# Ekonometrika Ilustrasi Permasalah Multiple Regression Dengan Software - PowerPoint PPT Presentation

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Ekonometrika Ilustrasi Permasalah Multiple Regression Dengan Software. Pendugaan Model Cobb Douglas. Data pada file Excell Tugas , sheet CobbDouglas

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Ekonometrika Ilustrasi Permasalah Multiple Regression Dengan Software

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## Ekonometrika Ilustrasi Permasalah Multiple Regression Dengan Software

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

### Pendugaan Model Cobb Douglas

• Data pada file ExcellTugas, sheet CobbDouglas

• Dari 51 perusahaandiamatiproduktivitas (OUTPUT dalam \$), investasiuntuk modal (CAPITAL dalam \$) daninvestasitenagakerja (LABOR dalam \$)

• Dilakukan pendugaan model

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

### UjiKeberartian Model secaraSimultan

• Menggunakanujihipotesis

• Model unrestricted:

• Model restricted

• Hipotesis

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

### 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 = -867.437

JKGU= 3.4155

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

### 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

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

### 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.

Statistikuji F

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

• Cukupbuktiuntukmenolak H0

• Koefisienbagipeubah Labour dan Capital tidaksamadengannol

• Unrestricted model berbedanyatadengan restricted model

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

### UjiLinear Restriction

• Menggunakanujihipotesis

• Model unrestricted:

• Model restricted:

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

### 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 = -867.437

JKGU= 3.4155

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

### 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 ***

• Mean dependent var 4.749135 S.D. dependent var 0.332104

• Sum squared resid 3.425582 S.E. of regression 0.264405

• R-squared 0.378823 Adjusted R-squared 0.366146

• F(1, 49) 29.88247 P-value(F) 1.54e-06

• Log-likelihood -3.501733 Akaike criterion 11.00347

• Schwarz criterion 14.86712 Hannan-Quinn 12.47988

• Log-likelihood for Out_Labor = -245.708

JKGR= 3.4255

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

### 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:

• coefficient std. error t-ratio p-value

• ----------------------------------------------------------

• const 3.75624 0.185368 20.26 1.82e-025 ***

• l_labor 0.476244 0.0958122 4.971 8.56e-06 ***

• l_capital 0.523756 0.0958122 5.466 1.54e-06 ***

• Standard error of the regression = 0.264405

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

• Karena p-value yang cukupbesar, tidakcukupbuktiuntukmenolak H0

• Restricted dan unrestricted model tidakberbedanyata

• Jumlahdarikedua 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)

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