Including Plots

##  Overall poverty Persistent poverty Total population (000s)
##  Min.   : 9.60   Min.   : 2.900     Min.   :  330823       
##  1st Qu.:13.82   1st Qu.: 7.375     1st Qu.: 2073586       
##  Median :16.30   Median : 9.950     Median : 5659715       
##  Mean   :16.76   Mean   :10.294     Mean   :16395592       
##  3rd Qu.:20.35   3rd Qu.:13.150     3rd Qu.:14054856       
##  Max.   :25.40   Max.   :19.300     Max.   :81197537       
##                                     NA's   :1

Análise de Correlação

Variável Persistent poverty x Overall poverty

## 
##  Pearson's product-moment correlation
## 
## data:  Persistent poverty and Overall poverty
## t = 10.319, df = 30, p-value = 2.191e-11
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  0.7725237 0.9418821
## sample estimates:
##       cor 
## 0.8832837

Variável Overall poverty x Total population (000s)

## 
##  Pearson's product-moment correlation
## 
## data:  Overall poverty and Total population (000s)
## t = 0.38284, df = 29, p-value = 0.7046
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.2907321  0.4148299
## sample estimates:
##        cor 
## 0.07091338

Variável Persistent poverty x Total population (000s)

## 
##  Pearson's product-moment correlation
## 
## data:  Persistent poverty and Total population (000s)
## t = 0.58897, df = 29, p-value = 0.5604
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.2554602  0.4458840
## sample estimates:
##       cor 
## 0.1087213

Modelo de Regressão Beta

## 
## Call:
## betareg(formula = `Persistent poverty` ~ `Overall poverty` + `Total population (000s)`, 
##     data = tabela1_tran)
## 
## Standardized weighted residuals 2:
##     Min      1Q  Median      3Q     Max 
## -2.5996 -0.6237  0.2707  0.6812  1.7994 
## 
## Coefficients (mean model with logit link):
##                             Estimate Std. Error z value Pr(>|z|)    
## (Intercept)               -3.705e+00  1.674e-01 -22.132   <2e-16 ***
## `Overall poverty`          8.717e+00  8.973e-01   9.715   <2e-16 ***
## `Total population (000s)`  1.503e-09  1.617e-09   0.929    0.353    
## 
## Phi coefficients (precision model with identity link):
##       Estimate Std. Error z value Pr(>|z|)    
## (phi)   251.27      63.87   3.934 8.35e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
## 
## Type of estimator: ML (maximum likelihood)
## Log-likelihood: 79.97 on 4 Df
## Pseudo R-squared: 0.7436
## Number of iterations: 222 (BFGS) + 5 (Fisher scoring)

Análise dos Resíduos

Normalidade dos Resíduos

shapiro.test(modelo_beta$residuals)
## 
##  Shapiro-Wilk normality test
## 
## data:  modelo_beta$residuals
## W = 0.97688, p-value = 0.7217

\(H_0:\) normal

\(H_1:\) nao normal

p-valor = 0.72, nao rejeito \(H_0\), ou seja os residuos sao normais.