Indeks Pembangunan Manusia (IPM)

Indeks Pembangunan Manusia atau Human Development Index adalah pengukuran perbandingan dari harapan hidup, melek huruf, pendidikan dan standar hidup. Pada bagian ini, saya akan melakukan pendeteksian autokorelasi terhadap data IPM Provinsi Kalimantan Timur selama 12 tahun terakhir beserta penanganannya (apabila terdapat autokorelasi).

Install Packages

library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(readxl)
library(forecast)
## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo
library(TTR)
library(tseries)
library(lmtest) #uji-Durbin Watson
## Loading required package: zoo
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
library(orcutt) #Cochrane-Orcutt
library(HoRM)#Hildreth Lu
library(ggplot2)

Data

#membuka file data
dataregresi <- read_excel("C:/SEMESTER 5/MPDW/dataregkaltim.xlsx")
knitr::kable(dataregresi,align = "c")
x y
2010 71.31
2011 72.02
2012 72.62
2013 73.21
2014 73.82
2015 74.17
2016 74.59
2017 75.12
2018 75.83
2019 76.61
2020 76.24
2021 76.88

Eksplorasi Data

x <- dataregresi$x
y <- dataregresi$y

#diagram pencar identifikasi model
ggplot(dataregresi, aes(x=x, y=y)) +
  geom_line(lwd=1.2,col="blue") +
  labs(x="Tahun",y="IPM_Kaltim",
       title="Time Series Plot IPM Kaltim",
       subtitle = "Tahun 2010-2021") +
  theme_bw()+
  theme(plot.title = element_text(size = 14L,
                                  face = "bold",
                                  hjust = 0.5),
        plot.subtitle = element_text(size = 11L,
                                     hjust = 0.5))+
  geom_point(size=2) +
  geom_text(aes(label=paste(y, "%")), vjust=-0.8, size=3)

#korelasi x dan y
cor(x,y)
## [1] 0.9913687

Model Regresi Deret Waktu

#model regresi
model <- lm(y~x, data = dataregresi)
summary(model)
## 
## Call:
## lm(formula = y ~ x, data = dataregresi)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.40351 -0.12214  0.00726  0.12866  0.47209 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -944.65719   42.61522  -22.17 7.83e-10 ***
## x              0.50559    0.02114   23.91 3.72e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2528 on 10 degrees of freedom
## Multiple R-squared:  0.9828, Adjusted R-squared:  0.9811 
## F-statistic: 571.8 on 1 and 10 DF,  p-value: 3.719e-10

Deteksi Autokorelasi

Grafik

1. Residual Plot

#sisaan dan fitted value
resi1 <- residuals(model)
fit <- predict(model)

#Diagnostik dengan eksploratif
par(mfrow = c(2,2))

qqnorm(resi1)
qqline(resi1, col = "steelblue", lwd = 2)

plot(fit, resi1, col = "steelblue", pch = 20, xlab = "Sisaan", 
     ylab = "Fitted Values", main = "Sisaan vs Fitted Values")
abline(a = 0, b = 0, lwd = 2)

hist(resi1, col = "steelblue")

plot(seq(1,12,1), resi1, col = "steelblue", pch = 20, 
     xlab = "Sisaan", ylab = "Order", main = "Sisaan vs Order")
lines(seq(1,12,1), resi1, col = "red")
abline(a = 0, b = 0, lwd = 2)

2. ACF dan PACF Plot

#ACF dan PACF identifikasi autokorelasi
par(mfrow = c(2,1))
acf(resi1)
pacf(resi1)

#Berdasarkna Plot ACF dan PACF dapat disimpulkan sisaan Saling Bebas

Uji Statistik

1. Durbin Watson Test

H0: tidak ada autokorelasi

H1: ada autokorelasi

lmtest::dwtest(model, alternative = 'two.sided')
## 
##  Durbin-Watson test
## 
## data:  model
## DW = 1.5684, p-value = 0.2418
## alternative hypothesis: true autocorrelation is not 0

2. Breusch-Godfrey Test

H0: tidak ada autokorelasi

H1: ada autokorelasi

lmtest::bgtest(y ~ x, data=dataregresi, order=1)
## 
##  Breusch-Godfrey test for serial correlation of order up to 1
## 
## data:  y ~ x
## LM test = 0.13912, df = 1, p-value = 0.7092

3. Run’s Test

lawstat::runs.test(resid(model), alternative = 'two.sided')
## 
##  Runs Test - Two sided
## 
## data:  resid(model)
## Standardized Runs Statistic = -1.2111, p-value = 0.2259

Simpulan:

Berdasarkan hasil uji statistik Durbin Watson Test, Breusch-Godfrey Test, dan Run’s Test ketiganya memberikan hasil nilai p-value > 0.05, sehingga Tak Tolak H0 yang berarti belum cukup bukti untuk menyatakan bahwa terdapat autokorelasi pada taraf 5%. Dengan demikian, tidak perlu dilakukan penanganan autokorelasi terhadap data IPM Kalimantan Timur.