Análisis descriptivo de los datos
str(datos)
## Classes 'tbl_df', 'tbl' and 'data.frame': 186 obs. of 31 variables:
## $ Country Name : chr "Afghanistan" "Albania" "Algeria" "Angola" ...
## $ Region : chr "Asia-Pacific" "Europe" "Middle East / North Africa" "Sub-Saharan Africa" ...
## $ World Rank : num 163 65 172 165 156 33 5 30 68 90 ...
## $ Region Rank : num 40 30 14 41 26 19 4 17 15 19 ...
## $ 2017 Score : num 48.9 64.4 46.5 48.5 50.4 ...
## $ Property Rights : num 12.6 54 38.2 36.4 32.4 ...
## $ Judical Effectiveness : num 28.4 28.5 29.6 19.8 39.6 ...
## $ Government Integrity : num 27.5 39.7 31.7 12.8 38.2 ...
## $ Tax Burden : num 91.6 86.9 81.1 87.7 62.6 ...
## $ Gov't Spending : num 79.9 72.5 51 58.6 54.6 ...
## $ Fiscal Health : num 97.3 51.5 19.8 70.7 56.4 ...
## $ Business Freedom : num 54.2 79.3 62.1 58.5 57.3 78.5 89.3 76.9 71.5 68.5 ...
## $ Labor Freedom : num 59.9 50.7 49.5 40.4 46.1 ...
## $ Monetary Freedom : num 69.3 81.4 67 70.6 50.9 ...
## $ Trade Freedom : num 66 87.7 63.3 56.7 66.7 ...
## $ Investment Freedom : num 0 70 35 30 50 80 80 90 55 50 ...
## $ Financial Freedom : num 0 70 30 40 50 70 90 70 50 60 ...
## $ Tariff Rate (%) : num 7 1.1 8.4 11.7 6.6 2.4 1.9 1.5 5.3 19.7 ...
## $ Income Tax Rate (%) : num 20 23 35 17 35 26 45 50 25 0 ...
## $ Corporate Tax Rate (%) : num 20 15 23 30 35 20 30 25 20 0 ...
## $ Tax Burden % of GDP : num 6.5 23.6 11.7 6.5 35.9 23.5 27.5 43 14.2 16.9 ...
## $ Gov't Expenditure % of GDP: num 27.1 30 44.4 28.9 43.9 ...
## $ Population (Millions) : num 32 2.8 39.5 25.1 42.4 3.3 23.9 8.6 9.5 0.4 ...
## $ GDP (Billions, PPP) : num 62.3 32.7 578.7 184.4 972 ...
## $ GDP Growth Rate (%) : num 1.5 2.6 3.7 3 1.2 3 2.5 0.9 1.1 0.5 ...
## $ 5 Year GDP Growth Rate (%): num 5.4 1.9 3.3 4.7 2.7 4.3 2.7 1 2.4 0.9 ...
## $ GDP per Capita (PPP) : num 1947 11301 14504 7344 22554 ...
## $ Unemployment (%) : num 9.6 17.3 10.5 7.6 6.7 16.3 6.3 5.7 4.7 14.4 ...
## $ Inflation (%) : num -1.5 1.9 4.8 10.3 26.5 3.7 1.5 0.8 4 1.9 ...
## $ FDI Inflow (Millions) : num 58 1003 -587 8681 11655 ...
## $ Public Debt (% of GDP) : num 6.8 71.9 8.7 62.3 56.5 46.6 36.8 86.2 36.1 65.7 ...
datos<-datos[complete.cases(datos), ]
datos1 <- subset(datos, select = c("2017 Score","GDP per Capita (PPP)"))
rownames(datos1)<- datos$`Country Name`
colnames(datos1)<- c("Índice de libertad económica","Renta per cápita")
summary(datos1)
## Índice de libertad económica Renta per cápita
## Min. :26.96 Min. : 629.7
## 1st Qu.:53.98 1st Qu.: 4324.4
## Median :61.10 Median : 12134.8
## Mean :61.51 Mean : 19836.9
## 3rd Qu.:68.58 3rd Qu.: 27965.9
## Max. :89.82 Max. :132098.7
par(mfrow = c(1, 2))
hist(datos1$`Renta per cápita`,labels=TRUE, col = "gold", main="",ylab="Frecuencia",
xlab="Renta per cápita",
border="tomato1")
hist(datos1$`Índice de libertad económica`, labels=TRUE,
col = "gold", xlab="Índice de libertad económica",main="",
ylab="Frecuencia",
border="tomato1")
boxplot(datos1$`Renta per cápita`,labels=TRUE, col = "gold", main="",
ylab="Renta per cápita ($)",
border="black")
text(0.82, 132098, "Qatar >-" ,cex = 1)
boxplot(datos1$`Índice de libertad económica`,labels=TRUE,
col = "gold", ylab="Índice de libertad económica (%)",main="",
border="black")
text(0.75, 26.96, "Venezuela >-" ,cex = 1)
par(mfrow = c(1, 1))
basicPlot <- function(){
plot(datos1$`Renta per cápita` ~ datos1$`Índice de libertad económica`,data=datos1, bty="n", lwd=2,
main="", col="#00526D", ylim=c(0,135000),xlim=c(0,100),
xlab="Indice de libertad económica",
ylab="Renta per cápita")
axis(side = 1, col="grey")
axis(side = 1, col="grey")
}
basicPlot()
Análisis cluster
datosz<- scale(datos1)
d <- dist(datosz, method = "euclidean")
fit <- hclust(d, method="ward.D")
plot(fit, cex = .6, xlab = "", ylab = "Distancia entre grupos", sub = "Cluster jerárquico por el método de Ward")
Numgrupos <- 3
library(scales)
library(RColorBrewer)
plot(fit, cex = .6, xlab = "", ylab = "Distancia entre grupos", sub = "Cluster jerárquico por el método de Ward ")
rect.hclust(fit, k = Numgrupos, border = brewer.pal(Numgrupos, "Dark2"))
grupos <- cutree(fit, k = Numgrupos)
datos1$GRUPOward <- factor(grupos)
palette(brewer.pal(Numgrupos, "Dark2"))
plot(datos1$`Renta per cápita` ~ datos1$`Índice de libertad económica`,
xlab="Índice de libertad económica", ylab="GDP",
col = alpha(GRUPOward, 1),data=datos1,
pch = 19,las = 1)
text(datos1, rownames(datos1), pos = 4, cex = .5)
fit2 <- hclust(d, method = "average")
plot(fit2, cex=.6,xlab = "", ylab = "Distancia entre grupos", sub = "Cluster jerárquico por el método average")
rect.hclust(fit2, k = 3, border = brewer.pal(Numgrupos, "Dark2"))
datos1$GRUPOaverage <- factor(cutree(fit2, 3))
colnames(datos1)<- c("Índice de libertad económica","Renta per cápita","GRUPOward","GRUPOaverage")
plot(datos1$`Renta per cápita` ~ datos1$`Índice de libertad económica`,
xlab="Índice de libertad económica", ylab="GDP",
col = alpha(GRUPOaverage, 1),data=datos1,
pch = 19,las = 1)
text(datos1, rownames(datos1), pos = 4, cex = .5)
fit3 <- hclust(d, method="complete")
plot(fit3, cex = .6, xlab = "", ylab = "Distancia entre grupos", sub = "Cluster jerárquico por el método complete")
rect.hclust(fit, k = 3, border = c("red","gold","green"))
grupos <- cutree(fit3, k = 3)
datos1$GRUPOcomplete <- factor(grupos)
colnames(datos1)<- c("Índice de libertad económica","Renta per cápita","GRUPOward","GRUPOaverage","GRUPOcomplete")
plot(datos1$`Renta per cápita` ~ datos1$`Índice de libertad económica`,
xlab="Índice de libertad económica", ylab="GDP",
col = alpha(GRUPOcomplete, 1),data=datos1,
pch = 19,las = 1)
text(datos1, rownames(datos1), pos = 4, cex = .5)
palette(brewer.pal(Numgrupos, "Dark2"))
Data.km <- kmeans(datos1, Numgrupos)
datos1 <- data.frame(datos1, GRUPO = factor(Data.km$cluster))
colnames(datos1)<- c("Índice de libertad económica","Renta per cápita","GRUPOward","GRUPOaverage","GRUPOcomplete","GRUPOkmeans")
plot(datos1$`Renta per cápita`~ datos1$`Índice de libertad económica`,
xlab="Índice de libertad económica", ylab="GDP",
col = alpha(GRUPOkmeans, 1),data=datos1,
pch = 19,las = 1)
text(datos1, rownames(datos1), pos = 4, cex = .5)
points(Data.km$centers,col = 1:Numgrupos, pch = 15, cex = 3)
Análisis de la varianza
modelo.aov <- aov(datos1$`Renta per cápita`~ GRUPOward, data = datos1)
summary(modelo.aov)
## Df Sum Sq Mean Sq F value Pr(>F)
## GRUPOward 2 3.909e+10 1.955e+10 80.49 <2e-16 ***
## Residuals 169 4.104e+10 2.428e+08
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
par(mfrow = c(1, 2))
boxplot(datos1$`Renta per cápita` ~ GRUPOward, main = "Boxplot GDP", col = 1:3, data = datos1, las = 1)
boxplot(datos1$`Índice de libertad económica` ~ GRUPOward, main = "Boxplot de libertad economica", col = 1:3, data = datos1, las = 1)
TukeyHSD(modelo.aov)
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = datos1$`Renta per cápita` ~ GRUPOward, data = datos1)
##
## $GRUPOward
## diff lwr upr p adj
## 2-1 1479.959 -5715.365 8675.282 0.8778828
## 3-1 31914.132 24814.626 39013.639 0.0000000
## 3-2 30434.174 23865.678 37002.670 0.0000000
modelo.aov2 <- aov(datos1$`Renta per cápita` ~ GRUPOaverage, data = datos1)
summary(modelo.aov2)
## Df Sum Sq Mean Sq F value Pr(>F)
## GRUPOaverage 2 3.461e+10 1.730e+10 64.24 <2e-16 ***
## Residuals 169 4.552e+10 2.694e+08
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
boxplot(datos1$`Renta per cápita` ~ GRUPOaverage, main = "Boxplot GDP", col = 1:3, data = datos1, las = 1)
boxplot(datos1$`Índice de libertad económica` ~ GRUPOaverage, main = "Boxplot de libertad economica", col = 1:3, data = datos1, las = 1)
TukeyHSD(modelo.aov2)
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = datos1$`Renta per cápita` ~ GRUPOaverage, data = datos1)
##
## $GRUPOaverage
## diff lwr upr p adj
## 2-1 71787.2851 56809.22 86765.35 0.0000000
## 3-1 -244.0006 -39170.81 38682.81 0.9998789
## 3-2 -72031.2857 -113519.50 -30543.08 0.0001847
modelo.aov3 <- aov(datos1$`Renta per cápita` ~ GRUPOcomplete, data = datos1)
summary(modelo.aov3)
## Df Sum Sq Mean Sq F value Pr(>F)
## GRUPOcomplete 2 3.994e+10 1.997e+10 83.98 <2e-16 ***
## Residuals 169 4.019e+10 2.378e+08
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
boxplot(datos1$`Renta per cápita` ~ GRUPOcomplete, main = "Boxplot GDP", col = 1:3, data = datos1, las = 1)
boxplot(datos1$`Índice de libertad económica` ~ GRUPOcomplete, main = "Boxplot de libertad economica", col = 1:3, data = datos1, las = 1)
TukeyHSD(modelo.aov3)
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = datos1$`Renta per cápita` ~ GRUPOcomplete, data = datos1)
##
## $GRUPOcomplete
## diff lwr upr p adj
## 2-1 17170.02 11252.90 23087.13 0
## 3-1 97018.74 78168.48 115869.00 0
## 3-2 79848.73 61288.14 98409.31 0
modelo.aov4 <- aov(datos1$`Índice de libertad económica` ~ GRUPOcomplete, data = datos1)
summary(modelo.aov4)
## Df Sum Sq Mean Sq F value Pr(>F)
## GRUPOcomplete 2 10150 5075 122.7 <2e-16 ***
## Residuals 169 6988 41
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
TukeyHSD(modelo.aov4)
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = datos1$`Índice de libertad económica` ~ GRUPOcomplete, data = datos1)
##
## $GRUPOcomplete
## diff lwr upr p adj
## 2-1 15.52866 13.061396 17.99592 0.0000000
## 3-1 26.10530 18.245286 33.96531 0.0000000
## 3-2 10.57664 2.837413 18.31586 0.0042063
modelo.aov5 <- aov(datos1$`Renta per cápita` ~ GRUPOkmeans, data = datos1)
summary(modelo.aov5)
## Df Sum Sq Mean Sq F value Pr(>F)
## GRUPOkmeans 2 6.752e+10 3.376e+10 452.6 <2e-16 ***
## Residuals 169 1.261e+10 7.460e+07
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
modelo.aov6 <- aov(datos1$`Índice de libertad económica` ~ GRUPOkmeans, data = datos1)
summary(modelo.aov6)
## Df Sum Sq Mean Sq F value Pr(>F)
## GRUPOkmeans 2 6880 3440 56.68 <2e-16 ***
## Residuals 169 10257 61
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
pirateplot(datos1$`Renta per cápita` ~ GRUPOkmeans,
hdi.o = 1, ylab="GDP",
point.o = 1,
point.pch = 1,
main = "Boxplot GDP", data = datos1)
pirateplot(datos1$`Índice de libertad económica` ~ GRUPOkmeans,
hdi.o = 1, ylab="GDP",point.o = 1,point.pch = 1,
main = "Boxplot ILE", data = datos1)
TukeyHSD(modelo.aov5)
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = datos1$`Renta per cápita` ~ GRUPOkmeans, data = datos1)
##
## $GRUPOkmeans
## diff lwr upr p adj
## 2-1 -49348.28 -57184.49 -41512.07 0
## 3-1 -79187.25 -86646.64 -71727.87 0
## 3-2 -29838.98 -33413.04 -26264.92 0
TukeyHSD(modelo.aov6)
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = datos1$`Índice de libertad económica` ~ GRUPOkmeans, data = datos1)
##
## $GRUPOkmeans
## diff lwr upr p adj
## 2-1 -3.941705 -11.00987 3.126460 0.3868
## 3-1 -16.939359 -23.66763 -10.211090 0.0000
## 3-2 -12.997655 -16.22141 -9.773898 0.0000
Comparación de grupos significativos
kable(tablaILE)
| Min. :26.96 |
Min. :55.00 |
Min. :70.67 |
| 1st Qu.:48.92 |
1st Qu.:61.09 |
1st Qu.:72.50 |
| Median :52.35 |
Median :65.18 |
Median :74.52 |
| Mean :50.97 |
Mean :66.50 |
Mean :77.07 |
| 3rd Qu.:53.98 |
3rd Qu.:70.63 |
3rd Qu.:79.10 |
| Max. :56.41 |
Max. :89.82 |
Max. :88.58 |
kable(tablaGDP)
| Min. : 629.7 |
Min. : 1462 |
Min. : 85253 |
| 1st Qu.: 1762.8 |
1st Qu.: 8528 |
1st Qu.: 94915 |
| Median : 3737.3 |
Median :18868 |
Median : 98561 |
| Mean : 6599.8 |
Mean :23770 |
Mean :103619 |
| 3rd Qu.:10440.4 |
3rd Qu.:35931 |
3rd Qu.:107265 |
| Max. :31757.7 |
Max. :79587 |
Max. :132099 |
levels(datos1$GRUPOcomplete)<- c("Bajo","Medio","Alto")
divisionILE<- cut(x = datos1$`Índice de libertad económica`,
breaks = seq(20, 100, by = 26),
labels = c("Economia intervencionista","Economia mixta","Economia de mercado"),
include.lowest = TRUE)
datosgrafico<- data.frame(divisionILE,datos1$`Renta per cápita`,datos1$GRUPOcomplete)
colnames(datosgrafico)<-c("Indice_libertad_economica","Renta_per_capita", "Cluster_por_el_metodo_complete")
table(divisionILE)
## divisionILE
## Economia intervencionista Economia mixta
## 5 137
## Economia de mercado
## 30
ggplot(datosgrafico, aes(Indice_libertad_economica ,Renta_per_capita, col=Cluster_por_el_metodo_complete)) + geom_point()
Regresiones
par(mfrow = c(1, 1))
lsq.mod <- lm(datos1$`Renta per cápita`~ datos1$`Índice de libertad económica`)
summary(lsq.mod)
##
## Call:
## lm(formula = datos1$`Renta per cápita` ~ datos1$`Índice de libertad económica`)
##
## Residuals:
## Min 1Q Median 3Q Max
## -30023 -10326 -3879 6685 96390
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -64344.3 8000.6 -8.042 1.44e-13
## datos1$`Índice de libertad económica` 1368.7 128.4 10.660 < 2e-16
##
## (Intercept) ***
## datos1$`Índice de libertad económica` ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 16810 on 170 degrees of freedom
## Multiple R-squared: 0.4006, Adjusted R-squared: 0.3971
## F-statistic: 113.6 on 1 and 170 DF, p-value: < 2.2e-16
basicPlot()
abline(lsq.mod, col="orange", lwd=3)
legend(x="topleft", bty="n", lwd=c(2,2), lty=c(NA,1),
legend=c("Paises", "Recta de regresión lineal"),
col=c("#00526D","orange"), pch=c(1,NA))
text(32.5, 90000, expression(R^2 ==0.4), cex = 1)
re <- lm(datos1$`Renta per cápita`~ poly(datos1$`Índice de libertad económica`,2))
summary(re)
##
## Call:
## lm(formula = datos1$`Renta per cápita` ~ poly(datos1$`Índice de libertad económica`,
## 2))
##
## Residuals:
## Min 1Q Median 3Q Max
## -33337 -8191 -3598 6099 95645
##
## Coefficients:
## Estimate Std. Error
## (Intercept) 19837 1221
## poly(datos1$`Índice de libertad económica`, 2)1 179172 16011
## poly(datos1$`Índice de libertad económica`, 2)2 68599 16011
## t value Pr(>|t|)
## (Intercept) 16.249 < 2e-16 ***
## poly(datos1$`Índice de libertad económica`, 2)1 11.190 < 2e-16 ***
## poly(datos1$`Índice de libertad económica`, 2)2 4.284 3.07e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 16010 on 169 degrees of freedom
## Multiple R-squared: 0.4593, Adjusted R-squared: 0.4529
## F-statistic: 71.79 on 2 and 169 DF, p-value: < 2.2e-16
basicPlot()
legend(x="topleft", bty="n", lwd=c(2,2), lty=c(NA,1),
legend=c("Paises", "Modelo polinomico^2"),
col=c("#00526D","orange"), pch=c(1,NA))
lines(sort(datos1$`Índice de libertad económica`), fitted(re)[order(datos1$`Índice de libertad económica`)], col='orange', type='l',lwd=3)
text(32.5, 90000, expression(R^2 ==0.45), cex = 1)
re2 <- lm(log(datos1$`Renta per cápita`)~ datos1$`Índice de libertad económica`)
summary(re2)
##
## Call:
## lm(formula = log(datos1$`Renta per cápita`) ~ datos1$`Índice de libertad económica`)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.24894 -0.56726 0.01879 0.63949 3.15734
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 4.449063 0.447960 9.932 <2e-16
## datos1$`Índice de libertad económica` 0.078450 0.007189 10.912 <2e-16
##
## (Intercept) ***
## datos1$`Índice de libertad económica` ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9411 on 170 degrees of freedom
## Multiple R-squared: 0.4119, Adjusted R-squared: 0.4085
## F-statistic: 119.1 on 1 and 170 DF, p-value: < 2.2e-16
basicPlot()
legend(x="topleft", bty="n", lwd=c(2,2), lty=c(NA,1),
legend=c("Paises", "Modelo exponencial"),
col=c("#00526D","orange"), pch=c(1,NA))
lines(sort(datos1$`Índice de libertad económica`),exp(fitted(re2))[order(datos1$`Índice de libertad económica`)], col='orange', type='l',lwd=3)
basicPlot()
abline(lsq.mod, col="green", lwd=3)
lines(sort(datos1$`Índice de libertad económica`), fitted(re)[order(datos1$`Índice de libertad económica`)], col='orange', type='l',lwd=3)
lines(sort(datos1$`Índice de libertad económica`),exp(fitted(re2))[order(datos1$`Índice de libertad económica`)], col='steelblue', type='l',lwd=3)
legend(x="topleft", bty="n", lwd=c(2,2), lty=c(NA,1,1,1),
legend=c("Paises", "Modelo lineal","Modelo polinomico ^2","Modelo exponencial"),
col=c("#00526D","green","orange","steelblue"), pch=c(1,NA,NA,NA))
