计量经济学作业.docx
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计量经济学作业.docx
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计量经济学作业
X
Y
80
55
100
65
85
70
110
80
120
79
115
84
130
98
140
95
125
90
90
75
105
74
160
110
150
113
165
125
145
108
180
115
225
140
200
120
240
145
185
130
220
152
210
144
245
175
260
180
190
135
205
140
265
178
270
191
230
137
250
189
第一次作业
第一题:
下列数据中,X表示家庭收入,Y表示家庭支出,请对如下数据运用戈德菲尔德-匡特检验。
第二题:
X代表职工的工龄,Y代表薪水。
要求:
1.通过散点图或残差图对样本进行初步观察。
2.对可能存在的问题进行检验。
3.采取措施消除问题。
4.写出最终表达式。
X
Y
0.5
69000
2.5
70500
4.5
74050
6.5
82600
8.5
91439
10.5
83127
12.5
84700
14.5
82601
16.5
93286
18.5
90400
20.5
98200
23
100000
26
99662
30
116012
34
85200
第一题:
步骤:
(1)、将样本数据排序,分组,剔除中间样本,然后做OLS回归
第一组:
80
55
85
70
90
75
100
65
105
74
110
80
115
84
120
79
125
90
130
98
140
95
DependentVariable:
Y
Method:
LeastSquares
Date:
04/18/11Time:
08:
52
Sample:
111
Includedobservations:
11
Y=C
(1)+C
(2)*X
Coefficient
Std.Error
t-Statistic
Prob.
C
(1)
12.53695
10.53870
1.189610
0.2646
C
(2)
0.605911
0.095271
6.359867
0.0001
R-squared
0.817990
Meandependentvar
78.63636
AdjustedR-squared
0.797767
S.D.dependentvar
12.87069
S.E.ofregression
5.787989
Akaikeinfocriterion
6.512413
Sumsquaredresid
301.5074
Schwarzcriterion
6.584757
Loglikelihood
-33.81827
Hannan-Quinncriter.
6.466810
F-statistic
40.44791
Durbin-Watsonstat
2.272765
Prob(F-statistic)
0.000131
第二组:
205
140
210
144
220
152
225
140
230
137
240
145
245
175
250
189
260
180
265
178
DependentVariable:
Y
Method:
LeastSquares
Date:
04/18/11Time:
08:
54
Sample:
111
Includedobservations:
11
Y=C
(1)+C
(2)*X
Coefficient
Std.Error
t-Statistic
Prob.
C
(1)
-36.60187
40.67131
-0.899943
0.3916
C
(2)
0.829626
0.170096
4.877405
0.0009
R-squared
0.725518
Meandependentvar
161.0000
AdjustedR-squared
0.695020
S.D.dependentvar
21.48022
S.E.ofregression
11.86244
Akaikeinfocriterion
7.947598
Sumsquaredresid
1266.458
Schwarzcriterion
8.019942
Loglikelihood
-41.71179
Hannan-Quinncriter.
7.901995
F-statistic
23.78908
Durbin-Watsonstat
1.178680
Prob(F-statistic)
0.000875
(2):
F=1266.458/301.5074=4.2004
给定a=5%
查表,得临界值:
F0.05(9,9)=2.97
判断F大于F0.05(9,9)否定两组子样本方差相同的假设,从而该总体随机项存在异方差性。
第二题:
做散点图:
DependentVariable:
Y
Method:
LeastSquares
Date:
04/18/11Time:
09:
04
Sample:
124
Includedobservations:
24
Y=C
(1)+C
(2)*X
Coefficient
Std.Error
t-Statistic
Prob.
C
(1)
-84.24803
11.17191
-7.541060
0.0000
C
(2)
7.783611
0.621134
12.53129
0.0000
R-squared
0.877118
Meandependentvar
51.27438
AdjustedR-squared
0.871532
S.D.dependentvar
38.30328
S.E.ofregression
13.72881
Akaikeinfocriterion
8.156526
Sumsquaredresid
4146.567
Schwarzcriterion
8.254697
Loglikelihood
-95.87831
Hannan-Quinncriter.
8.182571
F-statistic
157.0333
Durbin-Watsonstat
0.602173
Prob(F-statistic)
0.000000
由散点图可看出,该样本可能存在异方差性。
作G-Q检验:
将大样本分为两个小样本,
第二次上机
步骤:
先对全样本作整体回归:
DependentVariable:
Y
Method:
LeastSquares
Date:
04/18/11Time:
09:
04
Sample:
124
Includedobservations:
24
Y=C
(1)+C
(2)*X
Coefficient
Std.Error
t-Statistic
Prob.
C
(1)
-84.24803
11.17191
-7.541060
0.0000
C
(2)
7.783611
0.621134
12.53129
0.0000
R-squared
0.877118
Meandependentvar
51.27438
AdjustedR-squared
0.871532
S.D.dependentvar
38.30328
S.E.ofregression
13.72881
Akaikeinfocriterion
8.156526
Sumsquaredresid
4146.567
Schwarzcriterion
8.254697
Loglikelihood
-95.87831
Hannan-Quinncriter.
8.182571
F-statistic
157.0333
Durbin-Watsonstat
0.602173
Prob(F-statistic)
0.000000
将样本分组,分别作OLS回归,
Y
X
15.87
10.8
17.73
11.9
19.04
13.1
21.61
14.9
17.2
12.5
18.85
13.7
16.71
11.3
14.81
10.4
19.02
14.2
20.55
15.2
24.29
17.1
24.38
16.9
第一组:
DependentVariable:
Y
Method:
LeastSquares
Date:
04/18/11Time:
08:
42
Sample:
112
Includedobservations:
12
Y=C
(1)+C
(2)*X
Coefficient
Std.Error
t-Statistic
Prob.
C
(1)
1.149801
1.247010
0.922046
0.3782
C
(2)
1.334953
0.091224
14.63383
0.0000
R-squared
0.955387
Meandependentvar
19.17167
AdjustedR-squared
0.950926
S.D.dependentvar
3.063924
S.E.ofregression
0.678744
Akaikeinfocriterion
2.213866
Sumsquaredresid
4.606933
Schwarzcriterion
2.294684
Loglikelihood
-11.28320
Hannan-Quinncriter.
2.183944
F-statistic
214.1491
Durbin-Watsonstat
1.237672
Prob(F-statistic)
0.000000
第二组:
27.8
17.2
43.01
18.46
65.65
19.9
67.05
20.3
88.25
21.5
78.15
20.9
91.485
22.11
110.3
23.8
105.33
23.1
89.99
19.2
119.24
25.1
114.27
24.3
DependentVariable:
Y
Method:
LeastSquares
Date:
04/18/11Time:
08:
44
Sample:
112
Includedobservations:
12
Y=C
(1)+C
(2)*X
Coefficient
Std.Error
t-Statistic
Prob.
C
(1)
-147.5850
28.43609
-5.190061
0.0004
C
(2)
10.83185
1.325622
8.171147
0.0000
R-squared
0.869737
Meandependentvar
83.37708
AdjustedR-squared
0.856710
S.D.dependentvar
28.45566
S.E.ofregression
10.77149
Akaikeinfocriterion
7.742695
Sumsquaredresid
1160.250
Schwarzcriterion
7.823513
Loglikelihood
-44.45617
Hannan-Quinncriter.
7.712773
F-statistic
66.76765
Durbin-Watsonstat
1.798463
Prob(F-statistic)
0.000010
RSS(R)=4146.567
RSS(U)=RSS1+RSS2=4.606933+1160.250
=1164.856933
(4146.567-1164.856933)/12
F=————————————=4.2662035
1164.856933/(24-2*2)
给定显著性水平5%,F0.05(12,20)=2.28 所以,不显著,拒绝原假设。 第三次作业 步骤: 对整体样本作OLS回归: DependentVariable: Y Method: LeastSquares Date: 04/25/11Time: 08: 27 Sample: 130 Includedobservations: 30 Y=C (1)+C (2)*X1+C(3)*X2+C(4)*X3+C(5)*X4+C(6)*X5 Coefficient Std.Error t-Statistic Prob. C (1) 15.38369 14.01730 1.097479 0.2833 C (2) 0.020752 0.012865 1.613110 0.1198 C(3) -0.002178 0.133207 -0.016349 0.9871 C(4) 0.034338 0.013535 2.537008 0.0181 C(5) -0.003790 0.004617 -0.820953 0.4198 C(6) 0.011774 0.398255 0.029565 0.9767 R-squared 0.949200 Meandependentvar 45.63967 AdjustedR-squared 0.938616 S.D.dependentvar 21.74352 S.E.ofregression 5.387113 Akaikeinfocriterion 6.382753 Sumsquaredresid 696.5037 Schwarzcriterion 6.662992 Loglikelihood -89.74129 Hannan-Quinncriter. 6.472404 F-statistic 89.68776 Durbin-Watsonstat 0.983723 Prob(F-statistic) 0.000000 用软件得到参差序列: Lastupdated: 04/25/11-08: 32 Modified: 130//makeresid -2.387916742786327 -3.626222161418159 -6.831392318290824 -2.956212582870552 4.082095116985887 8.705595666216524 2.933711819027032 -1.374381856294256 2.855590708402779 2.512014926085435 0.906104137313708 1.218129548375583 1.130********2603 .0753******** -4.706987305005896 .010********* -2.727309400155605 -3.452771889540848 -2.604762777753955 7.683285351384584 .0875******** 5.786371769840066 -0.181********70489 7.468372960652204 2.206659904875522 -2.243012885258935 -6.286316222062766 -10.06359800777685 2.478021029106259 3.474021064943272 ~ 然后以et作为解释变量,做回归检验: DependentVariable: U Method: LeastSquares Date: 04/25/11Time: 08: 49 Sample(adjusted): 230 Includedobservations: 29afteradjustments U=C (1)*U(-1) Coefficient Std.Error t-Statistic Prob. C (1) 0.504117 0.164226 3.069644 0.0047 R-squared 0.251578 Meandependentvar 0.082342 AdjustedR-squared 0.251578 S.D.dependentvar 4.966333 S.E.ofregression 4.296443 Akaikeinfocriterion 5.787326 Sumsquaredresid 516.8637 Schwarzcriterion 5.834474 Loglikelihood -82.91623 Hannan-Quinncriter. 5.802092 Durbin-Watsonstat 1.727824 DependentVariable: U Method: LeastSquares Date: 04/25/11Time: 08: 51 Sample(adjusted): 330 Includedobservations: 28afteradjustments U=C (1)*U(-1)+C (2)*U(-2) Coefficient Std.Error t-Statistic Prob. C (1) 0.628738 0.188729 3.331425 0.0026 C (2) -0.268616 0.188790 -1.422823 0.1667 R-squared 0.299136 Meandependentvar 0.214791 AdjustedR-squared 0.272180 S.D.dependentvar 5.005036 S.E.ofregression 4.269915 Akaikeinfocriterion 5.809814 Sumsquaredresid 474.0366 Schwarzcriterion 5.904972 Loglikelihood -79.33740 Hannan-Quinncriter. 5.838905 Durbin-Watsonstat 2.047637 由上可知,存在着一阶滞后相关性。 然后,用广义差分法重新估计模型: DependentVariable: YT-0.628738*YT(-1) Method: LeastSquares Date: 04/25/11Time: 09: 21 Sample(adjusted): 630 Includedobservations: 25afteradjustments YT-0.628738*YT(-
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