Bai tập kinh tế lượng II. Mô hình hồi quy tổng thể PRICE = β 1 + β 2 * SQUARE + β 3 * DISTANCE + β 4 * PEOPLE + u i 1.kiểm định sự tồn tại của mô hình H 0 : Mô hình hồi quy không tồn tại H 1 : Mô hình hồi quy có tồn tại Dependent Variable: PRICE Method: Least Squares Date: 06/30/11 Time: 13:34 Sample: 1 85 Included observations: 85 Variable Coefficient Std. Error t-Statistic Prob. SQUARE 0.039932 0.007997 4.993083 0.0000 DISTANCE 0.004014 0.017489 0.229491 0.8191 PEOPLE 0.073233 0.066496 1.101317 0.2740 C 0.445857 0.184333 2.418751 0.0178 R-squared 0.367503 Mean dependent var 1.433412 Adjusted R-squared 0.344077 S.D. dependent var 0.787837 S.E. of regression 0.638062 Akaike info criterion 1.985153 Sum squared resid 32.97696 Schwarz criterion 2.100101 Log likelihood -80.36899 F-statistic 15.68793 Durbin-Watson stat 1.306837 Prob(F-statistic) 0.000000 Ta có: Prob(F) = 0.000000 < 5% Bác bỏ H 0 Mô hình hồi quy có tồn tại với α =5% 2. kiểm định đa cộng tuyến Chạy mô hình hồi quy phụ Dependent Variable: SQUARE Method: Least Squares Date: 06/30/11 Time: 13:44 Sample: 1 85 Included observations: 85 Variable Coefficient Std. Error t-Statistic Prob. DISTANCE 0.339706 0.238563 1.423970 0.1582 PEOPLE 4.396751 0.779324 5.641753 0.0000 C 5.547463 2.470537 2.245448 0.0274 R-squared 0.309660 Mean dependent var 19.22353 Adjusted R-squared 0.292822 S.D. dependent var 10.47716 S.E. of regression 8.810647 Akaike info criterion 7.224455 Sum squared resid 6365.455 Schwarz criterion 7.310666 Log likelihood -304.0393 F-statistic 18.39102 Durbin-Watson stat 1.995215 Prob(F-statistic) 0.000000 H 0 : mô hình hồi quy phụ không tồn tại H 1 : mô hình quy phụ có tồn tại Ta thấy Prob(F ) < 5% nên mô hình hồi quy phụ tồn tại do đó mô hình tổng thể bị đa cộng tuyến Tuy nhiên R^2 HQP = 0.309660 < R^2 HQC = 3067503 nên bỏ qua điều trị. 3. Kiểm định phương sai thay đổi ( HET) H 0 : mô hình không bị HET H 1 : mô hình bị HET - Dùng kiểm định white (no cross terms) White Heteroskedasticity Test: F-statistic 2.416418 Probability 0.034041 Obs*R-squared 13.32317 Probability 0.038182 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 06/30/11 Time: 14:01 Sample: 1 85 Included observations: 85 Variable Coefficient Std. Error t-Statistic Prob. C 0.113418 0.337901 0.335655 0.7380 SQUARE 0.040076 0.022170 1.807702 0.0745 SQUARE^2 -0.000335 0.000348 -0.961557 0.3392 PEOPLE -0.237844 0.220049 -1.080873 0.2831 PEOPLE^2 0.034115 0.033606 1.015139 0.3132 DISTANCE 0.014413 0.042061 0.342663 0.7328 DISTANCE^2 -0.001563 0.002423 -0.645073 0.5208 Ta thấy Prob F(White-net) = 0,034041 < α = 5% => Bác bỏ H 0 => Mô hình bị bệnh HET Dependent Variable: U2 Method: Least Squares Date: 06/30/11 Time: 19:21 Sample: 1 85 Included observations: 85 Variable Coefficient Std. Error t-Statistic Prob. SQUARE 0.040076 0.022170 1.807702 0.0745 DISTANCE 0.014413 0.042061 0.342663 0.7328 PEOPLE -0.237844 0.220049 -1.080873 0.2831 C 0.113418 0.337901 0.335655 0.7380 SQUARE^2 -0.000335 0.000348 -0.961557 0.3392 DISTANCE^2 -0.001563 0.002423 -0.645073 0.5208 PEOPLE^2 0.034115 0.033606 1.015139 0.3132 R-squared 0.156743 Mean dependent var 0.387964 Adjusted R-squared 0.091877 S.D. dependent var 0.571859 S.E. of regression 0.544956 Akaike info criterion 1.702539 Sum squared resid 23.16417 Schwarz criterion 1.903698 Log likelihood -65.35789 F-statistic 2.416418 Durbin-Watson stat 1.469243 Prob(F-statistic) 0.034041 - Trị bệnh HET Dependent Variable: PRICE Method: Least Squares Date: 06/30/11 Time: 19:25 Sample: 1 85 Included observations: 85 Weighting series: W Variable Coefficient Std. Error t-Statistic Prob. SQUARE 0.042208 0.009373 4.503102 0.0000 DISTANCE 0.007626 0.014901 0.511765 0.6102 PEOPLE 0.088639 0.067474 1.313684 0.1927 C 0.329234 0.159302 2.066725 0.0420 Weighted Statistics R-squared 0.092048 Mean dependent var 1.323050 Adjusted R-squared 0.058420 S.D. dependent var 0.577671 S.E. of regression 0.560543 Akaike info criterion 1.726093 Sum squared resid 25.45087 Schwarz criterion 1.841042 Log likelihood -69.35896 F-statistic 15.39420 Durbin-Watson stat 1.196347 Prob(F-statistic) 0.000000 Unweighted Statistics R-squared 0.364200 Mean dependent var 1.433412 Adjusted R-squared 0.340652 S.D. dependent var 0.787837 S.E. of regression 0.639726 Sum squared resid 33.14917 Durbin-Watson stat 1.352023 kiểm tra lại với white no cross terms White Heteroskedasticity Test: F-statistic 0.158176 Probability 0.986822 Obs*R-squared 1.021796 Probability 0.984773 Test Equation: Dependent Variable: STD_RESID^2 Method: Least Squares Date: 06/30/11 Time: 19:26 Sample: 1 85 Included observations: 85 Variable Coefficient Std. Error t-Statistic Prob. C 0.201271 0.223617 0.900071 0.3709 SQUARE 0.005995 0.014671 0.408649 0.6839 SQUARE^2 -8.25E-05 0.000231 -0.357866 0.7214 DISTANCE 0.005025 0.027835 0.180528 0.8572 DISTANCE^2 -0.000608 0.001603 -0.379374 0.7054 PEOPLE 0.001007 0.145624 0.006913 0.9945 PEOPLE^2 0.002145 0.022240 0.096460 0.9234 R-squared 0.012021 Mean dependent var 0.299422 Adjusted R-squared -0.063977 S.D. dependent var 0.349630 S.E. of regression 0.360641 Akaike info criterion 0.876898 Sum squared resid 10.14485 Schwarz criterion 1.078057 Log likelihood -30.26815 F-statistic 0.158176 Durbin-Watson stat 1.531565 Prob(F-statistic) 0.986822 ta thấy Prob > 5% nên mô hình hết bệnh 4. kiểm định tương quan chuỗi (AR) H 0 : mô hình không bị AR H 1 : mô hình bị AR Dùng kiểm định Correlogram-Qstat Date: 06/30/11 Time: 15:11 Sample: 1 85 Included observations: 85 Autocorrelation Partial Correlation AC PAC Q-Stat Prob . |** | . |** | 1 0.297 0.297 7.7818 0.005 . |** | . |** | 2 0.278 0.208 14.687 0.001 . |*. | . | . | 3 0.083 -0.051 15.309 0.002 . |*. | . | . | 4 0.084 0.020 15.949 0.003 . |*. | . |*. | 5 0.090 0.070 16.698 0.005 . | . | . | . | 6 0.033 -0.027 16.797 0.010 . | . | .*| . | 7 -0.033 -0.080 16.902 0.018 .*| . | .*| . | 8 -0.110 -0.099 18.075 0.021 .*| . | .*| . | 9 -0.188 -0.136 21.512 0.011 .*| . | . | . | 10 -0.147 -0.036 23.641 0.009 .*| . | .*| . | 11 -0.168 -0.062 26.460 0.006 . | . | . | . | 12 -0.055 0.055 26.768 0.008 . | . | . |*. | 13 -0.017 0.071 26.796 0.013 . | . | . | . | 14 -0.019 -0.001 26.836 0.020 . | . | . |*. | 15 0.050 0.073 27.097 0.028 . | . | .*| . | 16 -0.054 -0.089 27.414 0.037 . | . | . | . | 17 0.031 0.003 27.521 0.051 . |*. | . |*. | 18 0.082 0.070 28.264 0.058 . |*. | . | . | 19 0.071 -0.022 28.821 0.069 . |*. | . | . | 20 0.066 -0.021 29.320 0.082 . | . | . | . | 21 0.048 0.030 29.581 0.101 . | . | . | . | 22 -0.014 -0.049 29.605 0.128 .*| . | .*| . | 23 -0.058 -0.070 30.002 0.149 . | . | . | . | 24 -0.024 0.032 30.069 0.182 . | . | . | . | 25 0.000 0.022 30.069 0.222 . |*. | . |*. | 26 0.078 0.113 30.838 0.234 . |*. | . |*. | 27 0.089 0.082 31.849 0.238 . | . | .*| . | 28 -0.019 -0.079 31.897 0.279 . | . | . | . | 29 0.025 0.050 31.978 0.321 .*| . | .*| . | 30 -0.073 -0.101 32.694 0.336 . | . | . | . | 31 0.006 -0.012 32.699 0.383 . | . | . | . | 32 0.004 -0.001 32.701 0.432 . | . | . | . | 33 0.038 0.009 32.909 0.472 . | . | . | . | 34 0.034 0.051 33.081 0.512 . | . | . |*. | 35 0.034 0.073 33.253 0.553 . | . | . | . | 36 -0.033 -0.052 33.417 0.592 Ta thấy Prob F(Corelogram) < α = 5% => Bác bỏ H 0 => Mô hình bị AR -Trị bệnh AR Dependent Variable: PRICE Method: Least Squares Date: 06/30/11 Time: 19:35 Sample (adjusted): 2 85 Included observations: 84 after adjustments Convergence achieved after 7 iterations Variable Coefficient Std. Error t-Statistic Prob. SQUARE 0.036887 0.007044 5.236862 0.0000 DISTANCE -0.016605 0.017182 -0.966380 0.3368 PEOPLE 0.076219 0.061049 1.248477 0.2155 C 0.584153 0.189792 3.077865 0.0029 AR(1) 0.399006 0.114672 3.479530 0.0008 R-squared 0.451097 Mean dependent var 1.431429 Adjusted R-squared 0.423304 S.D. dependent var 0.792355 S.E. of regression 0.601718 Akaike info criterion 1.879624 Sum squared resid 28.60313 Schwarz criterion 2.024316 Log likelihood -73.94421 F-statistic 16.23086 Durbin-Watson stat 2.113651 Prob(F-statistic) 0.000000 Inverted AR Roots .40 Kiểm định lại với Corelogram Date: 06/30/11 Time: 15:12 Sample: 2 85 Included observations: 84 Q-statistic probabilities adjusted for 1 ARMA term(s) Autocorrelation Partial Correlation AC PAC Q-Stat Prob .*| . | .*| . | 1 -0.088 -0.088 0.6807 . |*. | . |*. | 2 0.153 0.146 2.7315 0.098 . | . | . | . | 3 -0.020 0.005 2.7666 0.251 . | . | . | . | 4 0.008 -0.016 2.7726 0.428 . |*. | . |*. | 5 0.116 0.121 4.0030 0.406 . | . | . | . | 6 -0.019 -0.000 4.0362 0.544 . | . | . | . | 7 0.019 -0.019 4.0703 0.667 . | . | . | . | 8 -0.050 -0.045 4.3041 0.744 .*| . | .*| . | 9 -0.085 -0.097 4.9991 0.758 . | . | . | . | 10 -0.040 -0.057 5.1518 0.821 .*| . | .*| . | 11 -0.161 -0.149 7.7096 0.657 . | . | . | . | 12 -0.008 -0.026 7.7154 0.739 . | . | . | . | 13 -0.016 0.038 7.7409 0.805 . | . | . | . | 14 -0.045 -0.025 7.9517 0.847 . |*. | . |*. | 15 0.090 0.104 8.8013 0.844 .*| . | . | . | 16 -0.080 -0.016 9.4752 0.851 . | . | . | . | 17 0.054 0.017 9.7939 0.877 . |*. | . |*. | 18 0.066 0.087 10.270 0.892 . | . | . | . | 19 0.007 -0.011 10.275 0.923 . | . | .*| . | 20 0.017 -0.059 10.307 0.945 . | . | . | . | 21 0.031 0.025 10.416 0.960 . | . | . | . | 22 -0.001 -0.037 10.416 0.973 . | . | .*| . | 23 -0.054 -0.096 10.758 0.978 . | . | . | . | 24 0.006 0.007 10.763 0.985 . | . | . | . | 25 -0.040 -0.028 10.958 0.989 . |*. | . |*. | 26 0.094 0.126 12.069 0.986 . |*. | . |*. | 27 0.090 0.151 13.104 0.983 .*| . | .*| . | 28 -0.088 -0.073 14.100 0.980 . | . | . |*. | 29 0.062 0.073 14.605 0.982 .*| . | .*| . | 30 -0.102 -0.077 15.985 0.976 . | . | .*| . | 31 0.012 -0.074 16.004 0.983 . | . | . | . | 32 -0.017 -0.034 16.046 0.988 . | . | . | . | 33 0.032 -0.003 16.189 0.991 . | . | . | . | 34 0.030 0.014 16.315 0.993 . | . | . |*. | 35 0.034 0.095 16.484 0.995 . | . | . | . | 36 -0.050 -0.051 16.864 0.996 ta thấy Prob > 5% mô hình đã hết bệnh AR tuy nhiên mô hình chưa tối ưu nên quyết định bỏ 2 biến DISTANCE và PEOPLE Dependent Variable: PRICE Method: Least Squares Date: 06/30/11 Time: 19:45 Sample (adjusted): 2 85 Included observations: 84 after adjustments Convergence achieved after 5 iterations Variable Coefficient Std. Error t-Statistic Prob. SQUARE 0.040373 0.006055 6.667209 0.0000 C 0.643249 0.155474 4.137341 0.0001 AR(1) 0.361104 0.107186 3.368958 0.0012 R-squared 0.435369 Mean dependent var 1.431429 Adjusted R-squared 0.421427 S.D. dependent var 0.792355 S.E. of regression 0.602697 Akaike info criterion 1.860257 Sum squared resid 29.42274 Schwarz criterion 1.947071 Log likelihood -75.13078 F-statistic 31.22820 Durbin-Watson stat 2.136175 Prob(F-statistic) 0.000000 Inverted AR Roots .36 Kiểm định lại với white no cross terms White Heteroskedasticity Test: F-statistic 5.458586 Probability 0.005971 Obs*R-squared 9.976834 Probability 0.006816 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 06/30/11 Time: 19:49 Sample: 2 85 Included observations: 84 Variable Coefficient Std. Error t-Statistic Prob. C -0.047827 0.229427 -0.208461 0.8354 SQUARE 0.022855 0.018703 1.221996 0.2253 SQUARE^2 -8.77E-05 0.000309 -0.284004 0.7771 R-squared 0.118772 Mean dependent var 0.350271 Adjusted R-squared 0.097013 S.D. dependent var 0.545166 S.E. of regression 0.518047 Akaike info criterion 1.557560 Sum squared resid 21.73820 Schwarz criterion 1.644375 Log likelihood -62.41752 F-statistic 5.458586 Durbin-Watson stat 1.840339 Prob(F-statistic) 0.005971 mô hình còn bệnh Mô hình tối ưu PRICE = 0.0403729702*SQUARE + 0.6432491035 + [AR(1)=0.3611040901] Giải thích ý nghĩa . Bai tập kinh tế lượng II. Mô hình hồi quy tổng thể PRICE = β 1 + β 2 * SQUARE + β 3 * DISTANCE