Bai tập kinh tế lượng pot

Error t-Statistic Prob... 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

Bai tập kinh tế lượng

II Mô hình hồi quy tổng thể

PRICE = β1 + β2* SQUARE + β3* DISTANCE + β4 * PEOPLE + ui

1.kiểm định sự tồn tại của mô hình

H0 : Mô hình hồi quy không tồn tại

H1 : 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

DISTANCE 0.004014 0.017489 0.229491 0.8191

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 H0  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

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

H0: mô hình hồi quy phụ không tồn tại

H1: 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^2HQC = 3067503 nên bỏ qua điều trị

3 Kiểm định phương sai thay đổi ( HET)

H0: mô hình không bị HET

H1: mô hình bị HET

- Dùng kiểm định white (no cross terms)

White Heteroskedasticity Test:

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

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 H0 => 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

DISTANCE 0.014413 0.042061 0.342663 0.7328

PEOPLE -0.237844 0.220049 -1.080873 0.2831

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

DISTANCE 0.007626 0.014901 0.511765 0.6102

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:

Test Equation:

Dependent Variable: STD_RESID^2

Sample: 1 85

Included observations: 85

Variable Coefficient Std Error t-Statistic Prob

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^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)

H0: mô hình không bị AR

H1: 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 H0 => 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

PEOPLE 0.076219 0.061049 1.248477 0.2155

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

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

F-statistic 5.458586 Probability 0.005971

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

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