 -1.107670563 0.160759558
## 120 -0.837261673 -1.154862080 -0.170432527 -1.207945443 0.113238708
## 121 -0.796657325 -1.107294243 0.273512686 -1.107670563 0.113238708
## 122 -0.761853597 -1.305160458 -0.071578330 -0.957258243 0.113238708
## 123 -0.721249248 -1.598162348 -0.475981863 -0.856983363 0.089478283
## 124 -0.709648006 -1.699693699 -0.943292613 -0.506021284 0.089478283
## 125 -0.703847384 -1.650526942 -0.591012202 -0.706571044 0.089478283
## 126 -0.622638687 -1.505425051 0.099169829 -0.756708483 -0.005563417
## 127 -0.622638687 -1.164455594 -0.283665516 -0.656433604 -0.005563417
## 128 -0.605236823 -1.102097756 -1.322533260 -0.706571044 -0.005563417
## 129 -0.611037444 -1.102497486 -0.919927076 -0.706571044 -0.029323841
## 130 -0.605236823 -1.391102349 -1.568770079 -0.806845923 -0.029323841
## 131 -0.593635580 -1.208026134 -0.382519713 -0.656433604 -0.029323841
## 132 -0.582034338 -1.127280729 -0.553267872 -0.455883844 0.041957433
## 133 -0.576233716 -1.157660188 -0.157851083 -0.405746404 0.041957433
## 134 -0.657442414 -1.070918838 -0.289057563 -0.355608964 0.041957433
## 135 -0.761853597 -0.817090461 -0.344775383 -0.155059204 0.113238708
## 136 -0.738651112 -0.861860190 -1.065512348 0.045490555 0.113238708
## 137 -0.738651112 -0.866257217 -0.346572732 0.145765435 0.113238708
## 138 -0.715448627 -0.976582622 -0.939697915 -0.004646885 0.303322107
## 139 -0.674844278 -1.020552892 -0.355559478 -0.104921765 0.303322107
## 140 -0.564632474 -1.077314513 -0.919927076 -0.255334084 0.303322107
## 141 -0.512426883 -1.172849918 -0.134485546 -0.405746404 0.327082532
## 142 -0.483423776 -0.983777757 -0.466995118 -0.355608964 0.327082532
## 143 -0.419616942 -0.994570460 -0.112917357 -0.255334084 0.327082532
## 144 -0.379012593 -0.788309920 -0.366343572 -0.104921765 0.422124231
## 145 -0.361610730 -0.635213435 -0.035631349 -0.205196644 0.422124231
## 146 -0.338408245 -0.547272895 -0.123701452 -0.104921765 0.422124231
## 147 -0.309405138 -0.415362085 -0.608985692 -0.155059204 0.350842957
## 148 -0.233997062 -0.328221004 -0.174027225 -0.155059204 0.350842957
## 149 -0.233997062 -0.458932625 -0.290854912 -0.104921765 0.350842957
## 150 0.003828410 -0.279453977 0.728241993 -0.004646885 0.232040832
## 151 0.102438972 -0.083586411 0.437071448 0.045490555 0.232040832
## 152 0.044432759 0.013148183 -0.452616326 0.195902875 0.232040832
## 153 -0.175990849 0.087098183 -0.833654322 0.246040315 0.113238708
## 154 -0.187592092 -0.120361546 -0.414871996 0.246040315 0.113238708
## 155 -0.193392713 0.006352778 -1.622690550 0.145765435 0.113238708
## 156 -0.274601411 0.218209533 0.825298841 -0.054784325 0.041957433
## 157 -0.350009487 -0.071594519 1.019412537 0.045490555 0.041957433
## 158 -0.332607623 -0.741541542 -0.502942099 -0.104921765 0.041957433
## 159 -0.367411351 -0.937808838 0.007505028 -0.255334084 0.113238708
## 160 -0.326807002 -0.614427489 0.156684998 -0.405746404 0.113238708
## 161 -0.309405138 -0.448939382 0.075804292 -0.455883844 0.113238708
## 162 -0.274601411 -0.354603166 0.672524172 -0.255334084 0.089478283
## 163 -0.251398926 -0.178322356 0.030870566 -0.205196644 0.089478283
## 164 -0.315205760 -0.510497760 -0.280070818 -0.305471524 0.089478283
## 165 -0.292003274 -0.428153436 -0.023049905 -0.405746404 0.136999133
## 166 -0.222395819 -0.483316138 0.654550682 -0.305471524 0.136999133
## 167 -0.245598304 -0.672788029 0.047046707 -0.355608964 0.136999133
## 168 -0.274601411 -0.658797489 -0.411277298 -0.355608964 0.041957433
## 169 -0.263000168 -0.680782624 1.202742139 -0.305471524 0.041957433
## 170 -0.263000168 -0.592842084 -0.724016031 -0.155059204 0.041957433
## 171 -0.239797683 -0.450138571 0.334622553 -0.054784325 -0.171886391
## 172 -0.204993956 -0.763526677 0.250147148 0.045490555 -0.171886391
## 173 -0.251398926 -1.068920189 0.356190742 -0.054784325 -0.171886391
## 174 -0.350009487 -2.179369372 0.300472921 -0.455883844 -0.860938713
## 175 -0.303604517 -2.078237751 -2.564501446 -1.057533123 -0.860938713
## 176 -0.280402032 -1.676109645 -0.044618094 -1.157808003 -0.860938713
## 177 -0.251398926 -1.443466943 1.835409000 -0.907120803 -5.090294343
## 178 -0.204993956 -1.357525052 2.613661134 -0.706571044 -5.090294343
## 179 -0.193392713 -1.278378566 0.464031684 -0.556158724 -5.090294343
## 180 -0.158588985 -1.451461538 2.033117395 -0.506021284 -1.621272309
## 181 -0.181791470 -1.590967213 2.065469677 -0.606296164 -1.621272309
## 182 -0.141187122 -1.186040999 1.152416366 -0.606296164 -1.621272309
## 183 -0.007772832 -1.017754784 1.806651416 -0.506021284 -1.811355708
## 184 0.050233380 -0.854665055 1.071535659 -0.506021284 -1.811355708
## 185 0.073435865 -0.444942084 1.305191034 -0.355608964 -1.811355708
## 186 0.050233380 -0.548472084 2.428534183 0.095627995 -1.146063811
## 187 0.177847048 -0.400172355 1.747338898 0.897827034 -1.146063811
## 188 0.183647669 -0.317428301 0.559291183 1.298926553 -1.146063811
## 189 0.195248912 -0.085185330 2.088835215 1.499476313 2.750645870
## 190 0.195248912 -0.037217762 0.561088532 1.499476313 2.750645870
## 191 0.496881218 -0.170727491 2.784409293 1.449338873 2.750645870
## 192 0.433074384 0.050323048 2.779017246 1.499476313 -2.096480807
## 193 0.485279975 0.284564668 2.814964226 1.900575832 -2.096480807
## 194 0.520083703 -0.267462085 1.492115334 2.201400472 -2.096480807
## 195 0.531684945 0.020743048 3.657920926 2.301675352 -0.171886391
## 196 0.485279975 0.557580072 1.431005467 2.552362551 -0.171886391
## 197 0.467878111 0.948515745 1.648484700 2.752912311 -0.171886391
## 198 0.456276869 1.225128717 2.868884698 3.053736951 0.160759558
## 199 0.276457609 1.282290068 2.308111798 2.953462071 0.160759558
## 200 0.293859473 1.821925200 0.370569534 3.103874390 0.160759558
## 201 0.073435865 1.500942229 2.016941253 3.354561590 1.087416128
## 202 0.085037108 1.309071959 0.890003406 3.053736951 1.087416128
## 203 0.027030895 0.768637368 1.150619017 2.953462071 1.087416128
## 204 -0.094782151 0.427667911 3.787330056 2.903324631 1.087416128
## 205 -0.187592092 0.702282233 3.787330056 2.903324631 1.087416128
## myrer outlier
## 1 0.158220697 0
## 2 0.163543850 0
## 3 0.167802371 0
## 4 0.106053807 0
## 5 0.030465048 0
## 6 -0.037458372 0
## 7 -0.161168425 0
## 8 -0.148392860 0
## 9 -0.055770015 0
## 10 -0.092393301 0
## 11 -0.041929820 0
## 12 -0.027024994 0
## 13 -0.099206936 0
## 14 -0.180331773 0
## 15 -0.369835986 0
## 16 -0.428603584 0
## 17 -0.422002876 0
## 18 -0.516542056 0
## 19 -0.593195446 0
## 20 -0.645362336 0
## 21 -0.524207395 0
## 22 -0.524207395 0
## 23 -0.424132137 0
## 24 -0.621088762 0
## 25 -0.769285315 0
## 26 -0.728616434 0
## 27 -0.828691692 0
## 28 -0.990515515 0
## 29 -1.078028134 0
## 30 -1.080157395 0
## 31 -1.151913485 0
## 32 -0.978804580 0
## 33 -0.924508429 0
## 34 -0.948994929 1
## 35 -0.653027675 1
## 36 -0.560404829 1
## 37 -0.324056878 0
## 38 -0.164362317 0
## 39 -0.496527004 0
## 40 -0.199495120 0
## 41 0.007894884 0
## 42 -0.113260057 0
## 43 -0.301486713 0
## 44 -0.439036962 0
## 45 -0.386657146 0
## 46 -0.379417659 0
## 47 -0.381546920 0
## 48 -0.509302569 0
## 49 -0.613636350 0
## 50 -0.656221566 0
## 51 -0.583826698 0
## 52 -0.619385354 0
## 53 -0.634290179 0
## 54 -0.930257433 0
## 55 -1.100598299 0
## 56 -0.935154733 0
## 57 -0.988386254 0
## 58 -1.104430968 0
## 59 -1.173631945 0
## 60 -1.306071968 0
## 61 -1.254543856 0
## 62 -1.136369881 0
## 63 -1.314163159 0
## 64 -1.362071527 0
## 65 -1.389751918 0
## 66 -1.437660287 0
## 67 -1.574997609 0
## 68 -1.462146786 0
## 69 -1.450435851 0
## 70 -1.560092784 0
## 71 -1.552001593 0
## 72 -1.089526143 0
## 73 -1.352489854 0
## 74 -1.109754120 0
## 75 -1.133814768 0
## 76 -1.406360153 0
## 77 -1.503667372 0
## 78 -1.356748375 0
## 79 -1.432337135 0
## 80 -1.117206533 0
## 81 -1.110818751 0
## 82 -1.214087901 0
## 83 -1.226863465 0
## 84 -1.367394680 0
## 85 -1.386558027 0
## 86 -1.407637709 0
## 87 -1.367394680 0
## 88 -1.266680643 0
## 89 -1.299258333 0
## 90 -1.292231773 0
## 91 -1.401462853 0
## 92 -1.288612029 0
## 93 -1.150210076 0
## 94 -0.972416798 1
## 95 -0.885755882 0
## 96 -0.939413255 0
## 97 -1.160430528 0
## 98 -1.017131275 0
## 99 -0.905345082 0
## 100 -0.753102933 0
## 101 -0.902151191 0
## 102 -0.926637690 0
## 103 -0.926637690 0
## 104 -1.038423883 0
## 105 -1.042682405 0
## 106 -1.075260095 0
## 107 -1.168308793 0
## 108 -0.894698778 0
## 109 -0.875535430 0
## 110 -0.676875396 0
## 111 -0.434778441 0
## 112 -0.152012604 0
## 113 -0.205457050 0
## 114 0.005978549 0
## 115 -0.296376487 0
## 116 -0.070674841 0
## 117 0.153962176 0
## 118 0.264683738 0
## 119 1.052510242 0
## 120 1.479427036 0
## 121 1.273314589 0
## 122 1.199429238 0
## 123 1.260113171 0
## 124 0.964571770 0
## 125 1.069544328 0
## 126 0.423313670 0
## 127 0.433959974 0
## 128 0.910914397 0
## 129 0.704376098 0
## 130 0.788056048 0
## 131 0.744832053 0
## 132 0.926245075 0
## 133 1.050380981 0
## 134 1.629965776 0
## 135 1.672550992 0
## 136 1.549692643 0
## 137 1.575243773 0
## 138 1.543304860 1
## 139 1.363382321 0
## 140 1.236265450 0
## 141 1.261816580 0
## 142 1.236265450 0
## 143 1.214334064 0
## 144 1.106806392 0
## 145 1.131292892 0
## 146 0.831067116 0
## 147 0.736315010 0
## 148 0.421184409 0
## 149 0.460575734 0
## 150 0.346660280 0
## 151 0.474415929 0
## 152 0.594293313 0
## 153 0.719280923 0
## 154 0.776132187 0
## 155 0.869393811 0
## 156 0.931781153 0
## 157 1.029514225 0
## 158 1.029514225 0
## 159 0.921560701 0
## 160 0.840222938 0
## 161 0.777409744 0
## 162 0.811903769 0
## 163 0.924115814 0
## 164 1.041863938 0
## 165 0.918366810 0
## 166 0.906655875 0
## 167 1.074867480 0
## 168 1.036966638 0
## 169 1.016738660 0
## 170 1.015886956 0
## 171 0.831067116 0
## 172 0.845971942 0
## 173 1.095095458 0
## 174 1.321222957 1
## 175 1.280767001 0
## 176 1.375093256 0
## 177 1.246911754 1
## 178 1.146836496 1
## 179 0.986503156 1
## 180 0.970533700 0
## 181 0.969043217 0
## 182 0.794443830 0
## 183 0.680528376 0
## 184 0.722474815 0
## 185 0.743341571 0
## 186 0.946047201 0
## 187 0.824679334 0
## 188 0.903887836 0
## 189 0.954564244 0
## 190 1.106806392 0
## 191 0.967765661 0
## 192 1.033772746 0
## 193 0.936039675 0
## 194 1.071247737 0
## 195 0.990761678 1
## 196 1.032282264 0
## 197 1.061666063 0
## 198 1.070608959 1
## 199 1.390636860 0
## 200 1.440035711 1
## 201 1.507107427 1
## 202 1.597175159 1
## 203 1.650832532 0
## 204 1.994708154 1
## 205 2.184638219 1Counting the number of outliers in each variable
outliers_z %>% group_by(df$mpr) %>% summarize(count=sum(outlier))## # A tibble: 9 × 2
## `df$mpr` count
## <dbl> <dbl>
## 1 1.75 4
## 2 2 3
## 3 2.25 1
## 4 2.5 3
## 5 2.7 0
## 6 2.75 0
## 7 3 2
## 8 3.25 0
## 9 3.5 3outliers_z %>% group_by(df$upr) %>% summarize(count=sum(outlier))## # A tibble: 22 × 2
## `df$upr` count
## <dbl> <dbl>
## 1 0.125 6
## 2 0.375 1
## 3 0.625 0
## 4 0.875 2
## 5 1 0
## 6 1.12 0
## 7 1.38 0
## 8 1.62 1
## 9 1.88 0
## 10 2 3
## # … with 12 more rowsoutliers_z %>% group_by(df$mcpi) %>% summarize(count=sum(outlier))## # A tibble: 62 × 2
## `df$mcpi` count
## <dbl> <dbl>
## 1 -2.9 0
## 2 -2.4 0
## 3 -2 0
## 4 -1.9 1
## 5 -1.7 0
## 6 -1.5 0
## 7 -1.4 1
## 8 -1.3 1
## 9 -0.7 0
## 10 -0.4 0
## # … with 52 more rowsoutliers_z %>% group_by(df$mnfbf) %>% summarize(count=sum(outlier))## # A tibble: 204 × 2
## `df$mnfbf` count
## <dbl> <dbl>
## 1 -23043. 1
## 2 -12466. 1
## 3 -12339. 1
## 4 -11546. 0
## 5 -8009. 0
## 6 -7446. 0
## 7 -7119. 0
## 8 -6634. 0
## 9 -6044. 0
## 10 -6007. 0
## # … with 194 more rowsoutliers_z %>% group_by(df$mfr) %>% summarize(count=sum(outlier))## # A tibble: 180 × 2
## `df$mfr` count
## <dbl> <dbl>
## 1 70.5 0
## 2 71.3 0
## 3 72.2 0
## 4 73.1 0
## 5 73.7 0
## 6 75.7 0
## 7 77.1 0
## 8 78.7 0
## 9 78.8 0
## 10 79.1 0
## # … with 170 more rowsoutliers_z %>% group_by(df$bco) %>% summarize(count=sum(outlier))## # A tibble: 203 × 2
## `df$bco` count
## <dbl> <dbl>
## 1 22.7 1
## 2 25.3 0
## 3 34.7 0
## 4 35.3 0
## 5 36.0 0
## 6 37.3 0
## 7 37.5 0
## 8 39.6 0
## 9 41.0 0
## 10 41.2 1
## # … with 193 more rowsoutliers_z %>% group_by(df$metb) %>% summarize(count=sum(outlier))## # A tibble: 189 × 2
## `df$metb` count
## <dbl> <dbl>
## 1 -3.63 0
## 2 1.04 0
## 3 1.15 0
## 4 1.61 0
## 5 1.91 0
## 6 2.38 0
## 7 2.86 1
## 8 2.88 0
## 9 3.27 0
## 10 3.28 0
## # … with 179 more rowsoutliers_z %>% group_by(df$uscpi) %>% summarize(count=sum(outlier))## # A tibble: 64 × 2
## `df$uscpi` count
## <dbl> <dbl>
## 1 -2.1 0
## 2 -1.5 0
## 3 -1.4 0
## 4 -1.3 0
## 5 -0.7 0
## 6 -0.4 0
## 7 -0.2 0
## 8 -0.1 0
## 9 0 0
## 10 0.1 0
## # … with 54 more rowsoutliers_z %>% group_by(df$mgdpqa) %>% summarize(count=sum(outlier))## # A tibble: 39 × 2
## `df$mgdpqa` count
## <dbl> <dbl>
## 1 -17.1 3
## 2 -5.8 0
## 3 -4.5 0
## 4 -3.7 0
## 5 -3.3 0
## 6 -2.5 0
## 7 -1.1 0
## 8 -0.5 0
## 9 0.3 0
## 10 0.7 1
## # … with 29 more rowsOnce we have identified the outliers in our dataset using the Z-score, there are several ways to handle them
Remove the outliers: One option is to simply remove the outliers from the dataset. This is a good option if the outliers are caused by errors or mistakes in the data.
Winsorize the outliers: Another option is to “winsorize” the outliers, which means replacing them with the nearest non-outlier value. For example, if an outlier is above the mean + 3 standard deviations, it can be replaced with the mean + 3 standard deviations. You can use the winsorize() function from the MASS library to winsorize the data.
Trim the outliers: A third option is to “trim” the outliers, which means removing a certain percentage of the lowest and highest values in the data. You can use the trim_mean() function from the stats library to trim the data.
Transform the data: In some cases, it may be appropriate to transform the data using a function such as log, square root, or Box-Cox to reduce the influence of the outliers. This can make the data more symmetrical and easier to model.
Use robust methods: Finally, we can use robust statistical methods that are less sensitive to outliers. For example, we can use the median instead of the mean to measure central tendency, or use robust regression methods such as the MM-estimator or the Tukey method to fit a model to the data.
Interquartile range (IQR) can be used to identify and handle outliers in a dataset. The IQR is the difference between the 75th percentile and the 25th percentile of the data, and values that are greater than the 75th percentile + 1.5 * IQR or less than the 25th percentile - 1.5 * IQR are considered to be outliers.
To fix outliers using the IQR, we can replace the outliers with the nearest non-outlier value. For example, if an outlier is above the 75th percentile + 1.5 * IQR, we can replace it with the 75th percentile + 1.5 * IQR. If an outlier is below the 25th percentile - 1.5 * IQR, you can replace it with the 25th percentile - 1.5 * IQR.