library(tidyverse)
## Warning: package 'tidyverse' was built under R version 4.4.2
## Warning: package 'lubridate' was built under R version 4.4.2
library(openintro)
## Warning: package 'openintro' was built under R version 4.4.3
## Warning: package 'airports' was built under R version 4.4.3
## Warning: package 'cherryblossom' was built under R version 4.4.3
## Warning: package 'usdata' was built under R version 4.4.3
library(statsr)
## Warning: package 'statsr' was built under R version 4.4.3
## Warning: package 'BayesFactor' was built under R version 4.4.3
## Warning: package 'coda' was built under R version 4.4.3
library(broom)
library(ggplot2)

Exercise 1

There are 1458 rows and 123 columns, each row represents a country in a specific year.

data(hfi, package = "openintro")
dim(hfi)
## [1] 1458  123
summary(hfi)
##       year        ISO_code          countries            region         
##  Min.   :2008   Length:1458        Length:1458        Length:1458       
##  1st Qu.:2010   Class :character   Class :character   Class :character  
##  Median :2012   Mode  :character   Mode  :character   Mode  :character  
##  Mean   :2012                                                           
##  3rd Qu.:2014                                                           
##  Max.   :2016                                                           
##                                                                         
##  pf_rol_procedural  pf_rol_civil   pf_rol_criminal     pf_rol     
##  Min.   :0.000     Min.   :0.000   Min.   :0.000   Min.   :0.000  
##  1st Qu.:4.133     1st Qu.:4.550   1st Qu.:3.790   1st Qu.:4.132  
##  Median :5.300     Median :5.300   Median :4.575   Median :4.911  
##  Mean   :5.589     Mean   :5.475   Mean   :5.044   Mean   :5.310  
##  3rd Qu.:7.389     3rd Qu.:6.411   3rd Qu.:6.400   3rd Qu.:6.513  
##  Max.   :9.700     Max.   :8.774   Max.   :8.720   Max.   :8.723  
##  NA's   :578       NA's   :578     NA's   :578     NA's   :80     
##  pf_ss_homicide  pf_ss_disappearances_disap pf_ss_disappearances_violent
##  Min.   :0.000   Min.   : 0.000             Min.   : 0.000              
##  1st Qu.:6.387   1st Qu.:10.000             1st Qu.:10.000              
##  Median :8.638   Median :10.000             Median :10.000              
##  Mean   :7.413   Mean   : 8.342             Mean   : 9.519              
##  3rd Qu.:9.454   3rd Qu.:10.000             3rd Qu.:10.000              
##  Max.   :9.927   Max.   :10.000             Max.   :10.000              
##  NA's   :80      NA's   :89                 NA's   :80                  
##  pf_ss_disappearances_organized pf_ss_disappearances_fatalities
##  Min.   : 0.000                 Min.   : 0.000                 
##  1st Qu.: 5.000                 1st Qu.: 9.943                 
##  Median : 7.500                 Median :10.000                 
##  Mean   : 6.773                 Mean   : 9.585                 
##  3rd Qu.:10.000                 3rd Qu.:10.000                 
##  Max.   :10.000                 Max.   :10.000                 
##  NA's   :179                    NA's   :80                     
##  pf_ss_disappearances_injuries pf_ss_disappearances pf_ss_women_fgm 
##  Min.   : 0.000                Min.   : 0.000       Min.   : 0.400  
##  1st Qu.: 9.938                1st Qu.: 8.457       1st Qu.: 9.600  
##  Median :10.000                Median : 9.500       Median :10.000  
##  Mean   : 9.599                Mean   : 8.812       Mean   : 9.237  
##  3rd Qu.:10.000                3rd Qu.:10.000       3rd Qu.:10.000  
##  Max.   :10.000                Max.   :10.000       Max.   :10.000  
##  NA's   :80                    NA's   :80           NA's   :172     
##  pf_ss_women_missing pf_ss_women_inheritance_widows
##  Min.   : 0.000      Min.   : 0.00                 
##  1st Qu.: 7.500      1st Qu.: 5.00                 
##  Median :10.000      Median : 5.00                 
##  Mean   : 9.126      Mean   : 6.27                 
##  3rd Qu.:10.000      3rd Qu.:10.00                 
##  Max.   :10.000      Max.   :10.00                 
##  NA's   :120         NA's   :541                   
##  pf_ss_women_inheritance_daughters pf_ss_women_inheritance  pf_ss_women    
##  Min.   : 0.00                     Min.   : 0.000          Min.   : 0.000  
##  1st Qu.: 5.00                     1st Qu.: 5.000          1st Qu.: 7.167  
##  Median : 5.00                     Median : 5.000          Median : 8.333  
##  Mean   : 6.26                     Mean   : 6.636          Mean   : 8.332  
##  3rd Qu.:10.00                     3rd Qu.:10.000          3rd Qu.:10.000  
##  Max.   :10.00                     Max.   :10.000          Max.   :10.000  
##  NA's   :541                       NA's   :119             NA's   :100     
##      pf_ss       pf_movement_domestic pf_movement_foreign pf_movement_women
##  Min.   :3.964   Min.   : 0.000       Min.   : 0.000      Min.   : 0.000   
##  1st Qu.:7.312   1st Qu.: 5.000       1st Qu.: 5.000      1st Qu.: 5.000   
##  Median :8.340   Median :10.000       Median :10.000      Median :10.000   
##  Mean   :8.181   Mean   : 7.702       Mean   : 7.676      Mean   : 8.045   
##  3rd Qu.:9.453   3rd Qu.:10.000       3rd Qu.:10.000      3rd Qu.:10.000   
##  Max.   :9.976   Max.   :10.000       Max.   :10.000      Max.   :10.000   
##  NA's   :80      NA's   :98           NA's   :98          NA's   :141      
##   pf_movement     pf_religion_estop_establish pf_religion_estop_operate
##  Min.   : 0.000   Min.   : 0.000              Min.   : 0.000           
##  1st Qu.: 6.667   1st Qu.: 5.000              1st Qu.: 6.667           
##  Median : 8.333   Median : 7.500              Median : 7.500           
##  Mean   : 7.824   Mean   : 7.524              Mean   : 7.495           
##  3rd Qu.:10.000   3rd Qu.:10.000              3rd Qu.:10.000           
##  Max.   :10.000   Max.   :10.000              Max.   :10.000           
##  NA's   :80       NA's   :731                 NA's   :731              
##  pf_religion_estop pf_religion_harassment pf_religion_restrictions
##  Min.   : 0.000    Min.   : 5.244         Min.   : 2.406          
##  1st Qu.: 5.833    1st Qu.: 8.289         1st Qu.: 6.189          
##  Median : 7.500    Median : 8.962         Median : 7.544          
##  Mean   : 7.449    Mean   : 8.782         Mean   : 7.298          
##  3rd Qu.:10.000    3rd Qu.: 9.513         3rd Qu.: 8.661          
##  Max.   :10.000    Max.   :10.000         Max.   :10.000          
##  NA's   :329       NA's   :94             NA's   :94              
##   pf_religion     pf_association_association pf_association_assembly
##  Min.   : 0.000   Min.   : 0.000             Min.   : 0.000         
##  1st Qu.: 7.175   1st Qu.: 7.500             1st Qu.: 5.000         
##  Median : 8.145   Median : 7.500             Median : 7.500         
##  Mean   : 7.875   Mean   : 7.825             Mean   : 7.418         
##  3rd Qu.: 8.858   3rd Qu.:10.000             3rd Qu.:10.000         
##  Max.   :10.000   Max.   :10.000             Max.   :10.000         
##  NA's   :90       NA's   :329                NA's   :329            
##  pf_association_political_establish pf_association_political_operate
##  Min.   : 0.000                     Min.   : 0.000                  
##  1st Qu.: 5.000                     1st Qu.: 4.167                  
##  Median : 7.500                     Median : 7.500                  
##  Mean   : 7.497                     Mean   : 6.652                  
##  3rd Qu.:10.000                     3rd Qu.:10.000                  
##  Max.   :10.000                     Max.   :10.000                  
##  NA's   :731                        NA's   :731                     
##  pf_association_political pf_association_prof_establish
##  Min.   : 0.000           Min.   : 0.000               
##  1st Qu.: 5.000           1st Qu.: 5.000               
##  Median : 7.500           Median : 7.500               
##  Mean   : 6.916           Mean   : 7.424               
##  3rd Qu.:10.000           3rd Qu.:10.000               
##  Max.   :10.000           Max.   :10.000               
##  NA's   :329              NA's   :731                  
##  pf_association_prof_operate pf_association_prof pf_association_sport_establish
##  Min.   : 0.000              Min.   : 0.000      Min.   : 2.500                
##  1st Qu.: 5.000              1st Qu.: 5.000      1st Qu.: 7.500                
##  Median : 7.500              Median : 7.500      Median :10.000                
##  Mean   : 6.959              Mean   : 7.003      Mean   : 8.332                
##  3rd Qu.:10.000              3rd Qu.:10.000      3rd Qu.:10.000                
##  Max.   :10.000              Max.   :10.000      Max.   :10.000                
##  NA's   :731                 NA's   :329         NA's   :731                   
##  pf_association_sport_operate pf_association_sport pf_association  
##  Min.   : 0.000               Min.   : 1.250       Min.   : 0.250  
##  1st Qu.: 6.667               1st Qu.: 6.250       1st Qu.: 6.000  
##  Median : 7.500               Median : 8.333       Median : 8.000  
##  Mean   : 7.309               Mean   : 7.804       Mean   : 7.424  
##  3rd Qu.:10.000               3rd Qu.:10.000       3rd Qu.: 9.500  
##  Max.   :10.000               Max.   :10.000       Max.   :10.000  
##  NA's   :731                  NA's   :329          NA's   :329     
##  pf_expression_killed pf_expression_jailed pf_expression_influence
##  Min.   : 0.000       Min.   : 0.000       Min.   :0.000          
##  1st Qu.:10.000       1st Qu.:10.000       1st Qu.:3.000          
##  Median :10.000       Median :10.000       Median :5.333          
##  Mean   : 9.231       Mean   : 9.657       Mean   :5.200          
##  3rd Qu.:10.000       3rd Qu.:10.000       3rd Qu.:7.333          
##  Max.   :10.000       Max.   :10.000       Max.   :9.667          
##  NA's   :80           NA's   :80           NA's   :80             
##  pf_expression_control pf_expression_cable pf_expression_newspapers
##  Min.   :0.000         Min.   : 0.000      Min.   : 0.000          
##  1st Qu.:3.750         1st Qu.: 7.500      1st Qu.: 7.500          
##  Median :5.250         Median :10.000      Median :10.000          
##  Mean   :5.259         Mean   : 9.039      Mean   : 8.588          
##  3rd Qu.:7.250         3rd Qu.:10.000      3rd Qu.:10.000          
##  Max.   :9.250         Max.   :10.000      Max.   :10.000          
##  NA's   :80            NA's   :335         NA's   :335             
##  pf_expression_internet pf_expression    pf_identity_legal
##  Min.   : 0.000         Min.   :0.2083   Min.   : 0.000   
##  1st Qu.: 7.500         1st Qu.:6.9167   1st Qu.: 7.000   
##  Median :10.000         Median :8.0833   Median : 7.000   
##  Mean   : 8.556         Mean   :7.8256   Mean   : 6.307   
##  3rd Qu.:10.000         3rd Qu.:9.0714   3rd Qu.:10.000   
##  Max.   :10.000         Max.   :9.7976   Max.   :10.000   
##  NA's   :329            NA's   :80       NA's   :1253     
##  pf_identity_parental_marriage pf_identity_parental_divorce
##  Min.   : 0.000                Min.   : 0.000              
##  1st Qu.: 5.000                1st Qu.: 5.000              
##  Median :10.000                Median :10.000              
##  Mean   : 7.248                Mean   : 7.633              
##  3rd Qu.:10.000                3rd Qu.:10.000              
##  Max.   :10.000                Max.   :10.000              
##  NA's   :535                   NA's   :535                 
##  pf_identity_parental pf_identity_sex_male pf_identity_sex_female
##  Min.   : 0.000       Min.   : 0.000       Min.   : 0.000        
##  1st Qu.: 5.000       1st Qu.: 0.000       1st Qu.:10.000        
##  Median :10.000       Median :10.000       Median :10.000        
##  Mean   : 7.428       Mean   : 6.709       Mean   : 7.935        
##  3rd Qu.:10.000       3rd Qu.:10.000       3rd Qu.:10.000        
##  Max.   :10.000       Max.   :10.000       Max.   :10.000        
##  NA's   :100          NA's   :83           NA's   :80            
##  pf_identity_sex  pf_identity_divorce  pf_identity        pf_score    
##  Min.   : 0.000   Min.   : 0.000      Min.   : 0.000   Min.   :2.167  
##  1st Qu.: 5.000   1st Qu.: 5.000      1st Qu.: 5.000   1st Qu.:6.197  
##  Median :10.000   Median :10.000      Median : 9.167   Median :7.189  
##  Mean   : 7.326   Mean   : 7.538      Mean   : 7.334   Mean   :7.201  
##  3rd Qu.:10.000   3rd Qu.:10.000      3rd Qu.:10.000   3rd Qu.:8.449  
##  Max.   :10.000   Max.   :10.000      Max.   :10.000   Max.   :9.568  
##  NA's   :80       NA's   :873         NA's   :80       NA's   :80     
##     pf_rank       ef_government_consumption ef_government_transfers
##  Min.   :  1.00   Min.   : 0.000            Min.   : 1.940         
##  1st Qu.: 39.00   1st Qu.: 4.242            1st Qu.: 6.084         
##  Median : 77.00   Median : 5.807            Median : 8.361         
##  Mean   : 77.22   Mean   : 5.636            Mean   : 7.624         
##  3rd Qu.:115.00   3rd Qu.: 7.319            3rd Qu.: 9.451         
##  Max.   :162.00   Max.   :10.000            Max.   :10.000         
##  NA's   :80       NA's   :66                NA's   :160            
##  ef_government_enterprises ef_government_tax_income ef_government_tax_payroll
##  Min.   : 0.000            Min.   : 0.00            Min.   : 0.000           
##  1st Qu.: 4.000            1st Qu.: 6.00            1st Qu.: 4.000           
##  Median : 7.000            Median : 8.00            Median : 5.000           
##  Mean   : 6.187            Mean   : 7.41            Mean   : 5.415           
##  3rd Qu.: 8.000            3rd Qu.:10.00            3rd Qu.: 7.000           
##  Max.   :10.000            Max.   :10.00            Max.   :10.000           
##  NA's   :104               NA's   :124              NA's   :193              
##  ef_government_tax ef_government   ef_legal_judicial ef_legal_courts
##  Min.   : 0.000    Min.   :3.175   Min.   :0.000     Min.   :0.000  
##  1st Qu.: 5.000    1st Qu.:5.541   1st Qu.:3.228     1st Qu.:3.251  
##  Median : 6.500    Median :6.485   Median :4.565     Median :4.120  
##  Mean   : 6.452    Mean   :6.456   Mean   :4.899     Mean   :4.397  
##  3rd Qu.: 8.000    3rd Qu.:7.403   3rd Qu.:6.532     3rd Qu.:5.319  
##  Max.   :10.000    Max.   :9.528   Max.   :9.697     Max.   :8.278  
##  NA's   :124       NA's   :80      NA's   :167       NA's   :80     
##  ef_legal_protection ef_legal_military ef_legal_integrity ef_legal_enforcement
##  Min.   :0.000       Min.   : 0.000    Min.   : 0.1667    Min.   :0.000       
##  1st Qu.:4.393       1st Qu.: 4.167    1st Qu.: 4.1667    1st Qu.:3.376       
##  Median :5.388       Median : 6.667    Median : 5.8333    Median :4.387       
##  Mean   :5.561       Mean   : 6.417    Mean   : 6.1773    Mean   :4.414       
##  3rd Qu.:6.847       3rd Qu.: 8.333    3rd Qu.: 8.3333    3rd Qu.:5.569       
##  Max.   :9.288       Max.   :10.000    Max.   :10.0000    Max.   :8.105       
##  NA's   :169         NA's   :80        NA's   :277        NA's   :90          
##  ef_legal_restrictions ef_legal_police ef_legal_crime  ef_legal_gender 
##  Min.   :0.000         Min.   :0.000   Min.   :0.000   Min.   :0.2857  
##  1st Qu.:6.395         1st Qu.:4.110   1st Qu.:4.696   1st Qu.:0.8148  
##  Median :7.693         Median :5.304   Median :6.074   Median :0.9444  
##  Mean   :7.350         Mean   :5.517   Mean   :5.912   Mean   :0.8870  
##  3rd Qu.:8.651         3rd Qu.:7.106   3rd Qu.:7.273   3rd Qu.:1.0000  
##  Max.   :9.981         Max.   :9.688   Max.   :9.673   Max.   :1.0000  
##  NA's   :100           NA's   :169     NA's   :169     NA's   :24      
##     ef_legal     ef_money_growth  ef_money_sd    ef_money_inflation
##  Min.   :1.430   Min.   :0.000   Min.   :0.000   Min.   : 0.000    
##  1st Qu.:4.122   1st Qu.:8.156   1st Qu.:7.927   1st Qu.: 8.580    
##  Median :5.229   Median :8.816   Median :8.985   Median : 9.263    
##  Mean   :5.280   Mean   :8.609   Mean   :8.312   Mean   : 8.878    
##  3rd Qu.:6.210   3rd Qu.:9.332   3rd Qu.:9.457   3rd Qu.: 9.694    
##  Max.   :8.907   Max.   :9.999   Max.   :9.950   Max.   :10.000    
##  NA's   :80      NA's   :70      NA's   :72      NA's   :72        
##  ef_money_currency    ef_money      ef_trade_tariffs_revenue
##  Min.   : 0.000    Min.   :0.9475   Min.   : 0.000          
##  1st Qu.: 5.000    1st Qu.:7.0266   1st Qu.: 7.753          
##  Median :10.000    Median :8.3296   Median : 9.000          
##  Mean   : 6.658    Mean   :8.1240   Mean   : 8.200          
##  3rd Qu.:10.000    3rd Qu.:9.3657   3rd Qu.: 9.607          
##  Max.   :10.000    Max.   :9.9222   Max.   :10.000          
##  NA's   :80        NA's   :82       NA's   :169             
##  ef_trade_tariffs_mean ef_trade_tariffs_sd ef_trade_tariffs
##  Min.   : 2.820        Min.   : 0.000      Min.   : 3.117  
##  1st Qu.: 7.620        1st Qu.: 5.364      1st Qu.: 6.698  
##  Median : 8.500        Median : 6.290      Median : 7.719  
##  Mean   : 8.232        Mean   : 5.934      Mean   : 7.444  
##  3rd Qu.: 8.940        3rd Qu.: 7.143      3rd Qu.: 8.315  
##  Max.   :10.000        Max.   :10.000      Max.   :10.000  
##  NA's   :92            NA's   :91          NA's   :85      
##  ef_trade_regulatory_nontariff ef_trade_regulatory_compliance
##  Min.   :0.000                 Min.   :0.000                 
##  1st Qu.:5.002                 1st Qu.:5.332                 
##  Median :5.663                 Median :7.293                 
##  Mean   :5.731                 Mean   :6.646                 
##  3rd Qu.:6.369                 3rd Qu.:8.680                 
##  Max.   :9.188                 Max.   :9.963                 
##  NA's   :170                   NA's   :90                    
##  ef_trade_regulatory ef_trade_black   ef_trade_movement_foreign
##  Min.   :0.000       Min.   : 0.000   Min.   :0.000            
##  1st Qu.:5.247       1st Qu.:10.000   1st Qu.:5.145            
##  Median :6.482       Median :10.000   Median :6.018            
##  Mean   :6.153       Mean   : 9.767   Mean   :5.930            
##  3rd Qu.:7.403       3rd Qu.:10.000   3rd Qu.:6.878            
##  Max.   :9.729       Max.   :10.000   Max.   :9.253            
##  NA's   :84          NA's   :87       NA's   :164              
##  ef_trade_movement_capital ef_trade_movement_visit ef_trade_movement
##  Min.   : 0.0000           Min.   : 0.000          Min.   :0.000    
##  1st Qu.: 0.7692           1st Qu.: 1.549          1st Qu.:3.454    
##  Median : 3.0769           Median : 6.416          Median :5.124    
##  Mean   : 3.5838           Mean   : 5.353          Mean   :4.883    
##  3rd Qu.: 6.1539           3rd Qu.: 7.854          3rd Qu.:6.351    
##  Max.   :10.0000           Max.   :10.000          Max.   :9.305    
##  NA's   :89                NA's   :85              NA's   :80       
##     ef_trade     ef_regulation_credit_ownership ef_regulation_credit_private
##  Min.   :1.782   Min.   : 0.0                   Min.   : 0.000              
##  1st Qu.:6.405   1st Qu.: 5.0                   1st Qu.: 7.243              
##  Median :7.149   Median : 8.0                   Median : 8.544              
##  Mean   :7.054   Mean   : 7.7                   Mean   : 7.899              
##  3rd Qu.:7.882   3rd Qu.:10.0                   3rd Qu.: 9.430              
##  Max.   :9.562   Max.   :10.0                   Max.   :10.000              
##  NA's   :81      NA's   :172                    NA's   :72                  
##  ef_regulation_credit_interest ef_regulation_credit ef_regulation_labor_minwage
##  Min.   : 0.000                Min.   : 2.207       Min.   : 0.000             
##  1st Qu.: 9.000                1st Qu.: 7.631       1st Qu.: 4.433             
##  Median :10.000                Median : 8.682       Median : 6.667             
##  Mean   : 9.331                Mean   : 8.314       Mean   : 6.446             
##  3rd Qu.:10.000                3rd Qu.: 9.380       3rd Qu.: 8.900             
##  Max.   :10.000                Max.   :10.000       Max.   :10.000             
##  NA's   :100                   NA's   :80           NA's   :91                 
##  ef_regulation_labor_firing ef_regulation_labor_bargain
##  Min.   :0.000              Min.   :0.000              
##  1st Qu.:3.898              1st Qu.:5.742              
##  Median :4.773              Median :6.725              
##  Mean   :4.741              Mean   :6.437              
##  3rd Qu.:5.509              3rd Qu.:7.386              
##  Max.   :8.511              Max.   :8.997              
##  NA's   :171                NA's   :170                
##  ef_regulation_labor_hours ef_regulation_labor_dismissal
##  Min.   : 2.000            Min.   : 0.000               
##  1st Qu.: 6.000            1st Qu.: 4.388               
##  Median : 8.000            Median : 7.381               
##  Mean   : 7.962            Mean   : 6.460               
##  3rd Qu.:10.000            3rd Qu.: 8.795               
##  Max.   :10.000            Max.   :10.000               
##  NA's   :88                NA's   :110                  
##  ef_regulation_labor_conscription ef_regulation_labor
##  Min.   : 0.000                   Min.   :2.099      
##  1st Qu.: 3.000                   1st Qu.:5.405      
##  Median :10.000                   Median :6.478      
##  Mean   : 6.555                   Mean   :6.440      
##  3rd Qu.:10.000                   3rd Qu.:7.572      
##  Max.   :10.000                   Max.   :9.725      
##  NA's   :81                       NA's   :84         
##  ef_regulation_business_adm ef_regulation_business_bureaucracy
##  Min.   :0.000              Min.   : 0.000                    
##  1st Qu.:3.203              1st Qu.: 3.333                    
##  Median :3.956              Median : 5.300                    
##  Mean   :3.971              Mean   : 5.271                    
##  3rd Qu.:4.643              3rd Qu.: 7.333                    
##  Max.   :7.687              Max.   :10.000                    
##  NA's   :169                NA's   :102                       
##  ef_regulation_business_start ef_regulation_business_bribes
##  Min.   :0.7764               Min.   :0.000                
##  1st Qu.:8.5270               1st Qu.:3.434                
##  Median :9.2470               Median :4.418                
##  Mean   :8.8534               Mean   :4.886                
##  3rd Qu.:9.6344               3rd Qu.:6.228                
##  Max.   :9.9808               Max.   :9.624                
##  NA's   :90                   NA's   :175                  
##  ef_regulation_business_licensing ef_regulation_business_compliance
##  Min.   : 0.000                   Min.   :0.000                    
##  1st Qu.: 6.875                   1st Qu.:6.368                    
##  Median : 8.074                   Median :7.467                    
##  Mean   : 7.698                   Mean   :6.982                    
##  3rd Qu.: 8.992                   3rd Qu.:8.209                    
##  Max.   :10.000                   Max.   :9.865                    
##  NA's   :101                      NA's   :90                       
##  ef_regulation_business ef_regulation      ef_score        ef_rank      
##  Min.   :2.010          Min.   :2.484   Min.   :2.880   Min.   :  1.00  
##  1st Qu.:5.592          1st Qu.:6.429   1st Qu.:6.250   1st Qu.: 38.00  
##  Median :6.265          Median :7.082   Median :6.900   Median : 77.00  
##  Mean   :6.318          Mean   :7.020   Mean   :6.786   Mean   : 76.97  
##  3rd Qu.:7.140          3rd Qu.:7.721   3rd Qu.:7.410   3rd Qu.:115.00  
##  Max.   :9.273          Max.   :9.440   Max.   :9.190   Max.   :162.00  
##  NA's   :84             NA's   :80      NA's   :80      NA's   :80      
##     hf_score        hf_rank        hf_quartile   
##  Min.   :3.766   Min.   :  1.00   Min.   :1.000  
##  1st Qu.:6.337   1st Qu.: 39.00   1st Qu.:1.000  
##  Median :6.924   Median : 76.00   Median :2.000  
##  Mean   :6.993   Mean   : 77.01   Mean   :2.491  
##  3rd Qu.:7.895   3rd Qu.:115.00   3rd Qu.:3.000  
##  Max.   :9.126   Max.   :162.00   Max.   :4.000  
##  NA's   :80      NA's   :80       NA's   :80

Exercise 2

hfi_2016 <- hfi %>%
  filter(year == 2016) %>%
  select(pf_expression_control, pf_identity, pf_score, pf_religion, pf_association_assembly, hf_score)

head(hfi_2016)
## # A tibble: 6 × 6
##   pf_expression_control pf_identity pf_score pf_religion pf_association_assembly
##                   <dbl>       <dbl>    <dbl>       <dbl>                   <dbl>
## 1                  5.25       6.25      7.60        9.19                    10  
## 2                  4          0.833     5.28        4.94                     5  
## 3                  2.5        7.5       6.11        8.79                     2.5
## 4                  5.5       10         8.10        7.80                    10  
## 5                  4.25       8         6.91        6.22                     7.5
## 6                  7.75       9.25      9.18        9.08                    10  
## # ℹ 1 more variable: hf_score <dbl>

Exercise 3

I used a scatter plot, the relationship looks linear. If I knew the pf_expression_control and the score out of 10 then I would be comfortable.

ggplot(hfi_2016, aes(x = pf_expression_control, y = pf_score)) +
  geom_point() +
  geom_smooth(method = "lm", se = FALSE, color = "blue") + 
  labs(title = "Relationship between Personal Freedom Score and Expression Control", x = "Personal Freedom Expression Control (0-10)", y = "Personal Freedom Score")
## `geom_smooth()` using formula = 'y ~ x'

hfi_2016 %>%
  summarise(cor(pf_expression_control, pf_score))
## # A tibble: 1 × 1
##   `cor(pf_expression_control, pf_score)`
##                                    <dbl>
## 1                                  0.845

Exercise 4

The form is linear, the direction is positive, the strength of the relationship is strong with a correlation of 0.845 and there is not a lot of unusual observations.

plot_ss(x = pf_expression_control, y = pf_score, data = hfi_2016)

## Click two points to make a line.                                
## Call:
## lm(formula = y ~ x, data = pts)
## 
## Coefficients:
## (Intercept)            x  
##      4.2838       0.5418  
## 
## Sum of Squares:  102.213

Exercise 5

The smallest sum of squares I got was 102.213

m1 <- lm(pf_score ~ pf_expression_control, data = hfi_2016)
tidy(m1)
## # A tibble: 2 × 5
##   term                  estimate std.error statistic  p.value
##   <chr>                    <dbl>     <dbl>     <dbl>    <dbl>
## 1 (Intercept)              4.28     0.149       28.8 4.23e-65
## 2 pf_expression_control    0.542    0.0271      20.0 2.31e-45
glance(m1)
## # A tibble: 1 × 12
##   r.squared adj.r.squared sigma statistic  p.value    df logLik   AIC   BIC
##       <dbl>         <dbl> <dbl>     <dbl>    <dbl> <dbl>  <dbl> <dbl> <dbl>
## 1     0.714         0.712 0.799      400. 2.31e-45     1  -193.  391.  400.
## # ℹ 3 more variables: deviance <dbl>, df.residual <int>, nobs <int>

Exercise 6

Insert any text here.

ggplot(hfi_2016, aes(x = pf_expression_control, y = pf_score)) +
  geom_point() +
  geom_smooth(method = "lm", se = FALSE)
## `geom_smooth()` using formula = 'y ~ x'

predicted <- predict(m1, newdata = data.frame(pf_expression_control = 3))
actual <- hfi_2016$pf_score[hfi_2016$pf_expression_control == 3]
residual <- actual - predicted

predict(m1, newdata = data.frame(pf_expression_control = 3))
##        1 
## 5.909351
print(actual)
## [1] 5.465632
print(residual)
##          1 
## -0.4437186

Exercise 7

The predicted value is 5.909351 whereas the actual value is 5.465632. This means that it is an overestimate and the residual is -0.4437186.

m1_aug <- augment(m1)

ggplot(m1_aug, aes(x = .fitted, y = .resid)) +
  geom_point() +
  geom_hline(yintercept = 0, linetype = "dashed", color = "red") +
  xlab("Fitted values") +
  ylab("Residuals")

Exercise 8

The residuals appear randomly scattered around 0, with no clear pattern → this supports the assumption of linearity.

ggplot(m1_aug, aes(x = .resid)) +
  geom_histogram(binwidth = 0.25) +
  xlab("Residuals")

Exercise 9

The histogram looks roughly symmetric and bell-shaped, so the nearly normal residuals condition is satisfied.

Exercise 10

If the residuals have a similar spread across all fitted values (no funnel shape), then constant variability holds. From what we saw, this condition is met.

m2 <- lm(pf_score ~ hf_score, data = hfi_2016)
glance(m2)$r.squared
## [1] 0.8978487
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