2  Basic Linear Regression

2.1 EDA

library(readxl)
data1 <- read_excel("Data/Bab 2/data1.xlsx")
head(data1)

# A tibble: 6 × 11
  Time                `Outstanding KPR (miliar)` LnKPR `PDB Nominal` LnPDB
  <dttm>                                   <dbl> <dbl>         <dbl> <dbl>
1 2014-10-01 00:00:00                     38047.  10.5       723518.  13.5
2 2014-11-01 00:00:00                     38526.  10.6       719996.  13.5
3 2014-12-01 00:00:00                     39221.  10.6       718040.  13.5
4 2015-01-01 00:00:00                     39023.  10.6       715580.  13.5
5 2015-02-01 00:00:00                     39756.  10.6       718307.  13.5
6 2015-03-01 00:00:00                     39954.  10.6       724152.  13.5
# ℹ 6 more variables: `Growth PDB YtY` <dbl>, Inflasi <dbl>, CreditRate <dbl>,
#   JII <dbl>, LnJII <dbl>, DFTV <dbl>

names(data1)[2] <- "Outstanding KPR"
names(data1)[7] <- "Inflasi"
names(data1)[8] <- "CreditRate"

data1baru = data1[,c(2,4,7,8,9)]
tsData = ts(data1baru, start=c(2014,10), frequency=12)
head(tsData,5)

     Outstanding KPR PDB Nominal Inflasi CreditRate    JII
[1,]        38047.46    723517.8    1.04       7.50 670.44
[2,]        38525.78    719995.7    0.49       7.75 683.02
[3,]        39220.50    718039.5    1.45       7.75 691.04
[4,]        39022.75    715580.1    0.80       7.75 706.68
[5,]        39755.80    718307.4    0.41       7.50 722.10

# Exploration
plot(tsData, type="l", main="Plot Data", xlab="Waktu")

# correlation
round(cor(tsData),3)

                Outstanding KPR PDB Nominal Inflasi CreditRate    JII
Outstanding KPR           1.000       0.968  -0.267     -0.548  0.218
PDB Nominal               0.968       1.000  -0.315     -0.590  0.204
Inflasi                  -0.267      -0.315   1.000      0.074  0.179
CreditRate               -0.548      -0.590   0.074      1.000 -0.624
JII                       0.218       0.204   0.179     -0.624  1.000

# Descriptive
summary(tsData)

 Outstanding KPR  PDB Nominal        Inflasi          CreditRate   
 Min.   :38047   Min.   :715580   Min.   :-0.4500   Min.   :4.250  
 1st Qu.:43622   1st Qu.:766385   1st Qu.: 0.1300   1st Qu.:4.750  
 Median :53612   Median :812954   Median : 0.2050   Median :5.875  
 Mean   :55303   Mean   :818266   Mean   : 0.2838   Mean   :5.896  
 3rd Qu.:65595   3rd Qu.:871216   3rd Qu.: 0.3125   3rd Qu.:7.312  
 Max.   :78998   Max.   :947281   Max.   : 1.4500   Max.   :7.750  
      JII       
 Min.   :556.1  
 1st Qu.:659.2  
 Median :691.5  
 Mean   :688.1  
 3rd Qu.:726.7  
 Max.   :787.1  

2.2 Ordinary Least Square (OLS)

# OLS
regresi1 = lm(LnKPR ~ LnPDB + Inflasi + CreditRate + LnJII + DFTV, data=data1)
summary(regresi1)

Call:
lm(formula = LnKPR ~ LnPDB + Inflasi + CreditRate + LnJII + DFTV, 
    data = data1)

Residuals:
      Min        1Q    Median        3Q       Max 
-0.138338 -0.029350  0.004568  0.029305  0.073667 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) -21.79826    2.19407  -9.935 8.61e-14 ***
LnPDB         2.29744    0.14887  15.432  < 2e-16 ***
Inflasi      -0.02407    0.02223  -1.083 0.283737    
CreditRate    0.04397    0.01081   4.067 0.000156 ***
LnJII         0.16152    0.10803   1.495 0.140715    
DFTV          0.18359    0.03372   5.444 1.31e-06 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.04381 on 54 degrees of freedom
Multiple R-squared:  0.9659,    Adjusted R-squared:  0.9627 
F-statistic: 305.6 on 5 and 54 DF,  p-value: < 2.2e-16

2.3 Diagnostic Gauss Markov

# Normality, Linearity, Heteroscedasticity
library(gvlma)
gvlma(regresi1)

Call:
lm(formula = LnKPR ~ LnPDB + Inflasi + CreditRate + LnJII + DFTV, 
    data = data1)

Coefficients:
(Intercept)        LnPDB      Inflasi   CreditRate        LnJII         DFTV  
  -21.79826      2.29744     -0.02407      0.04397      0.16152      0.18359  


ASSESSMENT OF THE LINEAR MODEL ASSUMPTIONS
USING THE GLOBAL TEST ON 4 DEGREES-OF-FREEDOM:
Level of Significance =  0.05 

Call:
 gvlma(x = regresi1) 

                     Value p-value                Decision
Global Stat        7.04469 0.13355 Assumptions acceptable.
Skewness           3.60383 0.05765 Assumptions acceptable.
Kurtosis           0.86268 0.35299 Assumptions acceptable.
Link Function      2.52749 0.11188 Assumptions acceptable.
Heteroscedasticity 0.05069 0.82187 Assumptions acceptable.

# Heteroscedasticity Test
library(car)

Loading required package: carData

# White test
ncvTest(regresi1)

Non-constant Variance Score Test 
Variance formula: ~ fitted.values 
Chisquare = 0.4905034, Df = 1, p = 0.4837

# Autocorrelation Test
library(lmtest)

Loading required package: zoo

Attaching package: 'zoo'

The following objects are masked from 'package:base':

    as.Date, as.Date.numeric

dwtest(regresi1)

    Durbin-Watson test

data:  regresi1
DW = 0.58729, p-value = 9.399e-13
alternative hypothesis: true autocorrelation is greater than 0

# Assumption: No perfect multicollinearity
vif(regresi1)

     LnPDB    Inflasi CreditRate      LnJII       DFTV 
  4.011533   1.412398   5.368989   1.828592   8.404443 

# Re-estimate Standard Error
library(sandwich)
# Account for heteroskedasticity
coeftest(regresi1, vcov = vcovHC(regresi1, "HC1"))

t test of coefficients:

              Estimate Std. Error  t value  Pr(>|t|)    
(Intercept) -21.798262   1.581079 -13.7870 < 2.2e-16 ***
LnPDB         2.297444   0.118364  19.4100 < 2.2e-16 ***
Inflasi      -0.024070   0.019603  -1.2279    0.2248    
CreditRate    0.043970   0.009386   4.6846 1.937e-05 ***
LnJII         0.161515   0.099960   1.6158    0.1120    
DFTV          0.183586   0.028221   6.5052 2.615e-08 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# Account for heteroskedasticity and autocorrelation
coeftest(regresi1, vcov = vcovHAC)

t test of coefficients:

              Estimate Std. Error  t value  Pr(>|t|)    
(Intercept) -21.798262   1.500741 -14.5250 < 2.2e-16 ***
LnPDB         2.297444   0.134419  17.0917 < 2.2e-16 ***
Inflasi      -0.024070   0.020238  -1.1894  0.239504    
CreditRate    0.043970   0.016296   2.6981  0.009286 ** 
LnJII         0.161515   0.117986   1.3689  0.176686    
DFTV          0.183586   0.041167   4.4595 4.197e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1