Bài tập và hướng dẫn phân tích số liệu bằng SPSS

Bài tập và hướng dẫn phân tích số liệu bằng SPSS Anh/Chị hãy vào trang web: http://www.fpts.com.vn/user/stock/thong-ke/ thu thập số liệu theo tháng của chỉ số giá chứng khoán VN Index (VNI) và giá của cổ phiếu của Công ty Chứng khoán Sài Gòn (SSI), và thực hiện các yêu cầu sau đây: - lưu số liệu vừa thu thập về dưới dạng tập tin .

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classify -> ta có bảng sau: Descriptive Statistics for COMPENS Categorized by values of PROF Date: 05/22/09 Time: 16:41 Sample: 1 50 Included observations: 50 PROF Mean Std. Dev. Obs. 1 1250.286 782.2090 7 2 2027.000 NA 1 3 1439.500 903.1546 6 4 1011.667 742.8256 6 5 825.7143 647.6346 7 6 1018.667 450.1959 3 7 1440.889 1117.068 9 8 1061.400 563.8123 5 9 1117.833 1129.092 6 All 1186.080 833.5558 50 Nhận xét: tổng tiền lương trung bình của giám đốc dự án ở mức cao nếu tham gia từ 1->3 khóa, từ 4-> 9 khóa : ở mức trung bình chung Xác định mô hình hồi quy phù hợp: (không chắc chắn) ls salary c bonus othercom compens age edu prof tenure exper value profit sales có bảng kết quả hồi quy sau: Dependent Variable: SALARY Method: Least Squares Date: 05/21/09 Time: 02:05 Sample: 1 50 Included observations: 50 Variable Coefficient Std. Error t-Statistic Prob. C 1.41E-12 8.48E-13 1.668228 0.1035 BONUS -1.000000 2.74E-16 -3.65E+15 0.0000 OTHERCOM -1.000000 2.41E-15 -4.16E+14 0.0000 COMPENS 1.000000 1.27E-16 7.87E+15 0.0000 AGE -9.43E-15 1.38E-14 -0.683261 0.4986 EDU -6.18E-14 1.31E-13 -0.472206 0.6395 PROF -9.82E-14 2.48E-14 -3.960393 0.0003 TENURE 8.39E-16 6.15E-15 0.136488 0.8922 EXPER -5.10E-16 9.80E-15 -0.052002 0.9588 VALUE 1.21E-16 2.80E-16 0.431854 0.6683 PROFIT -2.36E-16 2.12E-16 -1.115079 0.2718 SALES 0.000000 1.57E-17 0.000000 1.0000 R-squared 1.000000 Mean dependent var 920.1200 Adjusted R-squared 1.000000 S.D. dependent var 697.6053 S.E. of regression 4.18E-13 Sum squared resid 6.64E-24 F-statistic 1.24E+31 Durbin-Watson stat 1.842031 Prob(F-statistic) 0.000000 -> các hệ số b5, b6, b8,b9,b10,b11,b12 không có ý nghĩa thống kê ở mức ý nghĩa 11% kiểm định Wald: từ kết quả hồi quy-> view/Coefficient Tests/ Wald-Coefficient Restrictions/ gõ c(5)=c(6)=c(8)=c(9)=c(10)=c(11)=c(12)=0 (giả thiết Ho), ta có bảng: Wald Test: Equation: Untitled Test Statistic Value df Probability F-statistic 0.303039 (7, 38) 0.9481 Chi-square 2.121275 7 0.9528 Null Hypothesis Summary: Normalized Restriction (= 0) Value Std. Err. C(5) -9.43E-15 1.38E-14 C(6) -6.18E-14 1.31E-13 C(8) 8.39E-16 6.15E-15 C(9) -5.10E-16 9.80E-15 C(10) 1.21E-16 2.80E-16 C(11) -2.36E-16 2.12E-16 C(12) 0.000000 1.57E-17 Restrictions are linear in coefficients. p-value của F-statistic lớn (0.9481)-> chấp nhận Ho (cả age, edu, tenure, exper, value, profit, salé x8,x9,x10,x11,x12 đồng thời không ảnh hưởng đến Y) Hồi quy salary theo bonus, othercom, compens, prof: ls salary c bonus othercom compens prof Dependent Variable: SALARY Method: Least Squares Date: 05/21/09 Time: 10:25 Sample: 1 50 Included observations: 50 Variable Coefficient Std. Error t-Statistic Prob. C 7.72E-13 1.45E-13 5.305148 0.0000 BONUS -1.000000 2.00E-16 -5.00E+15 0.0000 OTHERCOM -1.000000 1.84E-15 -5.45E+14 0.0000 COMPENS 1.000000 8.75E-17 1.14E+16 0.0000 PROF -8.90E-14 2.06E-14 -4.322178 0.0001 R-squared 1.000000 Mean dependent var 920.1200 Adjusted R-squared 1.000000 S.D. dependent var 697.6053 S.E. of regression 3.72E-13 Sum squared resid 6.24E-24 F-statistic 4.30E+31 Durbin-Watson stat 1.807065 Prob(F-statistic) 0.000000 -> mô hình hôi quy: Salary = 7.72E-13 – bonus – othercom + compens – 8.90E-14 Các kiểm định cần thiết: Kiểm định phương sai thay đổi: B1: Vẽ đồ thị salary theo bonus: Quick/Graph/ bonus salary B2: ước lượng lại mô hình ls salary c bonus othercom compens prof Dependent Variable: SALARY Method: Least Squares Date: 05/21/09 Time: 10:25 Sample: 1 50 Included observations: 50 Variable Coefficient Std. Error t-Statistic Prob. C 7.72E-13 1.45E-13 5.305148 0.0000 BONUS -1.000000 2.00E-16 -5.00E+15 0.0000 OTHERCOM -1.000000 1.84E-15 -5.45E+14 0.0000 COMPENS 1.000000 8.75E-17 1.14E+16 0.0000 PROF -8.90E-14 2.06E-14 -4.322178 0.0001 R-squared 1.000000 Mean dependent var 920.1200 Adjusted R-squared 1.000000 S.D. dependent var 697.6053 S.E. of regression 3.72E-13 Sum squared resid 6.24E-24 F-statistic 4.30E+31 Durbin-Watson stat 1.807065 Prob(F-statistic) 0.000000 B3: Vẽ đồ thị phần dư theo giá trị ước lượng của salary Từ kết quả hồi quy, chọn View/Representative, rồi copy phương trình hồi quy, ra cửa sổ lệnh và ước lượng như sau: genr salaryhat= 7.71731845292e-13 - 1*BONUS - 1*OTHERCOM + 1*COMPENS - 8.90013815418e-14*PROF Vẽ đồ thị: Quick/Graph/ salaryhat resid có phương sai thay đổi B4: kiểm định thống kê Từ bảng kết quả hồi quy-> view/Residual Tests/ Heteroskedasticity Tests/ * nếu chọn Breusch-Pagan-Godfrey -> ta có bảng: Heteroskedasticity Test: Breusch-Pagan-Godfrey F-statistic 4.920500 Prob. F(4,45) 0.0022 Obs*R-squared 15.21443 Prob. Chi-Square(4) 0.0043 Scaled explained SS 23.41351 Prob. Chi-Square(4) 0.0001 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 05/21/09 Time: 10:56 Sample: 1 50 Included observations: 50 Variable Coefficient Std. Error t-Statistic Prob. C 4.29E-26 8.36E-26 0.513627 0.6100 BONUS -9.18E-29 1.15E-28 -0.799212 0.4284 OTHERCOM -2.83E-27 1.05E-27 -2.681876 0.0102 COMPENS 2.17E-28 5.03E-29 4.322641 0.0001 PROF -6.06E-27 1.18E-26 -0.512163 0.6110 R-squared 0.304289 Mean dependent var 1.25E-25 Adjusted R-squared 0.242448 S.D. dependent var 2.46E-25 S.E. of regression 2.14E-25 Sum squared resid 2.06E-48 F-statistic 4.920500 Durbin-Watson stat 2.394366 Prob(F-statistic) 0.002235 * nếu chọn Harvey -> ta có bảng : Heteroskedasticity Test: Harvey F-statistic 2.092208 Prob. F(4,45) 0.0976 Obs*R-squared 7.840561 Prob. Chi-Square(4) 0.0976 Scaled explained SS 5.869265 Prob. Chi-Square(4) 0.2091 Test Equation: Dependent Variable: LRESID2 Method: Least Squares Date: 05/21/09 Time: 11:01 Sample: 1 50 Included observations: 50 Variable Coefficient Std. Error t-Statistic Prob. C -57.35134 0.726762 -78.91346 0.0000 BONUS 0.000305 0.000999 0.304804 0.7619 OTHERCOM -0.011447 0.009172 -1.248043 0.2185 COMPENS 0.000462 0.000437 1.056523 0.2964 PROF -0.254434 0.102877 -2.473194 0.0172 R-squared 0.156811 Mean dependent var -58.56495 Adjusted R-squared 0.081861 S.D. dependent var 1.941512 S.E. of regression 1.860349 Akaike info criterion 4.174044 Sum squared resid 155.7404 Schwarz criterion 4.365247 Log likelihood -99.35111 Hannan-Quinn criter. 4.246855 F-statistic 2.092208 Durbin-Watson stat 1.975815 Prob(F-statistic) 0.097553 * nếu chọn Glejser -> ta có bảng: Heteroskedasticity Test: Glejser F-statistic 3.681065 Prob. F(4,45) 0.0112 Obs*R-squared 12.32687 Prob. Chi-Square(4) 0.0151 Scaled explained SS 12.27461 Prob. Chi-Square(4) 0.0154 Test Equation: Dependent Variable: ARESID Method: Least Squares Date: 05/21/09 Time: 11:02 Sample: 1 50 Included observations: 50 Variable Coefficient Std. Error t-Statistic Prob. C 3.28E-13 8.01E-14 4.093779 0.0002 BONUS -4.69E-17 1.10E-16 -0.426069 0.6721 OTHERCOM -1.98E-15 1.01E-15 -1.962031 0.0560 COMPENS 1.44E-16 4.82E-17 2.995479 0.0044 PROF -2.46E-14 1.13E-14 -2.172259 0.0351 R-squared 0.246537 Mean dependent var 2.73E-13 Adjusted R-squared 0.179563 S.D. dependent var 2.26E-13 S.E. of regression 2.05E-13 Sum squared resid 1.89E-24 F-statistic 3.681065 Durbin-Watson stat 2.093847 Prob(F-statistic) 0.011219 nếu chọn arch-> ta có bảng : Heteroskedasticity Test: ARCH F-statistic 0.058717 Prob. F(1,47) 0.8096 Obs*R-squared 0.061140 Prob. Chi-Square(1) 0.8047 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 05/21/09 Time: 11:05 Sample (adjusted): 2 50 Included observations: 49 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 1.28E-25 4.00E-26 3.201934 0.0024 RESID^2(-1) -0.035390 0.146048 -0.242317 0.8096 R-squared 0.001248 Mean dependent var 1.24E-25 Adjusted R-squared -0.020002 S.D. dependent var 2.48E-25 S.E. of regression 2.51E-25 Sum squared resid 2.95E-48 F-statistic 0.058717 Durbin-Watson stat 2.000941 Prob(F-statistic) 0.809589 * nếu chọn white -> ta có bảng: Heteroskedasticity Test: White F-statistic 62.57475 Prob. F(14,35) 0.0000 Obs*R-squared 48.07913 Prob. Chi-Square(14) 0.0000 Scaled explained SS 73.98905 Prob. Chi-Square(14) 0.0000 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 05/21/09 Time: 11:08 Sample: 1 50 Included observations: 50 Variable Coefficient Std. Error t-Statistic Prob. C 5.27E-25 5.66E-26 9.315531 0.0000 BONUS 5.10E-28 1.69E-28 3.009395 0.0048 BONUS^2 3.67E-31 1.18E-31 3.125379 0.0036 BONUS*OTHERCOM 7.98E-31 2.27E-30 0.352161 0.7268 BONUS*COMPENS -2.17E-31 7.88E-32 -2.755959 0.0092 BONUS*PROF -8.70E-29 1.72E-29 -5.052587 0.0000 OTHERCOM 7.63E-27 1.51E-27 5.069448 0.0000 OTHERCOM^2 1.27E-30 9.01E-30 0.141156 0.8886 OTHERCOM*COMPENS -2.91E-30 5.78E-31 -5.043283 0.0000 OTHERCOM*PROF -6.77E-28 1.39E-28 -4.887697 0.0000 COMPENS -5.27E-28 7.14E-29 -7.375194 0.0000 COMPENS^2 1.14E-31 1.66E-32 6.884827 0.0000 COMPENS*PROF 7.18E-29 6.21E-30 11.54878 0.0000 PROF -1.30E-25 1.72E-26 -7.567793 0.0000 PROF^2 7.55E-27 1.50E-27 5.045868 0.0000 R-squared 0.961583 Mean dependent var 1.25E-25 Adjusted R-squared 0.946216 S.D. dependent var 2.46E-25 S.E. of regression 5.70E-26 Sum squared resid 1.14E-49 F-statistic 62.57475 Durbin-Watson stat 1.420857 Prob(F-statistic) 0.000000 Nhận xét: Như vậy trừ kiểm định arch, tất cả các kiểm định còn lại điều cho thấy giá trị X2 (chi-squared) tính toán rất cao và giá trị xác suất rất thấp -> ta kết luận có hiện tượng phương sai thay đổi. Bài 4: a) ls log(imports) c log(gdp) log(cpi) Dependent Variable: LOG(IMPORTS) Method: Least Squares Date: 05/21/09 Time: 22:48 Sample: 1990Q1 2001Q3 Included observations: 47 Variable Coefficient Std. Error t-Statistic Prob. C 0.506395 0.295304 1.714828 0.0934 LOG(GDP) 2.136145 0.105433 20.26059 0.0000 LOG(CPI) 0.107142 0.050123 2.137587 0.0381 R-squared 0.977820 Mean dependent var 10.76531 Adjusted R-squared 0.976812 S.D. dependent var 0.164217 S.E. of regression 0.025007 Akaike info criterion -4.477653 Sum squared resid 0.027515 Schwarz criterion -4.359559 Log likelihood 108.2248 Hannan-Quinn criter. -4.433213 F-statistic 969.8746 Durbin-Watson stat 0.548284 Prob(F-statistic) 0.000000 b) Có hiện tượng đa cộng tuyến vì: sai dấu hệ số hồi quy b3 của biến log(cpi). Kỳ vọng b3 sản xuất giảm -> nhập khẩu (imports) giảm. R-squared = 0.977820 cao lập ma trận hệ số tương quan giữa các biến giải thích: View/ Group statistic/ Correlation/ nhập log(imports) log(gdp) log(cpi) LOG(IMPORTS) LOG(GDP) LOG(CPI) LOG(IMPORTS) 1.000000 0.987682 0.878005 LOG(GDP) 0.987682 1.000000 0.864534 LOG(CPI) 0.878005 0.864534 1.000000 Các hệ số tương quan giữa các biến cao -> có đa cộng tuyến, tương thích với kết quả ở câu b) Ước lượng mô hình: lnIMPORTt = B1 + B2lnGDPt + ut Dependent Variable: LOG(IMPORTS) Method: Least Squares Date: 05/21/09 Time: 23:13 Sample: 1990Q1 2001Q3 Included observations: 47 Variable Coefficient Std. Error t-Statistic Prob. C 0.143095 0.250887 0.570357 0.5713 LOG(GDP) 2.330987 0.055050 42.34344 0.0000 R-squared 0.975516 Mean dependent var 10.76531 Adjusted R-squared 0.974972 S.D. dependent var 0.164217 S.E. of regression 0.025979 Akaike info criterion -4.421405 Sum squared resid 0.030372 Schwarz criterion -4.342675 Log likelihood 105.9030 Hannan-Quinn criter. -4.391778 F-statistic 1792.967 Durbin-Watson stat 0.512036 Prob(F-statistic) 0.000000 Ước lượng mô hình: lnIMPORTt = B1 + B2lnCPIt + ut Dependent Variable: LOG(IMPORTS) Method: Least Squares Date: 05/21/09 Time: 23:15 Sample: 1990Q1 2001Q3 Included observations: 47 Variable Coefficient Std. Error t-Statistic Prob. C 5.942083 0.392142 15.15288 0.0000 LOG(CPI) 0.985095 0.080056 12.30506 0.0000 R-squared 0.770893 Mean dependent var 10.76531 Adjusted R-squared 0.765801 S.D. dependent var 0.164217 S.E. of regression 0.079471 Akaike info criterion -2.185217 Sum squared resid 0.284207 Schwarz criterion -2.106487 Log likelihood 53.35259 Hannan-Quinn criter. -2.155590 F-statistic 151.4145 Durbin-Watson stat 0.088172 Prob(F-statistic) 0.000000 Ước lượng mô hình: lnGDPt = B1 + B2lnCPIt + ut Dependent Variable: LOG(GDP) Method: Least Squares Date: 05/21/09 Time: 23:16 Sample: 1990Q1 2001Q3 Included observations: 47 Variable Coefficient Std. Error t-Statistic Prob. C 2.544625 0.174462 14.58552 0.0000 LOG(CPI) 0.410999 0.035617 11.53951 0.0000 R-squared 0.747419 Mean dependent var 4.556958 Adjusted R-squared 0.741806 S.D. dependent var 0.069582 S.E. of regression 0.035357 Akaike info criterion -3.805046 Sum squared resid 0.056254 Schwarz criterion -3.726316 Log likelihood 91.41858 Hannan-Quinn criter. -3.775419 F-statistic 133.1604 Durbin-Watson stat 0.051041 Prob(F-statistic) 0.000000 Rút ra kết luận về bản chất tự tương quan: tự tương quan là sự phụ thuộc giữa các biến trong mô hình. Bài 5: Dependent Variable: LOG(IMP) Method: Least Squares Date: 05/17/09 Time: 23:55 Sample: 1 24 Included observations: 24 Variable Coefficient Std. Error t-Statistic Prob. C 2.503281 0.298284 8.392276 0.0000 LOG(GDP) 2.158164 0.092647 23.29457 0.0000 LOG(CPI) -0.041740 0.030425 -1.371920 0.1846 R-squared 0.992698 Mean dependent var 11.81963 Adjusted R-squared 0.992003 S.D. dependent var 0.322220 S.E. of regression 0.028815 Akaike info criterion -4.139360 Sum squared resid 0.017437 Schwarz criterion -3.992103 Log likelihood 52.67231 Hannan-Quinn criter. -4.100292 F-statistic 1427.503 Durbin-Watson stat 1.192053 Prob(F-statistic) 0.000000 Dependent Variable: LOG(IMP) Method: Least Squares Date: 05/18/09 Time: 00:15 Sample: 1 24 Included observations: 24 Variable Coefficient Std. Error t-Statistic Prob. C 2.841244 0.171530 16.56410 0.0000 LOG(GDP) 2.042390 0.038996 52.37488 0.0000 R-squared 0.992044 Mean dependent var 11.81963 Adjusted R-squared 0.991682 S.D. dependent var 0.322220 S.E. of regression 0.029387 Akaike info criterion -4.136857 Sum squared resid 0.018999 Schwarz criterion -4.038686 Log likelihood 51.64229 Hannan-Quinn criter. -4.110813 F-statistic 2743.128 Durbin-Watson stat 1.114996 Prob(F-statistic) 0.000000 Breusch-Godfrey Serial Correlation LM Test: F-statistic 1.798545 Prob. F(1,21) 0.1942 Obs*R-squared 1.893326 Prob. Chi-Square(1) 0.1688 LOG(IMP) LOG(GDP) LOG(CPI) LOG(IMP) 1.000000 0.996014 0.896672 LOG(GDP) 0.996014 1.000000 0.910861 LOG(CPI) 0.896672 0.910861 1.000000 Dependent Variable: LOG(IMP) Method: Least Squares Date: 05/18/09 Time: 00:29 Sample: 1 24 Included observations: 24 Variable Coefficient Std. Error t-Statistic Prob. C 9.346217 0.262046 35.66637 0.0000 LOG(CPI) 0.603811 0.063557 9.500364 0.0000 R-squared 0.804021 Mean dependent var 11.81963 Adjusted R-squared 0.795113 S.D. dependent var 0.322220 S.E. of regression 0.145851 Akaike info criterion -0.932805 Sum squared resid 0.467996 Schwarz criterion -0.834634 Log likelihood 13.19366 Hannan-Quinn criter. -0.906760 F-statistic 90.25691 Durbin-Watson stat 0.251729 Prob(F-statistic) 0.000000 à tự tương quan Dependent Variable: LOG(GDP) Method: Least Squares Date: 05/18/09 Time: 00:30 Sample: 1 24 Included observations: 24 Variable Coefficient Std. Error t-Statistic Prob. C 3.170721 0.119137 26.61403 0.0000 LOG(CPI) 0.299120 0.028896 10.35178 0.0000 R-squared 0.829668 Mean dependent var 4.396017 Adjusted R-squared 0.821925 S.D. dependent var 0.157137 S.E. of regression 0.066310 Akaike info criterion -2.509291 Sum squared resid 0.096735 Schwarz criterion -2.411120 Log likelihood 32.11149 Hannan-Quinn criter. -2.483246 F-statistic 107.1593 Durbin-Watson stat 0.218168 Prob(F-statistic) 0.000000 à tự tương quan Bài 6: a) ls price c lotsize sqrft bdrms Dependent Variable: PRICE Method: Least Squares Date: 05/22/09 Time: 20:16 Sample: 1 88 Included observations: 88 Variable Coefficient Std. Error t-Statistic Prob. C -21770.31 29475.04 -0.738601 0.4622 LOTSIZE 2.067707 0.642126 3.220096 0.0018 SQRFT 122.7782 13.23741 9.275093 0.0000 BDRMS 13852.52 9010.145 1.537436 0.1279 R-squared 0.672362 Mean dependent var 293546.0 Adjusted R-squared 0.660661 S.D. dependent var 102713.4 S.E. of regression 59833.48 Akaike info criterion 24.88091 Sum squared resid 3.01E+11 Schwarz criterion 24.99351 Log likelihood -1090.760 Hannan-Quinn criter. 24.92627 F-statistic 57.46023 Durbin-Watson stat 2.109796 Prob(F-statistic) 0.000000 b) Kiểm định phương sai thay đổi: B1: Vẽ đồ thị price theo lotsize: Quick/Graph/ price lotsize B2: ước lượng lại mô hình ls price c lotsize sqrft bdrms Dependent Variable: PRICE Method: Least Squares Date: 05/22/09 Time: 20:23 Sample: 1 88 Included observations: 88 Variable Coefficient Std. Error t-Statistic Prob. C -21770.31 29475.04 -0.738601 0.4622 LOTSIZE 2.067707 0.642126 3.220096 0.0018 SQRFT 122.7782 13.23741 9.275093 0.0000 BDRMS 13852.52 9010.145 1.537436 0.1279 R-squared 0.672362 Mean dependent var 293546.0 Adjusted R-squared 0.660661 S.D. dependent var 102713.4 S.E. of regression 59833.48 Akaike info criterion 24.88091 Sum squared resid 3.01E+11 Schwarz criterion 24.99351 Log likelihood -1090.760 Hannan-Quinn criter. 24.92627 F-statistic 57.46023 Durbin-Watson stat 2.109796 Prob(F-statistic) 0.000000 B3: Vẽ đồ thị phần dư theo giá trị ước lượng của salary Từ kết quả hồi quy, chọn View/Representative, rồi copy phương trình hồi quy, ra cửa sổ lệnh và ước lượng như sau: genr pricehat = -21770.3086036 + 2.06770660199*LOTSIZE + 122.778185222*SQRFT + 13852.5218631*BDRMS Vẽ đồ thị: Quick/Graph/ pricehat resid -> có phương sai thay đổi B4: kiểm định thống kê Từ bảng kết quả hồi quy-> view/Residual Tests/ Heteroskedasticity Tests/ nếu chọn Breusch-Pagan-Godfrey -> ta có bảng Heteroskedasticity Test: Breusch-Pagan-Godfrey F-statistic 5.338919 Prob. F(3,84) 0.0020 Obs*R-squared 14.09239 Prob. Chi-Square(3) 0.0028 Scaled explained SS 27.35542 Prob. Chi-Square(3) 0.0000 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 05/22/09 Time: 20:31 Sample: 1 88 Included observations: 88 Variable Coefficient Std. Error t-Statistic Prob. C -5.52E+09 3.26E+09 -1.694380 0.0939 LOTSIZE 201520.9 71009.06 2.837961 0.0057 SQRFT 1691037. 1463850. 1.155198 0.2513 BDRMS 1.04E+09 9.96E+08 1.045544 0.2988 R-squared 0.160141 Mean dependent var 3.42E+09 Adjusted R-squared 0.130146 S.D. dependent var 7.09E+09 S.E. of regression 6.62E+09 Akaike info criterion 48.10798 Sum squared resid 3.68E+21 Schwarz criterion 48.22058 Log likelihood -2112.751 Hannan-Quinn criter. 48.15334 F-statistic 5.338919 Durbin-Watson stat 2.351111 Prob(F-statistic) 0.002048 * nếu chọn Harvey -> ta có bảng : Heteroskedasticity Test: Harvey F-statistic 2.883489 Prob. F(3,84) 0.0405 Obs*R-squared 8.216268 Prob. Chi-Square(3) 0.0417 Scaled explained SS 8.486394 Prob. Chi-Square(3) 0.0370 Test Equation: Dependent Variable: LRESID2 Method: Least Squares Date: 05/22/09 Time: 20:33 Sample: 1 88 Included observations: 88 Variable Coefficient Std. Error t-Statistic Prob. C 17.71619 1.083894 16.34494 0.0000 LOTSIZE 3.38E-05 2.36E-05 1.430733 0.1562 SQRFT 0.000515 0.000487 1.057938 0.2931 BDRMS 0.384611 0.331333 1.160801 0.2490 R-squared 0.093367 Mean dependent var 20.43030 Adjusted R-squared 0.060987 S.D. dependent var 2.270601 S.E. of regression 2.200274 Akaike info criterion 4.459430 Sum squared resid 406.6611 Schwarz criterion 4.572036 Log likelihood -192.2149 Hannan-Quinn criter. 4.504796 F-statistic 2.883489 Durbin-Watson stat 2.426777 Prob(F-statistic) 0.040533 * nếu chọn Glejser -> ta có bảng: Heteroskedasticity Test: Glejser F-statistic 7.185545 Prob. F(3,84) 0.0002 Obs*R-squared 17.97124 Prob. Chi-Square(3) 0.0004 Scaled explained SS 21.43101 Prob. Chi-Square(3) 0.0001 Test Equation: Dependent Variable: ARESID Method: Least Squares Date: 05/22/09 Time: 20:34 Sample: 1 88 Included observations: 88 Variable Coefficient Std. Error t-Statistic Prob. C -19500.44 17716.01 -1.100724 0.2742 LOTSIZE 1.129760 0.385951 2.927215 0.0044 SQRFT 10.69671 7.956360 1.344423 0.1824 BDRMS 8678.622 5415.559 1.602535 0.1128 R-squared 0.204219 Mean dependent var 43196.64 Adjusted R-squared 0.175798 S.D. dependent var 39613.11 S.E. of regression 35962.99 Akaike info criterion 23.86276 Sum squared resid 1.09E+11 Schwarz criterion 23.97536 Log likelihood -1045.961 Hannan-Quinn criter. 23.90812 F-statistic 7.185545 Durbin-Watson stat 2.538377 Prob(F-statistic) 0.000237 nếu chọn arch-> ta có bảng : Heteroskedasticity Test: ARCH F-statistic 0.125639 Prob. F(1,85) 0.7239 Obs*R-squared 0.128406 Prob. Chi-Square(1) 0.7201 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 05/22/09 Time: 20:36 Sample (adjusted): 2 88 Included observations: 87 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 3.57E+09 8.55E+08 4.169434 0.0001 RESID^2(-1) -0.038451 0.108478 -0.354457 0.7239 R-squared 0.001476 Mean dependent var 3.43E+09 Adjusted R-squared -0.010271 S.D. dependent var 7.13E+09 S.E. of regression 7.17E+09 Akaike info criterion 48.24710 Sum squared resid 4.37E+21 Schwarz criterion 48.30379 Log likelihood -2096.749 Hannan-Quinn criter. 48.26993 F-statistic 0.125639 Durbin-Watson stat 2.002935 Prob(F-statistic) 0.723875 * nếu chọn white -> ta có bảng: Heteroskedasticity Test: White F-statistic 5.386953 Prob. F(9,78) 0.0000 Obs*R-squared 33.73166 Prob. Chi-Square(9) 0.0001 Scaled explained SS 65.47818 Prob. Chi-Square(9) 0.0000 Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 05/22/09 Time: 20:37 Sample: 1 88 Included observations: 88 Variable Coefficient Std. Error t-Statistic Prob. C 1.56E+10 1.14E+10 1.374411 0.1733 LOTSIZE -1859507. 637097.0 -2.918719 0.0046 LOTSIZE^2 -0.497839 4.631155 -0.107498 0.9147 LOTSIZE*SQRFT 456.7785 276.8903 1.649673 0.1030 LOTSIZE*BDRMS 314646.9 252093.6 1.248135 0.2157 SQRFT -2673918. 8662183. -0.308689 0.7584 SQRFT^2 352.2553 1839.603 0.191484 0.8486 SQRFT*BDRMS -1020860. 1667154. -0.612337 0.5421 BDRMS -1.98E+09 5.44E+09 -0.364595 0.7164 BDRMS^2 2.90E+08 7.59E+08 0.381843 0.7036 R-squared 0.383314 Mean dependent var 3.42E+09 Adjusted R-squared 0.312158 S.D. dependent var 7.09E+09 S.E. of regression 5.88E+09 Akaike info criterion 47.93546 Sum squared resid 2.70E+21 Schwarz criterion 48.21698 Log likelihood -2099.160 Hannan-Quinn criter. 48.04888 F-statistic 5.386953 Durbin-Watson stat 2.052712 Prob(F-statistic) 0.000010 Nhận xét: Như vậy trừ kiểm định arch, tất cả các kiểm định còn lại điều cho thấy giá trị X2 (chi-squared) tính toán rất cao và giá trị xác suất rất thấp -> ta kết luận có hiện tượng phương sai thay đổi. c) ls price c log(lotsize) log(sqrft) log(bdrms) Dependent Variable: PRICE Method: Least Squares Date: 05/22/09 Time: 20:40 Sample: 1 88 Included observations: 88 Variable Coefficient Std. Error t-Statistic Prob. C -2082664. 206661.6 -10.07765 0.0000 LOG(LOTSIZE) 62344.58 12427.50 5.016663 0.0000 LOG(SQRFT) 230938.4 30176.04 7.653037 0.0000 LOG(BDRMS) 57951.03 32937.22 1.759439 0.0821 R-squared 0.671560 Mean dependent var 293546.0 Adjusted R-squared 0.659830 S.D. dependent var 102713.4 S.E. of regression 59906.72 Akaike info criterion 24.88335 Sum squared resid 3.01E+11 Schwarz criterion 24.99596 Log likelihood -1090.868 Hannan-Quinn criter. 24.92872 F-statistic 57.25139 Durbin-Watson stat 2.208456 Prob(F-statistic) 0.000000 Kiểm định phương sai thay đổi: B1: Vẽ đồ thị price theo lotsize: Quick/Graph/ price log(lotsize) B2: ước lượng lại mô hình ls price c log(lotsize) log(sqrft) log(bdrms) Dependent Variable: PRICE Method: Least Squares Date: 05/22/09 Time: 20:40 Sample: 1 88 Included observations: 88 Variable Coefficient Std. Error t-Statistic Prob. C -2082664. 206661.6 -10.07765 0.0000 LOG(LOTSIZE) 62344.58 12427.50 5.016663 0.0000 LOG(SQRFT) 230938.4 30176.04 7.653037 0.0000 LOG(BDRMS) 57951.03 32937.22 1.759439 0.0821 R-squared 0.671560 Mean dependent var 293546.0 Adjusted R-squared 0.659830 S.D. dependent var 102713.4 S.E. of regression 59906.72 Akaike info criterion 24.88335 Sum squared resid 3.01E+11 Schwarz criterion 24.99596 Log likelihood -1090.868 Hannan-Quinn criter. 24.92872 F-statistic 57.25139 Durbin-Watson stat 2.208456 Prob(F-statistic) 0.000000 B3: Vẽ đồ thị phần dư theo giá trị ước lượng của price Từ kết quả hồi quy, chọn View/Representative, rồi copy phương trình hồi quy, ra cửa sổ lệnh và ước lượng như sau: genr pricehat = -2082663.68199 + 62344.5769751*LOG(LOTSIZE) + 230938.364794*LOG(SQRFT) + 57951.0312542*LOG(BDRMS) Vẽ đồ thị: Quick/Graph/ pricehat resid -> có phương sai không đổi Bai 8: a) Chọn biến I -> view/Unit root test, chọn level, intercept -> có bảng: Null Hypothesis: I has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=7) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -1.158543 0.6782 Test critical values: 1% level -3.679322 5% level -2.967767 10% level -2.622989 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(I) Method: Least Squares Date: 05/22/09 Time: 20:58 Sample (adjusted): 2001Q4 2008Q4 Included observations: 29 after adjustments Variable Coefficient Std. Error t-Statistic Prob. I(-1) -0.108120 0.093324 -1.158543 0.2568 C 2.823139 1.970204 1.432917 0.1634 R-squared 0.047358 Mean dependent var 0.677586 Adjusted R-squared 0.012075 S.D. dependent var 3.642638 S.E. of regression 3.620580 Akaike info criterion 5.477617 Sum squared resid 353.9321 Schwarz criterion 5.571914 Log likelihood -77.42545 Hannan-Quinn criter. 5.507150 F-statistic 1.342222 Durbin-Watson stat 2.387635 Prob(F-statistic) 0.256787 Ho: chuỗi I không dừng P-value lớn -> chấp nhận Ho -> chuỗi I không dừng Chọn biến Y -> view/Unit root test, chọn level, intercept -> có bảng: Null Hypothesis: Y has a unit root Exogenous: Constant Lag Length: 2 (Automatic based on SIC, MAXLAG=7) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -0.551274 0.8657 Test critical values: 1% level -3.699871 5% level -2.976263 10% level -2.627420 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(Y) Method: Least Squares Date: 05/22/09 Time: 21:00 Sample (adjusted): 2002Q2 2008Q4 Included observations: 27 after adjustments Variable Coefficient Std. Error t-Statistic Prob. Y(-1) -0.022334 0.040514 -0.551274 0.5868 D(Y(-1)) -0.274478 0.185252 -1.481651 0.1520 D(Y(-2)) -0.450442 0.182826 -2.463769 0.0217 C 2.103577 0.920943 2.284154 0.0319 R-squared 0.263846 Mean dependent var 0.945185 Adjusted R-squared 0.167826 S.D. dependent var 1.780567 S.E. of regression 1.624297 Akaike info criterion 3.943981 Sum squared resid 60.68182 Schwarz criterion 4.135957 Log likelihood -49.24374 Hannan-Quinn criter. 4.001065 F-statistic 2.747820 Durbin-Watson stat 2.164554 Prob(F-statistic) 0.066029 -> chuỗi Y không dừng Chọn biến R -> view/Unit root test, chọn level, intercept -> có bảng: Null Hypothesis: R has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=7) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -6.909094 0.0000 Test critical values: 1% level -3.679322 5% level -2.967767 10% level -2.622989 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(R) Method: Least Squares Date: 05/22/09 Time: 21:01 Sample (adjusted): 2001Q4 2008Q4 Included observations: 29 after adjustments Variable Coefficient Std. Error t-Statistic Prob. R(-1) -1.267350 0.183432 -6.909094 0.0000 C 17.64524 2.717806 6.492458 0.0000 R-squared 0.638726 Mean dependent var -0.079310 Adjusted R-squared 0.625346 S.D. dependent var 7.894809 S.E. of regression 4.832334 Akaike info criterion 6.055008 Sum squared resid 630.4892 Schwarz criterion 6.149305 Log likelihood -85.79762 Hannan-Quinn criter. 6.084541 F-statistic 47.73559 Durbin-Watson stat 2.074225 Prob(F-statistic) 0.000000 -> chuỗi R dừng Nếu là chuỗi không dừng thì sẽ có trung bình và phương sai thay đổi thời gian -> không dự báo chính xác được -> nếu là chuỗi dừng thì nên chuyển sang dạng sai phân bậc 1 vì thông thường 1 chuỗi thời gian là không dừng thì sai phân bậc 1 có thể sẽ là một chuỗi dừng (có trung bình và phương sai không đổi theo thời gian) -> dự báo chính xác hơn. b) ls I c Y R Dependent Variable: I Method: Least Squares Date: 05/22/09 Time: 21:02 Sample: 2001Q3 2008Q4 Included observations: 30 Variable Coefficient Std. Error t-Statistic Prob. C 6.224938 2.510894 2.479172 0.0197 Y 0.769911 0.071791 10.72442 0.0000 R -0.184196 0.126416 -1.457068 0.1566 R-squared 0.816282 Mean dependent var 20.22200 Adjusted R-squared 0.802673 S.D. dependent var 7.495569 S.E. of regression 3.329642 Akaike info criterion 5.338246 Sum squared resid 299.3358 Schwarz criterion 5.478366 Log likelihood -77.07369 Hannan-Quinn criter. 5.383071 F-statistic 59.98221 Durbin-Watson stat 0.852153 Prob(F-statistic) 0.000000 Do d=0.85 -> có tự tương quan bậc 1 Ta kiểm tra xem có tự tương quan bặc cao hay không: Từ kết quả hồi quy -> view/Residual/ Serial Correlation LM Test -> có bảng: Breusch-Godfrey Serial Correlation LM Test: F-statistic 6.764643 Prob. F(2,25) 0.0045 Obs*R-squared 10.53429 Prob. Chi-Square(2) 0.0052 Test Equation: Dependent Variable: RESID Method: Least Squares Date: 05/22/09 Time: 21:04 Sample: 2001Q3 2008Q4 Included observations: 30 Presample missing value lagged residuals set to zero. Variable Coefficient Std. Error t-Statistic Prob. C 1.799886 2.202606 0.817162 0.4216 Y -0.012173 0.060373 -0.201637 0.8418 R -0.107141 0.112469 -0.952623 0.3499 RESID(-1) 0.697416 0.208636 3.342738 0.0026 RESID(-2) -0.165681 0.204936 -0.808452 0.4265 R-squared 0.351143 Mean dependent var -4.88E-16 Adjusted R-squared 0.247326 S.D. dependent var 3.212775 S.E. of regression 2.787301 Akaike info criterion 5.039036 Sum squared resid 194.2262 Schwarz criterion 5.272569 Log likelihood -70.58555 Hannan-Quinn criter. 5.113746 F-statistic 3.382321 Durbin-Watson stat 1.868584 Prob(F-statistic) 0.024177 Vì Prob.Square(2) = 0.0052 nhỏ -> có tự tương quan bậc cao c) ls log(I) c log(Y) log(R) Dependent Variable: LOG(I) Method: Least Squares Date: 05/22/09 Time: 21:10 Sample: 2001Q3 2008Q4 Included observations: 30 Variable Coefficient Std. Error t-Statistic Prob. C 1.023735 0.405353 2.525538 0.0177 LOG(Y) 0.734444 0.091028 8.068345 0.0000 LOG(R) -0.108312 0.102930 -1.052288 0.3020 R-squared 0.720742 Mean dependent var 2.933305 Adjusted R-squared 0.700056 S.D. dependent var 0.400720 S.E. of regression 0.219463 Akaike info criterion -0.100627 Sum squared resid 1.300428 Schwarz criterion 0.039493 Log likelihood 4.509408 Hannan-Quinn criter. -0.055802 F-statistic 34.84233 Durbin-Watson stat 0.619553 Prob(F-statistic) 0.000000 Do d=0.61 -> có tự tương quan bậc 1 Ta kiểm tra xem có tự tương quan bặc cao hay không: Từ kết quả hồi quy -> view/Residual/ Serial Correlation LM Test -> có bảng: Breusch-Godfrey Serial Correlation LM Test: F-statistic 11.32566 Prob. F(2,25) 0.0003 Obs*R-squared 14.26067 Prob. Chi-Square(2) 0.0008 Test Equation: Dependent Variable: RESID Method: Least Squares Date: 05/22/09 Time: 21:11 Sample: 2001Q3 2008Q4 Included observations: 30 Presample missing value lagged residuals set to zero. Variable Coefficient Std. Error t-Statistic Prob. C 0.128674 0.311885 0.412569 0.6834 LOG(Y) -0.009872 0.069046 -0.142978 0.8875 LOG(R) -0.037666 0.079057 -0.476442 0.6379 RESID(-1) 0.792038 0.201930 3.922330 0.0006 RESID(-2) -0.153046 0.203102 -0.753540 0.4582 R-squared 0.475356 Mean dependent var 5.12E-16 Adjusted R-squared 0.391412 S.D. dependent var 0.211760 S.E. of regression 0.165198 Akaike info criterion -0.612328 Sum squared resid 0.682262 Schwarz criterion -0.378795 Log likelihood 14.18492 Hannan-Quinn criter. -0.537619 F-statistic 5.662829 Durbin-Watson stat 1.992081 Prob(F-statistic) 0.002187 Vì Prob.Square(2) = 0.008 nhỏ -> có tự tương quan bậc cao ls I c y r @trend(2001Q3) Dependent Variable: I Method: Least Squares Date: 05/22/09 Time: 21:13 Sample: 2001Q3 2008Q4 Included observations: 30 Variable Coefficient Std. Error t-Statistic Prob. C 4.695682 3.912313 1.200232 0.2409 Y 0.992016 0.437555 2.267178 0.0319 R -0.187741 0.128357 -1.462647 0.1555 @TREND(2001Q3) -0.221050 0.429411 -0.514776 0.6111 R-squared 0.818136 Mean dependent var 20.22200 Adjusted R-squared 0.797151 S.D. dependent var 7.495569 S.E. of regression 3.375909 Akaike info criterion 5.394772 Sum squared resid 296.3158 Schwarz criterion 5.581598 Log likelihood -76.92158 Hannan-Quinn criter. 5.454539 F-statistic 38.98790 Durbin-Watson stat 0.916623 Prob(F-statistic) 0.000000 Do d=0.91 -> có tự tương quan bậc 1 Ta kiểm tra xem có tự tương quan bặc cao hay không: Từ kết quả hồi quy -> view/Residual/ Serial Correlation LM Test -> có bảng: Breusch-Godfrey Serial Correlation LM Test: F-statistic 7.743312 Prob. F(2,24) 0.0025 Obs*R-squared 11.76598 Prob. Chi-Square(2) 0.0028 Test Equation: Dependent Variable: RESID Method: Least Squares Date: 05/22/09 Time: 21:14 Sample: 2001Q3 2008Q4 Included observations: 30 Presample missing value lagged residuals set to zero. Variable Coefficient Std. Error t-Statistic Prob. C 7.156954 3.716978 1.925476 0.0661 Y -0.703810 0.399603 -1.761273 0.0909 R -0.133598 0.111906 -1.193840 0.2442 @TREND(2001Q3) 0.684778 0.391183 1.750530 0.0928 RESID(-1) 0.832667 0.227640 3.657818 0.0012 RESID(-2) -0.208571 0.202148 -1.031770 0.3125 R-squared 0.392199 Mean dependent var -8.88E-17 Adjusted R-squared 0.265574 S.D. dependent var 3.196527 S.E. of regression 2.739381 Akaike info criterion 5.030197 Sum squared resid 180.1009 Schwarz criterion 5.310437 Log likelihood -69.45296 Hannan-Quinn criter. 5.119848 F-statistic 3.097325 Durbin-Watson stat 1.871876 Prob(F-statistic) 0.026903 Vì Prob.Square(2) = 0.0028 nhỏ -> có tự tương quan bậc cao Mô hình 1 có tự tương quan, nhưng khi chuyển sang mô hình 2 và 3 vẫn còn tự tương quan (thay đổi dạng hàm) -> như vậy tự tương quan ở mô hình 1 là tự tương quan thuần túy. Khắc phục tự tương quan: thủ tục Cochrane-Orcutt B1: Ước lượng phương trình: Yt=b1+b2Xt+et ls I c Y R Dependent Variable: I Method: Least Squares Date: 05/22/09 Time: 22:05 Sample: 2001Q3 2008Q4 Included observations: 30 Variable Coefficient Std. Error t-Statistic Prob. C 6.224938 2.510894 2.479172 0.0197 Y 0.769911 0.071791 10.72442 0.0000 R -0.184196 0.126416 -1.457068 0.1566 R-squared 0.816282 Mean dependent var 20.22200 Adjusted R-squared 0.802673 S.D. dependent var 7.495569 S.E. of regression 3.329642 Akaike info criterion 5.338246 Sum squared resid 299.3358 Schwarz criterion 5.478366 Log likelihood -77.07369 Hannan-Quinn criter. 5.383071 F-statistic 59.98221 Durbin-Watson stat 0.852153 Prob(F-statistic) 0.000000 -> lưu et: genr pd=resid B2: Hồi quy: et=p^et-1+εt ls pd pd(-1) Dependent Variable: PD Method: Least Squares Date: 05/22/09 Time: 22:09 Sample (adjusted): 2001Q4 2008Q4 Included observations: 29 after adjustments Variable Coefficient Std. Error t-Statistic Prob. PD(-1) 0.567726 0.155221 3.657547 0.0010 R-squared 0.322978 Mean dependent var -0.070236 Adjusted R-squared 0.322978 S.D. dependent var 3.246119 S.E. of regression 2.670950 Akaike info criterion 4.836620 Sum squared resid 199.7512 Schwarz criterion 4.883768 Log likelihood -69.13098 Hannan-Quinn criter. 4.851386 Durbin-Watson stat 1.851803 -> p^=0.567726 lưu p^ genr rho=c(1) B3: Tính It*,Yt*,Rt* genr Ihat=I-rho*I(-1) genr yhat=y-rho*y(-1) genr rhat=r-rho*r(-1) B4: It*=B1*+B2*Yt*+B3*Rt*+ εt (2) ước lượng (2) theo OLS: ls Ihat c yhat rhat Dependent Variable: IHAT Method: Least Squares Date: 05/22/09 Time: 22:02 Sample (adjusted): 2001Q4 2008Q4 Included observations: 29 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 3.130112 1.442645 2.169704 0.0394 YHAT 0.787463 0.131353 5.995034 0.0000 RHAT -0.293100 0.080636 -3.634844 0.0012 R-squared 0.635559 Mean dependent var 9.255682 Adjusted R-squared 0.607525 S.D. dependent var 4.276520 S.E. of regression 2.679146 Akaike info criterion 4.906570 Sum squared resid 186.6234 Schwarz criterion 5.048015 Log likelihood -68.14527 Hannan-Quinn criter. 4.950869 F-statistic 22.67109 Durbin-Watson stat 1.547610 Prob(F-statistic) 0.000002 Do d=1.54->không có tự tương quan bậc 1 Ta kiểm tra xem có tự tương quan bặc cao hay không: Từ kết quả hồi quy -> view/Residual/ Serial Correlation LM Test -> có bảng: Breusch-Godfrey Serial Correlation LM Test: F-statistic 0.982814 Prob. F(2,24) 0.3888 Obs*R-squared 2.195333 Prob. Chi-Square(2) 0.3336 Test Equation: Dependent Variable: RESID Method: Least Squares Date: 05/22/09 Time: 22:18 Sample: 2001Q4 2008Q4 Included observations: 29 Presample missing value lagged residuals set to zero. Variable Coefficient Std. Error t-Statistic Prob. C 0.502257 1.492973 0.336414 0.7395 YHAT -0.027402 0.133920 -0.204616 0.8396 RHAT -0.036417 0.085114 -0.427866 0.6726 RESID(-1) 0.287089 0.214723 1.337020 0.1938 RESID(-2) -0.161041 0.209509 -0.768659 0.4496 R-squared 0.075701 Mean dependent var -1.36E-15 Adjusted R-squared -0.078349 S.D. dependent var 2.581690 S.E. of regression 2.680919 Akaike info criterion 4.965782 Sum squared resid 172.4958 Schwarz criterion 5.201522 Log likelihood -67.00383 Hannan-Quinn criter. 5.039613 F-statistic 0.491407 Durbin-Watson stat 1.931618 Prob(F-statistic) 0.742030 Vì Prob.Square(2) = 0.3336->không có tự tương quan bậc cao Bai 9: a) Chọn biến f -> view/Unit root test, chọn level, intercept -> có bảng: Null Hypothesis: F has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=7) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -0.853481 0.7888 Test critical values: 1% level -3.670170 5% level -2.963972 10% level -2.621007 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(F) Method: Least Squares Date: 05/22/09 Time: 14:52 Sample (adjusted): 1979 2008 Included observations: 30 after adjustments Variable Coefficient Std. Error t-Statistic Prob. F(-1) -0.022615 0.026497 -0.853481 0.4006 C 3.070566 2.897865 1.059596 0.2984 R-squared 0.025356 Mean dependent var 0.600000 Adjusted R-squared -0.009453 S.D. dependent var 0.739058 S.E. of regression 0.742543 Akaike info criterion 2.306869 Sum squared resid 15.43837 Schwarz criterion 2.400282 Log likelihood -32.60303 Hannan-Quinn criter. 2.336752 F-statistic 0.728430 Durbin-Watson stat 1.998903 Prob(F-statistic) 0.400635 Ho: chuỗi f không dừng P-value lớn -> chấp nhận Ho -> chuỗi f không dừng Chọn biến p -> view/Unit root test, chọn level, intercept -> có bảng: Null Hypothesis: P has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=7) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -3.156190 0.0330 Test critical values: 1% level -3.670170 5% level -2.963972 10% level -2.621007 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(P) Method: Least Squares Date: 05/22/09 Time: 14:56 Sample (adjusted): 1979 2008 Included observations: 30 after adjustments Variable Coefficient Std. Error t-Statistic Prob. P(-1) -0.518693 0.164342 -3.156190 0.0038 C 54.57645 17.21709 3.169900 0.0037 R-squared 0.262411 Mean dependent var 0.290000 Adjusted R-squared 0.236069 S.D. dependent var 4.806630 S.E. of regression 4.201146 Akaike info criterion 5.772932 Sum squared resid 494.1896 Schwarz criterion 5.866346 Log likelihood -84.59399 Hannan-Quinn criter. 5.802816 F-statistic 9.961532 Durbin-Watson stat 1.797577 Prob(F-statistic) 0.003803 p-value nhỏ -> bác bỏ Ho -> chuỗi p dừng Chọn biến q -> view/Unit root test, chọn level, intercept -> có bảng: Null Hypothesis: Q has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=7) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -3.297838 0.0243 Test critical values: 1% level -3.679322 5% level -2.967767 10% level -2.622989 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(Q) Method: Least Squares Date: 05/22/09 Time: 14:58 Sample (adjusted): 1980 2008 Included observations: 29 after adjustments Variable Coefficient Std. Error t-Statistic Prob. Q(-1) -0.529847 0.160665 -3.297838 0.0027 C 17.96495 5.512537 3.258927 0.0030 R-squared 0.287143 Mean dependent var -0.113793 Adjusted R-squared 0.260740 S.D. dependent var 3.629121 S.E. of regression 3.120325 Akaike info criterion 5.180224 Sum squared resid 262.8836 Schwarz criterion 5.274520 Log likelihood -73.11324 Hannan-Quinn criter. 5.209756 F-statistic 10.87573 Durbin-Watson stat 1.610096 Prob(F-statistic) 0.002736 -> chuỗi q dừng Chọn biến r -> view/Unit root test, chọn level, intercept -> có bảng: Null Hypothesis: R has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=7) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -4.342457 0.0019 Test critical values: 1% level -3.670170 5% level -2.963972 10% level -2.621007 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(R) Method: Least Squares Date: 05/22/09 Time: 14:59 Sample (adjusted): 1979 2008 Included observations: 30 after adjustments Variable Coefficient Std. Error t-Statistic Prob. R(-1) -0.758234 0.174610 -4.342457 0.0002 C 75.77033 20.14129 3.761940 0.0008 R-squared 0.402436 Mean dependent var -2.990000 Adjusted R-squared 0.381095 S.D. dependent var 60.97856 S.E. of regression 47.97216 Akaike info criterion 10.64346 Sum squared resid 64437.18 Schwarz criterion 10.73687 Log likelihood -157.6519 Hannan-Quinn criter. 10.67334 F-statistic 18.85693 Durbin-Watson stat 1.941030 Prob(F-statistic) 0.000167 chuỗi r dừngNếu là chuỗi không dừng thì sẽ có trung bình và phương sai thay đổi thời gian -> không dự báo chính xác được -> nếu là chuỗi dừng thì nên chuyển sang dạng sai phân bậc 1 vì thông thường 1 chuỗi thời gian là không dừng thì sai phân bậc 1 có thể sẽ là một chuỗi dừng (có trung bình và phương sai không đổi theo thời gian) -> dự báo chính xác hơn. ls q c p f r có bảng: Dependent Variable: Q Method: Least Squares Date: 05/22/09 Time: 15:04 Sample (adjusted): 1979 2008 Included observations: 30 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C -11.59809 14.96435 -0.775048 0.4453 P 0.316229 0.087615 3.609282 0.0013 F 0.061583 0.080990 0.760379 0.4539 R 0.058138 0.008069 7.205443 0.0000 R-squared 0.705547 Mean dependent var 34.22000 Adjusted R-squared 0.671571 S.D. dependent var 3.647238 S.E. of regression 2.090185 Akaike info criterion 4.435948 Sum squared resid 113.5907 Schwarz criterion 4.622774 Log likelihood -62.53922 Hannan-Quinn criter. 4.495715 F-statistic 20.76641 Durbin-Watson stat 1.805563 Prob(F-statistic) 0.000000 Do d=1.8 -> không có tự tương quan bậc 1 Ta kiểm tra xem có tự tương quan bặc cao hay không: Từ kết quả hồi quy -> view/Residual/ Serial Correlation LM Test -> có bảng: Breusch-Godfrey Serial Correlation LM Test: F-statistic 0.092111 Prob. F(2,24) 0.9123 Obs*R-squared 0.228522 Prob. Chi-Square(2) 0.8920 Test Equation: Dependent Variable: RESID Method: Least Squares Date: 05/22/09 Time: 16:25 Sample: 1979 2008 Included observations: 30 Presample missing value lagged residuals set to zero. Variable Coefficient Std. Error t-Statistic Prob. C -1.719567 16.31420 -0.105403 0.9169 P 0.012067 0.098153 0.122941 0.9032 F 0.004056 0.084654 0.047917 0.9622 R 3.77E-05 0.008387 0.004492 0.9965 RESID(-1) 0.038320 0.207442 0.184724 0.8550 RESID(-2) -0.085404 0.221688 -0.385242 0.7035 R-squared 0.007617 Mean dependent var -1.14E-14 Adjusted R-squared -0.199129 S.D. dependent var 1.979121 S.E. of regression 2.167231 Akaike info criterion 4.561634 Sum squared resid 112.7254 Schwarz criterion 4.841874 Log likelihood -62.42452 Hannan-Quinn criter. 4.651285 F-statistic 0.036844 Durbin-Watson stat 1.885074 Prob(F-statistic) 0.999170 Vì Prob.Square(2) = 0.8920 lớn -> không có tự tương quan bậc cao c) ls log(q) c log(p) log(f) log(r) -> có bảng : Dependent Variable: LOG(Q) Method: Least Squares Date: 05/22/09 Time: 16:33 Sample (adjusted): 1979 2008 Included observations: 30 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C -1.371261 1.866532 -0.734657 0.4691 LOG(P) 0.840709 0.249391 3.371041 0.0024 LOG(F) 0.070237 0.237214 0.296089 0.7695 LOG(R) 0.147023 0.017684 8.313880 0.0000 R-squared 0.760499 Mean dependent var 3.527108 Adjusted R-squared 0.732864 S.D. dependent var 0.109691 S.E. of regression 0.056694 Akaike info criterion -2.778730 Sum squared resid 0.083570 Schwarz criterion -2.591903 Log likelihood 45.68094 Hannan-Quinn criter. -2.718962 F-statistic 27.51971 Durbin-Watson stat 1.966064 Prob(F-statistic) 0.000000 d=1.966 -> không có tự tương quan bậc 1 Ta kiểm tra xem có tự tương quan bậc cao không Từ kết quả hồi quy -> view/Residual/ Serial Correlation LM Test -> có bảng: Breusch-Godfrey Serial Correlation LM Test: F-statistic 0.078943 Prob. F(2,24) 0.9243 Obs*R-squared 0.196069 Prob. Chi-Square(2) 0.9066 Test Equation: Dependent Variable: RESID Method: Least Squares Date: 05/22/09 Time: 16:36 Sample: 1979 2008 Included observations: 30 Presample missing value lagged residuals set to zero. Variable Coefficient Std. Error t-Statistic Prob. C -0.190791 2.001083 -0.095344 0.9248 LOG(P) 0.033717 0.273249 0.123393 0.9028 LOG(F) 0.007515 0.247028 0.030423 0.9760 LOG(R) -0.000363 0.018370 -0.019766 0.9844 RESID(-1) -0.041848 0.206665 -0.202493 0.8412 RESID(-2) -0.077912 0.218444 -0.356668 0.7245 R-squared 0.006536 Mean dependent var -6.98E-16 Adjusted R-squared -0.200436 S.D. dependent var 0.053682 S.E. of regression 0.058816 Akaike info criterion -2.651953 Sum squared resid 0.083023 Schwarz criterion -2.371714 Log likelihood 45.77930 Hannan-Quinn criter. -2.562302 F-statistic 0.031577 Durbin-Watson stat 1.878904 Prob(F-statistic) 0.999429 Vì Prob.Square(2) = 0.9066 lớn -> không có tự tương quan bậc cao

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