ekonometrika ilustrasi permasalah multiple regression dengan software

Dr. Rahma Fitriani, S.Si., M.Sc

Ekonometrika Ilustrasi Permasalah Multiple Regression Dengan

Software


Pendugaan Model Cobb Douglas Data pada file Excell Tugas, sheet CobbDouglas

Dari 51 perusahaan diamati produktivitas (OUTPUT dalam $), investasi untuk modal (CAPITAL dalam $) dan investasi tenaga kerja (LABOR dalam $)

Dilakukan pendugaan model

iiii uLaborCapitalOutput )ln()ln()ln( 321


Uji Keberartian Model secara Simultan Menggunakan uji hipotesis Model unrestricted:

Model restricted

Hipotesis


ii uOutput 1)ln(

0, keduanyaatau satu salah :

,0:

321

320

H

H


Output untuk Unrestricted Model Model 1: OLS, using observations 1-51 Dependent variable: l_output

coefficient std. error t-ratio p-value ---------------------------------------------------------- const 3.88760 0.396228 9.812 4.70e-013 *** l_labor 0.468332 0.0989259 4.734 1.98e-05 *** l_capital 0.521279 0.0968871 5.380 2.18e-06 ***

Mean dependent var 16.94139 S.D. dependent var 1.380870 Sum squared resid 3.415520 S.E. of regression 0.266752 R-squared 0.964175 Adjusted R-squared 0.962683 F(2, 48) 645.9311 P-value(F) 2.00e-35 Log-likelihood -3.426721 Akaike criterion 12.85344 Schwarz criterion 18.64892 Hannan-Quinn 15.06807

Log-likelihood for output = -867.437JKGU= 3.4155


Output Untuk Restricted Model Model 2: OLS, using observations 1-51 Dependent variable: l_output

coefficient std. error t-ratio p-value --------------------------------------------------------- const 16.9414 0.193361 87.62 2.12e-056 ***

Mean dependent var 16.94139 S.D. dependent var 1.380870 Sum squared resid 95.34013 S.E. of regression 1.380870 R-squared 0.000000 Adjusted R-squared 0.000000 Log-likelihood -88.31931 Akaike criterion 178.6386 Schwarz criterion 180.5704 Hannan-Quinn 179.3768

Log-likelihood for output = -952.33

JKGR= 95.34

UU

RUUR

kn

kkF

/JKG

/JKGJKG 931.645

351/4155.3

13/4155.334.95


Output Omitted variable Test Model 3: OLS, using observations 1-51

Dependent variable: l_output

coefficient std. error t-ratio p-value

---------------------------------------------------------

const 16.9414 0.193361 87.62 2.12e-056 ***

Mean dependent var 16.94139 S.D. dependent var 1.380870

Sum squared resid 95.34013 S.E. of regression 1.380870

R-squared 0.000000 Adjusted R-squared 0.000000

Log-likelihood -88.31931 Akaike criterion 178.6386

Schwarz criterion 180.5704 Hannan-Quinn 179.3768

Log-likelihood for output = -952.33

Comparison of Model 1 and Model 3:

Null hypothesis: the regression parameters are zero for the variables

l_labor, l_capital

Test statistic: F(2, 48) = 645.931, with p-value = 1.99686e-035

Of the 3 model selection statistics, 0 have improved.

Sama dengan output sebelumnya Restricted Model

Statistik uji F


Karena p-value relatif kecil, menuju nol Cukup bukti untuk menolak H0

Koefisien bagi peubah Labour dan Capital tidak sama dengan nol

Unrestricted model berbeda nyata dengan restricted model

Unrestricted model lebih baik menjelaskan keragaman Output produksi


Uji Linear Restriction Menggunakan uji hipotesis Model unrestricted:

Restritcion pada hipotesis:

Model restricted:


1:

,1:

321

320

H

H

iiiii uLaborCapitalββLaborOutput lnlnlnln 21

iLaborCapital

LaborOutput uββ

i

i

i

i lnln 21


Output untuk Unrestricted Model Model 1: OLS, using observations 1-51 Dependent variable: l_output



Log-likelihood for output = -867.437JKGU= 3.4155


Output Linear Restricted Model Model 4: OLS, using observations 1-51 Dependent variable: l_Out_Labor

coefficient std. error t-ratio p-value -------------------------------------------------------------- const 3.75624 0.185368 20.26 1.82e-025

*** l_Capital_Lab 0.523756 0.0958122 5.466 1.54e-06

***


Log-likelihood for Out_Labor = -245.708

JKGR= 3.4255

UU

RUUR

kn

kkF

/JKG

/JKGJKG 1414.0

351/4255.3

23/4155.34255.3


Output Linear Restriction Test Restriction: b[l_labor] + b[l_capital] = 1

Test statistic: F(1, 48) = 0.141406, with p-value = 0.708544

Restricted estimates:


Standard error of the regression = 0.264405


Karena p-value yang cukup besar, tidak cukup bukti untuk menolak H0

Restricted dan unrestricted model tidak berbeda nyata

Jumlah dari kedua parameter = 1 Penduga model:

^l_output = 3.89 + 0.468*l_labor + 0.521*l_capital (0.396)(0.0989) (0.0969)

n = 51, R-squared = 0.964 (standard errors in parentheses)

ekonometrika ilustrasi permasalah multiple regression dengan software

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