Simple Linear Regression

## Rows: 1,458
## Columns: 123
## $ year                               <dbl> 2016, 2016, 2016, 2016, 2016, 20...
## $ ISO_code                           <chr> "ALB", "DZA", "AGO", "ARG", "ARM...
## $ countries                          <chr> "Albania", "Algeria", "Angola", ...
## $ region                             <chr> "Eastern Europe", "Middle East &...
## $ pf_rol_procedural                  <dbl> 6.661503, NA, NA, 7.098483, NA, ...
## $ pf_rol_civil                       <dbl> 4.547244, NA, NA, 5.791960, NA, ...
## $ pf_rol_criminal                    <dbl> 4.666508, NA, NA, 4.343930, NA, ...
## $ pf_rol                             <dbl> 5.291752, 3.819566, 3.451814, 5....
## $ pf_ss_homicide                     <dbl> 8.920429, 9.456254, 8.060260, 7....
## $ pf_ss_disappearances_disap         <dbl> 10, 10, 5, 10, 10, 10, 10, 10, 1...
## $ pf_ss_disappearances_violent       <dbl> 10.000000, 9.294030, 10.000000, ...
## $ pf_ss_disappearances_organized     <dbl> 10.0, 5.0, 7.5, 7.5, 7.5, 10.0, ...
## $ pf_ss_disappearances_fatalities    <dbl> 10.000000, 9.926119, 10.000000, ...
## $ pf_ss_disappearances_injuries      <dbl> 10.000000, 9.990149, 10.000000, ...
## $ pf_ss_disappearances               <dbl> 10.000000, 8.842060, 8.500000, 9...
## $ pf_ss_women_fgm                    <dbl> 10.0, 10.0, 10.0, 10.0, 10.0, 10...
## $ pf_ss_women_missing                <dbl> 7.5, 7.5, 10.0, 10.0, 5.0, 10.0,...
## $ pf_ss_women_inheritance_widows     <dbl> 5, 0, 5, 10, 10, 10, 10, 5, NA, ...
## $ pf_ss_women_inheritance_daughters  <dbl> 5, 0, 5, 10, 10, 10, 10, 10, NA,...
## $ pf_ss_women_inheritance            <dbl> 5.0, 0.0, 5.0, 10.0, 10.0, 10.0,...
## $ pf_ss_women                        <dbl> 7.500000, 5.833333, 8.333333, 10...
## $ pf_ss                              <dbl> 8.806810, 8.043882, 8.297865, 9....
## $ pf_movement_domestic               <dbl> 5, 5, 0, 10, 5, 10, 10, 5, 10, 1...
## $ pf_movement_foreign                <dbl> 10, 5, 5, 10, 5, 10, 10, 5, 10, ...
## $ pf_movement_women                  <dbl> 5, 5, 10, 10, 10, 10, 10, 5, NA,...
## $ pf_movement                        <dbl> 6.666667, 5.000000, 5.000000, 10...
## $ pf_religion_estop_establish        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ pf_religion_estop_operate          <dbl> NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ pf_religion_estop                  <dbl> 10.0, 5.0, 10.0, 7.5, 5.0, 10.0,...
## $ pf_religion_harassment             <dbl> 9.566667, 6.873333, 8.904444, 9....
## $ pf_religion_restrictions           <dbl> 8.011111, 2.961111, 7.455556, 6....
## $ pf_religion                        <dbl> 9.192593, 4.944815, 8.786667, 7....
## $ pf_association_association         <dbl> 10.0, 5.0, 2.5, 7.5, 7.5, 10.0, ...
## $ pf_association_assembly            <dbl> 10.0, 5.0, 2.5, 10.0, 7.5, 10.0,...
## $ pf_association_political_establish <dbl> NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ pf_association_political_operate   <dbl> NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ pf_association_political           <dbl> 10.0, 5.0, 2.5, 5.0, 5.0, 10.0, ...
## $ pf_association_prof_establish      <dbl> NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ pf_association_prof_operate        <dbl> NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ pf_association_prof                <dbl> 10.0, 5.0, 5.0, 7.5, 5.0, 10.0, ...
## $ pf_association_sport_establish     <dbl> NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ pf_association_sport_operate       <dbl> NA, NA, NA, NA, NA, NA, NA, NA, ...
## $ pf_association_sport               <dbl> 10.0, 5.0, 7.5, 7.5, 7.5, 10.0, ...
## $ pf_association                     <dbl> 10.0, 5.0, 4.0, 7.5, 6.5, 10.0, ...
## $ pf_expression_killed               <dbl> 10.000000, 10.000000, 10.000000,...
## $ pf_expression_jailed               <dbl> 10.000000, 10.000000, 10.000000,...
## $ pf_expression_influence            <dbl> 5.0000000, 2.6666667, 2.6666667,...
## $ pf_expression_control              <dbl> 5.25, 4.00, 2.50, 5.50, 4.25, 7....
## $ pf_expression_cable                <dbl> 10.0, 10.0, 7.5, 10.0, 7.5, 10.0...
## $ pf_expression_newspapers           <dbl> 10.0, 7.5, 5.0, 10.0, 7.5, 10.0,...
## $ pf_expression_internet             <dbl> 10.0, 7.5, 7.5, 10.0, 7.5, 10.0,...
## $ pf_expression                      <dbl> 8.607143, 7.380952, 6.452381, 8....
## $ pf_identity_legal                  <dbl> 0, NA, 10, 10, 7, 7, 10, 0, NA, ...
## $ pf_identity_parental_marriage      <dbl> 10, 0, 10, 10, 10, 10, 10, 10, 1...
## $ pf_identity_parental_divorce       <dbl> 10, 5, 10, 10, 10, 10, 10, 10, 1...
## $ pf_identity_parental               <dbl> 10.0, 2.5, 10.0, 10.0, 10.0, 10....
## $ pf_identity_sex_male               <dbl> 10, 0, 0, 10, 10, 10, 10, 10, 10...
## $ pf_identity_sex_female             <dbl> 10, 0, 0, 10, 10, 10, 10, 10, 10...
## $ pf_identity_sex                    <dbl> 10, 0, 0, 10, 10, 10, 10, 10, 10...
## $ pf_identity_divorce                <dbl> 5, 0, 10, 10, 5, 10, 10, 5, NA, ...
## $ pf_identity                        <dbl> 6.2500000, 0.8333333, 7.5000000,...
## $ pf_score                           <dbl> 7.596281, 5.281772, 6.111324, 8....
## $ pf_rank                            <dbl> 57, 147, 117, 42, 84, 11, 8, 131...
## $ ef_government_consumption          <dbl> 8.232353, 2.150000, 7.600000, 5....
## $ ef_government_transfers            <dbl> 7.509902, 7.817129, 8.886739, 6....
## $ ef_government_enterprises          <dbl> 8, 0, 0, 6, 8, 10, 10, 0, 7, 10,...
## $ ef_government_tax_income           <dbl> 9, 7, 10, 7, 5, 5, 4, 9, 10, 10,...
## $ ef_government_tax_payroll          <dbl> 7, 2, 9, 1, 5, 5, 3, 4, 10, 10, ...
## $ ef_government_tax                  <dbl> 8.0, 4.5, 9.5, 4.0, 5.0, 5.0, 3....
## $ ef_government                      <dbl> 7.935564, 3.616782, 6.496685, 5....
## $ ef_legal_judicial                  <dbl> 2.6682218, 4.1867042, 1.8431292,...
## $ ef_legal_courts                    <dbl> 3.145462, 4.327113, 1.974566, 2....
## $ ef_legal_protection                <dbl> 4.512228, 4.689952, 2.512364, 4....
## $ ef_legal_military                  <dbl> 8.333333, 4.166667, 3.333333, 7....
## $ ef_legal_integrity                 <dbl> 4.166667, 5.000000, 4.166667, 3....
## $ ef_legal_enforcement               <dbl> 4.3874441, 4.5075380, 2.3022004,...
## $ ef_legal_restrictions              <dbl> 6.485287, 6.626692, 5.455882, 6....
## $ ef_legal_police                    <dbl> 6.933500, 6.136845, 3.016104, 3....
## $ ef_legal_crime                     <dbl> 6.215401, 6.737383, 4.291197, 4....
## $ ef_legal_gender                    <dbl> 0.9487179, 0.8205128, 0.8461538,...
## $ ef_legal                           <dbl> 5.071814, 4.690743, 2.963635, 3....
## $ ef_money_growth                    <dbl> 8.986454, 6.955962, 9.385679, 5....
## $ ef_money_sd                        <dbl> 9.484575, 8.339152, 4.986742, 5....
## $ ef_money_inflation                 <dbl> 9.743600, 8.720460, 3.054000, 2....
## $ ef_money_currency                  <dbl> 10, 5, 5, 10, 10, 10, 10, 5, 0, ...
## $ ef_money                           <dbl> 9.553657, 7.253894, 5.606605, 5....
## $ ef_trade_tariffs_revenue           <dbl> 9.626667, 8.480000, 8.993333, 6....
## $ ef_trade_tariffs_mean              <dbl> 9.24, 6.22, 7.72, 7.26, 8.76, 9....
## $ ef_trade_tariffs_sd                <dbl> 8.0240, 5.9176, 4.2544, 5.9448, ...
## $ ef_trade_tariffs                   <dbl> 8.963556, 6.872533, 6.989244, 6....
## $ ef_trade_regulatory_nontariff      <dbl> 5.574481, 4.962589, 3.132738, 4....
## $ ef_trade_regulatory_compliance     <dbl> 9.4053278, 0.0000000, 0.9171598,...
## $ ef_trade_regulatory                <dbl> 7.489905, 2.481294, 2.024949, 4....
## $ ef_trade_black                     <dbl> 10.00000, 5.56391, 10.00000, 0.0...
## $ ef_trade_movement_foreign          <dbl> 6.306106, 3.664829, 2.946919, 5....
## $ ef_trade_movement_capital          <dbl> 4.6153846, 0.0000000, 3.0769231,...
## $ ef_trade_movement_visit            <dbl> 8.2969231, 1.1062564, 0.1106256,...
## $ ef_trade_movement                  <dbl> 6.406138, 1.590362, 2.044823, 4....
## $ ef_trade                           <dbl> 8.214900, 4.127025, 5.264754, 3....
## $ ef_regulation_credit_ownership     <dbl> 5, 0, 8, 5, 10, 10, 8, 5, 10, 10...
## $ ef_regulation_credit_private       <dbl> 7.295687, 5.301526, 9.194715, 4....
## $ ef_regulation_credit_interest      <dbl> 9, 10, 4, 7, 10, 10, 10, 9, 10, ...
## $ ef_regulation_credit               <dbl> 7.098562, 5.100509, 7.064905, 5....
## $ ef_regulation_labor_minwage        <dbl> 5.566667, 5.566667, 8.900000, 2....
## $ ef_regulation_labor_firing         <dbl> 5.396399, 3.896912, 2.656198, 2....
## $ ef_regulation_labor_bargain        <dbl> 6.234861, 5.958321, 5.172987, 3....
## $ ef_regulation_labor_hours          <dbl> 8, 6, 4, 10, 10, 10, 6, 6, 8, 8,...
## $ ef_regulation_labor_dismissal      <dbl> 6.299741, 7.755176, 6.632764, 2....
## $ ef_regulation_labor_conscription   <dbl> 10, 1, 0, 10, 0, 10, 3, 1, 10, 1...
## $ ef_regulation_labor                <dbl> 6.916278, 5.029513, 4.560325, 5....
## $ ef_regulation_business_adm         <dbl> 6.072172, 3.722341, 2.758428, 2....
## $ ef_regulation_business_bureaucracy <dbl> 6.000000, 1.777778, 1.333333, 6....
## $ ef_regulation_business_start       <dbl> 9.713864, 9.243070, 8.664627, 9....
## $ ef_regulation_business_bribes      <dbl> 4.050196, 3.765515, 1.945540, 3....
## $ ef_regulation_business_licensing   <dbl> 7.324582, 8.523503, 8.096776, 5....
## $ ef_regulation_business_compliance  <dbl> 7.074366, 7.029528, 6.782923, 6....
## $ ef_regulation_business             <dbl> 6.705863, 5.676956, 4.930271, 5....
## $ ef_regulation                      <dbl> 6.906901, 5.268992, 5.518500, 5....
## $ ef_score                           <dbl> 7.54, 4.99, 5.17, 4.84, 7.57, 7....
## $ ef_rank                            <dbl> 34, 159, 155, 160, 29, 10, 27, 1...
## $ hf_score                           <dbl> 7.568140, 5.135886, 5.640662, 6....
## $ hf_rank                            <dbl> 48, 155, 142, 107, 57, 4, 16, 13...
## $ hf_quartile                        <dbl> 2, 4, 4, 3, 2, 1, 1, 4, 2, 2, 4,...

Actually, let’s see a fitted .

## `geom_smooth()` using formula 'y ~ x'
## Warning: Removed 80 rows containing non-finite values (stat_smooth).
## Warning: Removed 80 rows containing missing values (geom_point).

## 
## Call:
## lm(formula = pf_score ~ pf_expression_control, data = hfi)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.8467 -0.5704  0.1452  0.6066  3.2060 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)            4.61707    0.05745   80.36   <2e-16 ***
## pf_expression_control  0.49143    0.01006   48.85   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8318 on 1376 degrees of freedom
##   (80 observations deleted due to missingness)
## Multiple R-squared:  0.6342, Adjusted R-squared:  0.634 
## F-statistic:  2386 on 1 and 1376 DF,  p-value: < 2.2e-16
## 
## The equation of the regression line y^ = 4.61707 + 0.49143×pf_expression_control, b or y-intercept = 4.61707, slope or a-coeficient = 0.49143
## The following function calls produce the residuals plot for our model.

## 
## The Q-Q plot provides a nice visual indication of whether the residuals from the model are normally distributed.