Seorang penganalisis menganggarkan model pertumbuhan ekonomi berikut untuk tempoh 1971-2020 dan keputusan dipaparkan seperti dalam Jadual 1: An analyst estimates the following economic growth model over the period 1971-2020 for Malaysia and the results are displayed as per Table 1: GNIG =B + BINV + ME + INF + B5GEXP + ut, where GNIG, ialah pertumbuhan PNK (% tahunan), INV, ialah pembentukan model tetap kasar (% daripada KDNK), ME, ialah perbelanjaan ketenteraan (% daripada KDNK), INF ialah inflasi (% tahunan), GEXP, ialah perbelanjaan negara kasar (% daripada KDNK) dan u ialah ralat regresi. Ujian diagnostik dilaporkan dalam Jadual 2 dan Rajah 1. where GNIG, is GNI growth (annual %), INV, is gross fixed capital formation (% of GDP), ME, is military expenditure (% of GDP), INF, is inflation (annual %), GEXP, is gross national expenditure (% of GDP), and u, is the residual terms. Diagnostic tests are reported in Table 2 and Figure 1. Jadual 1: Keputusan Empirikal berdasarkan Kaedah Kuasa Dua Terkecil Table 1: Empirical Results based on Ordinary Least Square Dependent Variable: GNIG Method: Least Squares Sample: 1971 2020 Included observations: 50 Variable INV ME INF GEXP R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) Coefficient Std. Error t-Statistic Prob. 0.102924 0.112045 0.918588 0.3632 0.534077 0.529435 1.008768 0.162063 0.197007 0.822627 0.018032 0.099269 0.181653 0.8567 -0.482945 6.571272 -0.073493 0.9417 0.152282 Mean dependent var 0.076930 S.D. dependent var 0.3185 0.4151 3.589868 Akaike info criterion 579.9218 Schwarz criterion -132.2187 Hannan-Quinn criter. 2.020930 Durbin-Watson stat 0.107572 6.031855 3.736466 5.488747 5.679950 5.561558 1.510435 12 10 8 6 4 2 0 -12 -10 -8 White Test -6 -4-20 F-statistic Obs*R-squared Scaled explained SS Variable INV ME INF GEXP Variance Inflation Factors Sample: 1971 2020 Included observations: 50 Rajah 1 Figure 1 2 4 Jadual 2 Table 2 3.350054 Prob. F(14,35) 28.63268 58.85298 6 Series: Residuals Sample 1971 2020 Observations 50 Mean Median Maximum Minimum Std. Dev. Skewness Kurtasis Prob. Chi-Square(14) Prob. Chi-Square(14) Jarque-Bera 40.40880 Probability 0.000000 -1.146-15 0.755371 Coefficient Uncentered Centered Variance VIF VIF 5.203337 -12.97179 3.440224 -1.576348 6.075180 0.0018 0.0117 0.0000 0.012554 38.75422 2.055730 0.280301 10.24186 1.794831 0.038812 2.989785 1.281499 0.009854 325.0505 2.860312 43.18162 167.5375 Breusch-Godfrey Serial Correlation LM Test: Obs*R-squared Test Equation: Dependent Variable: RESID Method: Least Squares Sample: 1971 2020 Included observations: 50 Presample missing value lagged residuals set to zero. Coefficient Std. Error Variable INV ME INF GEXP RESID(-1) RESID(-2) R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) Prob. Chi-Square(2) 0.004591 0.111424 0.069228 0.556211 -0.020670 0.213094 0.244110 -0.152304 t-Statistic 0.041204 0.124463 -0.097001 -0.109957 6.755340 0.110978 -0.011073 0.100703 0.749697 3.564567 546.3639 0.170730 0.174807 -0.871273 0.057866 Mean dependent var -0.073594 S.D. dependent var 1.429799 0.1600 0.3884 Akaike info criterion Schwarz criterion -130.7285 Hannan-Quinn criter. 0.440179 Durbin-Watson stat 0.847804 Correlation ME INF 0.3049 0.2608 0.2075 1.0000 0.4567 0.2354 Prob. 0.9673 0.9015 0.9232 0.9130 0.9121 0.1887 0.4567 -1.14E-15 3.440224 5.509139 5.776823 5.611075 1.829234 GNIG INV GNIG 1.0000 0.2722 INV 0.2722 1.0000 ME 0.3049 0.2075 0.5584 INF 0.2608 0.1887 1.0000 0.3366 GEXP 0.3125 0.6843 0.5584 0.3366 1.0000 GEXP 0.3125 0.6843 Ramsey RESET Test Omitted Variables: Squares of fitted values Specification: GNIG INV ME INF GEXP C t-statistic F-statistic Likelihood ratio F-test summary: Test SSR Restricted SSR Unrestricted SSR LR test summary: Restricted LogL Unrestricted LogL Value 2.026744 44 4.107690 (1,44) 4.462621 1 F-statistic Obs*R-squared Sum of Sq. 49.51681 579.9218 530.4050 Value -132.2187 -129.9874 Breusch-Pagan-Godfrey Test df df 1 45 44 Probability 0.0488 0.0488 0.0346 Mean Squares 49.51681 12.88715 12.05466 0.307660 Prob. F(4,45) 1.330981 Prob. Chi-Square(4) Scaled explained SS 2.735762 Prob. Chi-Square(4) 0.8713 0.8561 0.6030 Berikan jawapan untuk soalan berikut berdasarkan keputusan yang tertera dalam Jadual di atas. Provide answers for the following questions based on the results tabulated in the above Tables. (a) Tetapkan hipotesis anda dengan sewajarnya. Uji sama ada pekali kecerunan bagi inflasi adalah uniti (bersamaan dengan 1) pada aras keertian 5%. Set your hypothesis appropriately. Test whether the slope coefficient for inflation is unity (equal to 1) at 5% significance level. (3 markah/marks) (b) Adakah terdapat autokorelasi dalam analisis anda pada tahap keertian 5%? Tunjukkan statistik ujian anda. Is there autocorrelation present in your analysis at 5% significance level? Show your test statistics. (2 markah/marks) (c) Diberi Jadual 3 Given Table 3 i. Dependent Variable: GNIG Method: Least Squares Sample: 1971 2020 Included observations: 50 ii. Variable INV ME INF GEXP DUMMY R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) Coefficient -0.029738 -0.403906 Jadual 3 Table 3 Std. Error t-Statistic 0.143418 -0.207349 0.830281 -0.486469 Prob. 0.8367 0.6290 0.171334 0.194713 0.879930 0.3837 0.133799 0.126295 1.059421 0.2952 -2.894680 1.990087 -1.454549 -4.133286 6.959526 -0.593903 0.191174 Mean dependent var 0.099262 S.D. dependent var 3.546176 Akaike info criterion 553.3159 Schwarz criterion -131.0446 Hannan-Quinn criter. 2.079971 Durbin-Watson stat 0.085970 0.1529 0.5556 di mana Dummy, ialah pembolehubah dummi (D=0 untuk pra-krisis 2008; D=1 untuk pasca-krisis 2008) where Dummy, is dummy variable (D=0 for pre-crisis 2008; D=1 for post-crisis 2008) 6.031855 3.736466 5.481783 5.711226 5.569156 1.529494 Adakah model ini menyuaikan data lebih baik daripada model dalam Jadual 1? Adakah model ini kelihatan menyuaikan data dengan baik? Is this model fits data better than the model in Table 1? Does this model seem fits the data well? (2 markah/marks) Bagaimanakah anda akan memutuskan model yang mana adalah spesifikasi yang lebih baik? Apakah kesimpulan keseluruhan yang anda akan buat? Berikan komen terhadap keputusan ujian RESET. How you decide which model is a better specification? What overall conclusion would you draw? Give comment on the result of RESET test. (3 markah/marks) (Jumlah/ Total: 10 markah/ marks) Seorang penganalisis menganggarkan model pertumbuhan ekonomi berikut untuk tempoh 1971-2020 dan keputusan dipaparkan seperti dalam Jadual 1: An analyst estimates the following economic growth model over the period 1971-2020 for Malaysia and the results are displayed as per Table 1: GNIG =B + BINV + ME + INF + B5GEXP + ut, where GNIG, ialah pertumbuhan PNK (% tahunan), INV, ialah pembentukan model tetap kasar (% daripada KDNK), ME, ialah perbelanjaan ketenteraan (% daripada KDNK), INF ialah inflasi (% tahunan), GEXP, ialah perbelanjaan negara kasar (% daripada KDNK) dan u ialah ralat regresi. Ujian diagnostik dilaporkan dalam Jadual 2 dan Rajah 1. where GNIG, is GNI growth (annual %), INV, is gross fixed capital formation (% of GDP), ME, is military expenditure (% of GDP), INF, is inflation (annual %), GEXP, is gross national expenditure (% of GDP), and u, is the residual terms. Diagnostic tests are reported in Table 2 and Figure 1. Jadual 1: Keputusan Empirikal berdasarkan Kaedah Kuasa Dua Terkecil Table 1: Empirical Results based on Ordinary Least Square Dependent Variable: GNIG Method: Least Squares Sample: 1971 2020 Included observations: 50 Variable INV ME INF GEXP R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) Coefficient Std. Error t-Statistic Prob. 0.102924 0.112045 0.918588 0.3632 0.534077 0.529435 1.008768 0.162063 0.197007 0.822627 0.018032 0.099269 0.181653 0.8567 -0.482945 6.571272 -0.073493 0.9417 0.152282 Mean dependent var 0.076930 S.D. dependent var 0.3185 0.4151 3.589868 Akaike info criterion 579.9218 Schwarz criterion -132.2187 Hannan-Quinn criter. 2.020930 Durbin-Watson stat 0.107572 6.031855 3.736466 5.488747 5.679950 5.561558 1.510435 12 10 8 6 4 2 0 -12 -10 -8 White Test -6 -4-20 F-statistic Obs*R-squared Scaled explained SS Variable INV ME INF GEXP Variance Inflation Factors Sample: 1971 2020 Included observations: 50 Rajah 1 Figure 1 2 4 Jadual 2 Table 2 3.350054 Prob. F(14,35) 28.63268 58.85298 6 Series: Residuals Sample 1971 2020 Observations 50 Mean Median Maximum Minimum Std. Dev. Skewness Kurtasis Prob. Chi-Square(14) Prob. Chi-Square(14) Jarque-Bera 40.40880 Probability 0.000000 -1.146-15 0.755371 Coefficient Uncentered Centered Variance VIF VIF 5.203337 -12.97179 3.440224 -1.576348 6.075180 0.0018 0.0117 0.0000 0.012554 38.75422 2.055730 0.280301 10.24186 1.794831 0.038812 2.989785 1.281499 0.009854 325.0505 2.860312 43.18162 167.5375 Breusch-Godfrey Serial Correlation LM Test: Obs*R-squared Test Equation: Dependent Variable: RESID Method: Least Squares Sample: 1971 2020 Included observations: 50 Presample missing value lagged residuals set to zero. Coefficient Std. Error Variable INV ME INF GEXP RESID(-1) RESID(-2) R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) Prob. Chi-Square(2) 0.004591 0.111424 0.069228 0.556211 -0.020670 0.213094 0.244110 -0.152304 t-Statistic 0.041204 0.124463 -0.097001 -0.109957 6.755340 0.110978 -0.011073 0.100703 0.749697 3.564567 546.3639 0.170730 0.174807 -0.871273 0.057866 Mean dependent var -0.073594 S.D. dependent var 1.429799 0.1600 0.3884 Akaike info criterion Schwarz criterion -130.7285 Hannan-Quinn criter. 0.440179 Durbin-Watson stat 0.847804 Correlation ME INF 0.3049 0.2608 0.2075 1.0000 0.4567 0.2354 Prob. 0.9673 0.9015 0.9232 0.9130 0.9121 0.1887 0.4567 -1.14E-15 3.440224 5.509139 5.776823 5.611075 1.829234 GNIG INV GNIG 1.0000 0.2722 INV 0.2722 1.0000 ME 0.3049 0.2075 0.5584 INF 0.2608 0.1887 1.0000 0.3366 GEXP 0.3125 0.6843 0.5584 0.3366 1.0000 GEXP 0.3125 0.6843 Ramsey RESET Test Omitted Variables: Squares of fitted values Specification: GNIG INV ME INF GEXP C t-statistic F-statistic Likelihood ratio F-test summary: Test SSR Restricted SSR Unrestricted SSR LR test summary: Restricted LogL Unrestricted LogL Value 2.026744 44 4.107690 (1,44) 4.462621 1 F-statistic Obs*R-squared Sum of Sq. 49.51681 579.9218 530.4050 Value -132.2187 -129.9874 Breusch-Pagan-Godfrey Test df df 1 45 44 Probability 0.0488 0.0488 0.0346 Mean Squares 49.51681 12.88715 12.05466 0.307660 Prob. F(4,45) 1.330981 Prob. Chi-Square(4) Scaled explained SS 2.735762 Prob. Chi-Square(4) 0.8713 0.8561 0.6030 Berikan jawapan untuk soalan berikut berdasarkan keputusan yang tertera dalam Jadual di atas. Provide answers for the following questions based on the results tabulated in the above Tables. (a) Tetapkan hipotesis anda dengan sewajarnya. Uji sama ada pekali kecerunan bagi inflasi adalah uniti (bersamaan dengan 1) pada aras keertian 5%. Set your hypothesis appropriately. Test whether the slope coefficient for inflation is unity (equal to 1) at 5% significance level. (3 markah/marks) (b) Adakah terdapat autokorelasi dalam analisis anda pada tahap keertian 5%? Tunjukkan statistik ujian anda. Is there autocorrelation present in your analysis at 5% significance level? Show your test statistics. (2 markah/marks) (c) Diberi Jadual 3 Given Table 3 i. Dependent Variable: GNIG Method: Least Squares Sample: 1971 2020 Included observations: 50 ii. Variable INV ME INF GEXP DUMMY R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) Coefficient -0.029738 -0.403906 Jadual 3 Table 3 Std. Error t-Statistic 0.143418 -0.207349 0.830281 -0.486469 Prob. 0.8367 0.6290 0.171334 0.194713 0.879930 0.3837 0.133799 0.126295 1.059421 0.2952 -2.894680 1.990087 -1.454549 -4.133286 6.959526 -0.593903 0.191174 Mean dependent var 0.099262 S.D. dependent var 3.546176 Akaike info criterion 553.3159 Schwarz criterion -131.0446 Hannan-Quinn criter. 2.079971 Durbin-Watson stat 0.085970 0.1529 0.5556 di mana Dummy, ialah pembolehubah dummi (D=0 untuk pra-krisis 2008; D=1 untuk pasca-krisis 2008) where Dummy, is dummy variable (D=0 for pre-crisis 2008; D=1 for post-crisis 2008) 6.031855 3.736466 5.481783 5.711226 5.569156 1.529494 Adakah model ini menyuaikan data lebih baik daripada model dalam Jadual 1? Adakah model ini kelihatan menyuaikan data dengan baik? Is this model fits data better than the model in Table 1? Does this model seem fits the data well? (2 markah/marks) Bagaimanakah anda akan memutuskan model yang mana adalah spesifikasi yang lebih baik? Apakah kesimpulan keseluruhan yang anda akan buat? Berikan komen terhadap keputusan ujian RESET. How you decide which model is a better specification? What overall conclusion would you draw? Give comment on the result of RESET test. (3 markah/marks) (Jumlah/ Total: 10 markah/ marks)