Thực hành assignment

g 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: