Bài tập thực hành cá nhân
b. Kiểm định giả thiết trên với mức ý nghĩa lần lượt như sau: = 1%, 5%, 10%, và 15%? Anh/Chị cho biết khi thay đổi thì quyết định chấp nhận hay bác bỏ giả thiết H0 sẽ thay đổi như thế nào? - Mở biến - Chọn View/ Descriptive Statistics & Tests/ Simple Hypothesis Tests - Xuất hiện hộp thoại Series Distribution Tests : - Trong Test value: nhập vào “MEAN” là 168 - Trong Mean test assumption: nhập vào “ENTER s.d. if known” là 24 ( do = N-1 = 25 -1) /OK Khi càng tăng thì càng “dễ” chấp nhận giả thiết Ho
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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:
Các file đính kèm theo tài liệu này:
_eco_assignment.doc
