计量经济小论文.docx
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计量经济小论文.docx
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计量经济小论文
成绩:
2011—2012学年第一学期
计量经济学综合作业1
学院:
理学院
专业:
统计学
班级:
09级1班
姓名:
雷文玉
学号:
091414753
单方程作业:
年份
总指数
建材类
农副产品类
纺织原料类
year
y
x1
x2
x3
lny
lnx1
lnx2
lnx3
1989
126.4
122.7
128.9
128.5
4.839451
4.809742
4.859037
4.855929
1990
105.6
115.2
107.8
107.4
4.659658
4.74667
4.680278
4.67656
1991
109.1
101.2
106.8
108.9
4.692265
4.617099
4.670958
4.69043
1992
111
118.8
103.4
100.5
4.70953
4.777441
4.638605
4.610158
1993
135.1
140.9
112.2
107.1
4.906015
4.94805
4.720283
4.673763
1994
118.2
114.3
148.3
139.6
4.772378
4.738827
4.999237
4.938781
1995
115.3
102.6
143.1
123.6
4.747537
4.630838
4.963544
4.817051
1996
103.9
102.5
114.7
94.5
4.643429
4.629863
4.74232
4.5486
1997
101.3
99.7
102
94.7
4.618086
4.602166
4.624973
4.550714
1998
95.8
98.6
94.5
94.3
4.562263
4.591071
4.5486
4.546481
1999
96.7
98.8
89.8
96.8
4.571613
4.593098
4.497585
4.572647
2000
105.1
101.5
99.9
102.4
4.654912
4.620059
4.60417
4.628887
2001
99.8
98.6
101.2
99.7
4.603168
4.591071
4.617099
4.602166
2002
97.7
98.2
95.7
97.1
4.581902
4.587006
4.561218
4.575741
2003
104.8
99.7
106.7
101.4
4.652054
4.602166
4.670021
4.619073
2004
111.4
105.1
114.2
104.7
4.713127
4.654912
4.737951
4.651099
2005
108.3
103.1
101.7
102.4
4.684905
4.635699
4.622027
4.628887
2006
106
101.9
104.3
102.9
4.663439
4.623992
4.647271
4.633758
2007
104.4
103
106.1
101.4
4.64823
4.634729
4.664382
4.619073
2008
110.5
109.5
107.5
103.1
4.705016
4.695925
4.677491
4.635699
2009
92.1
101.1
97
98.8
4.522875
4.61611
4.574711
4.593098
表一
9—15建材材料,农副产品和纺织类价格指数
数据来源《中中国统计年鉴2010》
1.对数据做回归处理:
1)原始数据的描述性统计量
X1
X2
X3
Y
Mean
106.5238
108.8476
105.2286
107.5476
Median
102.5000
106.1000
102.4000
105.6000
Maximum
140.9000
148.3000
139.6000
135.1000
Minimum
98.20000
89.80000
94.30000
92.10000
Std.Dev.
10.60301
14.82227
11.65003
10.14853
Skewness
1.910044
1.480493
1.746922
1.031591
Kurtosis
6.318668
4.571039
5.289888
4.079687
Jarque-Bera
22.40580
9.831154
15.26922
4.744637
Probability
0.000014
0.007331
0.000483
0.093264
Sum
2237.000
2285.800
2209.800
2258.500
SumSq.Dev.
2248.478
4393.992
2714.463
2059.852
Observations
21
21
21
21
表二
由上至下分别是均值,中位数,最大值,最小值,标准差,偏度,峰度,正态性检验,P值
等。
同时由EVIEWS软件输出的回归结果如下:
DependentVariable:
Y
Method:
LeastSquares
Date:
12/03/11Time:
18:
44
Sample:
19892009
Includedobservations:
21
Coefficient
Std.Error
t-Statistic
Prob.
C
6.019987
10.72765
0.561165
0.5820
X1
0.674173
0.097690
6.901132
0.0000
X2
0.249565
0.143440
1.739854
0.1000
X3
0.024210
0.187522
0.129105
0.8988
R-squared
0.855602
Meandependentvar
107.5476
AdjustedR-squared
0.830121
S.D.dependentvar
10.14853
S.E.ofregression
4.182861
Akaikeinfocriterion
5.869511
Sumsquaredresid
297.4376
Schwarzcriterion
6.068468
Loglikelihood
-57.62987
Hannan-Quinncriter.
5.912690
F-statistic
33.57685
Durbin-Watsonstat
2.375577
Prob(F-statistic)
0.000000
表三
(1)建立方程:
Y=6.01998690022+0.674172705671*X1+0.249565404554*X2+0.0242100329345*X3
2)为了消除异方差影响,对数据取对数,如第一个表。
DependentVariable:
LNY
Method:
LeastSquares
Date:
12/06/11Time:
16:
42
Sample:
19892009
Includedobservations:
21
Coefficient
Std.Error
t-Statistic
Prob.
C
0.181239
0.497311
0.364438
0.7200
LNX1
0.648378
0.107482
6.032412
0.0000
LNX2
0.276052
0.147168
1.875757
0.0780
LNX3
0.037858
0.186244
0.203269
0.8413
R-squared
0.842677
Meandependentvar
4.673898
AdjustedR-squared
0.814915
S.D.dependentvar
0.091020
S.E.ofregression
0.039158
Akaikeinfocriterion
-3.472766
Sumsquaredresid
0.026067
Schwarzcriterion
-3.273809
Loglikelihood
40.46404
Hannan-Quinncriter.
-3.429587
F-statistic
30.35273
Durbin-Watsonstat
2.257620
Prob(F-statistic)
0.000000
表四
1.建立方程:
LNY=C
(1)+C
(2)*LNX1+C(3)*LNX2+C(4)*LNX3
LNY=0.181238993815+0.648378343687*LNX1+0.27605201835*LNX2
+0.0378576549048*LNX3
拟合优度检验:
由上数据可知拟合程度较高.。
对变量进行T检验:
在10%的置信水平下
1.740,显然lnx1,lnx2通过了T检验
对方程进行F检验:
>
3.20所以通过了F检验
2.异方差性检验:
(1)怀特检验:
HeteroskedasticityTest:
White
F-statistic
0.266757
Prob.F(9,11)
0.9715
Obs*R-squared
3.762235
Prob.Chi-Square(9)
0.9264
ScaledexplainedSS
2.727734
Prob.Chi-Square(9)
0.9741
TestEquation:
DependentVariable:
RESID^2
Method:
LeastSquares
Date:
12/08/11Time:
11:
28
Sample:
19892009
Includedobservations:
21
Coefficient
Std.Error
t-Statistic
Prob.
C
-2.239234
2.259356
-0.991094
0.3429
LNX1
0.736741
0.753726
0.977465
0.3493
LNX1^2
0.009475
0.090587
0.104596
0.9186
LNX1*LNX2
-0.144341
0.404810
-0.356565
0.7282
LNX1*LNX3
-0.031443
0.343677
-0.091490
0.9287
LNX2
1.039238
1.989618
0.522331
0.6118
LNX2^2
0.022950
0.109283
0.210001
0.8375
LNX2*LNX3
-0.130151
0.247499
-0.525864
0.6094
LNX3
-0.824971
2.063398
-0.399812
0.6969
LNX3^2
0.172644
0.229574
0.752020
0.4678
R-squared
0.179154
Meandependentvar
0.001241
AdjustedR-squared
-0.492447
S.D.dependentvar
0.001892
S.E.ofregression
0.002311
Akaikeinfocriterion
-8.996128
Sumsquaredresid
5.88E-05
Schwarzcriterion
-8.498737
Loglikelihood
104.4593
Hannan-Quinncriter.
-8.888181
F-statistic
0.266757
Durbin-Watsonstat
1.522903
Prob(F-statistic)
0.971467
表五
怀特统计量
=21*0.179154=3.762234,该值小于在1%显著性水平下,自由
度为9的
分布的相应临界值
=21.66599,因此在1%的置信水平下接
受同方差的假设。
(2)G-Q检验:
将原始数据按X2排成升序,去掉中间5个数据,得两个容量为8的子样本。
对两个子样本分别作最小二乘回归,求各自的残差平方和RSS1和RSS2。
子样本1回归结果如下:
DependentVariable:
LNY
Method:
LeastSquares
Date:
12/08/11Time:
21:
14
Sample:
19891996
Includedobservations:
8
Coefficient
Std.Error
t-Statistic
Prob.
C
0.229786
1.205553
0.190606
0.8581
LNX1
0.655195
0.197101
3.324166
0.0293
LNX2
0.205655
0.301174
0.682844
0.5322
LNX3
0.090707
0.314272
0.288627
0.7872
R-squared
0.795096
Meandependentvar
4.746283
AdjustedR-squared
0.641418
S.D.dependentvar
0.090419
S.E.ofregression
0.054144
Akaikeinfocriterion
-2.687477
Sumsquaredresid
0.011726
Schwarzcriterion
-2.647756
Loglikelihood
14.74991
Hannan-Quinncriter.
-2.955377
F-statistic
5.173781
Durbin-Watsonstat
3.574743
Prob(F-statistic)
0.073121
表六
子样本一:
LNY=0.2297859988+0.655195068173*LNX1+0.20565484
7593*LNX2+0.0907073254034*LNX3
0.795096
0.641418
RSS1=0.011726
子样本2回归结果如下:
DependentVariable:
SER01
Method:
LeastSquares
Date:
12/08/11Time:
21:
38
Sample:
20022009
Includedobservations:
8
Coefficient
Std.Error
t-Statistic
Prob.
C
-5.063058
4.026459
-1.257447
0.2770
SER02
0.130886
0.627603
0.208549
0.8450
SER03
0.218024
0.571246
0.381664
0.7221
SER04
1.751412
1.517317
1.154282
0.3127
R-squared
0.792146
Meandependentvar
4.646443
AdjustedR-squared
0.636255
S.D.dependentvar
0.064493
S.E.ofregression
0.038896
Akaikeinfocriterion
-3.348983
Sumsquaredresid
0.006052
Schwarzcriterion
-3.309262
Loglikelihood
17.39593
Hannan-Quinncriter.
-3.616884
F-statistic
5.081426
Durbin-Watsonstat
1.617656
Prob(F-statistic)
0.075155
表七
子样本二:
SER01=-5.06305769616+0.130885629473*SER02+0.218023842813*SER03+1.75141205662*SER04
0.792146
0.636255
RSS2=0.006052
计算F的统计量:
0.516118
在5%的显著性水平下,
6.388233,由此可见接受原假设,即不存
在异方差性。
3.序列相关性检验:
(1)回归检验法:
DependentVariable:
E
Method:
LeastSquares
Date:
12/08/11Time:
22:
15
Sample(adjusted):
19902009
Includedobservations:
20afteradjustments
Coefficient
Std.Error
t-Statistic
Prob.
E1
-0.406218
0.266395
-1.524873
0.1447
C
0.001064
0.008060
0.132051
0.8964
R-squared
0.114402
Meandependentvar
-0.000725
AdjustedR-squared
0.065202
S.D.dependentvar
0.036883
S.E.ofregression
0.035660
Akaikeinfocriterion
-3.734923
Sumsquaredresid
0.022890
Schwarzcriterion
-3.635350
Loglikelihood
39.34923
Hannan-Quinncriter.
-3.715485
F-statistic
2.325239
Durbin-Watsonstat
1.236495
Prob(F-statistic)
0.144669
表八
由以上回归结果得到方程:
,由D.W=1.236495,dl=1.13,du=1.54,所以
正好落入盲区,不能确定。
(2)D.W检验法:
D.W.=2.257620在2的附近,dl=1.13,du=1.54,4-du=2.46,
所以不存在自相关性。
(3)LM检验法:
Breusch-GodfreySerialCorrelationLMTest:
F-statistic
2.129001
Prob.F(1,16)
0.1639
Obs*R-squared
2.466160
Prob.Chi-Square
(1)
0.1163
TestEquation:
DependentVariable:
RESID
Method:
LeastSquares
Date:
12/08/11Time:
22:
17
Sample:
19892009
Includedobservations:
21
Presamplemissingvaluelaggedresidualssettozero.
Coefficient
Std.Error
t-Statistic
Prob.
C
-0.008088
0.481608
-0.016793
0.9868
LNX1
0.017813
0.104795
0.169983
0.8672
LNX2
0.002032
0.142519
0.014256
0.9888
LNX3
-0.017794
0.180764
-0.098441
0.9228
RESID(-1)
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