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Ekonometrika

Ekonometrika. Program Studi Statistika, semester Ganjil 2012/2013. Contoh Aplikasi Regresi Dengan Peubah Dummy. Data tentang gaji ( wage ) dan IQ ( iq ) dari 935 individu Terdapat beberapa peubah dummy untuk menggambarkan karakteristik masing-masing individu selain IQ

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Ekonometrika

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  1. Ekonometrika Program Studi Statistika, semester Ganjil 2012/2013 Dr. Rahma Fitriani, S.Si., M.Sc

  2. ContohAplikasiRegresiDenganPeubah Dummy • Data tentanggaji (wage) dan IQ (iq) dari 935 individu • Terdapatbeberapapeubah dummy untukmenggambarkankarakteristikmasing-masingindividuselain IQ • Peubah dummy jeniskelamin (male): • Laki-laki: male =1 • Perempuan: male=0 • Peubah dummy tingkatpendidikan (educ1, educ2, educ3, daneduc4): • Lulusan SMP: educ1=1, selainnya 0 • Lulusan SMA: educ2=1, selainnya 0 • Lulusan S1: educ3=1, selainnya 0 • Lulusan S2: educ4=1, selainnya 0

  3. Ingindiperolehhubunganantaragajidantingkat IQ • Ingin diketahui apakah selain IQ, jenis kelamin juga mempengaruhi gaji, dengan pengaruh konstan (intersep dummy). • Ingin diketahui apakah jenis kelamin mempengaruhi marginal effect dari IQ terhadap gaji (slope dummy).

  4. Ingindiketahuiapakahselain IQ, jeniskelaminmempengaruhigajisecara konstan maupun secara marjinal (combined effect) • Ingindiketahuiapakahgajidipengaruhiolehtingkatpendidikan

  5. Gajiberdasarkan IQ • Model 1: OLS, using observations 1-935 • Dependent variable: WAGE • coefficient std. error t-ratio p-value • --------------------------------------------------------- • const 116.992 85.6415 1.366 0.1722 • IQ 8.30306 0.836395 9.927 3.79e-022 *** • Mean dependent var 957.9455 S.D. dependent var 404.3608 • Sum squared resid 1.38e+08 S.E. of regression 384.7667 • R-squared 0.095535 Adjusted R-squared 0.094566 • F(1, 933) 98.54936 P-value(F) 3.79e-22 • Log-likelihood -6891.422 Akaike criterion 13786.84 • Schwarz criterion 13796.53 Hannan-Quinn 13790.54 • IQ mempunyaihubunganpositifterhadapgaji (nyata) • Model kurangbaikkarena R2kecil

  6. Gajiberdasarkan IQ danJenisKelamin (Intercept dummy) • Model 2: OLS, using observations 1-935 • Dependent variable: WAGE • coefficient std. error t-ratio p-value • --------------------------------------------------------- • const 224.844 66.6424 3.374 0.0008 *** • IQ 5.07663 0.662354 7.665 4.50e-014 *** • MALE 498.049 20.0768 24.81 1.02e-104 *** • Mean dependent var 957.9455 S.D. dependent var 404.3608 • Sum squared resid 83193885 S.E. of regression 298.7705 • R-squared 0.455239 Adjusted R-squared 0.454070 • F(2, 932) 389.4203 P-value(F) 1.2e-123 • Log-likelihood -6654.402 Akaike criterion 13314.80 • Schwarz criterion 13329.33 Hannan-Quinn 13320.34 • Model lebihbaikkarena R2meningkat • 1 unit kenaikan IQ meningkatkangajisebesar 5.07 unit • Pegawailaki-lakimempunyaigajilebihbanyak 498 unit dibandingkandenganpegawaiperempuan, kenaikantsbnyatasecarastatistik

  7. Gaji GarisregresiuntukpegawaiLaki-laki Garisregresiuntukpegawaiperempuan 224.84+498.05=722.89 224.84 IQ

  8. Gajiberdasarkan IQ dan IQ*JenisKelamin (Slope dummy) • Model 3: OLS, using observations 1-935 • Dependent variable: WAGE • coefficient std. error t-ratio p-value • --------------------------------------------------------- • const 412.860 67.3637 6.129 1.31e-09 *** • IQ 3.18418 0.679283 4.688 3.18e-06 *** • MaleIQ 4.84013 0.193746 24.98 7.49e-106 *** • Mean dependent var 957.9455 S.D. dependent var 404.3608 • Sum squared resid 82728978 S.E. of regression 297.9346 • R-squared 0.458283 Adjusted R-squared 0.457120 • F(2, 932) 394.2274 P-value(F) 8.7e-125 • Log-likelihood -6651.782 Akaike criterion 13309.56 • Schwarz criterion 13324.09 Hannan-Quinn 13315.10 • R2meningkattapitidakterlalubesar • Padapegawaiperempuan 1 unit kenaikan IQ meningkatkangajisebesar 3.18 unit • Padapegawailaki-laki 1 unit kenaikan IQ meningkatkangajisebesar (3.18+4.84)=8.02 unit • Perbedaan yang nyataantarakenaikangajiantarakaryawanlaki-lakidanperempuan

  9. GarisregresiuntukpegawaiLaki-laki Slope: 3.18+4.84=8.02 Garisregresiuntukpegawaiperempuan Slope: 3.18

  10. Gajiberdasarkan IQ, JenisKelamindan IQ*JenisKelamin • Model 4: OLS, using observations 1-935 • Dependent variable: WAGE • coefficient std. error t-ratio p-value • -------------------------------------------------------- • const 357.857 84.7894 4.221 2.68e-05 *** • IQ 3.72852 0.849174 4.391 1.26e-05 *** • MaleIQ 3.41212 1.35097 2.526 0.0117 ** • MALE 149.104 139.602 1.068 0.2858 • Mean dependent var 957.9455 S.D. dependent var 404.3608 • Sum squared resid 82627733 S.E. of regression 297.9121 • R-squared 0.458946 Adjusted R-squared 0.457202 • F(3, 931) 263.2382 P-value(F) 1.1e-123 • Log-likelihood -6651.210 Akaike criterion 13310.42 • Schwarz criterion 13329.78 Hannan-Quinn 13317.80

  11. Gajiberdasarkan IQ, JenisKelamindan IQ*JenisKelamin • coefficient std. error t-ratio p-value • -------------------------------------------------------- • const 357.857 84.7894 4.221 2.68e-05 *** • IQ 3.72852 0.849174 4.391 1.26e-05 *** • MaleIQ 3.41212 1.35097 2.526 0.0117 ** • MALE 149.104 139.602 1.068 0.2858 • Pada IQ yang sama, gajipegawailaki-lakilebihbanyak 149.104 unit daripadagajipegawaiperempuan • Padapegawaiperempuan 1 unit kenaikan IQ meningkatkangajisebesar 3.72 unit • Padapegawailaki-laki 1 unit kenaikan IQ meningkatkangajisebesar (3.72+3.41)=7.13 unit

  12. GarisregresiuntukpegawaiLaki-laki Slope: 3.73+3.41=7.13 Garisregresiuntukpegawaiperempuan 357.86+149.10=506.96 Slope:3.73 357.86

  13. Gajiberdasarkantingkatpendidikan, Lulusan SMP sebagaireferensi • Model 5: OLS, using observations 1-935 • Dependent variable: WAGE • coefficient std. error t-ratio p-value • --------------------------------------------------------- • const 774.250 40.9511 18.91 1.00e-067 *** • EDUC2 88.4218 45.3045 1.952 0.0513 * • EDUC3 221.417 48.8868 4.529 6.69e-06 *** • EDUC4 369.118 47.6913 7.740 2.59e-014 *** • Mean dependent var 957.9455 S.D. dependent var 404.3608 • Sum squared resid 1.37e+08 S.E. of regression 384.1553 • R-squared 0.100340 Adjusted R-squared 0.097441 • F(3, 931) 34.61189 P-value(F) 3.27e-21 • Log-likelihood -6888.932 Akaike criterion 13785.86 • Schwarz criterion 13805.23 Hannan-Quinn 13793.25

  14. coefficient std. error t-ratio p-value --------------------------------------------------------- const 774.250 40.9511 18.91 1.00e-067 *** EDUC2 88.4218 45.3045 1.952 0.0513 * EDUC3 221.417 48.8868 4.529 6.69e-06 *** EDUC4 369.118 47.6913 7.740 2.59e-014 *** • Lulusan SMA mempunyaigaji 88.42 unit lebihbanyakdaripadalulusan SMP • Lulusan S1 mempunyaigaji 221.42 unit lebihbanyakdaripadalulusan SMP • Lulusan S2 mempunyaigaji 369.118 unit lebihbanyakdaripadalulusan SMP

  15. Gajiberdasarkantingkatpendidikan, Lulusan S2 sebagaireferensi • Model 6: OLS, using observations 1-935 • Dependent variable: WAGE • coefficient std. error t-ratio p-value • --------------------------------------------------------- • const 1143.37 24.4432 46.78 1.18e-246 *** • EDUC1 -369.118 47.6913 -7.740 2.59e-014 *** • EDUC2 -280.697 31.1926 -8.999 1.26e-018 *** • EDUC3 -147.702 36.1994 -4.080 4.88e-05 *** • Mean dependent var 957.9455 S.D. dependent var 404.3608 • Sum squared resid 1.37e+08 S.E. of regression 384.1553 • R-squared 0.100340 Adjusted R-squared 0.097441 • F(3, 931) 34.61189 P-value(F) 3.27e-21 • Log-likelihood -6888.932 Akaike criterion 13785.86 • Schwarz criterion 13805.23 Hannan-Quinn 13793.25

  16. coefficient std. error t-ratio p-value --------------------------------------------------------- const 1143.37 24.4432 46.78 1.18e-246 *** EDUC1 -369.118 47.6913 -7.740 2.59e-014 *** EDUC2 -280.697 31.1926 -8.999 1.26e-018 *** EDUC3 -147.702 36.1994 -4.080 4.88e-05 *** • Lulusan SMP mempunyaigaji 369.12 unit lebihsedikitdaripadalulusan S2 • Lulusan SMA mempunyaigaji 280.7 unit lebihsedikitdaripadalulusan S2 • Lulusan S1 mempunyaigaji 147.7 unit lebihsedikitdaripadalulusan S2

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