Chow Test (Pengujian F Statistic)
H0 : Model pooled least square (restricted)
H1 : Model fixed effect (unrestricted)
dimana:
RRSS : restricted residual sum square
URSS : unrestricted residual sum square
N : jumlah data unit individ
T : jumlah data deret-waktu
K : jumlah peubah bebas
Hipotesis dalam uji chow adalah:
Chow test berfungsi untuk menentukan apakah model yang digunakan pooled least square atau fixed effect. Dalam pengujian ini dilakukan dengan hipotesis sebagai berikut:
H1 : Model fixed effect (unrestricted)
Tolak H0 jika nilai Chow statistik (F-statistic) lebih besar dari F tabel. Dengan demikian, model yang dipilih adalah model fixed effect, dan sebaliknya. Besaran nilai Chow itu sendiri didapat dari perhitungan di bawah ini.
dimana:
RRSS : restricted residual sum square
URSS : unrestricted residual sum square
N : jumlah data unit individ
T : jumlah data deret-waktu
K : jumlah peubah bebas
H0 : Common Effect Model atau pooled
OLS
H1 : Fixed Effect Model
Dimana:
SSE1 : Sum Square Error dari model
Common Effect
SSE2 : Sum Square Error dari model
Fixed Effect
n : Jumlah perusahaan (cross
section)
nt : Jumlah cross
section x jumlah time series
k : Jumlah variabel
independen
Dimana:
α : Tingkat
signifikasi yang dipakai (alfa)
n : Jumlah perusahaan
(cross section)
nt : Jumlah cross
section x jumlah time series
k : Jumlah
variabel independen
Untuk menghitung kita lihat hasil Common Effect dan Fixed Effect dibawah ini:
Hasil Regresi Panel dengan Common Effect
Dependent
Variable: LDR
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Method:
Panel Least Squares
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Date:
04/29/13 Time: 07:21
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Sample:
2007 2011
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Periods
included: 5
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Cross-sections
included: 10
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Total
panel (balanced) observations: 50
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Variable
|
Coefficient
|
Std.
Error
|
t-Statistic
|
Prob.
|
C
|
101.5206
|
33.72252
|
3.010470
|
0.0042
|
NPL
|
8.066572
|
3.574101
|
2.256951
|
0.0287
|
KURS
|
-0.003213
|
0.003595
|
-0.893980
|
0.3759
|
R-squared
|
0.105314
|
Mean dependent var
|
79.28840
|
|
Adjusted
R-squared
|
0.067243
|
S.D. dependent var
|
14.93432
|
|
S.E. of
regression
|
14.42347
|
Akaike info criterion
|
8.233715
|
|
Sum
squared resid
|
9777.711
|
Schwarz criterion
|
8.348436
|
|
Log
likelihood
|
-202.8429
|
Hannan-Quinn criter.
|
8.277401
|
|
F-statistic
|
2.766212
|
Durbin-Watson stat
|
0.235459
|
|
Prob(F-statistic)
|
0.073157
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Hasil Regresi Panel dengan Fixed Effect
Dependent
Variable: LDR
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Method:
Panel Least Squares
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Date:
04/29/13 Time: 07:22
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Sample:
2007 2011
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Periods
included: 5
|
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Cross-sections
included: 10
|
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Total
panel (balanced) observations: 50
|
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Variable
|
Coefficient
|
Std.
Error
|
t-Statistic
|
Prob.
|
C
|
101.6511
|
11.83352
|
8.590096
|
0.0000
|
NPL
|
-9.442499
|
3.187997
|
-2.961891
|
0.0052
|
KURS
|
-0.001377
|
0.001298
|
-1.060954
|
0.2954
|
Effects Specification
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Cross-section
fixed (dummy variables)
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R-squared
|
0.910928
|
Mean dependent var
|
79.28840
|
|
Adjusted
R-squared
|
0.885144
|
S.D. dependent var
|
14.93432
|
|
S.E. of
regression
|
5.061309
|
Akaike info criterion
|
6.286690
|
|
Sum
squared resid
|
973.4401
|
Schwarz criterion
|
6.745576
|
|
Log likelihood
|
-145.1673
|
Hannan-Quinn criter.
|
6.461437
|
|
F-statistic
|
35.32908
|
Durbin-Watson stat
|
1.590946
|
|
Prob(F-statistic)
|
0.000000
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Fn-1,nt,n-k (ROE) = (9777,711- 973,4401) / (10 -1)
973,4401/ (10.5
- 10 – 2)
= 978,252322222
20,2800020833
= 48,237289
F-tabel = ⎨ ⍺ ;
df (n-1, nT-n-k)⎬
= 5% ; (10 - 1, 10.5 -
10 - 2)
=
5% ; (9, 50 - 10 - 2)
=
5% ; (9, 48) = 2,08
Hasil dari perhitungan F-hitung
didapat sebesar 48,237289 sedangkan F-tabel dari numerator 9 dan
denumenator 48 pada ⍺: 5%
adalah 2,08. Dari hipotesis diatas dapat disimpulkan bahwa H0 ditolak karena
F-hitung lebih besar dari F-tabel (48,237289 > 2,08), sehingga model yang
dipakai dalam penelitian ini adalah Fixed Effect Model.
Berikut ini hasil regresi panel dengan model Fixed Effect:
Dependent
Variable: LDR
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Method:
Panel Least Squares
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Date:
04/29/13 Time: 07:22
|
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Sample:
2007 2011
|
||||
Periods
included: 5
|
||||
Cross-sections
included: 10
|
||||
Total
panel (balanced) observations: 50
|
||||
Variable
|
Coefficient
|
Std.
Error
|
t-Statistic
|
Prob.
|
C
|
101.6511
|
11.83352
|
8.590096
|
0.0000
|
NPL
|
-9.442499
|
3.187997
|
-2.961891
|
0.0052
|
KURS
|
-0.001377
|
0.001298
|
-1.060954
|
0.2954
|
Effects Specification
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Cross-section
fixed (dummy variables)
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R-squared
|
0.910928
|
Mean dependent var
|
79.28840
|
|
Adjusted
R-squared
|
0.885144
|
S.D. dependent var
|
14.93432
|
|
S.E. of
regression
|
5.061309
|
Akaike info criterion
|
6.286690
|
|
Sum
squared resid
|
973.4401
|
Schwarz criterion
|
6.745576
|
|
Log
likelihood
|
-145.1673
|
Hannan-Quinn criter.
|
6.461437
|
|
F-statistic
|
35.32908
|
Durbin-Watson stat
|
1.590946
|
|
Prob(F-statistic)
|
0.000000
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