input data excel

indikator_IPM <-read_excel(path="D:/data_komlan.xlsx",col_names=TRUE)
indikator_IPM
## # A tibble: 38 × 6
##    Provinsi               UHH   HLS   RLS Pengeluaran   IPM
##    <chr>                <dbl> <dbl> <dbl>       <dbl> <dbl>
##  1 Aceh                  73.5  14.4  9.95       11191  76.2
##  2 Sumatera Utara        74.2  13.5 10.1        11898  76.5
##  3 Sumatera Barat        74.7  14.3  9.77       12041  77.3
##  4 Riau                  74.7  13.4  9.55       12233  76.3
##  5 Jambi                 74.4  13.3  8.95       12018  75.1
##  6 Sumatera Selatan      74.6  12.6  8.91       12416  74.8
##  7 Bengkulu              73.6  13.8  9.23       12197  75.7
##  8 Lampung               74.7  12.8  8.61       11683  74.0
##  9 Kep. Bangka Belitung  74.5  12.5  8.65       13837  75.3
## 10 Kep. Riau             75.5  13.3 10.7        15881  80.5
## # ℹ 28 more rows

deskripsi data

summary(indikator_IPM)
##    Provinsi              UHH             HLS             RLS        
##  Length:38          Min.   :67.55   Min.   : 9.64   Min.   : 4.300  
##  Class :character   1st Qu.:71.45   1st Qu.:12.99   1st Qu.: 8.445  
##  Mode  :character   Median :74.17   Median :13.34   Median : 9.050  
##                     Mean   :73.18   Mean   :13.26   Mean   : 9.029  
##                     3rd Qu.:74.73   3rd Qu.:13.76   3rd Qu.: 9.765  
##                     Max.   :76.27   Max.   :15.78   Max.   :11.590  
##   Pengeluaran         IPM       
##  Min.   : 5861   Min.   :54.91  
##  1st Qu.:10598   1st Qu.:72.67  
##  Median :11978   Median :74.81  
##  Mean   :11962   Mean   :74.25  
##  3rd Qu.:12766   3rd Qu.:76.29  
##  Max.   :20676   Max.   :85.05

Rata-rata IPM adalah 74.25

plot

Matrix Plot Hubungan Variabel

Matrix Plot Hubungan Variabel

model regresi

Bentuk persamaan yang digunakan adalah: \[ IPM = \beta_0 + \beta_1 UHH + \beta_2 HLS + \beta_3 RLS + \beta_4 Pengeluaran + \epsilon \] ## estimasi parameter

model = lm(IPM ~ UHH + HLS + RLS + Pengeluaran, data = indikator_IPM)
summary(model)
## 
## Call:
## lm(formula = IPM ~ UHH + HLS + RLS + Pengeluaran, data = indikator_IPM)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.42545 -0.17094  0.09716  0.23276  0.68412 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -7.023e+00  3.350e+00  -2.096   0.0438 *  
## UHH          6.182e-01  5.194e-02  11.902 1.75e-13 ***
## HLS          1.182e+00  1.132e-01  10.440 5.45e-12 ***
## RLS          1.366e+00  1.130e-01  12.086 1.15e-13 ***
## Pengeluaran  6.708e-04  5.323e-05  12.601 3.69e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4358 on 33 degrees of freedom
## Multiple R-squared:  0.9937, Adjusted R-squared:  0.993 
## F-statistic:  1307 on 4 and 33 DF,  p-value: < 2.2e-16

Model Akhir: \[ IPM = -7.0225 + 0.6182 UHH + 1.1815 HLS + 1.3662 RLS + 7\times 10^{-4} Pengeluaran \]

Pengujian Hipotesis

Uji Normalitas Residual

error = model$residuals
ks.test(error,"pnorm",mean(error),sqrt(var(error)))
## 
##  Exact one-sample Kolmogorov-Smirnov test
## 
## data:  error
## D = 0.15349, p-value = 0.3006
## alternative hypothesis: two-sided

Uji Autokorelasi

dwtest(model)
## 
##  Durbin-Watson test
## 
## data:  model
## DW = 1.6362, p-value = 0.06968
## alternative hypothesis: true autocorrelation is greater than 0

Plot Model Regresi

Scatter plot dari setiap variabel independen (X) terhadap IPM (Y) dan garis regresinya.

Scatterplot Variabel X vs IPM

Scatterplot Variabel X vs IPM