Ekonometrika Ilustrasi Permasalah Multiple Regression Dengan Software Dr. Rahma Fitriani, S.Si., M.Sc

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

Uji Keberartian Model secara Simultan Menggunakan uji hipotesis 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 Sama dengan output sebelumnya Restricted Model 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. Statistik uji F Dr. Rahma Fitriani, S.Si., M.Sc

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

Uji Linear Restriction Menggunakan uji hipotesis Model unrestricted: Restritcion pada hipotesis: 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 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 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) Dr. Rahma Fitriani, S.Si., M.Sc