计量经济学庞皓第三版课后答案 本文简介：
第二章简单线性回归模型2.1（1）①首先分析人均寿命与人均GDP的数量关系，用Eviews分析：DependentVariable:YMethod:LeastSquaresDate:12/27/14Time:21:00Sample:122Includedobservations:22Variable
计量经济学庞皓第三版课后答案 本文内容：
第二章
简单线性回归模型
2.1
（1）
①首先分析人均寿命与人均GDP的数量关系，用Eviews分析：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/27/14
Time:
21:00
Sample:
1
22Included
observations:
22
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
C
56.64794
1.960820
28.88992
0.0000
X1
0.128360
0.027242
4.711834
0.0001
R-squared
0.526082
????Mean
dependent
var
62.50000
Adjusted
R-squared
0.502386
????S.D.
dependent
var
10.08889
S.E.
of
regression
7.116881
????Akaike
info
criterion
6.849324
Sum
squared
resid
1013.000
????Schwarz
criterion
6.948510
Log
likelihood
-73.34257
????Hannan-Quinn
criter.
6.872689
F-statistic
22.20138
????Durbin-Watson
stat
0.629074
Prob(F-statistic)
0.000134
有上可知，关系式为y=56.64794+0.128360x1
②关于人均寿命与成人识字率的关系，用Eviews分析如下：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
11/26/14
Time:
21:10
Sample:
1
22Included
observations:
22
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
C
38.79424
3.532079
10.98340
0.0000
X2
0.331971
0.046656
7.115308
0.0000
R-squared
0.716825
????Mean
dependent
var
62.50000
Adjusted
R-squared
0.702666
????S.D.
dependent
var
10.08889
S.E.
of
regression
5.501306
????Akaike
info
criterion
6.334356
Sum
squared
resid
605.2873
????Schwarz
criterion
6.433542
Log
likelihood
-67.67792
????Hannan-Quinn
criter.
6.357721
F-statistic
50.62761
????Durbin-Watson
stat
1.846406
Prob(F-statistic)
0.000001
由上可知，关系式为y=38.79424+0.331971x2
③关于人均寿命与一岁儿童疫苗接种率的关系，用Eviews分析如下：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
11/26/14
Time:
21:14
Sample:
1
22Included
observations:
22
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
C
31.79956
6.536434
4.864971
0.0001
X3
0.387276
0.080260
4.825285
0.0001
R-squared
0.537929
????Mean
dependent
var
62.50000
Adjusted
R-squared
0.514825
????S.D.
dependent
var
10.08889
S.E.
of
regression
7.027364
????Akaike
info
criterion
6.824009
Sum
squared
resid
987.6770
????Schwarz
criterion
6.923194
Log
likelihood
-73.06409
????Hannan-Quinn
criter.
6.847374
F-statistic
23.28338
????Durbin-Watson
stat
0.952555
Prob(F-statistic)
0.000103
由上可知，关系式为y=31.79956+0.387276x3
（2）①关于人均寿命与人均GDP模型，由上可知，可决系数为0.526082，说明所建模型整体上对样本数据拟合较好。
对于回归系数的t检验：t（β1）=4.711834>t0.025(20)=2.086，对斜率系数的显著性检验表明，人均GDP对人均寿命有显著影响。
②关于人均寿命与成人识字率模型，由上可知，可决系数为0.716825，说明所建模型整体上对样本数据拟合较好。
对于回归系数的t检验：t（β2）=7.115308>t0.025(20)=2.086，对斜率系数的显著性检验表明，成人识字率对人均寿命有显著影响。
③关于人均寿命与一岁儿童疫苗的模型，由上可知，可决系数为0.537929，说明所建模型整体上对样本数据拟合较好。
对于回归系数的t检验：t（β3）=4.825285>t0.025(20)=2.086，对斜率系数的显著性检验表明，一岁儿童疫苗接种率对人均寿命有显著影响。
2.2
（1）
①对于浙江省预算收入与全省生产总值的模型，用Eviews分析结果如下：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/03/14
Time:
17:00
Sample
(adjusted):
1
33
Included
observations:
33
after
adjustmentsVariable
Coefficient
Std.
Error
t-Statistic
Prob.??
X
0.176124
0.004072
43.25639
0.0000
C
-154.3063
39.08196
-3.948274
0.0004
R-squared
0.983702
????Mean
dependent
var
902.5148
Adjusted
R-squared
0.983177
????S.D.
dependent
var
1351.009
S.E.
of
regression
175.2325
????Akaike
info
criterion
13.22880
Sum
squared
resid
951899.7
????Schwarz
criterion
13.31949
Log
likelihood
-216.2751
????Hannan-Quinn
criter.
13.25931
F-statistic
1871.115
????Durbin-Watson
stat
0.100021
Prob(F-statistic)
0.000000
②由上可知，模型的参数：斜率系数0.176124，截距为—154.3063
③关于浙江省财政预算收入与全省生产总值的模型，检验模型的显著性：
1）可决系数为0.983702，说明所建模型整体上对样本数据拟合较好。
2）对于回归系数的t检验：t（β2）=43.25639>t0.025(31)=2.0395，对斜率系数的显著性检验表明，全省生产总值对财政预算总收入有显著影响。
④用规范形式写出检验结果如下：
Y=0.176124X—154.3063
(0.004072)
(39.08196)
t=
(43.25639)（-3.948274）
R2=0.983702
F=1871.115
n=33
⑤经济意义是：全省生产总值每增加1亿元，财政预算总收入增加0.176124亿元。
（2）当x=32000时，
①进行点预测，由上可知Y=0.176124X—154.3063，代入可得：
Y=
Y=0.176124*32000—154.3063=5481.6617
②进行区间预测：
先由Eviews分析：
X
Y
?Mean
?6000.441
?902.5148
?Median
?2689.280
?209.3900
?Maximum
?27722.31
?4895.410
?Minimum
?123.7200
?25.87000
?Std.
Dev.
?7608.021
?1351.009
?Skewness
?1.432519
?1.663108
?Kurtosis
?4.010515
?4.590432?Jarque-Bera
?12.69068
?18.69063
?Probability
?0.001755
?0.000087?Sum
?198014.5
?29782.99
?Sum
Sq.
Dev.
?1.85E+09
?58407195?Observations
?33
?33
由上表可知，
∑x2=∑（Xi—X）2=δ2x(n—1)=
?7608.0212
x
(33—1)=1852223.473
(Xf—X)2=(32000—?6000.441)2=675977068.2
当Xf=32000时，将相关数据代入计算得到：
5481.6617—2.0395x175.2325x√1/33+1852223.473/675977068.2≤
Yf≤5481.6617+2.0395x175.2325x√1/33+1852223.473/675977068.2
即Yf的置信区间为（5481.6617—64.9649,
5481.6617+64.9649）
(3)
对于浙江省预算收入对数与全省生产总值对数的模型，由Eviews分析结果如下：
Dependent
Variable:
LNY
Method:
Least
Squares
Date:
12/03/14
Time:
18:00
Sample
(adjusted):
1
33
Included
observations:
33
after
adjustmentsVariable
Coefficient
Std.
Error
t-Statistic
Prob.??
LNX
0.980275
0.034296
28.58268
0.0000
C
-1.918289
0.268213
-7.152121
0.0000
R-squared
0.963442
????Mean
dependent
var
5.573120
Adjusted
R-squared
0.962263
????S.D.
dependent
var
1.684189
S.E.
of
regression
0.327172
????Akaike
info
criterion
0.662028
Sum
squared
resid
3.318281
????Schwarz
criterion
0.752726
Log
likelihood
-8.923468
????Hannan-Quinn
criter.
0.692545
F-statistic
816.9699
????Durbin-Watson
stat
0.096208
Prob(F-statistic)
0.000000
①模型方程为：lnY=0.980275lnX-1.918289
②由上可知，模型的参数：斜率系数为0.980275，截距为-1.918289
③关于浙江省财政预算收入与全省生产总值的模型，检验其显著性：
1）可决系数为0.963442，说明所建模型整体上对样本数据拟合较好。
2）对于回归系数的t检验：t（β2）=28.58268>t0.025(31)=2.0395，对斜率系数的显著性检验表明，全省生产总值对财政预算总收入有显著影响。
④经济意义：全省生产总值每增长1%，财政预算总收入增长0.980275%
2.4
（1）对建筑面积与建造单位成本模型，用Eviews分析结果如下：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/01/14
Time:
12:40
Sample:
1
12Included
observations:
12
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X
-64.18400
4.809828
-13.34434
0.0000
C
1845.475
19.26446
95.79688
0.0000
R-squared
0.946829
????Mean
dependent
var
1619.333
Adjusted
R-squared
0.941512
????S.D.
dependent
var
131.2252
S.E.
of
regression
31.73600
????Akaike
info
criterion
9.903792
Sum
squared
resid
10071.74
????Schwarz
criterion
9.984610
Log
likelihood
-57.42275
????Hannan-Quinn
criter.
9.873871
F-statistic
178.0715
????Durbin-Watson
stat
1.172407
Prob(F-statistic)
0.000000
由上可得：建筑面积与建造成本的回归方程为：
Y=1845.475--64.18400X
（2）经济意义：建筑面积每增加1万平方米，建筑单位成本每平方米减少64.18400元。
（3）
①首先进行点预测，由Y=1845.475--64.18400X得，当x=4.5，y=1556.647
②再进行区间估计：
用Eviews分析：
Y
X
?Mean
?1619.333
?3.523333
?Median
?1630.000
?3.715000
?Maximum
?1860.000
?6.230000
?Minimum
?1419.000
?0.600000
?Std.
Dev.
?131.2252
?1.989419
?Skewness
?0.003403
-0.060130
?Kurtosis
?2.346511
?1.664917?Jarque-Bera
?0.213547
?0.898454
?Probability
?0.898729
?0.638121?Sum
?19432.00
?42.28000
?Sum
Sq.
Dev.
?189420.7
?43.53567?Observations
?12
?12
由上表可知，
∑x2=∑（Xi—X）2=δ2x(n—1)=
?1.9894192
x
(12—1)=43.5357
(Xf—X)2=(4.5—?3.523333)2=0.95387843
当Xf=4.5时，将相关数据代入计算得到：
1556.647—2.228x31.73600x√1/12+43.5357/0.95387843≤
Yf≤1556.647+2.228x31.73600x√1/12+43.5357/0.95387843
即Yf的置信区间为（1556.647—478.1231,
1556.647+478.1231）3.1
（1）
①对百户拥有家用汽车量计量经济模型，用Eviews分析结果如下：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
11/25/14
Time:
12:38
Sample:
1
31Included
observations:
31
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X2
5.996865
1.406058
4.265020
0.0002
X3
-0.524027
0.179280
-2.922950
0.0069
X4
-2.265680
0.518837
-4.366842
0.0002
C
246.8540
51.97500
4.749476
0.0001
R-squared
0.666062
????Mean
dependent
var
16.77355
Adjusted
R-squared
0.628957
????S.D.
dependent
var
8.252535
S.E.
of
regression
5.026889
????Akaike
info
criterion
6.187394
Sum
squared
resid
682.2795
????Schwarz
criterion
6.372424
Log
likelihood
-91.90460
????Hannan-Quinn
criter.
6.247709
F-statistic
17.95108
????Durbin-Watson
stat
1.147253
Prob(F-statistic)
0.000001
②得到模型得：
Y=246.8540+5.996865X2- 0.524027
X3-2.265680
X4
③对模型进行检验：
1）
可决系数是0.666062，修正的可决系数为0.628957，说明模型对样本拟合较好
2）
F检验，F=17.95108>F（3,27）=3.65，回归方程显著。
3）t检验，t统计量分别为4.749476，4.265020，-2.922950，-4.366842，均大于
t（27）=2.0518，所以这些系数都是显著的。
④依据：
1）
可决系数越大，说明拟合程度越好
2）
F的值与临界值比较，若大于临界值，则否定原假设，回归方程是显著的；若小于临界值，则接受原假设，回归方程不显著。
3）
t的值与临界值比较，若大于临界值，则否定原假设，系数都是显著的；若小于临界值，则接受原假设，系数不显著。
（2）经济意义：人均ＧＤＰ增加１万元，百户拥有家用汽车增加5.996865辆，城镇人口比重增加１个百分点，百户拥有家用汽车减少0.524027辆，交通工具消费价格指数每上升１，百户拥有家用汽车减少2.265680辆。
（3）用EViews分析得：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/08/14
Time:
17:28
Sample:
1
31Included
observations:
31
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X2
5.135670
1.010270
5.083465
0.0000
LNX3
-22.81005
6.771820
-3.368378
0.0023
LNX4
-230.8481
49.46791
-4.666624
0.0001
C
1148.758
228.2917
5.031974
0.0000
R-squared
0.691952
????Mean
dependent
var
16.77355
Adjusted
R-squared
0.657725
????S.D.
dependent
var
8.252535
S.E.
of
regression
4.828088
????Akaike
info
criterion
6.106692
Sum
squared
resid
629.3818
????Schwarz
criterion
6.291723
Log
likelihood
-90.65373
????Hannan-Quinn
criter.
6.167008
F-statistic
20.21624
????Durbin-Watson
stat
1.150090
Prob(F-statistic)
0.000000
模型方程为：
Y=5.135670
X2-22.81005
LNX3-230.8481
LNX4+1148.758
此分析得出的可决系数为0.691952>0.666062，拟合程度得到了提高，可这样改进。
3.2
（１）对出口货物总额计量经济模型，用Eviews分析结果如下：：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/01/14
Time:
20:25
Sample:
1994
2011
Included
observations:
18
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X2
0.135474
0.012799
10.58454
0.0000
X3
18.85348
9.776181
1.928512
0.0729
C
-18231.58
8638.216
-2.110573
0.0520
R-squared
0.985838
????Mean
dependent
var
6619.191
Adjusted
R-squared
0.983950
????S.D.
dependent
var
5767.152
S.E.
of
regression
730.6306
????Akaike
info
criterion
16.17670
Sum
squared
resid
8007316.
????Schwarz
criterion
16.32510
Log
likelihood
-142.5903
????Hannan-Quinn
criter.
16.19717
F-statistic
522.0976
????Durbin-Watson
stat
1.173432
Prob(F-statistic)
0.000000
①由上可知，模型为：
Y
=
0.135474X2
+
18.85348X3
-
18231.58
②对模型进行检验：
1）可决系数是0.985838，修正的可决系数为0.983950，说明模型对样本拟合较好
2）F检验，F=522.0976>F（2,15）=4.77，回归方程显著
3）t检验，t统计量分别为X2的系数对应t值为10.58454，大于t（15）=2.131，系数是显著的，X3的系数对应t值为1.928512，小于t（15）=2.131，说明此系数是不显著的。
（2）对于对数模型，用Eviews分析结果如下：
Dependent
Variable:
LNY
Method:
Least
Squares
Date:
12/01/14
Time:
20:25
Sample:
1994
2011
Included
observations:
18
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
LNX2
1.564221
0.088988
17.57789
0.0000
LNX3
1.760695
0.682115
2.581229
0.0209
C
-20.52048
5.432487
-3.777363
0.0018
R-squared
0.986295
????Mean
dependent
var
8.400112
Adjusted
R-squared
0.984467
????S.D.
dependent
var
0.941530
S.E.
of
regression
0.117343
????Akaike
info
criterion
-1.296424
Sum
squared
resid
0.206540
????Schwarz
criterion
-1.148029
Log
likelihood
14.66782
????Hannan-Quinn
criter.
-1.275962
F-statistic
539.7364
????Durbin-Watson
stat
0.686656
Prob(F-statistic)
0.000000
①由上可知，模型为：
LNY=-20.52048+1.564221
LNX2+1.760695
LNX3
②对模型进行检验：
1）可决系数是0.986295，修正的可决系数为0.984467，说明模型对样本拟合较好。
2）F检验，F=539.7364>
F（2,15）=4.77，回归方程显著。
3）t检验，t统计量分别为-3.777363，17.57789，2.581229，均大于t（15）=2.131，所以这些系数都是显著的。
（3）
①（1）式中的经济意义：工业增加1亿元，出口货物总额增加0.135474亿元，人民币汇率增加1，出口货物总额增加18.85348亿元。
②（2）式中的经济意义：工业增加额每增加1%，出口货物总额增加1.564221%，人民币汇率每增加1%，出口货物总额增加1.760695%
3.3
（1）对家庭书刊消费对家庭月平均收入和户主受教育年数计量模型，由Eviews分析结果如下：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/01/14
Time:
20:30
Sample:
1
18Included
observations:
18
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X
0.086450
0.029363
2.944186
0.0101
T
52.37031
5.202167
10.06702
0.0000
C
-50.01638
49.46026
-1.011244
0.3279
R-squared
0.951235
????Mean
dependent
var
755.1222
Adjusted
R-squared
0.944732
????S.D.
dependent
var
258.7206
S.E.
of
regression
60.82273
????Akaike
info
criterion
11.20482
Sum
squared
resid
55491.07
????Schwarz
criterion
11.35321
Log
likelihood
-97.84334
????Hannan-Quinn
criter.
11.22528
F-statistic
146.2974
????Durbin-Watson
stat
2.605783
Prob(F-statistic)
0.000000
①模型为：Y
=
0.086450X
+
52.37031T-50.01638
②对模型进行检验：
1）可决系数是0.951235，修正的可决系数为0.944732，说明模型对样本拟合较好。
2）F检验，F=539.7364>
F（2,15）=4.77，回归方程显著。
3）t检验，t统计量分别为2.944186，10.06702，均大于t（15）=2.131，所以这些系数都是显著的。
③经济意义：家庭月平均收入增加1元，家庭书刊年消费支出增加0.086450元，户主受教育年数增加1年，家庭书刊年消费支出增加52.37031元。
（2）用Eviews分析：
①
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/01/14
Time:
22:30
Sample:
1
18Included
observations:
18
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
T
63.01676
4.548581
13.85416
0.0000
C
-11.58171
58.02290
-0.199606
0.8443
R-squared
0.923054
????Mean
dependent
var
755.1222
Adjusted
R-squared
0.918245
????S.D.
dependent
var
258.7206
S.E.
of
regression
73.97565
????Akaike
info
criterion
11.54979
Sum
squared
resid
87558.36
????Schwarz
criterion
11.64872
Log
likelihood
-101.9481
????Hannan-Quinn
criter.
11.56343
F-statistic
191.9377
????Durbin-Watson
stat
2.134043
Prob(F-statistic)
0.000000
②
Dependent
Variable:
X
Method:
Least
Squares
Date:
12/01/14
Time:
22:34
Sample:
1
18Included
observations:
18
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
T
123.1516
31.84150
3.867644
0.0014
C
444.5888
406.1786
1.094565
0.2899
R-squared
0.483182
????Mean
dependent
var
1942.933
Adjusted
R-squared
0.450881
????S.D.
dependent
var
698.8325
S.E.
of
regression
517.8529
????Akaike
info
criterion
15.44170
Sum
squared
resid
4290746.
????Schwarz
criterion
15.54063
Log
likelihood
-136.9753
????Hannan-Quinn
criter.
15.45534
F-statistic
14.95867
????Durbin-Watson
stat
1.052251
Prob(F-statistic)
0.001364
以上分别是y与T，X与T的一元回归
模型分别是：
Y
=
63.01676T
-
11.58171
X
=
123.1516T
+
444.5888
（3）对残差进行模型分析，用Eviews分析结果如下：
Dependent
Variable:
E1
Method:
Least
Squares
Date:
12/03/14
Time:
20:39
Sample:
1
18Included
observations:
18
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
E2
0.086450
0.028431
3.040742
0.0078
C
3.96E-14
13.88083
2.85E-15
1.0000
R-squared
0.366239
????Mean
dependent
var
2.30E-14
Adjusted
R-squared
0.326629
????S.D.
dependent
var
71.76693
S.E.
of
regression
58.89136
????Akaike
info
criterion
11.09370
Sum
squared
resid
55491.07
????Schwarz
criterion
11.19264
Log
likelihood
-97.84334
????Hannan-Quinn
criter.
11.10735
F-statistic
9.246111
????Durbin-Watson
stat
2.605783
Prob(F-statistic)
0.007788
模型为：
E1
=
0.086450E2
+
3.96e-14
参数：斜率系数α为0.086450，截距为3.96e-14
（3）由上可知，β2与α2的系数是一样的。回归系数与被解释变量的残差系数是一样的，它们的变化规律是一致的。
3.6
（1）预期的符号是X1，X2,X3,X4,X5的符号为正，X6的符号为负
（2）根据Eviews分析得到数据如下：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/04/14
Time:
13:24
Sample:
1994
2011
Included
observations:
18
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X2
0.001382
0.001102
1.254330
0.2336
X3
0.001942
0.003960
0.490501
0.6326
X4
-3.579090
3.559949
-1.005377
0.3346
X5
0.004791
0.005034
0.951671
0.3600
X6
0.045542
0.095552
0.476621
0.6422
C
-13.77732
15.73366
-0.875659
0.3984
R-squared
0.994869
????Mean
dependent
var
12.76667
Adjusted
R-squared
0.992731
????S.D.
dependent
var
9.746631
S.E.
of
regression
0.830963
????Akaike
info
criterion
2.728738
Sum
squared
resid
8.285993
????Schwarz
criterion
3.025529
Log
likelihood
-18.55865
????Hannan-Quinn
criter.
2.769662
F-statistic
465.3617
????Durbin-Watson
stat
1.553294
Prob(F-statistic)
0.000000
①与预期不相符。
②评价：
1）
可决系数为0.994869，数据相当大，可以认为拟合程度很好。
2）
F检验，F=465.3617>F（5.12）=3,89，回归方程显著
3）
T检验，X1，X2,X3,X4,X5，X6
系数对应的t值分别为：1.254330，0.490501，-1.005377，0.951671，0.476621，均小于t（12）=2.179，所以所得系数都是不显著的。
（3）根据Eviews分析得到数据如下：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/03/14
Time:
11:12
Sample:
1994
2011
Included
observations:
18
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X5
0.001032
2.20E-05
46.79946
0.0000
X6
-0.054965
0.031184
-1.762581
0.0983
C
4.205481
3.335602
1.260786
0.2266
R-squared
0.993601
????Mean
dependent
var
12.76667
Adjusted
R-squared
0.992748
????S.D.
dependent
var
9.746631
S.E.
of
regression
0.830018
????Akaike
info
criterion
2.616274
Sum
squared
resid
10.33396
????Schwarz
criterion
2.764669
Log
likelihood
-20.54646
????Hannan-Quinn
criter.
2.636736
F-statistic
1164.567
????Durbin-Watson
stat
1.341880
Prob(F-statistic)
0.000000
①得到模型的方程为：
Y=0.001032
X5-0.054965
X6+4.205481
②评价：
1）
可决系数为0.993601，数据相当大，可以认为拟合程度很好。
2）
F检验，F=1164.567>F（5.12）=3,89，回归方程显著
3）
T检验，X5
系数对应的t值为46.79946，大于t（12）=2.179，所以系数是显著的，即人均GDP对年底存款余额有显著影响。
X6
系数对应的t值为-1.762581，小于t（12）=2.179，所以系数是不显著的。4.3
（1）根据Eviews分析得到数据如下：
Dependent
Variable:
LNY
Method:
Least
Squares
Date:
12/05/14
Time:
11:39
Sample:
1985
2011
Included
observations:
27
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
LNGDP
1.338533
0.088610
15.10582
0.0000
LNCPI
-0.421791
0.233295
-1.807975
0.0832
C
-3.111486
0.463010
-6.720126
0.0000
R-squared
0.988051
????Mean
dependent
var
9.484710
Adjusted
R-squared
0.987055
????S.D.
dependent
var
1.425517
S.E.
of
regression
0.162189
????Akaike
info
criterion
-0.695670
Sum
squared
resid
0.631326
????Schwarz
criterion
-0.551689
Log
likelihood
12.39155
????Hannan-Quinn
criter.
-0.652857
F-statistic
992.2582
????Durbin-Watson
stat
0.522613
Prob(F-statistic)
0.000000
得到的模型方程为：
LNY=1.338533
LNGDPt-0.421791
LNCPIt-3.111486
（2）
①
该模型的可决系数为0.988051，可决系数很高，F检验值为992.2582，
明显显著。但当α=0.05时，t（24）=2.064，LNCPI的系数不显著，可能存在多重共线性。
②得到相关系数矩阵如下：
LNY
LNGDP
LNCPI
LNY
?1.000000
?0.993189
?0.935116
LNGDP
?0.993189
?1.000000
?0.953740
LNCPI
?0.935116
?0.953740
?1.000000
LNGDP，
LNCPI之间的相关系数很高，证实确实存在多重共线性。
（3）由Eviews得：
a）
Dependent
Variable:
LNY
Method:
Least
Squares
Date:
12/03/14
Time:
14:41
Sample:
1985
2011
Included
observations:
27
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
LNGDP
1.185739
0.027822
42.61933
0.0000
C
-3.750670
0.312255
-12.01156
0.0000
R-squared
0.986423
????Mean
dependent
var
9.484710
Adjusted
R-squared
0.985880
????S.D.
dependent
var
1.425517
S.E.
of
regression
0.169389
????Akaike
info
criterion
-0.642056
Sum
squared
resid
0.717312
????Schwarz
criterion
-0.546068
Log
likelihood
10.66776
????Hannan-Quinn
criter.
-0.613514
F-statistic
1816.407
????Durbin-Watson
stat
0.471111
Prob(F-statistic)
0.000000
b)
Dependent
Variable:
LNY
Method:
Least
Squares
Date:
12/03/14
Time:
14:41
Sample:
1985
2011
Included
observations:
27
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
LNCPI
2.939295
0.222756
13.19511
0.0000
C
-6.854535
1.242243
-5.517871
0.0000
R-squared
0.874442
????Mean
dependent
var
9.484710
Adjusted
R-squared
0.869419
????S.D.
dependent
var
1.425517
S.E.
of
regression
0.515124
????Akaike
info
criterion
1.582368
Sum
squared
resid
6.633810
????Schwarz
criterion
1.678356
Log
likelihood
-19.36196
????Hannan-Quinn
criter.
1.610910
F-statistic
174.1108
????Durbin-Watson
stat
0.137042
Prob(F-statistic)
0.000000
c)
Dependent
Variable:
LNGDP
Method:
Least
Squares
Date:
12/05/14
Time:
11:11
Sample:
1985
2011
Included
observations:
27
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
LNCPI
2.511022
0.158302
15.86227
0.0000
C
-2.796381
0.882798
-3.167634
0.0040
R-squared
0.909621
????Mean
dependent
var
11.16214
Adjusted
R-squared
0.906005
????S.D.
dependent
var
1.194029
S.E.
of
regression
0.366072
????Akaike
info
criterion
0.899213
Sum
squared
resid
3.350216
????Schwarz
criterion
0.995201
Log
likelihood
-10.13938
????Hannan-Quinn
criter.
0.927755
F-statistic
251.6117
????Durbin-Watson
stat
0.099623
Prob(F-statistic)
0.000000
①得到的回归方程分别为
1）LNY=1.185739
LNGDPt-3.750670
2）LNY=2.939295
LNCPIt-6.854535
3）LNGDPt=2.511022
LNCPIt-2.796381
②对多重共线性的认识：
单方程拟合效果都很好，回归系数显著，判定系数较高，GDP和CPI对进口的显著的单一影响，在这两个变量同时引入模型时影响方向发生了改变，这只有通过相关系数的分析才能发现。
（4）建议：如果仅仅是作预测，可以不在意这种多重共线性，但如果是进行结构分析，还是应该引起注意的。4.4
（1）按照设计的理论模型，由Eviews分析得：
Dependent
Variable:
CZSR
Method:
Least
Squares
Date:
12/03/14
Time:
11:40
Sample:
1985
2011
Included
observations:
27
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
CZZC
0.090114
0.044367
2.031129
0.0540
GDP
-0.025334
0.005069
-4.998036
0.0000
SSZE
1.176894
0.062162
18.93271
0.0000
C
-221.8540
130.6532
-1.698038
0.1030
R-squared
0.999857
????Mean
dependent
var
22572.56
Adjusted
R-squared
0.999838
????S.D.
dependent
var
27739.49
S.E.
of
regression
353.0540
????Akaike
info
criterion
14.70707
Sum
squared
resid
2866884.
????Schwarz
criterion
14.89905
Log
likelihood
-194.5455
????Hannan-Quinn
criter.
14.76416
F-statistic
53493.93
????Durbin-Watson
stat
1.458128
Prob(F-statistic)
0.000000
从回归结果可见，可决系数为0.999857，校正的可决系数为0.999838，模型拟合的很好。F的统计量为53493.93，说明在α=0.05,水平下，回归方程回归方程整体上是显著的。但是t检验结果表明，国内生产总值对财政收入的影响显著，但回归系数的符号为负，与实际不符合。由此可得知，该方程可能存在多重共线性。
（2）得到相关系数矩阵如下：
CZSR
CZZC
GDP
SSZE
CZSR
?1.000000
?0.998729
?0.992838
?0.999832
CZZC
?0.998729
?1.000000
?0.992536
?0.998575
GDP
?0.992838
?0.992536
?1.000000
?0.994370
SSZE
?0.999832
?0.998575
?0.994370
?1.000000
由上表可知，CZZC与GDP，CZZC与SSZE，GDP与SSZE之间的相关系数都非常高，说明确实存在多重共线性。
（3）做辅助回归
被解释变量
可决系数
方差扩大因子
CZZC
0.997168
353
GDP
0.988833
90
SSZE
0.997862
468
方差扩大因子均大于10，存在严重多重共线性。并且通过以上分析，两两被解释变量之间相关性都很高。
（4）解决方式：分别作出财政收入与财政支出、国内生产总值、税收总额之间的一元回归。
5.2
（1）
①用图形法检验
绘制e2的散点图，用Eviews分析如下：
由上图可知，模型可能存在异方差，
②
Goldfeld-Quanadt检验
1）定义区间为1-7时，由软件分析得：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/10/14
Time:
14:52
Sample:
1
7Included
observations:
7
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
T
35.20664
4.901492
7.182843
0.0020
X
0.109949
0.061965
1.774380
0.1507
C
77.12588
82.32844
0.936807
0.4019
R-squared
0.943099
????Mean
dependent
var
565.6857
Adjusted
R-squared
0.914649
????S.D.
dependent
var
108.2755
S.E.
of
regression
31.63265
????Akaike
info
criterion
10.04378
Sum
squared
resid
4002.499
????Schwarz
criterion
10.02060
Log
likelihood
-32.15324
????Hannan-Quinn
criter.
9.757267
F-statistic
33.14880
????Durbin-Watson
stat
1.426262
Prob(F-statistic)
0.003238
得∑e1i2=4002.499
2）定义区间为12-18时，由软件分析得：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/10/14
Time:
13:50
Sample:
12
18Included
observations:
7
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
T
52.40588
6.923378
7.569409
0.0016
X
0.068689
0.053763
1.277635
0.2705
C
-8.789265
79.92542
-0.109968
0.9177
R-squared
0.984688
????Mean
dependent
var
887.6143
Adjusted
R-squared
0.977032
????S.D.
dependent
var
274.4148
S.E.
of
regression
41.58810
????Akaike
info
criterion
10.59103
Sum
squared
resid
6918.280
????Schwarz
criterion
10.56785
Log
likelihood
-34.06861
????Hannan-Quinn
criter.
10.30451
F-statistic
128.6166
????Durbin-Watson
stat
2.390329
Prob(F-statistic)
0.000234
得∑e2i2=6918.280
3）根据Goldfeld-Quanadt检验，F统计量为：
F=∑e2i2
/∑e1i2
=6918.280/4002.499=1.7285
在α=0.05水平下，分子分母的自由度均为4，查分布表得临界值F0.05（4,4）=6.39，因为F=1.7285<
F0.05（4,4）=6.39，所以接受原假设，此检验表明模型不存在异方差。
（2）存在异方差，估计参数的方法：
①可以对模型进行变换
②使用加权最小二乘法进行计算，得出模型方程，并对其进行相关检验
③对模型进行对数变换，进行分析
（3）评价：
3.3所得结论是可以相信的，随机扰动项之间不存在异方差。回归方程是显著的。
5.3
(1)由Eviews软件分析得：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/10/14
Time:
16:00
Sample:
1
31Included
observations:
31
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X
1.244281
0.079032
15.74411
0.0000
C
242.4488
291.1940
0.832602
0.4119
R-squared
0.895260
????Mean
dependent
var
4443.526
Adjusted
R-squared
0.891649
????S.D.
dependent
var
1972.072
S.E.
of
regression
649.1426
????Akaike
info
criterion
15.85152
Sum
squared
resid
12220196
????Schwarz
criterion
15.94404
Log
likelihood
-243.6986
????Hannan-Quinn
criter.
15.88168
F-statistic
247.8769
????Durbin-Watson
stat
1.078581
Prob(F-statistic)
0.000000
由上表可知，2007年我国农村居民家庭人均消费支出（x）对人均纯收入（y）的模型为：
Y=1.244281X+242.4488
（2）
①由图形法检验
由上图可知，模型可能存在异方差。
②Goldfeld-Quanadt检验
1）定义区间为1-12时，由软件分析得：
Dependent
Variable:
Y1
Method:
Least
Squares
Date:
12/10/14
Time:
11:34
Sample:
1
12Included
observations:
12
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X1
1.485296
0.500386
2.968297
0.0141
C
-550.5492
1220.063
-0.451247
0.6614
R-squared
0.468390
????Mean
dependent
var
3052.950
Adjusted
R-squared
0.415229
????S.D.
dependent
var
550.5148
S.E.
of
regression
420.9803
????Akaike
info
criterion
15.07406
Sum
squared
resid
1772245.
????Schwarz
criterion
15.15488
Log
likelihood
-88.44437
????Hannan-Quinn
criter.
15.04414
F-statistic
8.810789
????Durbin-Watson
stat
2.354167
Prob(F-statistic)
0.014087
得∑e1i2=1772245.
2）定义区间为20-31时，由软件分析得：
Dependent
Variable:
Y1
Method:
Least
Squares
Date:
12/10/14
Time:
16:36
Sample:
20
31Included
observations:
12
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X1
1.086940
0.148863
7.301623
0.0000
C
1173.307
733.2520
1.600141
0.1407
R-squared
0.842056
????Mean
dependent
var
6188.329
Adjusted
R-squared
0.826262
????S.D.
dependent
var
2133.692
S.E.
of
regression
889.3633
????Akaike
info
criterion
16.56990
Sum
squared
resid
7909670.
????Schwarz
criterion
16.65072
Log
likelihood
-97.41940
????Hannan-Quinn
criter.
16.53998
F-statistic
53.31370
????Durbin-Watson
stat
2.339767
Prob(F-statistic)
0.000026
得∑e2i2=7909670.
3）根据Goldfeld-Quanadt检验，F统计量为：
F=∑e2i2
/∑e1i2
=7909670./
1772245=4.4631
在α=0.05水平下，分子分母的自由度均为10，查分布表得临界值F0.05（10,10）=2.98，因为F=4.4631>
F0.05（10,10）=2.98，所以拒绝原假设，此检验表明模型存在异方差。
（3）
1）采用WLS法估计过程中，
①用权数w1=1/X,建立回归得：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/09/14
Time:
11:13
Sample:
1
31Included
observations:
31
Weighting
series:
W1
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X
1.425859
0.119104
11.97157
0.0000
C
-334.8131
344.3523
-0.972298
0.3389Weighted
Statistics
R-squared
0.831707
????Mean
dependent
var
3946.082
Adjusted
R-squared
0.825904
????S.D.
dependent
var
536.1907
S.E.
of
regression
536.6796
????Akaike
info
criterion
15.47102
Sum
squared
resid
8352726.
????Schwarz
criterion
15.56354
Log
likelihood
-237.8008
????Hannan-Quinn
criter.
15.50118
F-statistic
143.3184
????Durbin-Watson
stat
1.369081
Prob(F-statistic)
0.000000
Unweighted
Statistics
R-squared
0.875855
????Mean
dependent
var
4443.526
Adjusted
R-squared
0.871574
????S.D.
dependent
var
1972.072
S.E.
of
regression
706.7236
????Sum
squared
resid
14484289
Durbin-Watson
stat
1.532908
对此模型进行White检验得：
Heteroskedasticity
Test:
WhiteF-statistic
0.299395
????Prob.
F(2,28)
0.7436
Obs*R-squared
0.649065
????Prob.
Chi-Square(2)
0.7229
Scaled
explained
SS
1.798067
????Prob.
Chi-Square(2)
0.4070Test
Equation:Dependent
Variable:
WGT_RESID^2
Method:
Least
Squares
Date:
12/10/14
Time:
21:13
Sample:
1
31Included
observations:
31
Collinear
test
regressors
dropped
from
specification
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
C
61927.89
1045682.
0.059222
0.9532
WGT^2
-593927.9
1173622.
-0.506064
0.6168
X*WGT^2
282.4407
747.9780
0.377606
0.7086
R-squared
0.020938
????Mean
dependent
var
269442.8
Adjusted
R-squared
-0.048995
????S.D.
dependent
var
689166.5
S.E.
of
regression
705847.6
????Akaike
info
criterion
29.86395
Sum
squared
resid
1.40E+13
????Schwarz
criterion
30.00273
Log
likelihood
-459.8913
????Hannan-Quinn
criter.
29.90919
F-statistic
0.299395
????Durbin-Watson
stat
1.922336
Prob(F-statistic)
0.743610
从上可知，nR2=0.649065，比较计算的统计量的临界值，因为nR2=0.649065<0.05（2）=5.9915，所以接受原假设，该模型消除了异方差。
估计结果为：
Y=1.425859X-334.8131
t=（11.97157）（-0.972298）
R2=0.875855
F=143.3184
DW=1.369081
②用权数w2=1/x2,用回归分析得：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/09/14
Time:
21:08
Sample:
1
31Included
observations:
31
Weighting
series:
W2
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X
1.557040
0.145392
10.70922
0.0000
C
-693.1946
376.4760
-1.841272
0.0758Weighted
Statistics
R-squared
0.798173
????Mean
dependent
var
3635.028
Adjusted
R-squared
0.791214
????S.D.
dependent
var
1029.830
S.E.
of
regression
466.8513
????Akaike
info
criterion
15.19224
Sum
squared
resid
6320554.
????Schwarz
criterion
15.28475
Log
likelihood
-233.4797
????Hannan-Quinn
criter.
15.22240
F-statistic
114.6875
????Durbin-Watson
stat
1.562975
Prob(F-statistic)
0.000000
Unweighted
Statistics
R-squared
0.834850
????Mean
dependent
var
4443.526
Adjusted
R-squared
0.829156
????S.D.
dependent
var
1972.072
S.E.
of
regression
815.1229
????Sum
squared
resid
19268334
Durbin-Watson
stat
1.678365
对此模型进行White检验得：
Heteroskedasticity
Test:
WhiteF-statistic
0.299790
????Prob.
F(3,27)
0.8252
Obs*R-squared
0.999322
????Prob.
Chi-Square(3)
0.8014
Scaled
explained
SS
1.789507
????Prob.
Chi-Square(3)
0.6172Test
Equation:Dependent
Variable:
WGT_RESID^2
Method:
Least
Squares
Date:
12/10/14
Time:
21:29
Sample:
1
31Included
observations:
31
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
C
-111661.8
549855.7
-0.203075
0.8406
WGT^2
426220.2
2240181.
0.190262
0.8505
X^2*WGT^2
0.194888
0.516395
0.377402
0.7088
X*WGT^2
-583.2151
2082.820
-0.280012
0.7816
R-squared
0.032236
????Mean
dependent
var
203888.8
Adjusted
R-squared
-0.075293
????S.D.
dependent
var
419282.0
S.E.
of
regression
434780.1
????Akaike
info
criterion
28.92298
Sum
squared
resid
5.10E+12
????Schwarz
criterion
29.10801
Log
likelihood
-444.3062
????Hannan-Quinn
criter.
28.98330
F-statistic
0.299790
????Durbin-Watson
stat
1.835854
Prob(F-statistic)
0.825233
从上可知，nR2=0.999322，比较计算的统计量的临界值，因为nR2=0.999322<0.05（2）=5.9915，所以接受原假设，该模型消除了异方差。
估计结果为：
Y=1.557040X-693.1946
t=（10.70922）（-1.841272）
R2=0.798173
F=114.6875
DW=1.562975
③用权数w3=1/sqr（x）,用回归分析得：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/09/14
Time:
21:35
Sample:
1
31Included
observations:
31
Weighting
series:
W3
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X
1.330130
0.098345
13.52507
0.0000
C
-47.40242
313.1154
-0.151390
0.8807Weighted
Statistics
R-squared
0.863161
????Mean
dependent
var
4164.118
Adjusted
R-squared
0.858442
????S.D.
dependent
var
991.2079
S.E.
of
regression
586.9555
????Akaike
info
criterion
15.65012
Sum
squared
resid
9990985.
????Schwarz
criterion
15.74263
Log
likelihood
-240.5768
????Hannan-Quinn
criter.
15.68027
F-statistic
182.9276
????Durbin-Watson
stat
1.237664
Prob(F-statistic)
0.000000
Unweighted
Statistics
R-squared
0.890999
????Mean
dependent
var
4443.526
Adjusted
R-squared
0.887240
????S.D.
dependent
var
1972.072
S.E.
of
regression
662.2171
????Sum
squared
resid
12717412
Durbin-Watson
stat
1.314859
对此模型进行White检验得：
Heteroskedasticity
Test:
WhiteF-statistic
0.423886
????Prob.
F(2,28)
0.6586
Obs*R-squared
0.911022
????Prob.
Chi-Square(2)
0.6341
Scaled
explained
SS
2.768332
????Prob.
Chi-Square(2)
0.2505Test
Equation:Dependent
Variable:
WGT_RESID^2
Method:
Least
Squares
Date:
12/09/14
Time:
20:36
Sample:
1
31Included
observations:
31
Collinear
test
regressors
dropped
from
specification
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
C
1212308.
2141958.
0.565981
0.5759
WGT^2
-715673.0
1301839.
-0.549740
0.5869
X^2*WGT^2
-0.015194
0.082276
-0.184677
0.8548
R-squared
0.029388
????Mean
dependent
var
322289.8
Adjusted
R-squared
-0.039942
????S.D.
dependent
var
863356.7
S.E.
of
regression
880429.8
????Akaike
info
criterion
30.30597
Sum
squared
resid
2.17E+13
????Schwarz
criterion
30.44475
Log
likelihood
-466.7426
????Hannan-Quinn
criter.
30.35121
F-statistic
0.423886
????Durbin-Watson
stat
1.887426
Prob(F-statistic)
0.658628
从上可知，nR2=0.911022，比较计算的统计量的临界值，因为nR2=0.911022<0.05（2）=5.9915，所以接受原假设，该模型消除了异方差。
估计结果为：
Y=1.330130X-47.40242
t=（13.52507）（-0.151390）
R2=0.863161
F=182.9276
DW=1.237664
经过检验发现，用权数w1的效果最好，所以综上可知，即修改后的结果为：
Y=1.425859X-334.8131
t=（11.97157）（-0.972298）
R2=0.875855
F=143.3184
DW=1.3690815.6
(1)
a)用Eviews模型分析得：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/10/14
Time:
20:16
Sample:
1978
2011
Included
observations:
34
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X
0.746241
0.019120
39.03027
0.0000
C
92.55422
42.80529
2.162215
0.0382
R-squared
0.979426
????Mean
dependent
var
1295.802
Adjusted
R-squared
0.978783
????S.D.
dependent
var
1188.791
S.E.
of
regression
173.1597
????Akaike
info
criterion
13.20333
Sum
squared
resid
959497.2
????Schwarz
criterion
13.29311
Log
likelihood
-222.4566
????Hannan-Quinn
criter.
13.23395
F-statistic
1523.362
????Durbin-Watson
stat
1.534491
Prob(F-statistic)
0.000000
得回归模型为：
Y=0.746241
X+92.55422
b)检验是否存在异方差：
①用Goldfeld-Quanadt检验如下：
1）当定义区间为1-13时，由软件分析得：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/11/14
Time:
11:47
Sample:
1
13Included
observations:
13
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X
0.967839
0.026879
36.00771
0.0000
C
-18.86861
8.963780
-2.104984
0.0591
R-squared
0.991587
????Mean
dependent
var
280.1377
Adjusted
R-squared
0.990823
????S.D.
dependent
var
127.0409
S.E.
of
regression
12.17039
????Akaike
info
criterion
7.976527
Sum
squared
resid
1629.301
????Schwarz
criterion
8.063442
Log
likelihood
-49.84742
????Hannan-Quinn
criter.
7.958662
F-statistic
1296.555
????Durbin-Watson
stat
1.071505
Prob(F-statistic)
0.000000
得∑e1i2=1629.301
2）当定义区间为1-13时，由软件分析得：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/11/14
Time:
12:21
Sample:
22
34Included
observations:
13
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X
0.719567
0.058312
12.33998
0.0000
C
179.3950
202.8764
0.884258
0.3955
R-squared
0.932629
????Mean
dependent
var
2496.127
Adjusted
R-squared
0.926504
????S.D.
dependent
var
1022.591
S.E.
of
regression
277.2250
????Akaike
info
criterion
14.22817
Sum
squared
resid
845390.4
????Schwarz
criterion
14.31509
Log
likelihood
-90.48313
????Hannan-Quinn
criter.
14.21031
F-statistic
152.2752
????Durbin-Watson
stat
1.658418
Prob(F-statistic)
0.000000
得∑e2i2=845390.4
3）根据Goldfeld-Quanadt检验，F统计量为：
F=∑e2i2
/∑e1i2
=845390.4/
1629.301=518.8669
在α=0.05水平下，分子分母的自由度均为11，查分布表得临界值F0.05（11,11）=4.47，因为F=518.8669>
F0.05（11,11）=4.47，所以拒绝原假设，此检验表明模型存在异方差。
②White检验
用EViews软件分析得：
Heteroskedasticity
Test:
WhiteF-statistic
10.36759
????Prob.
F(2,31)
0.0004
Obs*R-squared
13.62701
????Prob.
Chi-Square(2)
0.0011
Scaled
explained
SS
76.13635
????Prob.
Chi-Square(2)
0.0000Test
Equation:Dependent
Variable:
RESID^2
Method:
Least
Squares
Date:
12/11/14
Time:
12:56
Sample:
1
34Included
observations:
34
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
C
11581.11
26117.11
0.443430
0.6605
X
-27.69901
27.86540
-0.994029
0.3279
X^2
0.012230
0.005156
2.371861
0.0241
R-squared
0.400795
????Mean
dependent
var
28220.51
Adjusted
R-squared
0.362136
????S.D.
dependent
var
101738.9
S.E.
of
regression
81255.15
????Akaike
info
criterion
25.53267
Sum
squared
resid
2.05E+11
????Schwarz
criterion
25.66735
Log
likelihood
-431.0554
????Hannan-Quinn
criter.
25.57860
F-statistic
10.36759
????Durbin-Watson
stat
3.021651
Prob(F-statistic)
0.000357
从上图中可以看出，nR2=13.62701，比较计算的统计量的临界值，因为nR2=13.62701>0.05（2）=5.9915，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差。
用以上两种方法，可以检验模型是存在异方差的。
c)修正模型
1）用加权二乘法修正异方差现象步骤如下：
①当权数w1=1/x时，用软件分析得：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/11/14
Time:
13:22
Sample:
1
34Included
observations:
34
Weighting
series:
W1
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X
0.821013
0.016866
48.67993
0.0000
C
17.69318
6.283256
2.815926
0.0083Weighted
Statistics
R-squared
0.986676
????Mean
dependent
var
457.8505
Adjusted
R-squared
0.986260
????S.D.
dependent
var
41.70384
S.E.
of
regression
37.91285
????Akaike
info
criterion
10.16548
Sum
squared
resid
45996.29
????Schwarz
criterion
10.25527
Log
likelihood
-170.8132
????Hannan-Quinn
criter.
10.19610
F-statistic
2369.735
????Durbin-Watson
stat
0.605852
Prob(F-statistic)
0.000000
Unweighted
Statistics
R-squared
0.968070
????Mean
dependent
var
1295.802
Adjusted
R-squared
0.967072
????S.D.
dependent
var
1188.791
S.E.
of
regression
215.7175
????Sum
squared
resid
1489089.
Durbin-Watson
stat
1.079107
得方程模型为：
Y=0.821013X-17.69318
t=（48.67993）（2.815926）
R2=0.986676
F=2369.735
DW=0.605852
对此模型进行White检验如下：
Heteroskedasticity
Test:
WhiteF-statistic
1.348072
????Prob.
F(2,31)
0.2745
Obs*R-squared
2.720457
????Prob.
Chi-Square(2)
0.2566
Scaled
explained
SS
1.221901
????Prob.
Chi-Square(2)
0.5428Test
Equation:Dependent
Variable:
WGT_RESID^2
Method:
Least
Squares
Date:
12/11/14
Time:
11:20
Sample:
1
34Included
observations:
34
Collinear
test
regressors
dropped
from
specification
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
C
1678.870
416.5417
4.030498
0.0003
WGT^2
-32.13071
187.6175
-0.171257
0.8651
X*WGT^2
-0.484040
1.279449
-0.378319
0.7078
R-squared
0.080013
????Mean
dependent
var
1352.832
Adjusted
R-squared
0.020659
????S.D.
dependent
var
1382.825
S.E.
of
regression
1368.467
????Akaike
info
criterion
17.36487
Sum
squared
resid
58053732
????Schwarz
criterion
17.49955
Log
likelihood
-292.2027
????Hannan-Quinn
criter.
17.41080
F-statistic
1.348072
????Durbin-Watson
stat
1.199640
Prob(F-statistic)
0.274545
从上图中可以看出，nR2=2.720457，比较计算的统计量的临界值，
因为nR2=2.720457<0.05（2）=5.9915，所以接受原假设，即该模型消除了异方差的影响。
②当权数w2=1/x2时，用软件分析得：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/11/14
Time:
13:27
Sample:
1
34Included
observations:
34
Weighting
series:
W2
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X
0.852193
0.020150
42.29335
0.0000
C
8.890886
3.604301
2.466744
0.0192Weighted
Statistics
R-squared
0.982425
????Mean
dependent
var
230.2433
Adjusted
R-squared
0.981875
????S.D.
dependent
var
247.1718
S.E.
of
regression
16.20273
????Akaike
info
criterion
8.465259
Sum
squared
resid
8400.912
????Schwarz
criterion
8.555045
Log
likelihood
-141.9094
????Hannan-Quinn
criter.
8.495879
F-statistic
1788.728
????Durbin-Watson
stat
0.604647
Prob(F-statistic)
0.000000
Unweighted
Statistics
R-squared
0.954142
????Mean
dependent
var
1295.802
Adjusted
R-squared
0.952709
????S.D.
dependent
var
1188.791
S.E.
of
regression
258.5207
????Sum
squared
resid
2138654.
Durbin-Watson
stat
0.781788
得方程模型为：
Y=0.852193X+8.890886
t=（42.29335）（2.466744）
R2=0.982425
F=1788.728
DW=0.604647
用White检验模型得：
Heteroskedasticity
Test:
WhiteF-statistic
7.462185
????Prob.
F(3,30)
0.0007
Obs*R-squared
14.52935
????Prob.
Chi-Square(3)
0.0023
Scaled
explained
SS
19.40139
????Prob.
Chi-Square(3)
0.0002Test
Equation:Dependent
Variable:
WGT_RESID^2
Method:
Least
Squares
Date:
12/11/14
Time:
11:19
Sample:
1
34Included
observations:
34
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
C
-7.684700
85.76169
-0.089605
0.9292
WGT^2
64.20016
96.11160
0.667975
0.5093
X^2*WGT^2
0.006306
0.003431
1.838317
0.0759
X*WGT^2
-1.247222
1.163558
-1.071903
0.2923
R-squared
0.427334
????Mean
dependent
var
247.0857
Adjusted
R-squared
0.370067
????S.D.
dependent
var
435.4791
S.E.
of
regression
345.6323
????Akaike
info
criterion
14.63876
Sum
squared
resid
3583851.
????Schwarz
criterion
14.81833
Log
likelihood
-244.8589
????Hannan-Quinn
criter.
14.70000
F-statistic
7.462185
????Durbin-Watson
stat
1.586012
Prob(F-statistic)
0.000712
从上图中可以看出，nR2=14.52935，比较计算的统计量的临界值，因为nR2=14.52935>0.05（2）=5.9915，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差。此模型并未消除异方差。
③当权数w3=1/sqr(x)时，用软件分析得：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/11/14
Time:
13:21
Sample:
1
34Included
observations:
34
Weighting
series:
W3
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X
0.778551
0.015677
49.66347
0.0000
C
40.45770
14.57528
2.775775
0.0091Weighted
Statistics
R-squared
0.987192
????Mean
dependent
var
776.3266
Adjusted
R-squared
0.986792
????S.D.
dependent
var
367.3152
S.E.
of
regression
79.19828
????Akaike
info
criterion
11.63881
Sum
squared
resid
200715.8
????Schwarz
criterion
11.72859
Log
likelihood
-195.8597
????Hannan-Quinn
criter.
11.66943
F-statistic
2466.460
????Durbin-Watson
stat
1.178340
Prob(F-statistic)
0.000000
Unweighted
Statistics
R-squared
0.977590
????Mean
dependent
var
1295.802
Adjusted
R-squared
0.976890
????S.D.
dependent
var
1188.791
S.E.
of
regression
180.7210
????Sum
squared
resid
1045123.
Durbin-Watson
stat
1.460832
得方程模型为：
Y=0.778551X+40.45770
t=（49.66347）（2.775775）
R2=0.986792
F=2466.460
DW=1.178340
对所得模型进行White检验：
Heteroskedasticity
Test:
WhiteF-statistic
8.158958
????Prob.
F(2,31)
0.0014
Obs*R-squared
11.72514
????Prob.
Chi-Square(2)
0.0028
Scaled
explained
SS
28.08353
????Prob.
Chi-Square(2)
0.0000Test
Equation:Dependent
Variable:
WGT_RESID^2
Method:
Least
Squares
Date:
12/10/14
Time:
13:23
Sample:
1
34Included
observations:
34
Collinear
test
regressors
dropped
from
specification
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
C
-7585.186
5311.263
-1.428132
0.1633
WGT^2
2468.369
1996.041
1.236632
0.2255
X^2*WGT^2
0.009139
0.002481
3.684177
0.0009
R-squared
0.344857
????Mean
dependent
var
5903.405
Adjusted
R-squared
0.302590
????S.D.
dependent
var
13934.64
S.E.
of
regression
11636.97
????Akaike
info
criterion
21.64586
Sum
squared
resid
4.20E+09
????Schwarz
criterion
21.78054
Log
likelihood
-364.9796
????Hannan-Quinn
criter.
21.69179
F-statistic
8.158958
????Durbin-Watson
stat
2.344068
Prob(F-statistic)
0.001423
从上图中可以看出，nR2=11.72514，比较计算的统计量的临界值，因为nR2=11.72514>0.05（2）=5.9915，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差。此模型并未消除异方差。
综上所述，用加权二乘法w1的效果最好，所以模型为：
得方程模型为：
Y=0.821013X-17.69318
t=（48.67993）（2.815926）
R2=0.986676
F=2369.735
DW=0.605852
2）用对数模型法
用软件分析得：
Dependent
Variable:
LNY
Method:
Least
Squares
Date:
12/11/14
Time:
09:54
Sample:
1
34Included
observations:
34
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
LNX
0.946887
0.011228
84.33549
0.0000
C
0.201861
0.077905
2.591100
0.0143
R-squared
0.995521
????Mean
dependent
var
6.687779
Adjusted
R-squared
0.995381
????S.D.
dependent
var
1.067124
S.E.
of
regression
0.072525
????Akaike
info
criterion
-2.352753
Sum
squared
resid
0.168315
????Schwarz
criterion
-2.262967
Log
likelihood
41.99680
????Hannan-Quinn
criter.
-2.322134
F-statistic
7112.475
????Durbin-Watson
stat
0.812150
Prob(F-statistic)
0.000000
得到模型为：
LnY=0.946887
LNX+0.201861
对此模型进行White检验得：
Heteroskedasticity
Test:
WhiteF-statistic
1.003964
????Prob.
F(2,31)
0.3780
Obs*R-squared
2.068278
????Prob.
Chi-Square(2)
0.3555
Scaled
explained
SS
1.469638
????Prob.
Chi-Square(2)
0.4796Test
Equation:Dependent
Variable:
RESID^2
Method:
Least
Squares
Date:
12/11/14
Time:
09:55
Sample:
1
34Included
observations:
34
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
C
0.039547
0.046759
0.845753
0.4042
LNX
-0.011601
0.014012
-0.827969
0.4140
LNX^2
0.000932
0.001028
0.906774
0.3715
R-squared
0.060832
????Mean
dependent
var
0.004950
Adjusted
R-squared
0.000240
????S.D.
dependent
var
0.006365
S.E.
of
regression
0.006364
????Akaike
info
criterion
-7.192271
Sum
squared
resid
0.001255
????Schwarz
criterion
-7.057592
Log
likelihood
125.2686
????Hannan-Quinn
criter.
-7.146342
F-statistic
1.003964
????Durbin-Watson
stat
2.022904
Prob(F-statistic)
0.378027
从上图中可以看出，nR2=2.068278，比较计算的统计量的临界值，因为nR2=2.068278<0.05（2）=5.9915，所以接受原假设，此模型消除了异方差。
综合两种方法，改进后的模型最好为：
LnY=0.946887
LNX+0.201861
(2)
1）考虑价格因素，首先用软件三者关系进行分析如下：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/12/14
Time:
19:26
Sample:
1
34Included
observations:
34
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X
0.741684
0.019905
37.26095
0.0000
P
0.235025
0.271701
0.865012
0.3937
C
43.41715
71.22946
0.609539
0.5466
R-squared
0.979911
????Mean
dependent
var
1295.802
Adjusted
R-squared
0.978615
????S.D.
dependent
var
1188.791
S.E.
of
regression
173.8449
????Akaike
info
criterion
13.23830
Sum
squared
resid
936883.7
????Schwarz
criterion
13.37298
Log
likelihood
-222.0511
????Hannan-Quinn
criter.
13.28423
F-statistic
756.0627
????Durbin-Watson
stat
1.681521
Prob(F-statistic)
0.000000
1）用Goldfeld-Quanadt检验如下：
①当样本为1-13时，进行回归分析：
Dependent
Variable:
P
Method:
Least
Squares
Date:
12/14/14
Time:
19:26
Sample:
1
13Included
observations:
13
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X
-0.170484
0.203868
-0.836247
0.4225
Y
0.458660
0.209755
2.186646
0.0536
C
59.50496
7.385841
8.056627
0.0000
R-squared
0.956255
????Mean
dependent
var
135.3231
Adjusted
R-squared
0.947506
????S.D.
dependent
var
36.95380
S.E.
of
regression
8.466678
????Akaike
info
criterion
7.309328
Sum
squared
resid
716.8464
????Schwarz
criterion
7.439701
Log
likelihood
-44.51063
????Hannan-Quinn
criter.
7.282530
F-statistic
109.2993
????Durbin-Watson
stat
0.637181
Prob(F-statistic)
0.000000
得∑e1i2=716.8464
②当样本为22-34时，做回归分析得：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/14/14
Time:20:39
Sample:
22
34Included
observations:
13
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X
0.641197
0.092678
6.918569
0.0000
P
-1.206222
1.114278
-1.082514
0.3044
C
795.6887
603.8605
1.317670
0.2170
R-squared
0.939696
????Mean
dependent
var
2496.127
Adjusted
R-squared
0.927635
????S.D.
dependent
var
1022.591
S.E.
of
regression
275.0847
????Akaike
info
criterion
14.27121
Sum
squared
resid
756715.7
????Schwarz
criterion
14.40158
Log
likelihood
-89.76286
????Hannan-Quinn
criter.
14.24441
F-statistic
77.91291
????Durbin-Watson
stat
1.128778
Prob(F-statistic)
0.000001
得∑e2i2=756715.7
③根据Goldfeld-Quanadt检验，F统计量为：
F=∑e2i2
/∑e1i2
=756715.7/
716.8464=1055.6176
在α=0.05水平下，分子分母的自由度均为11，查分布表得临界值F0.05（10,10）=2.98，因为F=1055.6176>
F0.05（10,10）=2.98，所以拒绝原假设，此检验表明模型存在异方差。
2）用White检验，软件分析结果为：
Heteroskedasticity
Test:
WhiteF-statistic
7.312529
????Prob.
F(5,28)
0.0002
Obs*R-squared
19.25463
????Prob.
Chi-Square(5)
0.0017
Scaled
explained
SS
119.3072
????Prob.
Chi-Square(5)
0.0000Test
Equation:Dependent
Variable:
RESID^2
Method:
Least
Squares
Date:
12/12/14
Time:
19:31
Sample:
1
34Included
observations:
34
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
C
79541.08
112647.3
0.706107
0.4860
X
209.4964
63.90400
3.278298
0.0028
X^2
-0.024133
0.010712
-2.252841
0.0323
X*P
-0.235137
0.106647
-2.204822
0.0358
P
-1175.326
1156.253
-1.016495
0.3181
P^2
1.637366
2.600020
0.629751
0.5340
R-squared
0.566313
????Mean
dependent
var
27555.40
Adjusted
R-squared
0.488869
????S.D.
dependent
var
107990.9
S.E.
of
regression
77206.44
????Akaike
info
criterion
25.50514
Sum
squared
resid
1.67E+11
????Schwarz
criterion
25.77450
Log
likelihood
-427.5874
????Hannan-Quinn
criter.
25.59700
F-statistic
7.312529
????Durbin-Watson
stat
2.787044
Prob(F-statistic)
0.000171
从上图中可以看出，nR2=19.25463，比较计算的统计量的临界值，因为nR2=19.25463>0.05（5）=11.0705，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差。
2）修正
①建立对数模型，用软件分析如下：
Dependent
Variable:
LNY
Method:
Least
Squares
Date:
12/12/14
Time:
19:24
Sample:
1
34Included
observations:
34
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
LNX
0.939605
0.013645
68.86088
0.0000
LNP
0.026821
0.028454
0.942609
0.3532
C
0.108230
0.126322
0.856784
0.3981
R-squared
0.995646
????Mean
dependent
var
6.687779
Adjusted
R-squared
0.995365
????S.D.
dependent
var
1.067124
S.E.
of
regression
0.072652
????Akaike
info
criterion
-2.322188
Sum
squared
resid
0.163625
????Schwarz
criterion
-2.187509
Log
likelihood
42.47720
????Hannan-Quinn
criter.
-2.276259
F-statistic
3544.292
????Durbin-Watson
stat
0.930109
Prob(F-statistic)
0.000000
对此模型进行White检验：
Heteroskedasticity
Test:
WhiteF-statistic
3.523832
????Prob.
F(5,28)
0.0135
Obs*R-squared
13.13158
????Prob.
Chi-Square(5)
0.0222
Scaled
explained
SS
12.14373
????Prob.
Chi-Square(5)
0.0329Test
Equation:Dependent
Variable:
RESID^2
Method:
Least
Squares
Date:
12/12/14
Time:
19:24
Sample:
1
34Included
observations:
34
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
C
0.422872
0.273746
1.544759
0.1336
LNX
0.080712
0.031833
2.535502
0.0171
LNX^2
-0.003917
0.003037
-1.289564
0.2078
LNX*LNP
-0.004955
0.005136
-0.964765
0.3429
LNP
-0.254992
0.129858
-1.963631
0.0596
LNP^2
0.026470
0.012675
2.088390
0.0460
R-squared
0.386223
????Mean
dependent
var
0.004813
Adjusted
R-squared
0.276620
????S.D.
dependent
var
0.007286
S.E.
of
regression
0.006197
????Akaike
info
criterion
-7.170690
Sum
squared
resid
0.001075
????Schwarz
criterion
-6.901332
Log
likelihood
127.9017
????Hannan-Quinn
criter.
-7.078831
F-statistic
3.523832
????Durbin-Watson
stat
2.264261
Prob(F-statistic)
0.013502
从上图中可以看出，nR2=13.13158，比较计算的统计量的临界值，因为nR2=13.13158>0.05（5）=11.0705，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差，所以此模型没有消除异方差。
②当w1=1/x时，用软件分析如下：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/13/14
Time:
18:49
Sample:
1
34Included
observations:
34
Weighting
series:
W1
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X
0.723218
0.022965
31.49212
0.0000
P
0.719506
0.141085
5.099795
0.0000
C
-44.72084
13.11268
-3.410502
0.0018Weighted
Statistics
R-squared
0.992755
????Mean
dependent
var
457.8505
Adjusted
R-squared
0.992287
????S.D.
dependent
var
41.70384
S.E.
of
regression
28.40494
????Akaike
info
criterion
9.615100
Sum
squared
resid
25012.05
????Schwarz
criterion
9.749779
Log
likelihood
-160.4567
????Hannan-Quinn
criter.
9.661030
F-statistic
2123.843
????Durbin-Watson
stat
1.298389
Prob(F-statistic)
0.000000
Unweighted
Statistics
R-squared
0.977704
????Mean
dependent
var
1295.802
Adjusted
R-squared
0.976266
????S.D.
dependent
var
1188.791
S.E.
of
regression
183.1446
????Sum
squared
resid
1039800.
Durbin-Watson
stat
1.740795
所得模型为：
Y=0.723218X+0.719506p-44.72084
对此模型进行White检验得：
Heteroskedasticity
Test:
WhiteF-statistic
2.088840
????Prob.
F(5,28)
0.0966
Obs*R-squared
9.236835
????Prob.
Chi-Square(5)
0.1000
Scaled
explained
SS
25.50696
????Prob.
Chi-Square(5)
0.0001Test
Equation:Dependent
Variable:
WGT_RESID^2
Method:
Least
Squares
Date:
12/14/14
Time:
19:57
Sample:
1
34Included
observations:
34
Collinear
test
regressors
dropped
from
specification
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
C
3861.793
1068.806
3.613183
0.0012
WGT^2
3260.199
4309.988
0.756429
0.4557
X*WGT^2
13.72241
8.453473
1.623287
0.1157
X*P*WGT^2
-0.151725
0.061588
-2.463567
0.0202
P^2*WGT^2
0.431162
0.278315
1.549186
0.1326
P*WGT^2
-76.13221
73.40636
-1.037134
0.3085
R-squared
0.271672
????Mean
dependent
var
735.6486
Adjusted
R-squared
0.141613
????S.D.
dependent
var
1924.655
S.E.
of
regression
1783.177
????Akaike
info
criterion
17.96897
Sum
squared
resid
89032169
????Schwarz
criterion
18.23832
Log
likelihood
-299.4724
????Hannan-Quinn
criter.
18.06082
F-statistic
2.088840
????Durbin-Watson
stat
2.336495
Prob(F-statistic)
0.096616
因为nR2=9.236835<0.05（5）=11.0705，所以接受原假设。该模型不存在异方差，所以此模型消除了异方差。
③当w2=1/x2，用软件分析得：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/15/14
Time:
20:02
Sample:
1
34Included
observations:
34
Weighting
series:
W2
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X
0.639012
0.039216
16.29477
0.0000
P
1.200751
0.206023
5.828234
0.0000
C
-81.85973
15.77499
-5.189209
0.0000Weighted
Statistics
R-squared
0.991614
????Mean
dependent
var
230.2433
Adjusted
R-squared
0.991073
????S.D.
dependent
var
247.1718
S.E.
of
regression
11.37136
????Akaike
info
criterion
7.784170
Sum
squared
resid
4008.543
????Schwarz
criterion
7.918849
Log
likelihood
-129.3309
????Hannan-Quinn
criter.
7.830100
F-statistic
1832.775
????Durbin-Watson
stat
1.167961
Prob(F-statistic)
0.000000
Unweighted
Statistics
R-squared
0.956816
????Mean
dependent
var
1295.802
Adjusted
R-squared
0.954030
????S.D.
dependent
var
1188.791
S.E.
of
regression
254.8849
????Sum
squared
resid
2013955.
Durbin-Watson
stat
1.002870
所得模型为：
Y=0.639012X+1.200751p-81.85973
对该模型进行White检验得：
Heteroskedasticity
Test:
WhiteF-statistic
43.19853
????Prob.
F(6,27)
0.0000
Obs*R-squared
30.79235
????Prob.
Chi-Square(6)
0.0000
Scaled
explained
SS
47.42430
????Prob.
Chi-Square(6)
0.0000Test
Equation:Dependent
Variable:
WGT_RESID^2
Method:
Least
Squares
Date:
12/14/14
Time:
19:20
Sample:
1
34Included
observations:
34
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
C
27.51002
20.12556
1.366919
0.1829
WGT^2
-1245.193
837.2352
-1.487268
0.1485
X^2*WGT^2
0.007732
0.005450
1.418649
0.1674
X*WGT^2
7.948582
4.884597
1.627275
0.1153
X*P*WGT^2
-0.111755
0.064061
-1.744525
0.0924
P^2*WGT^2
0.184342
0.164562
1.120199
0.2725
P*WGT^2
-3.127017
23.56724
-0.132685
0.8954
R-squared
0.905657
????Mean
dependent
var
117.8983
Adjusted
R-squared
0.884692
????S.D.
dependent
var
230.3570
S.E.
of
regression
78.22224
????Akaike
info
criterion
11.73823
Sum
squared
resid
165205.4
????Schwarz
criterion
12.05248
Log
likelihood
-192.5498
????Hannan-Quinn
criter.
11.84539
F-statistic
43.19853
????Durbin-Watson
stat
1.794799
Prob(F-statistic)
0.000000
因为nR2=30.79235>0.05（5）=11.0705，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差，所以此模型没有消除异方差。
④当w3=1/sqr(x)时，用软件分析得：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/14/14
Time:
19:06
Sample:
1
34Included
observations:
34
Weighting
series:
W3
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X
0.744661
0.019825
37.56252
0.0000
P
0.451861
0.179971
2.510739
0.0175
C
-13.49643
25.37768
-0.531823
0.5986Weighted
Statistics
R-squared
0.989356
????Mean
dependent
var
776.3266
Adjusted
R-squared
0.988670
????S.D.
dependent
var
367.3152
S.E.
of
regression
73.35237
????Akaike
info
criterion
11.51252
Sum
squared
resid
166797.7
????Schwarz
criterion
11.64720
Log
likelihood
-192.7129
????Hannan-Quinn
criter.
11.55845
F-statistic
1440.783
????Durbin-Watson
stat
1.599590
Prob(F-statistic)
0.000000
Unweighted
Statistics
R-squared
0.979407
????Mean
dependent
var
1295.802
Adjusted
R-squared
0.978079
????S.D.
dependent
var
1188.791
S.E.
of
regression
176.0098
????Sum
squared
resid
960362.6
Durbin-Watson
stat
1.761225
所得模型为：
Y=0.744661X+0.451861p-13.49643
对所得模型进行White检验得：
Heteroskedasticity
Test:
WhiteF-statistic
4.459272
????Prob.
F(5,28)
0.0041
Obs*R-squared
15.07219
????Prob.
Chi-Square(5)
0.0101
Scaled
explained
SS
72.39077
????Prob.
Chi-Square(5)
0.0000Test
Equation:Dependent
Variable:
WGT_RESID^2
Method:
Least
Squares
Date:
12/14/14
Time:
19:08
Sample:
1
34Included
observations:
34
Collinear
test
regressors
dropped
from
specification
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
C
61163.22
27531.93
2.221538
0.0346
WGT^2
28251.98
17350.39
1.628320
0.1147
X^2*WGT^2
-0.001093
0.006624
-0.164950
0.8702
X*P*WGT^2
-0.235836
0.077110
-3.058447
0.0049
P^2*WGT^2
1.236884
0.644872
1.918030
0.0654
P*WGT^2
-503.3080
262.5884
-1.916718
0.0655
R-squared
0.443300
????Mean
dependent
var
4905.814
Adjusted
R-squared
0.343889
????S.D.
dependent
var
16926.97
S.E.
of
regression
13710.96
????Akaike
info
criterion
22.04856
Sum
squared
resid
5.26E+09
????Schwarz
criterion
22.31792
Log
likelihood
-368.8256
????Hannan-Quinn
criter.
22.14042
F-statistic
4.459272
????Durbin-Watson
stat
2.450171
Prob(F-statistic)
0.004103
因为nR2=15.07219>0.05（5）=11.0705，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差，所以此模型没有消除异方差。
综上所述，修改后的模型为：
Y=
Y=0.723218X+0.719506p-44.72084
t=(31.49212)
(5.099705)
(-3.410502)
R2=0.992755
F=2123.843
DW=1.298389
(3)体会：对于不同的模型，可采取对数模型法或者加权二乘法对具有异方差性的模型进行改进，从而消除异方差。但对于不同的模型，自由度的不同，可能导致改进的方法不同，所以要对改进的模型进行进一步的检验才行。
6.1
(1)建立居民收入-消费模型，用Eviews分析结果如下：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/20/14
Time:
14:22
Sample:
1
19Included
observations:
19
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X
0.690488
0.012877
53.62068
0.0000
C
79.93004
12.39919
6.446390
0.0000
R-squared
0.994122
????Mean
dependent
var
700.2747
Adjusted
R-squared
0.993776
????S.D.
dependent
var
246.4491
S.E.
of
regression
19.44245
????Akaike
info
criterion
8.872095
Sum
squared
resid
6426.149
????Schwarz
criterion
8.971510
Log
likelihood
-82.28490
????Hannan-Quinn
criter.
8.888920
F-statistic
2875.178
????Durbin-Watson
stat
0.574663
Prob(F-statistic)
0.000000
所得模型为：
Y=0.690488X+79.93004
Se=(0.012877)(12.39919)
t=(53.62068)(6.446390)
R2=0.994122
F=2875.178
DW=0.574663
（2）
1）检验模型中存在的问题
①做出残差图如下：
残差的变动有系统模式，连续为正和连续为负，表明残差项存在一阶自相关。
②该回归方程可决系数较高，回归系数均显著。对样本量为19，一个解释变量的模型，5%的显著水平，查DW统计表可知，dL=1.180，dU=1.401，模型中DW=0.574663,<
dL,显然模型中有自相关。
③对模型进行BG检验，用Eviews分析结果如下：
Breusch-Godfrey
Serial
Correlation
LM
Test:F-statistic
4.811108
????Prob.
F(2,15)
0.0243
Obs*R-squared
7.425088
????Prob.
Chi-Square(2)
0.0244Test
Equation:Dependent
Variable:
RESID
Method:
Least
Squares
Date:
12/20/14
Time:
15:03
Sample:
1
19Included
observations:
19
Presample
missing
value
lagged
residuals
set
to
zero.
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
X
-0.003275
0.010787
-0.303586
0.7656
C
1.929546
10.35593
0.186323
0.8547
RESID(-1)
0.608886
0.292707
2.080189
0.0551
RESID(-2)
0.089988
0.291120
0.309110
0.7615
R-squared
0.390794
????Mean
dependent
var
-1.65E-13
Adjusted
R-squared
0.268953
????S.D.
dependent
var
18.89466
S.E.
of
regression
16.15518
????Akaike
info
criterion
8.587023
Sum
squared
resid
3914.848
????Schwarz
criterion
8.785852
Log
likelihood
-77.57671
????Hannan-Quinn
criter.
8.620672
F-statistic
3.207406
????Durbin-Watson
stat
1.570723
Prob(F-statistic)
0.053468
如上表显示，LM=TR2=7.425088，其p值为0.0244，表明存在自相关。
2）对模型进行处理：
①采取广义差分法
a)为估计自相关系数ρ。对et进行滞后一期的自回归，用EViews分析结果如下：
Dependent
Variable:
E
Method:
Least
Squares
Date:
12/20/14
Time:
15:04
Sample
(adjusted):
2
19
Included
observations:
18
after
adjustmentsVariable
Coefficient
Std.
Error
t-Statistic
Prob.??
E(-1)
0.657352
0.177626
3.700759
0.0018
R-squared
0.440747
????Mean
dependent
var
1.717433
Adjusted
R-squared
0.440747
????S.D.
dependent
var
17.85134
S.E.
of
regression
13.34980
????Akaike
info
criterion
8.074833
Sum
squared
resid
3029.692
????Schwarz
criterion
8.124298
Log
likelihood
-71.67349
????Hannan-Quinn
criter.
8.081653
Durbin-Watson
stat
1.634573
由上可知，ρ=0.657352
b)对原模型进行广义差分回归，用Eviews进行分析所得结果如下：
Dependent
Variable:
Y-0.657352*Y(-1)
Method:
Least
Squares
Date:
12/20/14
Time:
15:04
Sample
(adjusted):
2
19
Included
observations:
18
after
adjustmentsVariable
Coefficient
Std.
Error
t-Statistic
Prob.??
C
35.97761
8.103546
4.439737
0.0004
X-0.657352*X(-1)
0.668695
0.020642
32.39512
0.0000
R-squared
0.984983
????Mean
dependent
var
278.1002
Adjusted
R-squared
0.984044
????S.D.
dependent
var
105.1781
S.E.
of
regression
13.28570
????Akaike
info
criterion
8.115693
Sum
squared
resid
2824.158
????Schwarz
criterion
8.214623
Log
likelihood
-71.04124
????Hannan-Quinn
criter.
8.129334
F-statistic
1049.444
????Durbin-Watson
stat
1.830746
Prob(F-statistic)
0.000000
由上图可知回归方程为：
Yt*=35.97761+0.668695Xt*
Se=(8.103546)(0.020642)
t=(4.439737)(32.39512)
R2=0.984983
F=1049.444
DW=1.830746
式中，Yt*=Yt-0.657352Yt-1,
Xt*=Xt-0.657352Xt-1
由于使用了广义差分数据，样本容量减少了1个，为18个。查5%显著水平的DW统计表可知，dL=1.158,dU=1.391模型中DW=1,830746，du
dU，说明在5%的显著水平下广义差分模型中已无自相关。可决系数R2，t，F统计量也均达到理想水平。
由差分方程，β1=35.97761/(1-0.657352)=104.9987
由此最终的消费模型为：
Yt=104.9987+0.668695Xt
②用科克伦-奥克特迭代法，用EVIews分析结果如下：
Dependent
Variable:
Y
Method:
Least
Squares
Date:
12/20/14
Time:
15:15
Sample
(adjusted):
2
19
Included
observations:
18
after
adjustments
Convergence
achieved
after
5
iterationsVariable
Coefficient
Std.
Error
t-Statistic
Prob.??
C
104.0449
23.87618
4.357687
0.0006
X
0.669262
0.020831
32.12757
0.0000
AR(1)
0.630015
0.164218
3.836462
0.0016
R-squared
0.997097
????Mean
dependent
var
719.1867
Adjusted
R-squared
0.996710
????S.D.
dependent
var
238.9866
S.E.
of
regression
13.70843
????Akaike
info
criterion
8.224910
Sum
squared
resid
2818.814
????Schwarz
criterion
8.373306
Log
likelihood
-71.02419
????Hannan-Quinn
criter.
8.245372
F-statistic
2575.896
????Durbin-Watson
stat
1.787878
Prob(F-statistic)
0.000000
Inverted
AR
Roots
??????.63
所得方程为：
Yt=104.0449+0.669262Xt
（3）经济意义：人均实际收入每增加1元，平均说来人均时间消费支出将增加0.669262元。
6.4
（1）
1）针对对数模型，用Eviews分析结果如下：
Dependent
Variable:
LNY
Method:
Least
Squares
Date:
12/27/14
Time:
16:13
Sample:
1980
2000
Included
observations:
21
Variable
Coefficient
Std.
Error
t-Statistic
Prob.??
LNX
0.951090
0.038897
24.45123
0.0000
C
2.171041
0.241025
9.007529
0.0000
R-squared
0.969199
????Mean
dependent
var
8.039307
Adjusted
R-squared
0.967578
????S.D.
dependent
var
0.565486
S.E.
of
regression
0.101822
????Akaike
info
criterion
-1.640785
Sum
squared
resid
0.196987
????Schwarz
criterion
-1.541307
Log
likelihood
19.22825
????Hannan-Quinn
criter.
-1.619196
F-statistic
597.8626
????Durbin-Watson
stat
1.159788
Prob(F-statistic)
0.000000
所得模型为：
lnY=0,951090lnX+2.171041
se=(0.038897)
(0.241025)
t=(24.45123)
(9.007529)
R2=0.969199
F=597.8626
DW=1.159788
2）检验模型的自相关性
该回归方程可决系数较高，回归系数均显著。对样本量为21，一个解释变量的模型，5%的显著水平，查DW统计表可知，dL=1.221，dU=1.420，模型中DW=1.159788<
dL,显然模型中有自相关。
(2)用广义差分法处理模型：
1）为估计自相关系数ρ。对et进行滞后一期的自回归，用EViews分析结果如下：
Dependent
Variable:
E
Method:
Least
Squares
Date:
12/27/14
Time:
16:18
Sample
(adjusted):
1982
2000
Included
observations:
19
after
adjustmentsVariable
Coefficient
Std.
Error
t-Statistic
Prob.??
E(-1)
-0.012872
0.280581
-0.045878
0.9639
R-squared
0.000073
????Mean
dependent
var
-2.556737
Adjusted
R-squared
0.000073
????S.D.
dependent
var
397.7924
S.E.
of
regression
397.7778
????Akaike
info
criterion
14.86086
Sum
squared
resid
2848090.
????Schwarz
criterion
14.91057
Log
likelihood
-140.1782
????Hannan-Quinn
criter.
14.86927
Durbin-Watson
stat
1.700254
由上可知，ρ=-0.012872
2）对原模型进行广义差分回归，用Eviews进行分析所得结果如下：
Dependent
Variable:
Y+0.012872*Y(-1)
Method:
Least
Squares
Date:
12/27/14
Time:
21:06
Sample
(adjusted):
1981
2000
Included
observations:
20
after
adjustmentsVariable
Coefficient
Std.
Error
t-Statistic
Prob.??
C
-104.9645
197.7928
-0.530679
0.6021
X+0.012872*X(-1)
6.653757
0.304157
21.87605
0.0000
R-squared
0.963751
????Mean
dependent
var
3753.934
Adjusted
R-squared
0.961737
????S.D.
dependent
var
2045.606
S.E.
of
regression
400.1404
????Akaike
info
criterion
14.91615
Sum
squared
resid
2882022.
????Schwarz
criterion
15.01572
Log
likelihood
-147.1615
????Hannan-Quinn
criter.
14.93559
F-statistic
478.5614
????Durbin-Watson
stat
1.822259
Prob(F-statistic)
0.000000
由上图可知回归方程为：
Yt*=-104.9645+6.653757Xt*
Se=(197.7928)(
0.304157)
t=(-0.530679)(
21.87605)
R2=0.963751
F=478.5614DW=1.8222596
式中，Yt*=Yt+0.012872Yt-1,
Xt*=Xt+0.012872Xt-1
由于使用了广义差分数据，样本容量减少了1个，为20个。查5%显著水平的DW统计表可知，dL=1.201,dU=1.411模型中DW=1.8222596，dudU，说明在5%的显著水平下广义差分模型中已无自相关。可决系数R2，t，F统计量也均达到理想水平。
由差分方程，β1=-104.9645/(1+0.012872)=-103.6306
由此最终的模型为：
Yt=-103.6306+6.653757Xt
（3）对于此模型，用Eviews分析结果如下：
Dependent
Variable:
LNY1
Method:
Least
Squares
Date:
12/27/14
Time:
22:16
Sample
(adjusted):
1981
2000
Included
observations:
20
after
adjustmentsVariable
Coefficient
Std.
Error
t-Statistic
Prob.??
LNX1
0.442224
0.066024
6.697901
0.0000
C
0.054047
0.013322
4.056896
0.0007
R-squared
0.713658
????Mean
dependent
var
0.091592
Adjusted
R-squared
0.697750
????S.D.
dependent
var
0.098311
S.E.
of
regression
0.054049
????Akaike
info
criterion
-2.903219
Sum
squared
resid
0.052583
????Schwarz
criterion
-2.803646
Log
likelihood
31.03219
????Hannan-Quinn
criter.
-2.883781
F-statistic
44.86188
????Durbin-Watson
stat
1.590363
Prob(F-statistic)
0.000003
由题目可知，此模型样本容量为20，查5%显著水平的DW统计表可知，dL=1.201,dU=1.411模型中DW=1.590363，dudU，说明在5%的显著水平此模型中无自相关。可决系数R2，t，F统计量也均达到理想水平
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