Start fresh

code for starting fresh?

rm(list = ls()) #this function clears the memory.

get the data

code for opening a file from a url (file in Excel), name it ‘fragility23’?

linkGit="https://github.com/DACSS-Fundamentals/overview/raw/refs/heads/main/FSI-2023-DOWNLOAD.xlsx" #this function obtains the data we are seeking to analyze
library(rio) # package needed
fragility23=rio::import(file = linkGit) #this function loads the rio package into the r session which is necessary step in obtaining the data.

exploratory commands

find out column names in ‘fragility23’?

names(x = fragility23)#this function provides the column names of the dataset.
##  [1] "Country"                          "Year"                            
##  [3] "Rank"                             "Total"                           
##  [5] "S1: Demographic Pressures"        "S2: Refugees and IDPs"           
##  [7] "C3: Group Grievance"              "E3: Human Flight and Brain Drain"
##  [9] "E2: Economic Inequality"          "E1: Economy"                     
## [11] "P1: State Legitimacy"             "P2: Public Services"             
## [13] "P3: Human Rights"                 "C1: Security Apparatus"          
## [15] "C2: Factionalized Elites"         "X1: External Intervention"

Check the data types in df?

str(object = fragility23) #this function provides the format type of the numeric columns. 
## 'data.frame':    179 obs. of  16 variables:
##  $ Country                         : chr  "Somalia" "Yemen" "South Sudan" "Congo Democratic Republic" ...
##  $ Year                            : num  2023 2023 2023 2023 2023 ...
##  $ Rank                            : chr  "1st" "2nd" "3rd" "4th" ...
##  $ Total                           : num  112 109 109 107 107 ...
##  $ S1: Demographic Pressures       : num  10 9.6 9.7 9.7 7.4 9.2 8.8 9.3 9.5 8.8 ...
##  $ S2: Refugees and IDPs           : num  9 9.6 10 9.8 9.1 8.6 9.6 9.5 9 7.7 ...
##  $ C3: Group Grievance             : num  8.7 8.8 8.6 9.4 9.1 8.3 9.3 8.1 8.1 5.5 ...
##  $ E3: Human Flight and Brain Drain: num  8.6 6.4 6.5 6.4 8 8.5 7.5 6.2 7.7 8.3 ...
##  $ E2: Economic Inequality         : num  9.1 7.9 8.6 8.4 6.5 8.2 8.5 9.6 8.7 9.2 ...
##  $ E1: Economy                     : num  9.5 9.9 8.6 8.1 9.6 9.6 9.3 8.2 8.4 8.9 ...
##  $ P1: State Legitimacy            : num  9.6 9.8 9.8 9.3 10 9.4 9.4 8.9 9.1 9.9 ...
##  $ P2: Public Services             : num  9.8 9.6 9.7 9.3 9 10 8.6 10 9.6 9.8 ...
##  $ P3: Human Rights                : num  9 9.6 8.7 9.3 9.1 8.7 9.2 9.1 8.4 8.7 ...
##  $ C1: Security Apparatus          : num  9.5 8.6 9.9 8.8 9.4 9.7 8.3 8 8.7 6.8 ...
##  $ C2: Factionalized Elites        : num  10 9.9 9.2 9.6 9.9 8.7 9.6 9.4 9.5 9.7 ...
##  $ X1: External Intervention       : num  9.1 9.2 9.2 9.1 10 7.7 8.1 9.4 7.9 9.6 ...

show me the first 10 rows?

head(x = fragility23,10)  #this function provides a view of the first ten rows of data.
##                      Country Year Rank Total S1: Demographic Pressures
## 1                    Somalia 2023  1st 111.9                      10.0
## 2                      Yemen 2023  2nd 108.9                       9.6
## 3                South Sudan 2023  3rd 108.5                       9.7
## 4  Congo Democratic Republic 2023  4th 107.2                       9.7
## 5                      Syria 2023  5th 107.1                       7.4
## 6                Afghanistan 2023  6th 106.6                       9.2
## 7                      Sudan 2023  7th 106.2                       8.8
## 8   Central African Republic 2023  8th 105.7                       9.3
## 9                       Chad 2023  9th 104.6                       9.5
## 10                     Haiti 2023 10th 102.9                       8.8
##    S2: Refugees and IDPs C3: Group Grievance E3: Human Flight and Brain Drain
## 1                    9.0                 8.7                              8.6
## 2                    9.6                 8.8                              6.4
## 3                   10.0                 8.6                              6.5
## 4                    9.8                 9.4                              6.4
## 5                    9.1                 9.1                              8.0
## 6                    8.6                 8.3                              8.5
## 7                    9.6                 9.3                              7.5
## 8                    9.5                 8.1                              6.2
## 9                    9.0                 8.1                              7.7
## 10                   7.7                 5.5                              8.3
##    E2: Economic Inequality E1: Economy P1: State Legitimacy P2: Public Services
## 1                      9.1         9.5                  9.6                 9.8
## 2                      7.9         9.9                  9.8                 9.6
## 3                      8.6         8.6                  9.8                 9.7
## 4                      8.4         8.1                  9.3                 9.3
## 5                      6.5         9.6                 10.0                 9.0
## 6                      8.2         9.6                  9.4                10.0
## 7                      8.5         9.3                  9.4                 8.6
## 8                      9.6         8.2                  8.9                10.0
## 9                      8.7         8.4                  9.1                 9.6
## 10                     9.2         8.9                  9.9                 9.8
##    P3: Human Rights C1: Security Apparatus C2: Factionalized Elites
## 1               9.0                    9.5                     10.0
## 2               9.6                    8.6                      9.9
## 3               8.7                    9.9                      9.2
## 4               9.3                    8.8                      9.6
## 5               9.1                    9.4                      9.9
## 6               8.7                    9.7                      8.7
## 7               9.2                    8.3                      9.6
## 8               9.1                    8.0                      9.4
## 9               8.4                    8.7                      9.5
## 10              8.7                    6.8                      9.7
##    X1: External Intervention
## 1                        9.1
## 2                        9.2
## 3                        9.2
## 4                        9.1
## 5                       10.0
## 6                        7.7
## 7                        8.1
## 8                        9.4
## 9                        7.9
## 10                       9.6

show me the last 10 rows?

tail(fragility23,10)  #this function provides a view of the final ten rows of data.
##         Country Year  Rank Total S1: Demographic Pressures
## 170      Sweden 2023 170th  20.6                       3.0
## 171  Luxembourg 2023 172nd  19.5                       2.4
## 172     Ireland 2023 171st  19.5                       2.8
## 173      Canada 2023 173rd  18.9                       1.2
## 174     Denmark 2023 174th  17.9                       2.3
## 175 Switzerland 2023 175th  17.8                       2.4
## 176 New Zealand 2023 176th  16.7                       1.1
## 177     Finland 2023 177th  16.0                       1.7
## 178     Iceland 2023 178th  15.7                       1.5
## 179      Norway 2023 179th  14.5                       1.4
##     S2: Refugees and IDPs C3: Group Grievance E3: Human Flight and Brain Drain
## 170                   3.7                 2.3                              0.6
## 171                   2.8                 1.5                              1.7
## 172                   1.6                 0.5                              2.5
## 173                   2.0                 2.0                              0.7
## 174                   3.0                 3.1                              1.0
## 175                   3.2                 2.1                              1.0
## 176                   1.2                 2.0                              1.6
## 177                   1.9                 0.3                              1.5
## 178                   1.5                 0.5                              1.6
## 179                   1.7                 3.1                              0.7
##     E2: Economic Inequality E1: Economy P1: State Legitimacy
## 170                     2.3         1.3                  0.5
## 171                     1.8         2.4                  0.3
## 172                     1.8         1.7                  0.5
## 173                     2.5         1.4                  0.4
## 174                     1.8         1.0                  0.3
## 175                     2.4         1.6                  0.3
## 176                     2.6         2.6                  0.5
## 177                     1.6         2.7                  0.4
## 178                     1.5         2.6                  0.4
## 179                     1.4         1.4                  0.4
##     P2: Public Services P3: Human Rights C1: Security Apparatus
## 170                 1.0              1.5                    2.1
## 171                 1.3              1.1                    0.4
## 172                 1.9              1.6                    2.1
## 173                 1.7              1.9                    2.2
## 174                 1.7              0.6                    1.1
## 175                 1.6              0.4                    1.4
## 176                 1.1              0.5                    1.6
## 177                 1.0              0.5                    2.0
## 178                 0.9              0.4                    0.4
## 179                 1.0              0.4                    1.4
##     C2: Factionalized Elites X1: External Intervention
## 170                      1.8                       0.5
## 171                      3.4                       0.4
## 172                      1.5                       1.0
## 173                      2.5                       0.4
## 174                      1.4                       0.6
## 175                      1.0                       0.4
## 176                      1.4                       0.5
## 177                      1.4                       1.0
## 178                      1.8                       2.6
## 179                      1.1                       0.5

transformative commands

subsetting

keep some columns: Country, Total, S1: Demographic Pressures, P1: State Legitimacy, E2: Economic Inequality into object ‘frag23_sub’

fragility23[,c(5,11,9)] #this function subfilters by specified columns.
##     S1: Demographic Pressures P1: State Legitimacy E2: Economic Inequality
## 1                        10.0                  9.6                     9.1
## 2                         9.6                  9.8                     7.9
## 3                         9.7                  9.8                     8.6
## 4                         9.7                  9.3                     8.4
## 5                         7.4                 10.0                     6.5
## 6                         9.2                  9.4                     8.2
## 7                         8.8                  9.4                     8.5
## 8                         9.3                  8.9                     9.6
## 9                         9.5                  9.1                     8.7
## 10                        8.8                  9.9                     9.2
## 11                        9.8                  8.2                     7.5
## 12                        7.0                  9.3                     7.3
## 13                        8.8                  8.6                     7.2
## 14                        8.8                  9.7                     7.5
## 15                        9.6                  8.2                     8.1
## 16                        8.7                  8.9                     7.8
## 17                        6.0                  9.6                     6.4
## 18                        7.3                  6.4                     4.9
## 19                        7.7                  9.7                     7.9
## 20                        8.7                  9.1                     7.2
## 21                        8.3                  7.4                     8.3
## 22                        9.6                  7.1                     9.2
## 23                        9.0                  8.8                     7.4
## 24                        8.9                  6.6                     7.8
## 25                        5.8                  7.7                     6.6
## 26                        9.2                  8.2                     7.4
## 27                        8.2                  8.3                     5.7
## 28                        8.5                  9.1                     7.5
## 29                        6.5                  9.6                     6.9
## 30                        7.2                  8.0                     6.0
## 31                        8.9                  9.1                     8.9
## 32                        8.3                  7.4                     4.9
## 33                        8.4                  6.2                     7.5
## 34                        8.3                  9.1                     4.9
## 35                        8.1                  7.3                     7.4
## 36                        8.6                  7.5                     7.5
## 37                        8.6                  7.8                     7.2
## 38                        7.3                  9.8                     7.3
## 39                        9.3                  8.1                     8.8
## 40                        6.8                  9.8                     4.5
## 41                        7.7                  7.5                     5.9
## 42                        9.1                  9.9                     7.6
## 43                        9.6                  7.5                     7.8
## 44                        7.2                  6.7                     7.8
## 45                        8.2                  8.0                     7.7
## 46                        7.1                  8.8                     7.2
## 47                        7.4                  7.6                     8.1
## 48                        9.4                  6.7                     9.1
## 49                        9.6                  6.7                     9.2
## 50                        6.7                  8.6                     4.5
## 51                        8.4                  5.5                     7.5
## 52                        4.5                  7.3                     6.6
## 53                        4.8                  9.1                     5.2
## 54                        6.4                  9.1                     6.4
## 55                        8.1                  6.6                     5.3
## 56                        7.1                  6.2                     7.8
## 57                        6.9                  6.8                     6.7
## 58                        8.7                  8.8                     7.8
## 59                        7.8                  5.3                     6.4
## 60                        7.4                  5.7                     8.2
## 61                        7.9                  6.8                     4.7
## 62                        5.0                  9.1                     6.7
## 63                        8.7                  4.9                     5.9
## 64                        7.1                  6.8                     6.5
## 65                        8.6                  6.9                     7.3
## 66                        8.6                  4.9                     7.9
## 67                        8.2                  6.4                     5.9
## 68                        6.3                  6.9                     4.4
## 69                        5.7                  8.2                     4.9
## 70                        6.4                  8.9                     5.3
## 71                        8.7                  7.1                     6.8
## 72                        7.0                  9.4                     4.3
## 73                        8.5                  4.5                     5.8
## 74                        8.0                  5.3                     7.8
## 75                        7.6                  7.3                     6.2
## 76                        3.8                  9.2                     4.5
## 77                        6.1                  6.4                     3.9
## 78                        8.0                  6.1                     6.9
## 79                        4.7                  8.0                     4.4
## 80                        7.4                  3.7                     6.3
## 81                        6.9                  6.4                     7.6
## 82                        4.6                  6.1                     5.0
## 83                        5.0                  7.6                     5.2
## 84                        4.8                  9.4                     3.3
## 85                        6.9                  6.3                     5.7
## 86                        6.9                  3.8                     6.7
## 87                        6.7                  6.4                     6.2
## 88                        5.8                  4.1                     6.8
## 89                        6.8                  5.2                     5.1
## 90                        4.4                  6.8                     4.8
## 91                        6.1                  7.5                     4.3
## 92                        4.1                  5.6                     4.3
## 93                        3.8                  6.3                     2.8
## 94                        5.4                  4.9                     3.6
## 95                        4.3                  9.0                     5.3
## 96                        5.4                  2.8                     4.3
## 97                        4.3                  5.7                     4.1
## 98                        7.0                  4.7                     4.4
## 99                        6.7                  8.1                     5.8
## 100                       4.3                  7.6                     4.8
## 101                       4.7                  4.1                     3.7
## 102                       4.1                  8.0                     5.7
## 103                       6.5                  8.1                     6.1
## 104                       5.6                  9.8                     5.6
## 105                       5.7                  6.4                     6.9
## 106                       5.2                  6.9                     2.6
## 107                       7.4                  3.2                     6.6
## 108                       4.8                  4.2                     5.3
## 109                       5.8                  4.4                     3.9
## 110                       6.4                  5.4                     4.7
## 111                       4.1                  8.4                     2.6
## 112                       8.1                  3.1                     6.9
## 113                       4.2                  4.5                     4.3
## 114                       6.2                  3.5                     5.0
## 115                       5.0                  3.4                     3.6
## 116                       5.5                  4.0                     4.7
## 117                       5.9                  7.6                     3.8
## 118                       4.4                  8.0                     3.5
## 119                       4.1                  3.9                     2.4
## 120                       3.4                  4.2                     4.5
## 121                       4.1                  5.0                     2.9
## 122                       7.8                  2.5                     6.8
## 123                       4.1                  5.8                     3.2
## 124                       5.1                  6.5                     3.5
## 125                       2.8                  7.7                     6.9
## 126                       3.7                  3.6                     5.1
## 127                       4.1                  3.7                     4.6
## 128                       4.2                  3.5                     5.3
## 129                       4.5                  4.4                     4.0
## 130                       4.1                  3.5                     4.7
## 131                       5.4                  3.5                     4.7
## 132                       4.8                  4.0                     5.2
## 133                       4.4                  7.2                     4.8
## 134                       6.3                  1.8                     4.7
## 135                       3.5                  6.2                     2.6
## 136                       4.9                  3.7                     6.0
## 137                       4.2                  7.2                     4.1
## 138                       4.8                  2.3                     2.9
## 139                       5.7                  3.4                     5.3
## 140                       3.7                  1.2                     5.0
## 141                       5.2                  4.2                     4.0
## 142                       3.8                  3.7                     2.4
## 143                       4.8                  3.3                     3.6
## 144                       3.3                  6.3                     3.5
## 145                       3.2                  1.8                     3.7
## 146                       4.6                  2.0                     2.9
## 147                       5.9                  4.4                     4.9
## 148                       3.4                  3.6                     3.7
## 149                       3.0                  6.4                     5.3
## 150                       2.9                  1.2                     5.1
## 151                       3.2                  3.9                     1.9
## 152                       3.6                  1.2                     4.1
## 153                       2.9                  1.0                     3.0
## 154                       3.1                  2.3                     3.1
## 155                       2.6                  3.2                     2.2
## 156                       3.6                  6.4                     3.1
## 157                       3.4                  0.4                     3.3
## 158                       3.7                  2.9                     2.3
## 159                       2.5                  2.4                     2.8
## 160                       4.2                  0.8                     2.2
## 161                       5.9                  0.3                     2.9
## 162                       3.1                  1.0                     2.9
## 163                       3.6                  1.4                     2.7
## 164                       4.0                  0.8                     2.4
## 165                       2.5                  3.7                     3.4
## 166                       2.3                  0.7                     2.7
## 167                       3.6                  0.6                     2.5
## 168                       3.8                  0.4                     2.6
## 169                       2.5                  0.3                     1.8
## 170                       3.0                  0.5                     2.3
## 171                       2.4                  0.3                     1.8
## 172                       2.8                  0.5                     1.8
## 173                       1.2                  0.4                     2.5
## 174                       2.3                  0.3                     1.8
## 175                       2.4                  0.3                     2.4
## 176                       1.1                  0.5                     2.6
## 177                       1.7                  0.4                     1.6
## 178                       1.5                  0.4                     1.5
## 179                       1.4                  0.4                     1.4
grep(pattern = "Country|S1|P1|E2|Total",x = names(fragility23),fixed = F,value = T) #this function searches for a specified set of characters  It is test function.
## [1] "Country"                   "Total"                    
## [3] "S1: Demographic Pressures" "E2: Economic Inequality"  
## [5] "P1: State Legitimacy"
keep=grep("Country|S1|P1|E2|Total",names(fragility23),fixed = F,value = T)
frag23_sub=fragility23[,keep] # this function keeps the results that match most to the intial grep pattern search.

renaming

rename ‘frag23_sub’ columns, keep var codes only

names(frag23_sub)[3:5]=c("S1","E2", "P1") #this function renames specified columns to the abbreviations noted in the code.

filtering

get me the top ten best countries on the ‘E2’ measure from ‘frag23_sub’

tail(frag23_sub[order(x=-frag23_sub$E2),],10) #Option 1, we are requesting the tail figures, because the lower scores are more impressive.  
##             Country Total  S1  E2  P1
## 155 Slovak Republic  37.8 2.6 2.2 3.2
## 160         Belgium  31.4 4.2 2.2 0.8
## 151  Czech Republic  40.2 3.2 1.9 3.9
## 169     Netherlands  21.0 2.5 1.8 0.3
## 171      Luxembourg  19.5 2.4 1.8 0.3
## 172         Ireland  19.5 2.8 1.8 0.5
## 174         Denmark  17.9 2.3 1.8 0.3
## 177         Finland  16.0 1.7 1.6 0.4
## 178         Iceland  15.7 1.5 1.5 0.4
## 179          Norway  14.5 1.4 1.4 0.4
tail(frag23_sub[order(x=-frag23_sub$E2),'Country'],10) #Option 2,but accomplished the same request.  This function just lists the countries.
##  [1] "Slovak Republic" "Belgium"         "Czech Republic"  "Netherlands"    
##  [5] "Luxembourg"      "Ireland"         "Denmark"         "Finland"        
##  [9] "Iceland"         "Norway"

some computations

give the statistical description of “frag23_sub”

summary(object = frag23_sub) #this function provides basic statistical information for S1, E2, and P1, along with totals
##    Country              Total              S1               E2       
##  Length:179         Min.   : 14.50   Min.   : 1.100   Min.   :1.400  
##  Class :character   1st Qu.: 49.00   1st Qu.: 4.100   1st Qu.:3.650  
##  Mode  :character   Median : 68.20   Median : 5.900   Median :5.200  
##                     Mean   : 65.83   Mean   : 5.956   Mean   :5.323  
##                     3rd Qu.: 82.20   3rd Qu.: 8.050   3rd Qu.:7.200  
##                     Max.   :111.90   Max.   :10.000   Max.   :9.600  
##        P1        
##  Min.   : 0.300  
##  1st Qu.: 3.650  
##  Median : 6.400  
##  Mean   : 5.741  
##  3rd Qu.: 8.100  
##  Max.   :10.000

the value of the worst quartile in Total

q3_Total=quantile(x = frag23_sub$Total, 
                  probs = 0.75, 
                  na.rm = TRUE) #this function provides the 75th percentile numbers as the higher value scores indicate a less positive condition

show correlations between “S1”,“E2”, “P1”

cor(x=frag23_sub[,-c(1,2)]) #shows the correlations among the selected variables
##           S1        E2        P1
## S1 1.0000000 0.8537425 0.6571171
## E2 0.8537425 1.0000000 0.6661759
## P1 0.6571171 0.6661759 1.0000000
library(corrtable)
corrtable::correlation_matrix(df = frag23_sub[,-c(1,2)]) #shows the correlations among the selections, similar to the above but contains asterisks to note stiatitical significance
##    S1         E2         P1        
## S1 "1.000   " "0.854***" "0.657***"
## E2 "0.854***" "1.000   " "0.666***"
## P1 "0.657***" "0.666***" "1.000   "

regress P1 and E2 on S1

lm(S1~P1+E2,data=frag23_sub)
## 
## Call:
## lm(formula = S1 ~ P1 + E2, data = frag23_sub)
## 
## Coefficients:
## (Intercept)           P1           E2  
##      0.8536       0.1248       0.8239
model <- lm(S1 ~ P1 + E2, data = frag23_sub) #models the regression expressed.
summary(model) #provides a summary
## 
## Call:
## lm(formula = S1 ~ P1 + E2, data = frag23_sub)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.6991 -0.8670  0.1260  0.7808  2.6197 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.85359    0.24234   3.522 0.000545 ***
## P1           0.12477    0.04024   3.100 0.002250 ** 
## E2           0.82389    0.05645  14.594  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.162 on 176 degrees of freedom
## Multiple R-squared:  0.7429, Adjusted R-squared:   0.74 
## F-statistic: 254.3 on 2 and 176 DF,  p-value: < 2.2e-16

some plotting

give me a plot for the ‘P1’ variable

hist(x = frag23_sub$P1) #creates a histogram based on P1

visual correlation between S1 and E2

plot(x=frag23_sub$S1, y=frag23_sub$E2) #plots the correlations of the specified variables.

Color points if country is on worst quartile of total.

frag23_sub$Total>=q3_Total
##   [1]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
##  [13]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
##  [25]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
##  [37]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE FALSE
##  [49] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [61] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [73] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [85] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
##  [97] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [109] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [121] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [133] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [145] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [157] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
## [169] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE
frag23_sub$worstQt=frag23_sub$Total>=q3_Total #provides the listing of countries that meet or do not meet the condition of worst quartile, true or false.
plot(frag23_sub$S1, 
     frag23_sub$E2,pch=20,
     col = as.factor(frag23_sub$worstQt))#actual color plots of the worst quartile

visual of the regression P1 and E2 on S1

library(sjPlot)
plot_models(model) #provides a visual model of the regression P1 and E2 on S1
## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## ℹ The deprecated feature was likely used in the sjPlot package.
##   Please report the issue at <https://github.com/strengejacke/sjPlot/issues>.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
## Ignoring unknown labels:
## • shape : "p-level"