第二章 简单线性回模型
21
（1） ①首先分析均寿命均GDP数量关系Eviews分析：
Dependent Variable Y
Method Least Squares
Date 122714 Time 2100
Sample 1 22
Included observations 22
Variable
Coefficient
Std Error
tStatistic
Prob
C
5664794
1960820
2888992
00000
X1
0128360
0027242
4711834
00001
Rsquared
0526082
Mean dependent var
6250000
Adjusted Rsquared
0502386
SD dependent var
1008889
SE of regression
7116881
Akaike info criterion
6849324
Sum squared resid
1013000
Schwarz criterion
6948510
Log likelihood
7334257
HannanQuinn criter
6872689
Fstatistic
2220138
DurbinWatson stat
0629074
Prob(Fstatistic)
0000134
知关系式y5664794+0128360x1
②关均寿命成识字率关系Eviews分析：
Dependent Variable Y
Method Least Squares
Date 112614 Time 2110
Sample 1 22
Included observations 22
Variable
Coefficient
Std Error
tStatistic
Prob
C
3879424
3532079
1098340
00000
X2
0331971
0046656
7115308
00000
Rsquared
0716825
Mean dependent var
6250000
Adjusted Rsquared
0702666
SD dependent var
1008889
SE of regression
5501306
Akaike info criterion
6334356
Sum squared resid
6052873
Schwarz criterion
6433542
Log likelihood
6767792
HannanQuinn criter
6357721
Fstatistic
5062761
DurbinWatson stat
1846406
Prob(Fstatistic)
0000001
知关系式y3879424+0331971x2
③关均寿命岁童疫苗接种率关系Eviews分析：
Dependent Variable Y
Method Least Squares
Date 112614 Time 2114
Sample 1 22
Included observations 22
Variable
Coefficient
Std Error
tStatistic
Prob
C
3179956
6536434
4864971
00001
X3
0387276
0080260
4825285
00001
Rsquared
0537929
Mean dependent var
6250000
Adjusted Rsquared
0514825
SD dependent var
1008889
SE of regression
7027364
Akaike info criterion
6824009
Sum squared resid
9876770
Schwarz criterion
6923194
Log likelihood
7306409
HannanQuinn criter
6847374
Fstatistic
2328338
DurbinWatson stat
0952555
Prob(Fstatistic)
0000103
知关系式y3179956+0387276x3
（2）①关均寿命均GDP模型知决系数0526082说明建模型整体样数拟合较
回系数t检验：t（β1）4711834>t0025(20)2086斜率系数显著性检验表明均GDP均寿命显著影响
②关均寿命成识字率模型知决系数0716825说明建模型整体样数拟合较
回系数t检验：t（β2）7115308>t0025(20)2086斜率系数显著性检验表明成识字率均寿命显著影响
③关均寿命岁童疫苗模型知决系数0537929说明建模型整体样数拟合较
回系数t检验：t（β3）4825285>t0025(20)2086斜率系数显著性检验表明岁童疫苗接种率均寿命显著影响
22
（1）
①浙江省预算收入全省生产总值模型Eviews分析结果：
Dependent Variable Y
Method Least Squares
Date 120314 Time 1700
Sample (adjusted) 1 33
Included observations 33 after adjustments
Variable
Coefficient
Std Error
tStatistic
Prob
X
0176124
0004072
4325639
00000
C
1543063
3908196
3948274
00004
Rsquared
0983702
Mean dependent var
9025148
Adjusted Rsquared
0983177
SD dependent var
1351009
SE of regression
1752325
Akaike info criterion
1322880
Sum squared resid
9518997
Schwarz criterion
1331949
Log likelihood
2162751
HannanQuinn criter
1325931
Fstatistic
1871115
DurbinWatson stat
0100021
Prob(Fstatistic)
0000000
②知模型参数：斜率系数0176124截距—1543063
③关浙江省财政预算收入全省生产总值模型检验模型显著性：
1）决系数0983702说明建模型整体样数拟合较
2）回系数t检验：t（β2）4325639>t0025(31)20395斜率系数显著性检验表明全省生产总值财政预算总收入显著影响
④规范形式写出检验结果：
Y0176124X—1543063
(0004072) (3908196)
t (4325639) （3948274）
R20983702 F1871115 n33
⑤济意义：全省生产总值增加1亿元财政预算总收入增加0176124亿元
（2）x32000时
①进行点预测知Y0176124X—1543063代入：
Y Y0176124*32000—154306354816617
②进行区间预测：
先Eviews分析：
X
Y
Mean
6000441
9025148
Median
2689280
2093900
Maximum
2772231
4895410
Minimum
1237200
2587000
Std Dev
7608021
1351009
Skewness
1432519
1663108
Kurtosis
4010515
4590432
JarqueBera
1269068
1869063
Probability
0001755
0000087
Sum
1980145
2978299
Sum Sq Dev
185E+09
58407195
Observations
33
33
表知
∑x2∑（Xi—X）2δ2x(n—1) 76080212 x (33—1)1852223473
(Xf—X)2(32000— 6000441)26759770682
Xf32000时相关数代入计算：
54816617—20395x1752325x√133+18522234736759770682≤
Yf≤54816617+20395x1752325x√133+18522234736759770682
Yf置信区间（54816617—649649 54816617+649649）
(3) 浙江省预算收入数全省生产总值数模型Eviews分析结果：
Dependent Variable LNY
Method Least Squares
Date 120314 Time 1800
Sample (adjusted) 1 33
Included observations 33 after adjustments
Variable
Coefficient
Std Error
tStatistic
Prob
LNX
0980275
0034296
2858268
00000
C
1918289
0268213
7152121
00000
Rsquared
0963442
Mean dependent var
5573120
Adjusted Rsquared
0962263
SD dependent var
1684189
SE of regression
0327172
Akaike info criterion
0662028
Sum squared resid
3318281
Schwarz criterion
0752726
Log likelihood
8923468
HannanQuinn criter
0692545
Fstatistic
8169699
DurbinWatson stat
0096208
Prob(Fstatistic)
0000000
①模型方程：lnY0980275lnX1918289
②知模型参数：斜率系数0980275截距1918289
③关浙江省财政预算收入全省生产总值模型检验显著性：
1）决系数0963442说明建模型整体样数拟合较
2）回系数t检验：t（β2）2858268>t0025(31)20395斜率系数显著性检验表明全省生产总值财政预算总收入显著影响
④济意义：全省生产总值增长1财政预算总收入增长0980275
24
（1）建筑面积建造单位成模型Eviews分析结果：
Dependent Variable Y
Method Least Squares
Date 120114 Time 1240
Sample 1 12
Included observations 12
Variable
Coefficient
Std Error
tStatistic
Prob
X
6418400
4809828
1334434
00000
C
1845475
1926446
9579688
00000
Rsquared
0946829
Mean dependent var
1619333
Adjusted Rsquared
0941512
SD dependent var
1312252
SE of regression
3173600
Akaike info criterion
9903792
Sum squared resid
1007174
Schwarz criterion
9984610
Log likelihood
5742275
HannanQuinn criter
9873871
Fstatistic
1780715
DurbinWatson stat
1172407
Prob(Fstatistic)
0000000
：建筑面积建造成回方程：
Y18454756418400X
（2）济意义：建筑面积增加1万方米建筑单位成方米减少6418400元
（3）
①首先进行点预测Y18454756418400Xx45y1556647
②进行区间估计：
Eviews分析：
Y
X
Mean
1619333
3523333
Median
1630000
3715000
Maximum
1860000
6230000
Minimum
1419000
0600000
Std Dev
1312252
1989419
Skewness
0003403
0060130
Kurtosis
2346511
1664917
JarqueBera
0213547
0898454
Probability
0898729
0638121
Sum
1943200
4228000
Sum Sq Dev
1894207
4353567
Observations
12
12
表知
∑x2∑（Xi—X）2δ2x(n—1) 19894192 x (12—1)435357
(Xf—X)2(45— 3523333)2095387843
Xf45时相关数代入计算：
1556647—2228x3173600x√112+435357095387843≤
Yf≤1556647+2228x3173600x√112+435357095387843
Yf置信区间（1556647—4781231 1556647+4781231）
31
（1）
①百户拥家汽车量计量济模型Eviews分析结果：
Dependent Variable Y
Method Least Squares
Date 112514 Time 1238
Sample 1 31
Included observations 31
Variable
Coefficient
Std Error
tStatistic
Prob
X2
5996865
1406058
4265020
00002
X3
0524027
0179280
2922950
00069
X4
2265680
0518837
4366842
00002
C
2468540
5197500
4749476
00001
Rsquared
0666062
Mean dependent var
1677355
Adjusted Rsquared
0628957
SD dependent var
8252535
SE of regression
5026889
Akaike info criterion
6187394
Sum squared resid
6822795
Schwarz criterion
6372424
Log likelihood
9190460
HannanQuinn criter
6247709
Fstatistic
1795108
DurbinWatson stat
1147253
Prob(Fstatistic)
0000001
②模型：
Y2468540+5996865X2 0524027 X32265680 X4
③模型进行检验：
1） 决系数0666062修正决系数0628957说明模型样拟合较
2） F检验F1795108>F（327）365回方程显著
3）t检验t统计量分4749476426502029229504366842均
t（27）20518系数显著
④：
1） 决系数越说明拟合程度越
2） F值界值较界值否定原假设回方程显著界值接受原假设回方程显著
3） t值界值较界值否定原假设系数显著界值接受原假设系数显著
（2）济意义：均ＧＤＰ增加１万元百户拥家汽车增加5996865辆城镇口重增加１百分点百户拥家汽车减少0524027辆交通工具消费价格指数升１百户拥家汽车减少2265680辆
（3）EViews分析：
Dependent Variable Y
Method Least Squares
Date 120814 Time 1728
Sample 1 31
Included observations 31
Variable
Coefficient
Std Error
tStatistic
Prob
X2
5135670
1010270
5083465
00000
LNX3
2281005
6771820
3368378
00023
LNX4
2308481
4946791
4666624
00001
C
1148758
2282917
5031974
00000
Rsquared
0691952
Mean dependent var
1677355
Adjusted Rsquared
0657725
SD dependent var
8252535
SE of regression
4828088
Akaike info criterion
6106692
Sum squared resid
6293818
Schwarz criterion
6291723
Log likelihood
9065373
HannanQuinn criter
6167008
Fstatistic
2021624
DurbinWatson stat
1150090
Prob(Fstatistic)
0000000
模型方程：
Y5135670 X22281005 LNX32308481 LNX4+1148758
分析出决系数0691952>0666062拟合程度提高样改进
32
（１）出口货物总额计量济模型Eviews分析结果：：
Dependent Variable Y
Method Least Squares
Date 120114 Time 2025
Sample 1994 2011
Included observations 18
Variable
Coefficient
Std Error
tStatistic
Prob
X2
0135474
0012799
1058454
00000
X3
1885348
9776181
1928512
00729
C
1823158
8638216
2110573
00520
Rsquared
0985838
Mean dependent var
6619191
Adjusted Rsquared
0983950
SD dependent var
5767152
SE of regression
7306306
Akaike info criterion
1617670
Sum squared resid
8007316
Schwarz criterion
1632510
Log likelihood
1425903
HannanQuinn criter
1619717
Fstatistic
5220976
DurbinWatson stat
1173432
Prob(Fstatistic)
0000000
①知模型：
Y 0135474X2 + 1885348X3 1823158
②模型进行检验：
1）决系数0985838修正决系数0983950说明模型样拟合较
2）F检验F5220976>F（215）477回方程显著
3）t检验t统计量分X2系数应t值1058454t（15）2131系数显著X3系数应t值1928512t（15）2131说明系数显著
（2）数模型Eviews分析结果：
Dependent Variable LNY
Method Least Squares
Date 120114 Time 2025
Sample 1994 2011
Included observations 18
Variable
Coefficient
Std Error
tStatistic
Prob
LNX2
1564221
0088988
1757789
00000
LNX3
1760695
0682115
2581229
00209
C
2052048
5432487
3777363
00018
Rsquared
0986295
Mean dependent var
8400112
Adjusted Rsquared
0984467
SD dependent var
0941530
SE of regression
0117343
Akaike info criterion
1296424
Sum squared resid
0206540
Schwarz criterion
1148029
Log likelihood
1466782
HannanQuinn criter
1275962
Fstatistic
5397364
DurbinWatson stat
0686656
Prob(Fstatistic)
0000000
①知模型：
LNY2052048+1564221 LNX2+1760695 LNX3
②模型进行检验：
1）决系数0986295修正决系数0984467说明模型样拟合较
2）F检验F5397364> F（215）477回方程显著
3）t检验t统计量分377736317577892581229均t（15）2131系数显著
（3）
①（1）式中济意义：工业增加1亿元出口货物总额增加0135474亿元民币汇率增加1出口货物总额增加1885348亿元
②（2）式中济意义：工业增加额增加1出口货物总额增加1564221民币汇率增加1出口货物总额增加1760695
33
（1）家庭书刊消费家庭月均收入户受教育年数计量模型Eviews分析结果：
Dependent Variable Y
Method Least Squares
Date 120114 Time 2030
Sample 1 18
Included observations 18
Variable
Coefficient
Std Error
tStatistic
Prob
X
0086450
0029363
2944186
00101
T
5237031
5202167
1006702
00000
C
5001638
4946026
1011244
03279
Rsquared
0951235
Mean dependent var
7551222
Adjusted Rsquared
0944732
SD dependent var
2587206
SE of regression
6082273
Akaike info criterion
1120482
Sum squared resid
5549107
Schwarz criterion
1135321
Log likelihood
9784334
HannanQuinn criter
1122528
Fstatistic
1462974
DurbinWatson stat
2605783
Prob(Fstatistic)
0000000
①模型：Y 0086450X + 5237031T5001638
②模型进行检验：
1）决系数0951235修正决系数0944732说明模型样拟合较
2）F检验F5397364> F（215）477回方程显著
3）t检验t统计量分29441861006702均t（15）2131系数显著
③济意义：家庭月均收入增加1元家庭书刊年消费支出增加0086450元户受教育年数增加1年家庭书刊年消费支出增加5237031元
（2）Eviews分析：
①
Dependent Variable Y
Method Least Squares
Date 120114 Time 2230
Sample 1 18
Included observations 18
Variable
Coefficient
Std Error
tStatistic
Prob
T
6301676
4548581
1385416
00000
C
1158171
5802290
0199606
08443
Rsquared
0923054
Mean dependent var
7551222
Adjusted Rsquared
0918245
SD dependent var
2587206
SE of regression
7397565
Akaike info criterion
1154979
Sum squared resid
8755836
Schwarz criterion
1164872
Log likelihood
1019481
HannanQuinn criter
1156343
Fstatistic
1919377
DurbinWatson stat
2134043
Prob(Fstatistic)
0000000
②
Dependent Variable X
Method Least Squares
Date 120114 Time 2234
Sample 1 18
Included observations 18
Variable
Coefficient
Std Error
tStatistic
Prob
T
1231516
3184150
3867644
00014
C
4445888
4061786
1094565
02899
Rsquared
0483182
Mean dependent var
1942933
Adjusted Rsquared
0450881
SD dependent var
6988325
SE of regression
5178529
Akaike info criterion
1544170
Sum squared resid
4290746
Schwarz criterion
1554063
Log likelihood
1369753
HannanQuinn criter
1545534
Fstatistic
1495867
DurbinWatson stat
1052251
Prob(Fstatistic)
0001364
分yTXT元回
模型分：
Y 6301676T 1158171
X 1231516T + 4445888
（3）残差进行模型分析Eviews分析结果：
Dependent Variable E1
Method Least Squares
Date 120314 Time 2039
Sample 1 18
Included observations 18
Variable
Coefficient
Std Error
tStatistic
Prob
E2
0086450
0028431
3040742
00078
C
396E14
1388083
285E15
10000
Rsquared
0366239
Mean dependent var
230E14
Adjusted Rsquared
0326629
SD dependent var
7176693
SE of regression
5889136
Akaike info criterion
1109370
Sum squared resid
5549107
Schwarz criterion
1119264
Log likelihood
9784334
HannanQuinn criter
1110735
Fstatistic
9246111
DurbinWatson stat
2605783
Prob(Fstatistic)
0007788
模型：
E1 0086450E2 + 396e14
参数：斜率系数α0086450截距396e14
（3）知β2α2系数样回系数解释变量残差系数样变化规律致
36
（1）预期符号X1X2X3X4X5符号正X6符号负
（2）根Eviews分析数：
Dependent Variable Y
Method Least Squares
Date 120414 Time 1324
Sample 1994 2011
Included observations 18
Variable
Coefficient
Std Error
tStatistic
Prob
X2
0001382
0001102
1254330
02336
X3
0001942
0003960
0490501
06326
X4
3579090
3559949
1005377
03346
X5
0004791
0005034
0951671
03600
X6
0045542
0095552
0476621
06422
C
1377732
1573366
0875659
03984
Rsquared
0994869
Mean dependent var
1276667
Adjusted Rsquared
0992731
SD dependent var
9746631
SE of regression
0830963
Akaike info criterion
2728738
Sum squared resid
8285993
Schwarz criterion
3025529
Log likelihood
1855865
HannanQuinn criter
2769662
Fstatistic
4653617
DurbinWatson stat
1553294
Prob(Fstatistic)
0000000
①预期相符
②评价：
1） 决系数0994869数相认拟合程度
2） F检验F4653617>F（512）389回方程显著
3） T检验X1X2X3X4X5X6 系数应t值分：12543300490501100537709516710476621均t（12）2179系数显著
（3）根Eviews分析数：
Dependent Variable Y
Method Least Squares
Date 120314 Time 1112
Sample 1994 2011
Included observations 18
Variable
Coefficient
Std Error
tStatistic
Prob
X5
0001032
220E05
4679946
00000
X6
0054965
0031184
1762581
00983
C
4205481
3335602
1260786
02266
Rsquared
0993601
Mean dependent var
1276667
Adjusted Rsquared
0992748
SD dependent var
9746631
SE of regression
0830018
Akaike info criterion
2616274
Sum squared resid
1033396
Schwarz criterion
2764669
Log likelihood
2054646
HannanQuinn criter
2636736
Fstatistic
1164567
DurbinWatson stat
1341880
Prob(Fstatistic)
0000000
①模型方程：
Y0001032 X50054965 X6+4205481
②评价：
1） 决系数0993601数相认拟合程度
2） F检验F1164567>F（512）389回方程显著
3） T检验X5 系数应t值4679946t（12）2179系数显著均GDP年底存款余额显著影响 X6 系数应t值1762581t（12）2179系数显著
43
（1）根Eviews分析数：
Dependent Variable LNY
Method Least Squares
Date 120514 Time 1139
Sample 1985 2011
Included observations 27
Variable
Coefficient
Std Error
tStatistic
Prob
LNGDP
1338533
0088610
1510582
00000
LNCPI
0421791
0233295
1807975
00832
C
3111486
0463010
6720126
00000
Rsquared
0988051
Mean dependent var
9484710
Adjusted Rsquared
0987055
SD dependent var
1425517
SE of regression
0162189
Akaike info criterion
0695670
Sum squared resid
0631326
Schwarz criterion
0551689
Log likelihood
1239155
HannanQuinn criter
0652857
Fstatistic
9922582
DurbinWatson stat
0522613
Prob(Fstatistic)
0000000
模型方程：
LNY1338533 LNGDPt0421791 LNCPIt3111486
（2）
① 该模型决系数0988051决系数高F检验值9922582
明显显著α005时t（24）2064LNCPI系数显著存重线性
②相关系数矩阵：
LNY
LNGDP
LNCPI
LNY
1000000
0993189
0935116
LNGDP
0993189
1000000
0953740
LNCPI
0935116
0953740
1000000
LNGDP LNCPI间相关系数高证实确实存重线性
（3）Eviews：
a）
Dependent Variable LNY
Method Least Squares
Date 120314 Time 1441
Sample 1985 2011
Included observations 27
Variable
Coefficient
Std Error
tStatistic
Prob
LNGDP
1185739
0027822
4261933
00000
C
3750670
0312255
1201156
00000
Rsquared
0986423
Mean dependent var
9484710
Adjusted Rsquared
0985880
SD dependent var
1425517
SE of regression
0169389
Akaike info criterion
0642056
Sum squared resid
0717312
Schwarz criterion
0546068
Log likelihood
1066776
HannanQuinn criter
0613514
Fstatistic
1816407
DurbinWatson stat
0471111
Prob(Fstatistic)
0000000
b)
Dependent Variable LNY
Method Least Squares
Date 120314 Time 1441
Sample 1985 2011
Included observations 27
Variable
Coefficient
Std Error
tStatistic
Prob
LNCPI
2939295
0222756
1319511
00000
C
6854535
1242243
5517871
00000
Rsquared
0874442
Mean dependent var
9484710
Adjusted Rsquared
0869419
SD dependent var
1425517
SE of regression
0515124
Akaike info criterion
1582368
Sum squared resid
6633810
Schwarz criterion
1678356
Log likelihood
1936196
HannanQuinn criter
1610910
Fstatistic
1741108
DurbinWatson stat
0137042
Prob(Fstatistic)
0000000
c)
Dependent Variable LNGDP
Method Least Squares
Date 120514 Time 1111
Sample 1985 2011
Included observations 27
Variable
Coefficient
Std Error
tStatistic
Prob
LNCPI
2511022
0158302
1586227
00000
C
2796381
0882798
3167634
00040
Rsquared
0909621
Mean dependent var
1116214
Adjusted Rsquared
0906005
SD dependent var
1194029
SE of regression
0366072
Akaike info criterion
0899213
Sum squared resid
3350216
Schwarz criterion
0995201
Log likelihood
1013938
HannanQuinn criter
0927755
Fstatistic
2516117
DurbinWatson stat
0099623
Prob(Fstatistic)
0000000
①回方程分
1）LNY1185739 LNGDPt3750670
2）LNY2939295 LNCPIt6854535
3）LNGDPt2511022 LNCPIt2796381
②重线性认识：
单方程拟合效果回系数显著判定系数较高GDPCPI进口显著单影响两变量时引入模型时影响方发生改变通相关系数分析发现
（4）建议：果仅仅作预测意种重线性果进行结构分析应该引起注意
44
（1）设计理模型Eviews分析：
Dependent Variable CZSR
Method Least Squares
Date 120314 Time 1140
Sample 1985 2011
Included observations 27
Variable
Coefficient
Std Error
tStatistic
Prob
CZZC
0090114
0044367
2031129
00540
GDP
0025334
0005069
4998036
00000
SSZE
1176894
0062162
1893271
00000
C
2218540
1306532
1698038
01030
Rsquared
0999857
Mean dependent var
2257256
Adjusted Rsquared
0999838
SD dependent var
2773949
SE of regression
3530540
Akaike info criterion
1470707
Sum squared resid
2866884
Schwarz criterion
1489905
Log likelihood
1945455
HannanQuinn criter
1476416
Fstatistic
5349393
DurbinWatson stat
1458128
Prob(Fstatistic)
0000000
回结果见决系数0999857校正决系数0999838模型拟合F统计量5349393说明α005水回方程回方程整体显著t检验结果表明国生产总值财政收入影响显著回系数符号负实际符合知该方程存重线性
（2）相关系数矩阵：
CZSR
CZZC
GDP
SSZE
CZSR
1000000
0998729
0992838
0999832
CZZC
0998729
1000000
0992536
0998575
GDP
0992838
0992536
1000000
0994370
SSZE
0999832
0998575
0994370
1000000
表知CZZCGDPCZZCSSZEGDPSSZE间相关系数非常高说明确实存重线性
（3）做辅助回
解释变量
决系数
方差扩子
CZZC
0997168
353
GDP
0988833
90
SSZE
0997862
468
方差扩子均10存严重重线性通分析两两解释变量间相关性高
（4）解决方式：分作出财政收入财政支出国生产总值税收总额间元回
52
（1）
①图形法检验
绘制e2散点图Eviews分析：
图知模型存异方差
② GoldfeldQuanadt检验
1）定义区间17时软件分析：
Dependent Variable Y
Method Least Squares
Date 121014 Time 1452
Sample 1 7
Included observations 7
Variable
Coefficient
Std Error
tStatistic
Prob
T
3520664
4901492
7182843
00020
X
0109949
0061965
1774380
01507
C
7712588
8232844
0936807
04019
Rsquared
0943099
Mean dependent var
5656857
Adjusted Rsquared
0914649
SD dependent var
1082755
SE of regression
3163265
Akaike info criterion
1004378
Sum squared resid
4002499
Schwarz criterion
1002060
Log likelihood
3215324
HannanQuinn criter
9757267
Fstatistic
3314880
DurbinWatson stat
1426262
Prob(Fstatistic)
0003238
∑e1i24002499
2）定义区间1218时软件分析：
Dependent Variable Y
Method Least Squares
Date 121014 Time 1350
Sample 12 18
Included observations 7
Variable
Coefficient
Std Error
tStatistic
Prob
T
5240588
6923378
7569409
00016
X
0068689
0053763
1277635
02705
C
8789265
7992542
0109968
09177
Rsquared
0984688
Mean dependent var
8876143
Adjusted Rsquared
0977032
SD dependent var
2744148
SE of regression
4158810
Akaike info criterion
1059103
Sum squared resid
6918280
Schwarz criterion
1056785
Log likelihood
3406861
HannanQuinn criter
1030451
Fstatistic
1286166
DurbinWatson stat
2390329
Prob(Fstatistic)
0000234
∑e2i26918280
3）根GoldfeldQuanadt检验F统计量：
F∑e2i2 ∑e1i2 6918280400249917285
α005水分子分母度均4查分布表界值F005（44）639F17285< F005（44）639接受原假设检验表明模型存异方差
（2）存异方差估计参数方法：
①模型进行变换
②加权二法进行计算出模型方程进行相关检验
③模型进行数变换进行分析
（3）评价：
33结相信机扰动项间存异方差回方程显著
53
(1)Eviews软件分析：
Dependent Variable Y
Method Least Squares
Date 121014 Time 1600
Sample 1 31
Included observations 31
Variable
Coefficient
Std Error
tStatistic
Prob
X
1244281
0079032
1574411
00000
C
2424488
2911940
0832602
04119
Rsquared
0895260
Mean dependent var
4443526
Adjusted Rsquared
0891649
SD dependent var
1972072
SE of regression
6491426
Akaike info criterion
1585152
Sum squared resid
12220196
Schwarz criterion
1594404
Log likelihood
2436986
HannanQuinn criter
1588168
Fstatistic
2478769
DurbinWatson stat
1078581
Prob(Fstatistic)
0000000
表知2007年国农村居民家庭均消费支出（x）均纯收入（y）模型：
Y1244281X+2424488
（2）
①图形法检验
图知模型存异方差
②GoldfeldQuanadt检验
1）定义区间112时软件分析：
Dependent Variable Y1
Method Least Squares
Date 121014 Time 1134
Sample 1 12
Included observations 12
Variable
Coefficient
Std Error
tStatistic
Prob
X1
1485296
0500386
2968297
00141
C
5505492
1220063
0451247
06614
Rsquared
0468390
Mean dependent var
3052950
Adjusted Rsquared
0415229
SD dependent var
5505148
SE of regression
4209803
Akaike info criterion
1507406
Sum squared resid
1772245
Schwarz criterion
1515488
Log likelihood
8844437
HannanQuinn criter
1504414
Fstatistic
8810789
DurbinWatson stat
2354167
Prob(Fstatistic)
0014087
∑e1i21772245
2）定义区间2031时软件分析：
Dependent Variable Y1
Method Least Squares
Date 121014 Time 1636
Sample 20 31
Included observations 12
Variable
Coefficient
Std Error
tStatistic
Prob
X1
1086940
0148863
7301623
00000
C
1173307
7332520
1600141
01407
Rsquared
0842056
Mean dependent var
6188329
Adjusted Rsquared
0826262
SD dependent var
2133692
SE of regression
8893633
Akaike info criterion
1656990
Sum squared resid
7909670
Schwarz criterion
1665072
Log likelihood
9741940
HannanQuinn criter
1653998
Fstatistic
5331370
DurbinWatson stat
2339767
Prob(Fstatistic)
0000026
∑e2i27909670
3）根GoldfeldQuanadt检验F统计量：
F∑e2i2 ∑e1i2 7909670 177224544631
α005水分子分母度均10查分布表界值F005（1010）298F44631> F005（1010）298拒绝原假设检验表明模型存异方差
（3）
1）采WLS法估计程中
①权数w11X建立回：
Dependent Variable Y
Method Least Squares
Date 120914 Time 1113
Sample 1 31
Included observations 31
Weighting series W1
Variable
Coefficient
Std Error
tStatistic
Prob
X
1425859
0119104
1197157
00000
C
3348131
3443523
0972298
03389
Weighted Statistics
Rsquared
0831707
Mean dependent var
3946082
Adjusted Rsquared
0825904
SD dependent var
5361907
SE of regression
5366796
Akaike info criterion
1547102
Sum squared resid
8352726
Schwarz criterion
1556354
Log likelihood
2378008
HannanQuinn criter
1550118
Fstatistic
1433184
DurbinWatson stat
1369081
Prob(Fstatistic)
0000000
Unweighted Statistics
Rsquared
0875855
Mean dependent var
4443526
Adjusted Rsquared
0871574
SD dependent var
1972072
SE of regression
7067236
Sum squared resid
14484289
DurbinWatson stat
1532908
模型进行White检验：
Heteroskedasticity Test White
Fstatistic
0299395
Prob F(228)
07436
Obs*Rsquared
0649065
Prob ChiSquare(2)
07229
Scaled explained SS
1798067
Prob ChiSquare(2)
04070
Test Equation
Dependent Variable WGT_RESID^2
Method Least Squares
Date 121014 Time 2113
Sample 1 31
Included observations 31
Collinear test regressors dropped from specification
Variable
Coefficient
Std Error
tStatistic
Prob
C
6192789
1045682
0059222
09532
WGT^2
5939279
1173622
0506064
06168
X*WGT^2
2824407
7479780
0377606
07086
Rsquared
0020938
Mean dependent var
2694428
Adjusted Rsquared
0048995
SD dependent var
6891665
SE of regression
7058476
Akaike info criterion
2986395
Sum squared resid
140E+13
Schwarz criterion
3000273
Log likelihood
4598913
HannanQuinn criter
2990919
Fstatistic
0299395
DurbinWatson stat
1922336
Prob(Fstatistic)
0743610
知nR20649065较计算统计量界值nR20649065<005（2）59915接受原假设该模型消异方差
估计结果：
Y1425859X3348131
t（1197157）（0972298）
R20875855 F1433184 DW1369081
②权数w21x2回分析：
Dependent Variable Y
Method Least Squares
Date 120914 Time 2108
Sample 1 31
Included observations 31
Weighting series W2
Variable
Coefficient
Std Error
tStatistic
Prob
X
1557040
0145392
1070922
00000
C
6931946
3764760
1841272
00758
Weighted Statistics
Rsquared
0798173
Mean dependent var
3635028
Adjusted Rsquared
0791214
SD dependent var
1029830
SE of regression
4668513
Akaike info criterion
1519224
Sum squared resid
6320554
Schwarz criterion
1528475
Log likelihood
2334797
HannanQuinn criter
1522240
Fstatistic
1146875
DurbinWatson stat
1562975
Prob(Fstatistic)
0000000
Unweighted Statistics
Rsquared
0834850
Mean dependent var
4443526
Adjusted Rsquared
0829156
SD dependent var
1972072
SE of regression
8151229
Sum squared resid
19268334
DurbinWatson stat
1678365
模型进行White检验：
Heteroskedasticity Test White
Fstatistic
0299790
Prob F(327)
08252
Obs*Rsquared
0999322
Prob ChiSquare(3)
08014
Scaled explained SS
1789507
Prob ChiSquare(3)
06172
Test Equation
Dependent Variable WGT_RESID^2
Method Least Squares
Date 121014 Time 2129
Sample 1 31
Included observations 31
Variable
Coefficient
Std Error
tStatistic
Prob
C
1116618
5498557
0203075
08406
WGT^2
4262202
2240181
0190262
08505
X^2*WGT^2
0194888
0516395
0377402
07088
X*WGT^2
5832151
2082820
0280012
07816
Rsquared
0032236
Mean dependent var
2038888
Adjusted Rsquared
0075293
SD dependent var
4192820
SE of regression
4347801
Akaike info criterion
2892298
Sum squared resid
510E+12
Schwarz criterion
2910801
Log likelihood
4443062
HannanQuinn criter
2898330
Fstatistic
0299790
DurbinWatson stat
1835854
Prob(Fstatistic)
0825233
知nR20999322较计算统计量界值nR20999322<005（2）59915接受原假设该模型消异方差
估计结果：
Y1557040X6931946
t（1070922）（1841272）
R20798173 F1146875 DW1562975
③权数w31sqr（x）回分析：
Dependent Variable Y
Method Least Squares
Date 120914 Time 2135
Sample 1 31
Included observations 31
Weighting series W3
Variable
Coefficient
Std Error
tStatistic
Prob
X
1330130
0098345
1352507
00000
C
4740242
3131154
0151390
08807
Weighted Statistics
Rsquared
0863161
Mean dependent var
4164118
Adjusted Rsquared
0858442
SD dependent var
9912079
SE of regression
5869555
Akaike info criterion
1565012
Sum squared resid
9990985
Schwarz criterion
1574263
Log likelihood
2405768
HannanQuinn criter
1568027
Fstatistic
1829276
DurbinWatson stat
1237664
Prob(Fstatistic)
0000000
Unweighted Statistics
Rsquared
0890999
Mean dependent var
4443526
Adjusted Rsquared
0887240
SD dependent var
1972072
SE of regression
6622171
Sum squared resid
12717412
DurbinWatson stat
1314859
模型进行White检验：
Heteroskedasticity Test White
Fstatistic
0423886
Prob F(228)
06586
Obs*Rsquared
0911022
Prob ChiSquare(2)
06341
Scaled explained SS
2768332
Prob ChiSquare(2)
02505
Test Equation
Dependent Variable WGT_RESID^2
Method Least Squares
Date 120914 Time 2036
Sample 1 31
Included observations 31
Collinear test regressors dropped from specification
Variable
Coefficient
Std Error
tStatistic
Prob
C
1212308
2141958
0565981
05759
WGT^2
7156730
1301839
0549740
05869
X^2*WGT^2
0015194
0082276
0184677
08548
Rsquared
0029388
Mean dependent var
3222898
Adjusted Rsquared
0039942
SD dependent var
8633567
SE of regression
8804298
Akaike info criterion
3030597
Sum squared resid
217E+13
Schwarz criterion
3044475
Log likelihood
4667426
HannanQuinn criter
3035121
Fstatistic
0423886
DurbinWatson stat
1887426
Prob(Fstatistic)
0658628
知nR20911022较计算统计量界值nR20911022<005（2）59915接受原假设该模型消异方差
估计结果：
Y1330130X4740242
t（1352507）（0151390）
R20863161 F1829276 DW1237664
检验发现权数w1效果综知修改结果：
Y1425859X3348131
t（1197157）（0972298）
R20875855 F1433184 DW1369081
56
(1)
a)Eviews模型分析：
Dependent Variable Y
Method Least Squares
Date 121014 Time 2016
Sample 1978 2011
Included observations 34
Variable
Coefficient
Std Error
tStatistic
Prob
X
0746241
0019120
3903027
00000
C
9255422
4280529
2162215
00382
Rsquared
0979426
Mean dependent var
1295802
Adjusted Rsquared
0978783
SD dependent var
1188791
SE of regression
1731597
Akaike info criterion
1320333
Sum squared resid
9594972
Schwarz criterion
1329311
Log likelihood
2224566
HannanQuinn criter
1323395
Fstatistic
1523362
DurbinWatson stat
1534491
Prob(Fstatistic)
0000000
回模型：
Y0746241 X+9255422
b)检验否存异方差：
①GoldfeldQuanadt检验：
1）定义区间113时软件分析：
Dependent Variable Y
Method Least Squares
Date 121114 Time 1147
Sample 1 13
Included observations 13
Variable
Coefficient
Std Error
tStatistic
Prob
X
0967839
0026879
3600771
00000
C
1886861
8963780
2104984
00591
Rsquared
0991587
Mean dependent var
2801377
Adjusted Rsquared
0990823
SD dependent var
1270409
SE of regression
1217039
Akaike info criterion
7976527
Sum squared resid
1629301
Schwarz criterion
8063442
Log likelihood
4984742
HannanQuinn criter
7958662
Fstatistic
1296555
DurbinWatson stat
1071505
Prob(Fstatistic)
0000000
∑e1i21629301
2）定义区间113时软件分析：
Dependent Variable Y
Method Least Squares
Date 121114 Time 1221
Sample 22 34
Included observations 13
Variable
Coefficient
Std Error
tStatistic
Prob
X
0719567
0058312
1233998
00000
C
1793950
2028764
0884258
03955
Rsquared
0932629
Mean dependent var
2496127
Adjusted Rsquared
0926504
SD dependent var
1022591
SE of regression
2772250
Akaike info criterion
1422817
Sum squared resid
8453904
Schwarz criterion
1431509
Log likelihood
9048313
HannanQuinn criter
1421031
Fstatistic
1522752
DurbinWatson stat
1658418
Prob(Fstatistic)
0000000
∑e2i28453904
3）根GoldfeldQuanadt检验F统计量：
F∑e2i2 ∑e1i2 8453904 16293015188669
α005水分子分母度均11查分布表界值F005（1111）447F5188669> F005（1111）447拒绝原假设检验表明模型存异方差
②White检验
EViews软件分析：
Heteroskedasticity Test White
Fstatistic
1036759
Prob F(231)
00004
Obs*Rsquared
1362701
Prob ChiSquare(2)
00011
Scaled explained SS
7613635
Prob ChiSquare(2)
00000
Test Equation
Dependent Variable RESID^2
Method Least Squares
Date 121114 Time 1256
Sample 1 34
Included observations 34
Variable
Coefficient
Std Error
tStatistic
Prob
C
1158111
2611711
0443430
06605
X
2769901
2786540
0994029
03279
X^2
0012230
0005156
2371861
00241
Rsquared
0400795
Mean dependent var
2822051
Adjusted Rsquared
0362136
SD dependent var
1017389
SE of regression
8125515
Akaike info criterion
2553267
Sum squared resid
205E+11
Schwarz criterion
2566735
Log likelihood
4310554
HannanQuinn criter
2557860
Fstatistic
1036759
DurbinWatson stat
3021651
Prob(Fstatistic)
0000357
图中出nR21362701较计算统计量界值nR21362701>005（2）59915拒绝原假设拒绝备择假设表明模型存异方差
两种方法检验模型存异方差
c)修正模型
1）加权二法修正异方差现象步骤：
①权数w11x时软件分析：
Dependent Variable Y
Method Least Squares
Date 121114 Time 1322
Sample 1 34
Included observations 34
Weighting series W1
Variable
Coefficient
Std Error
tStatistic
Prob
X
0821013
0016866
4867993
00000
C
1769318
6283256
2815926
00083
Weighted Statistics
Rsquared
0986676
Mean dependent var
4578505
Adjusted Rsquared
0986260
SD dependent var
4170384
SE of regression
3791285
Akaike info criterion
1016548
Sum squared resid
4599629
Schwarz criterion
1025527
Log likelihood
1708132
HannanQuinn criter
1019610
Fstatistic
2369735
DurbinWatson stat
0605852
Prob(Fstatistic)
0000000
Unweighted Statistics
Rsquared
0968070
Mean dependent var
1295802
Adjusted Rsquared
0967072
SD dependent var
1188791
SE of regression
2157175
Sum squared resid
1489089
DurbinWatson stat
1079107
方程模型：
Y0821013X1769318
t（4867993）（2815926）
R20986676 F2369735 DW0605852
模型进行White检验：
Heteroskedasticity Test White
Fstatistic
1348072
Prob F(231)
02745
Obs*Rsquared
2720457
Prob ChiSquare(2)
02566
Scaled explained SS
1221901
Prob ChiSquare(2)
05428
Test Equation
Dependent Variable WGT_RESID^2
Method Least Squares
Date 121114 Time 1120
Sample 1 34
Included observations 34
Collinear test regressors dropped from specification
Variable
Coefficient
Std Error
tStatistic
Prob
C
1678870
4165417
4030498
00003
WGT^2
3213071
1876175
0171257
08651
X*WGT^2
0484040
1279449
0378319
07078
Rsquared
0080013
Mean dependent var
1352832
Adjusted Rsquared
0020659
SD dependent var
1382825
SE of regression
1368467
Akaike info criterion
1736487
Sum squared resid
58053732
Schwarz criterion
1749955
Log likelihood
2922027
HannanQuinn criter
1741080
Fstatistic
1348072
DurbinWatson stat
1199640
Prob(Fstatistic)
0274545
图中出nR22720457较计算统计量界值
nR22720457<005（2）59915接受原假设该模型消异方差影响
②权数w21x2时软件分析：
Dependent Variable Y
Method Least Squares
Date 121114 Time 1327
Sample 1 34
Included observations 34
Weighting series W2
Variable
Coefficient
Std Error
tStatistic
Prob
X
0852193
0020150
4229335
00000
C
8890886
3604301
2466744
00192
Weighted Statistics
Rsquared
0982425
Mean dependent var
2302433
Adjusted Rsquared
0981875
SD dependent var
2471718
SE of regression
1620273
Akaike info criterion
8465259
Sum squared resid
8400912
Schwarz criterion
8555045
Log likelihood
1419094
HannanQuinn criter
8495879
Fstatistic
1788728
DurbinWatson stat
0604647
Prob(Fstatistic)
0000000
Unweighted Statistics
Rsquared
0954142
Mean dependent var
1295802
Adjusted Rsquared
0952709
SD dependent var
1188791
SE of regression
2585207
Sum squared resid
2138654
DurbinWatson stat
0781788
方程模型：
Y0852193X+8890886
t（4229335）（2466744）
R20982425 F1788728 DW0604647
White检验模型：
Heteroskedasticity Test White
Fstatistic
7462185
Prob F(330)
00007
Obs*Rsquared
1452935
Prob ChiSquare(3)
00023
Scaled explained SS
1940139
Prob ChiSquare(3)
00002
Test Equation
Dependent Variable WGT_RESID^2
Method Least Squares
Date 121114 Time 1119
Sample 1 34
Included observations 34
Variable
Coefficient
Std Error
tStatistic
Prob
C
7684700
8576169
0089605
09292
WGT^2
6420016
9611160
0667975
05093
X^2*WGT^2
0006306
0003431
1838317
00759
X*WGT^2
1247222
1163558
1071903
02923
Rsquared
0427334
Mean dependent var
2470857
Adjusted Rsquared
0370067
SD dependent var
4354791
SE of regression
3456323
Akaike info criterion
1463876
Sum squared resid
3583851
Schwarz criterion
1481833
Log likelihood
2448589
HannanQuinn criter
1470000
Fstatistic
7462185
DurbinWatson stat
1586012
Prob(Fstatistic)
0000712
图中出nR21452935较计算统计量界值nR21452935>005（2）59915拒绝原假设拒绝备择假设表明模型存异方差模型未消异方差
③权数w31sqr(x)时软件分析：
Dependent Variable Y
Method Least Squares
Date 121114 Time 1321
Sample 1 34
Included observations 34
Weighting series W3
Variable
Coefficient
Std Error
tStatistic
Prob
X
0778551
0015677
4966347
00000
C
4045770
1457528
2775775
00091
Weighted Statistics
Rsquared
0987192
Mean dependent var
7763266
Adjusted Rsquared
0986792
SD dependent var
3673152
SE of regression
7919828
Akaike info criterion
1163881
Sum squared resid
2007158
Schwarz criterion
1172859
Log likelihood
1958597
HannanQuinn criter
1166943
Fstatistic
2466460
DurbinWatson stat
1178340
Prob(Fstatistic)
0000000
Unweighted Statistics
Rsquared
0977590
Mean dependent var
1295802
Adjusted Rsquared
0976890
SD dependent var
1188791
SE of regression
1807210
Sum squared resid
1045123
DurbinWatson stat
1460832
方程模型：
Y0778551X+4045770
t（4966347）（2775775）
R20986792 F2466460 DW1178340
模型进行White检验：
Heteroskedasticity Test White
Fstatistic
8158958
Prob F(231)
00014
Obs*Rsquared
1172514
Prob ChiSquare(2)
00028
Scaled explained SS
2808353
Prob ChiSquare(2)
00000
Test Equation
Dependent Variable WGT_RESID^2
Method Least Squares
Date 121014 Time 1323
Sample 1 34
Included observations 34
Collinear test regressors dropped from specification
Variable
Coefficient
Std Error
tStatistic
Prob
C
7585186
5311263
1428132
01633
WGT^2
2468369
1996041
1236632
02255
X^2*WGT^2
0009139
0002481
3684177
00009
Rsquared
0344857
Mean dependent var
5903405
Adjusted Rsquared
0302590
SD dependent var
1393464
SE of regression
1163697
Akaike info criterion
2164586
Sum squared resid
420E+09
Schwarz criterion
2178054
Log likelihood
3649796
HannanQuinn criter
2169179
Fstatistic
8158958
DurbinWatson stat
2344068
Prob(Fstatistic)
0001423
图中出nR21172514较计算统计量界值nR21172514>005（2）59915拒绝原假设拒绝备择假设表明模型存异方差模型未消异方差
综述加权二法w1效果模型：
方程模型：
Y0821013X1769318
t（4867993）（2815926）
R20986676 F2369735 DW0605852
2）数模型法
软件分析：
Dependent Variable LNY
Method Least Squares
Date 121114 Time 0954
Sample 1 34
Included observations 34
Variable
Coefficient
Std Error
tStatistic
Prob
LNX
0946887
0011228
8433549
00000
C
0201861
0077905
2591100
00143
Rsquared
0995521
Mean dependent var
6687779
Adjusted Rsquared
0995381
SD dependent var
1067124
SE of regression
0072525
Akaike info criterion
2352753
Sum squared resid
0168315
Schwarz criterion
2262967
Log likelihood
4199680
HannanQuinn criter
2322134
Fstatistic
7112475
DurbinWatson stat
0812150
Prob(Fstatistic)
0000000
模型：
LnY0946887 LNX+0201861
模型进行White检验：
Heteroskedasticity Test White
Fstatistic
1003964
Prob F(231)
03780
Obs*Rsquared
2068278
Prob ChiSquare(2)
03555
Scaled explained SS
1469638
Prob ChiSquare(2)
04796
Test Equation
Dependent Variable RESID^2
Method Least Squares
Date 121114 Time 0955
Sample 1 34
Included observations 34
Variable
Coefficient
Std Error
tStatistic
Prob
C
0039547
0046759
0845753
04042
LNX
0011601
0014012
0827969
04140
LNX^2
0000932
0001028
0906774
03715
Rsquared
0060832
Mean dependent var
0004950
Adjusted Rsquared
0000240
SD dependent var
0006365
SE of regression
0006364
Akaike info criterion
7192271
Sum squared resid
0001255
Schwarz criterion
7057592
Log likelihood
1252686
HannanQuinn criter
7146342
Fstatistic
1003964
DurbinWatson stat
2022904
Prob(Fstatistic)
0378027
图中出nR22068278较计算统计量界值nR22068278<005（2）59915接受原假设模型消异方差
综合两种方法改进模型：
LnY0946887 LNX+0201861
(2)
1）考虑价格素首先软件三者关系进行分析：
Dependent Variable Y
Method Least Squares
Date 121214 Time 1926
Sample 1 34
Included observations 34
Variable
Coefficient
Std Error
tStatistic
Prob
X
0741684
0019905
3726095
00000
P
0235025
0271701
0865012
03937
C
4341715
7122946
0609539
05466
Rsquared
0979911
Mean dependent var
1295802
Adjusted Rsquared
0978615
SD dependent var
1188791
SE of regression
1738449
Akaike info criterion
1323830
Sum squared resid
9368837
Schwarz criterion
1337298
Log likelihood
2220511
HannanQuinn criter
1328423
Fstatistic
7560627
DurbinWatson stat
1681521
Prob(Fstatistic)
0000000
1）GoldfeldQuanadt检验：
①样113时进行回分析：
Dependent Variable P
Method Least Squares
Date 121414 Time 1926
Sample 1 13
Included observations 13
Variable
Coefficient
Std Error
tStatistic
Prob
X
0170484
0203868
0836247
04225
Y
0458660
0209755
2186646
00536
C
5950496
7385841
8056627
00000
Rsquared
0956255
Mean dependent var
1353231
Adjusted Rsquared
0947506
SD dependent var
3695380
SE of regression
8466678
Akaike info criterion
7309328
Sum squared resid
7168464
Schwarz criterion
7439701
Log likelihood
4451063
HannanQuinn criter
7282530
Fstatistic
1092993
DurbinWatson stat
0637181
Prob(Fstatistic)
0000000
∑e1i27168464
②样2234时做回分析：
Dependent Variable Y
Method Least Squares
Date 121414 Time2039
Sample 22 34
Included observations 13
Variable
Coefficient
Std Error
tStatistic
Prob
X
0641197
0092678
6918569
00000
P
1206222
1114278
1082514
03044
C
7956887
6038605
1317670
02170
Rsquared
0939696
Mean dependent var
2496127
Adjusted Rsquared
0927635
SD dependent var
1022591
SE of regression
2750847
Akaike info criterion
1427121
Sum squared resid
7567157
Schwarz criterion
1440158
Log likelihood
8976286
HannanQuinn criter
1424441
Fstatistic
7791291
DurbinWatson stat
1128778
Prob(Fstatistic)
0000001
∑e2i27567157
③根GoldfeldQuanadt检验F统计量：
F∑e2i2 ∑e1i2 7567157 716846410556176
α005水分子分母度均11查分布表界值F005（1010）298F10556176> F005（1010）298拒绝原假设检验表明模型存异方差
2）White检验软件分析结果：
Heteroskedasticity Test White
Fstatistic
7312529
Prob F(528)
00002
Obs*Rsquared
1925463
Prob ChiSquare(5)
00017
Scaled explained SS
1193072
Prob ChiSquare(5)
00000
Test Equation
Dependent Variable RESID^2
Method Least Squares
Date 121214 Time 1931
Sample 1 34
Included observations 34
Variable
Coefficient
Std Error
tStatistic
Prob
C
7954108
1126473
0706107
04860
X
2094964
6390400
3278298
00028
X^2
0024133
0010712
2252841
00323
X*P
0235137
0106647
2204822
00358
P
1175326
1156253
1016495
03181
P^2
1637366
2600020
0629751
05340
Rsquared
0566313
Mean dependent var
2755540
Adjusted Rsquared
0488869
SD dependent var
1079909
SE of regression
7720644
Akaike info criterion
2550514
Sum squared resid
167E+11
Schwarz criterion
2577450
Log likelihood
4275874
HannanQuinn criter
2559700
Fstatistic
7312529
DurbinWatson stat
2787044
Prob(Fstatistic)
0000171
图中出nR21925463较计算统计量界值nR21925463>005（5）110705拒绝原假设拒绝备择假设表明模型存异方差
2）修正
①建立数模型软件分析：
Dependent Variable LNY
Method Least Squares
Date 121214 Time 1924
Sample 1 34
Included observations 34
Variable
Coefficient
Std Error
tStatistic
Prob
LNX
0939605
0013645
6886088
00000
LNP
0026821
0028454
0942609
03532
C
0108230
0126322
0856784
03981
Rsquared
0995646
Mean dependent var
6687779
Adjusted Rsquared
0995365
SD dependent var
1067124
SE of regression
0072652
Akaike info criterion
2322188
Sum squared resid
0163625
Schwarz criterion
2187509
Log likelihood
4247720
HannanQuinn criter
2276259
Fstatistic
3544292
DurbinWatson stat
0930109
Prob(Fstatistic)
0000000
模型进行White检验：
Heteroskedasticity Test White
Fstatistic
3523832
Prob F(528)
00135
Obs*Rsquared
1313158
Prob ChiSquare(5)
00222
Scaled explained SS
1214373
Prob ChiSquare(5)
00329
Test Equation
Dependent Variable RESID^2
Method Least Squares
Date 121214 Time 1924
Sample 1 34
Included observations 34
Variable
Coefficient
Std Error
tStatistic
Prob
C
0422872
0273746
1544759
01336
LNX
0080712
0031833
2535502
00171
LNX^2
0003917
0003037
1289564
02078
LNX*LNP
0004955
0005136
0964765
03429
LNP
0254992
0129858
1963631
00596
LNP^2
0026470
0012675
2088390
00460
Rsquared
0386223
Mean dependent var
0004813
Adjusted Rsquared
0276620
SD dependent var
0007286
SE of regression
0006197
Akaike info criterion
7170690
Sum squared resid
0001075
Schwarz criterion
6901332
Log likelihood
1279017
HannanQuinn criter
7078831
Fstatistic
3523832
DurbinWatson stat
2264261
Prob(Fstatistic)
0013502
图中出nR21313158较计算统计量界值nR21313158>005（5）110705拒绝原假设拒绝备择假设表明模型存异方差模型没消异方差
②w11x时软件分析：
Dependent Variable Y
Method Least Squares
Date 121314 Time 1849
Sample 1 34
Included observations 34
Weighting series W1
Variable
Coefficient
Std Error
tStatistic
Prob
X
0723218
0022965
3149212
00000
P
0719506
0141085
5099795
00000
C
4472084
1311268
3410502
00018
Weighted Statistics
Rsquared
0992755
Mean dependent var
4578505
Adjusted Rsquared
0992287
SD dependent var
4170384
SE of regression
2840494
Akaike info criterion
9615100
Sum squared resid
2501205
Schwarz criterion
9749779
Log likelihood
1604567
HannanQuinn criter
9661030
Fstatistic
2123843
DurbinWatson stat
1298389
Prob(Fstatistic)
0000000
Unweighted Statistics
Rsquared
0977704
Mean dependent var
1295802
Adjusted Rsquared
0976266
SD dependent var
1188791
SE of regression
1831446
Sum squared resid
1039800
DurbinWatson stat
1740795
模型：
Y0723218X+0719506p4472084
模型进行White检验：
Heteroskedasticity Test White
Fstatistic
2088840
Prob F(528)
00966
Obs*Rsquared
9236835
Prob ChiSquare(5)
01000
Scaled explained SS
2550696
Prob ChiSquare(5)
00001
Test Equation
Dependent Variable WGT_RESID^2
Method Least Squares
Date 121414 Time 1957
Sample 1 34
Included observations 34
Collinear test regressors dropped from specification
Variable
Coefficient
Std Error
tStatistic
Prob
C
3861793
1068806
3613183
00012
WGT^2
3260199
4309988
0756429
04557
X*WGT^2
1372241
8453473
1623287
01157
X*P*WGT^2
0151725
0061588
2463567
00202
P^2*WGT^2
0431162
0278315
1549186
01326
P*WGT^2
7613221
7340636
1037134
03085
Rsquared
0271672
Mean dependent var
7356486
Adjusted Rsquared
0141613
SD dependent var
1924655
SE of regression
1783177
Akaike info criterion
1796897
Sum squared resid
89032169
Schwarz criterion
1823832
Log likelihood
2994724
HannanQuinn criter
1806082
Fstatistic
2088840
DurbinWatson stat
2336495
Prob(Fstatistic)
0096616
nR29236835<005（5）110705接受原假设该模型存异方差模型消异方差
③w21x2软件分析：
Dependent Variable Y
Method Least Squares
Date 121514 Time 2002
Sample 1 34
Included observations 34
Weighting series W2
Variable
Coefficient
Std Error
tStatistic
Prob
X
0639012
0039216
1629477
00000
P
1200751
0206023
5828234
00000
C
8185973
1577499
5189209
00000
Weighted Statistics
Rsquared
0991614
Mean dependent var
2302433
Adjusted Rsquared
0991073
SD dependent var
2471718
SE of regression
1137136
Akaike info criterion
7784170
Sum squared resid
4008543
Schwarz criterion
7918849
Log likelihood
1293309
HannanQuinn criter
7830100
Fstatistic
1832775
DurbinWatson stat
1167961
Prob(Fstatistic)
0000000
Unweighted Statistics
Rsquared
0956816
Mean dependent var
1295802
Adjusted Rsquared
0954030
SD dependent var
1188791
SE of regression
2548849
Sum squared resid
2013955
DurbinWatson stat
1002870
模型：
Y0639012X+1200751p8185973
该模型进行White检验：
Heteroskedasticity Test White
Fstatistic
4319853
Prob F(627)
00000
Obs*Rsquared
3079235
Prob ChiSquare(6)
00000
Scaled explained SS
4742430
Prob ChiSquare(6)
00000
Test Equation
Dependent Variable WGT_RESID^2
Method Least Squares
Date 121414 Time 1920
Sample 1 34
Included observations 34
Variable
Coefficient
Std Error
tStatistic
Prob
C
2751002
2012556
1366919
01829
WGT^2
1245193
8372352
1487268
01485
X^2*WGT^2
0007732
0005450
1418649
01674
X*WGT^2
7948582
4884597
1627275
01153
X*P*WGT^2
0111755
0064061
1744525
00924
P^2*WGT^2
0184342
0164562
1120199
02725
P*WGT^2
3127017
2356724
0132685
08954
Rsquared
0905657
Mean dependent var
1178983
Adjusted Rsquared
0884692
SD dependent var
2303570
SE of regression
7822224
Akaike info criterion
1173823
Sum squared resid
1652054
Schwarz criterion
1205248
Log likelihood
1925498
HannanQuinn criter
1184539
Fstatistic
4319853
DurbinWatson stat
1794799
Prob(Fstatistic)
0000000
nR23079235>005（5）110705拒绝原假设拒绝备择假设表明模型存异方差模型没消异方差
④w31sqr(x)时软件分析：
Dependent Variable Y
Method Least Squares
Date 121414 Time 1906
Sample 1 34
Included observations 34
Weighting series W3
Variable
Coefficient
Std Error
tStatistic
Prob
X
0744661
0019825
3756252
00000
P
0451861
0179971
2510739
00175
C
1349643
2537768
0531823
05986
Weighted Statistics
Rsquared
0989356
Mean dependent var
7763266
Adjusted Rsquared
0988670
SD dependent var
3673152
SE of regression
7335237
Akaike info criterion
1151252
Sum squared resid
1667977
Schwarz criterion
1164720
Log likelihood
1927129
HannanQuinn criter
1155845
Fstatistic
1440783
DurbinWatson stat
1599590
Prob(Fstatistic)
0000000
Unweighted Statistics
Rsquared
0979407
Mean dependent var
1295802
Adjusted Rsquared
0978079
SD dependent var
1188791
SE of regression
1760098
Sum squared resid
9603626
DurbinWatson stat
1761225
模型：
Y0744661X+0451861p1349643
模型进行White检验：
Heteroskedasticity Test White
Fstatistic
4459272
Prob F(528)
00041
Obs*Rsquared
1507219
Prob ChiSquare(5)
00101
Scaled explained SS
7239077
Prob ChiSquare(5)
00000
Test Equation
Dependent Variable WGT_RESID^2
Method Least Squares
Date 121414 Time 1908
Sample 1 34
Included observations 34
Collinear test regressors dropped from specification
Variable
Coefficient
Std Error
tStatistic
Prob
C
6116322
2753193
2221538
00346
WGT^2
2825198
1735039
1628320
01147
X^2*WGT^2
0001093
0006624
0164950
08702
X*P*WGT^2
0235836
0077110
3058447
00049
P^2*WGT^2
1236884
0644872
1918030
00654
P*WGT^2
5033080
2625884
1916718
00655
Rsquared
0443300
Mean dependent var
4905814
Adjusted Rsquared
0343889
SD dependent var
1692697
SE of regression
1371096
Akaike info criterion
2204856
Sum squared resid
526E+09
Schwarz criterion
2231792
Log likelihood
3688256
HannanQuinn criter
2214042
Fstatistic
4459272
DurbinWatson stat
2450171
Prob(Fstatistic)
0004103
nR21507219>005（5）110705拒绝原假设拒绝备择假设表明模型存异方差模型没消异方差
综述修改模型：
Y Y0723218X+0719506p4472084
t(3149212) (5099705) (3410502)
R20992755 F2123843 DW1298389
(3)体会：模型采取数模型法者加权二法具异方差性模型进行改进消异方差模型度导致改进方法改进模型进行进步检验行
61
(1)建立居民收入消费模型Eviews分析结果：
Dependent Variable Y
Method Least Squares
Date 122014 Time 1422
Sample 1 19
Included observations 19
Variable
Coefficient
Std Error
tStatistic
Prob
X
0690488
0012877
5362068
00000
C
7993004
1239919
6446390
00000
Rsquared
0994122
Mean dependent var
7002747
Adjusted Rsquared
0993776
SD dependent var
2464491
SE of regression
1944245
Akaike info criterion
8872095
Sum squared resid
6426149
Schwarz criterion
8971510
Log likelihood
8228490
HannanQuinn criter
8888920
Fstatistic
2875178
DurbinWatson stat
0574663
Prob(Fstatistic)
0000000
模型：
Y0690488X+7993004
Se(0012877)(1239919)
t(5362068)(6446390)
R20994122 F2875178 DW0574663
（2）
1）检验模型中存问题
①做出残差图：
残差变动系统模式连续正连续负表明残差项存阶相关
②该回方程决系数较高回系数均显著样量19解释变量模型5显著水查DW统计表知dL1180dU1401模型中DW0574663< dL显然模型中相关
③模型进行BG检验Eviews分析结果：
BreuschGodfrey Serial Correlation LM Test
Fstatistic
4811108
Prob F(215)
00243
Obs*Rsquared
7425088
Prob ChiSquare(2)
00244
Test Equation
Dependent Variable RESID
Method Least Squares
Date 122014 Time 1503
Sample 1 19
Included observations 19
Presample missing value lagged residuals set to zero
Variable
Coefficient
Std Error
tStatistic
Prob
X
0003275
0010787
0303586
07656
C
1929546
1035593
0186323
08547
RESID(1)
0608886
0292707
2080189
00551
RESID(2)
0089988
0291120
0309110
07615
Rsquared
0390794
Mean dependent var
165E13
Adjusted Rsquared
0268953
SD dependent var
1889466
SE of regression
1615518
Akaike info criterion
8587023
Sum squared resid
3914848
Schwarz criterion
8785852
Log likelihood
7757671
HannanQuinn criter
8620672
Fstatistic
3207406
DurbinWatson stat
1570723
Prob(Fstatistic)
0053468
表显示LMTR27425088p值00244表明存相关
2）模型进行处理：
①采取广义差分法
a)估计相关系数ρet进行滞期回EViews分析结果：
Dependent Variable E
Method Least Squares
Date 122014 Time 1504
Sample (adjusted) 2 19
Included observations 18 after adjustments
Variable
Coefficient
Std Error
tStatistic
Prob
E(1)
0657352
0177626
3700759
00018
Rsquared
0440747
Mean dependent var
1717433
Adjusted Rsquared
0440747
SD dependent var
1785134
SE of regression
1334980
Akaike info criterion
8074833
Sum squared resid
3029692
Schwarz criterion
8124298
Log likelihood
7167349
HannanQuinn criter
8081653
DurbinWatson stat
1634573
知ρ0657352
b)原模型进行广义差分回Eviews进行分析结果：
Dependent Variable Y0657352*Y(1)
Method Least Squares
Date 122014 Time 1504
Sample (adjusted) 2 19
Included observations 18 after adjustments
Variable
Coefficient
Std Error
tStatistic
Prob
C
3597761
8103546
4439737
00004
X0657352*X(1)
0668695
0020642
3239512
00000
Rsquared
0984983
Mean dependent var
2781002
Adjusted Rsquared
0984044
SD dependent var
1051781
SE of regression
1328570
Akaike info criterion
8115693
Sum squared resid
2824158
Schwarz criterion
8214623
Log likelihood
7104124
HannanQuinn criter
8129334
Fstatistic
1049444
DurbinWatson stat
1830746
Prob(Fstatistic)
0000000
图知回方程：
Yt*3597761+0668695Xt*
Se(8103546)(0020642)
t(4439737)(3239512)
R20984983 F1049444 DW1830746
式中Yt*Yt0657352Yt1 Xt*Xt0657352Xt1
广义差分数样容量减少118查5显著水DW统计表知dL1158dU1391模型中DW1830746du差分方程β13597761(10657352)1049987
终消费模型：
Yt1049987+0668695Xt
②科克伦奥克特迭代法EVIews分析结果：
Dependent Variable Y
Method Least Squares
Date 122014 Time 1515
Sample (adjusted) 2 19
Included observations 18 after adjustments
Convergence achieved after 5 iterations
Variable
Coefficient
Std Error
tStatistic
Prob
C
1040449
2387618
4357687
00006
X
0669262
0020831
3212757
00000
AR(1)
0630015
0164218
3836462
00016
Rsquared
0997097
Mean dependent var
7191867
Adjusted Rsquared
0996710
SD dependent var
2389866
SE of regression
1370843
Akaike info criterion
8224910
Sum squared resid
2818814
Schwarz criterion
8373306
Log likelihood
7102419
HannanQuinn criter
8245372
Fstatistic
2575896
DurbinWatson stat
1787878
Prob(Fstatistic)
0000000
Inverted AR Roots
63
方程：
Yt1040449+0669262Xt
（3）济意义：均实际收入增加1元均说均时间消费支出增加0669262元
64
（1）
1）针数模型Eviews分析结果：
Dependent Variable LNY
Method Least Squares
Date 122714 Time 1613
Sample 1980 2000
Included observations 21
Variable
Coefficient
Std Error
tStatistic
Prob
LNX
0951090
0038897
2445123
00000
C
2171041
0241025
9007529
00000
Rsquared
0969199
Mean dependent var
8039307
Adjusted Rsquared
0967578
SD dependent var
0565486
SE of regression
0101822
Akaike info criterion
1640785
Sum squared resid
0196987
Schwarz criterion
1541307
Log likelihood
1922825
HannanQuinn criter
1619196
Fstatistic
5978626
DurbinWatson stat
1159788
Prob(Fstatistic)
0000000
模型：
lnY0951090lnX+2171041
se(0038897) (0241025)
t(2445123) (9007529)
R20969199 F5978626 DW1159788
2）检验模型相关性
该回方程决系数较高回系数均显著样量21解释变量模型5显著水查DW统计表知dL1221dU1420模型中DW1159788< dL显然模型中相关
(2)广义差分法处理模型：
1）估计相关系数ρet进行滞期回EViews分析结果：
Dependent Variable E
Method Least Squares
Date 122714 Time 1618
Sample (adjusted) 1982 2000
Included observations 19 after adjustments
Variable
Coefficient
Std Error
tStatistic
Prob
E(1)
0012872
0280581
0045878
09639
Rsquared
0000073
Mean dependent var
2556737
Adjusted Rsquared
0000073
SD dependent var
3977924
SE of regression
3977778
Akaike info criterion
1486086
Sum squared resid
2848090
Schwarz criterion
1491057
Log likelihood
1401782
HannanQuinn criter
1486927
DurbinWatson stat
1700254
知ρ0012872
2）原模型进行广义差分回Eviews进行分析结果：
Dependent Variable Y+0012872*Y(1)
Method Least Squares
Date 122714 Time 2106
Sample (adjusted) 1981 2000
Included observations 20 after adjustments
Variable
Coefficient
Std Error
tStatistic
Prob
C
1049645
1977928
0530679
06021
X+0012872*X(1)
6653757
0304157
2187605
00000
Rsquared
0963751
Mean dependent var
3753934
Adjusted Rsquared
0961737
SD dependent var
2045606
SE of regression
4001404
Akaike info criterion
1491615
Sum squared resid
2882022
Schwarz criterion
1501572
Log likelihood
1471615
HannanQuinn criter
1493559
Fstatistic
4785614
DurbinWatson stat
1822259
Prob(Fstatistic)
0000000
图知回方程：
Yt*1049645+6653757Xt*
Se(1977928)( 0304157)
t(0530679)( 2187605)
R20963751 F4785614DW18222596
式中Yt*Yt+0012872Yt1 Xt*Xt+0012872Xt1
广义差分数样容量减少120查5显著水DW统计表知dL1201dU1411模型中DW18222596du差分方程β11049645(1+0012872)1036306
终模型：
Yt1036306+6653757Xt
（3）模型Eviews分析结果：
Dependent Variable LNY1
Method Least Squares
Date 122714 Time 2216
Sample (adjusted) 1981 2000
Included observations 20 after adjustments
Variable
Coefficient
Std Error
tStatistic
Prob
LNX1
0442224
0066024
6697901
00000
C
0054047
0013322
4056896
00007
Rsquared
0713658
Mean dependent var
0091592
Adjusted Rsquared
0697750
SD dependent var
0098311
SE of regression
0054049
Akaike info criterion
2903219
Sum squared resid
0052583
Schwarz criterion
2803646
Log likelihood
3103219
HannanQuinn criter
2883781
Fstatistic
4486188
DurbinWatson stat
1590363
Prob(Fstatistic)
0000003
题目知模型样容量20查5显著水DW统计表知dL1201dU1411模型中DW1590363du
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21
（1） ①首先分析均寿命均GDP数量关系Eviews分析：
Dependent Variable Y
Method Least Squares
Date 122714 Time 2100
Sample 1 22
Included observations 22
Variable
Coefficient
Std Error
tStatistic
Prob
C
5664794
1960820
2888992
00000
X1
0128360
0027242
4711834
00001
Rsquared
0526082
Mean dependent var
6250000
Adjusted Rsquared
0502386
SD dependent var
1008889
SE of regression
7116881
Akaike info criterion
6849324
Sum squared resid
1013000
Schwarz criterion
6948510
Log likelihood
7334257
HannanQuinn criter
6872689
Fstatistic
2220138
DurbinWatson stat
0629074
Prob(Fstatistic)
0000134
知关系式y5664794+0128360x1
②关均寿命成识字率关系Eviews分析：
Dependent Variable Y
Method Least Squares
Date 112614 Time 2110
Sample 1 22
Included observations 22
Variable
Coefficient
Std Error
tStatistic
Prob
C
3879424
3532079
1098340
00000
X2
0331971
0046656
7115308
00000
Rsquared
0716825
Mean dependent var
6250000
Adjusted Rsquared
0702666
SD dependent var
1008889
SE of regression
5501306
Akaike info criterion
6334356
Sum squared resid
6052873
Schwarz criterion
6433542
Log likelihood
6767792
HannanQuinn criter
6357721
Fstatistic
5062761
DurbinWatson stat
1846406
Prob(Fstatistic)
0000001
知关系式y3879424+0331971x2
③关均寿命岁童疫苗接种率关系Eviews分析：
Dependent Variable Y
Method Least Squares
Date 112614 Time 2114
Sample 1 22
Included observations 22
Variable
Coefficient
Std Error
tStatistic
Prob
C
3179956
6536434
4864971
00001
X3
0387276
0080260
4825285
00001
Rsquared
0537929
Mean dependent var
6250000
Adjusted Rsquared
0514825
SD dependent var
1008889
SE of regression
7027364
Akaike info criterion
6824009
Sum squared resid
9876770
Schwarz criterion
6923194
Log likelihood
7306409
HannanQuinn criter
6847374
Fstatistic
2328338
DurbinWatson stat
0952555
Prob(Fstatistic)
0000103
知关系式y3179956+0387276x3
（2）①关均寿命均GDP模型知决系数0526082说明建模型整体样数拟合较
回系数t检验：t（β1）4711834>t0025(20)2086斜率系数显著性检验表明均GDP均寿命显著影响
②关均寿命成识字率模型知决系数0716825说明建模型整体样数拟合较
回系数t检验：t（β2）7115308>t0025(20)2086斜率系数显著性检验表明成识字率均寿命显著影响
③关均寿命岁童疫苗模型知决系数0537929说明建模型整体样数拟合较
回系数t检验：t（β3）4825285>t0025(20)2086斜率系数显著性检验表明岁童疫苗接种率均寿命显著影响
22
（1）
①浙江省预算收入全省生产总值模型Eviews分析结果：
Dependent Variable Y
Method Least Squares
Date 120314 Time 1700
Sample (adjusted) 1 33
Included observations 33 after adjustments
Variable
Coefficient
Std Error
tStatistic
Prob
X
0176124
0004072
4325639
00000
C
1543063
3908196
3948274
00004
Rsquared
0983702
Mean dependent var
9025148
Adjusted Rsquared
0983177
SD dependent var
1351009
SE of regression
1752325
Akaike info criterion
1322880
Sum squared resid
9518997
Schwarz criterion
1331949
Log likelihood
2162751
HannanQuinn criter
1325931
Fstatistic
1871115
DurbinWatson stat
0100021
Prob(Fstatistic)
0000000
②知模型参数：斜率系数0176124截距—1543063
③关浙江省财政预算收入全省生产总值模型检验模型显著性：
1）决系数0983702说明建模型整体样数拟合较
2）回系数t检验：t（β2）4325639>t0025(31)20395斜率系数显著性检验表明全省生产总值财政预算总收入显著影响
④规范形式写出检验结果：
Y0176124X—1543063
(0004072) (3908196)
t (4325639) （3948274）
R20983702 F1871115 n33
⑤济意义：全省生产总值增加1亿元财政预算总收入增加0176124亿元
（2）x32000时
①进行点预测知Y0176124X—1543063代入：
Y Y0176124*32000—154306354816617
②进行区间预测：
先Eviews分析：
X
Y
Mean
6000441
9025148
Median
2689280
2093900
Maximum
2772231
4895410
Minimum
1237200
2587000
Std Dev
7608021
1351009
Skewness
1432519
1663108
Kurtosis
4010515
4590432
JarqueBera
1269068
1869063
Probability
0001755
0000087
Sum
1980145
2978299
Sum Sq Dev
185E+09
58407195
Observations
33
33
表知
∑x2∑（Xi—X）2δ2x(n—1) 76080212 x (33—1)1852223473
(Xf—X)2(32000— 6000441)26759770682
Xf32000时相关数代入计算：
54816617—20395x1752325x√133+18522234736759770682≤
Yf≤54816617+20395x1752325x√133+18522234736759770682
Yf置信区间（54816617—649649 54816617+649649）
(3) 浙江省预算收入数全省生产总值数模型Eviews分析结果：
Dependent Variable LNY
Method Least Squares
Date 120314 Time 1800
Sample (adjusted) 1 33
Included observations 33 after adjustments
Variable
Coefficient
Std Error
tStatistic
Prob
LNX
0980275
0034296
2858268
00000
C
1918289
0268213
7152121
00000
Rsquared
0963442
Mean dependent var
5573120
Adjusted Rsquared
0962263
SD dependent var
1684189
SE of regression
0327172
Akaike info criterion
0662028
Sum squared resid
3318281
Schwarz criterion
0752726
Log likelihood
8923468
HannanQuinn criter
0692545
Fstatistic
8169699
DurbinWatson stat
0096208
Prob(Fstatistic)
0000000
①模型方程：lnY0980275lnX1918289
②知模型参数：斜率系数0980275截距1918289
③关浙江省财政预算收入全省生产总值模型检验显著性：
1）决系数0963442说明建模型整体样数拟合较
2）回系数t检验：t（β2）2858268>t0025(31)20395斜率系数显著性检验表明全省生产总值财政预算总收入显著影响
④济意义：全省生产总值增长1财政预算总收入增长0980275
24
（1）建筑面积建造单位成模型Eviews分析结果：
Dependent Variable Y
Method Least Squares
Date 120114 Time 1240
Sample 1 12
Included observations 12
Variable
Coefficient
Std Error
tStatistic
Prob
X
6418400
4809828
1334434
00000
C
1845475
1926446
9579688
00000
Rsquared
0946829
Mean dependent var
1619333
Adjusted Rsquared
0941512
SD dependent var
1312252
SE of regression
3173600
Akaike info criterion
9903792
Sum squared resid
1007174
Schwarz criterion
9984610
Log likelihood
5742275
HannanQuinn criter
9873871
Fstatistic
1780715
DurbinWatson stat
1172407
Prob(Fstatistic)
0000000
：建筑面积建造成回方程：
Y18454756418400X
（2）济意义：建筑面积增加1万方米建筑单位成方米减少6418400元
（3）
①首先进行点预测Y18454756418400Xx45y1556647
②进行区间估计：
Eviews分析：
Y
X
Mean
1619333
3523333
Median
1630000
3715000
Maximum
1860000
6230000
Minimum
1419000
0600000
Std Dev
1312252
1989419
Skewness
0003403
0060130
Kurtosis
2346511
1664917
JarqueBera
0213547
0898454
Probability
0898729
0638121
Sum
1943200
4228000
Sum Sq Dev
1894207
4353567
Observations
12
12
表知
∑x2∑（Xi—X）2δ2x(n—1) 19894192 x (12—1)435357
(Xf—X)2(45— 3523333)2095387843
Xf45时相关数代入计算：
1556647—2228x3173600x√112+435357095387843≤
Yf≤1556647+2228x3173600x√112+435357095387843
Yf置信区间（1556647—4781231 1556647+4781231）
31
（1）
①百户拥家汽车量计量济模型Eviews分析结果：
Dependent Variable Y
Method Least Squares
Date 112514 Time 1238
Sample 1 31
Included observations 31
Variable
Coefficient
Std Error
tStatistic
Prob
X2
5996865
1406058
4265020
00002
X3
0524027
0179280
2922950
00069
X4
2265680
0518837
4366842
00002
C
2468540
5197500
4749476
00001
Rsquared
0666062
Mean dependent var
1677355
Adjusted Rsquared
0628957
SD dependent var
8252535
SE of regression
5026889
Akaike info criterion
6187394
Sum squared resid
6822795
Schwarz criterion
6372424
Log likelihood
9190460
HannanQuinn criter
6247709
Fstatistic
1795108
DurbinWatson stat
1147253
Prob(Fstatistic)
0000001
②模型：
Y2468540+5996865X2 0524027 X32265680 X4
③模型进行检验：
1） 决系数0666062修正决系数0628957说明模型样拟合较
2） F检验F1795108>F（327）365回方程显著
3）t检验t统计量分4749476426502029229504366842均
t（27）20518系数显著
④：
1） 决系数越说明拟合程度越
2） F值界值较界值否定原假设回方程显著界值接受原假设回方程显著
3） t值界值较界值否定原假设系数显著界值接受原假设系数显著
（2）济意义：均ＧＤＰ增加１万元百户拥家汽车增加5996865辆城镇口重增加１百分点百户拥家汽车减少0524027辆交通工具消费价格指数升１百户拥家汽车减少2265680辆
（3）EViews分析：
Dependent Variable Y
Method Least Squares
Date 120814 Time 1728
Sample 1 31
Included observations 31
Variable
Coefficient
Std Error
tStatistic
Prob
X2
5135670
1010270
5083465
00000
LNX3
2281005
6771820
3368378
00023
LNX4
2308481
4946791
4666624
00001
C
1148758
2282917
5031974
00000
Rsquared
0691952
Mean dependent var
1677355
Adjusted Rsquared
0657725
SD dependent var
8252535
SE of regression
4828088
Akaike info criterion
6106692
Sum squared resid
6293818
Schwarz criterion
6291723
Log likelihood
9065373
HannanQuinn criter
6167008
Fstatistic
2021624
DurbinWatson stat
1150090
Prob(Fstatistic)
0000000
模型方程：
Y5135670 X22281005 LNX32308481 LNX4+1148758
分析出决系数0691952>0666062拟合程度提高样改进
32
（１）出口货物总额计量济模型Eviews分析结果：：
Dependent Variable Y
Method Least Squares
Date 120114 Time 2025
Sample 1994 2011
Included observations 18
Variable
Coefficient
Std Error
tStatistic
Prob
X2
0135474
0012799
1058454
00000
X3
1885348
9776181
1928512
00729
C
1823158
8638216
2110573
00520
Rsquared
0985838
Mean dependent var
6619191
Adjusted Rsquared
0983950
SD dependent var
5767152
SE of regression
7306306
Akaike info criterion
1617670
Sum squared resid
8007316
Schwarz criterion
1632510
Log likelihood
1425903
HannanQuinn criter
1619717
Fstatistic
5220976
DurbinWatson stat
1173432
Prob(Fstatistic)
0000000
①知模型：
Y 0135474X2 + 1885348X3 1823158
②模型进行检验：
1）决系数0985838修正决系数0983950说明模型样拟合较
2）F检验F5220976>F（215）477回方程显著
3）t检验t统计量分X2系数应t值1058454t（15）2131系数显著X3系数应t值1928512t（15）2131说明系数显著
（2）数模型Eviews分析结果：
Dependent Variable LNY
Method Least Squares
Date 120114 Time 2025
Sample 1994 2011
Included observations 18
Variable
Coefficient
Std Error
tStatistic
Prob
LNX2
1564221
0088988
1757789
00000
LNX3
1760695
0682115
2581229
00209
C
2052048
5432487
3777363
00018
Rsquared
0986295
Mean dependent var
8400112
Adjusted Rsquared
0984467
SD dependent var
0941530
SE of regression
0117343
Akaike info criterion
1296424
Sum squared resid
0206540
Schwarz criterion
1148029
Log likelihood
1466782
HannanQuinn criter
1275962
Fstatistic
5397364
DurbinWatson stat
0686656
Prob(Fstatistic)
0000000
①知模型：
LNY2052048+1564221 LNX2+1760695 LNX3
②模型进行检验：
1）决系数0986295修正决系数0984467说明模型样拟合较
2）F检验F5397364> F（215）477回方程显著
3）t检验t统计量分377736317577892581229均t（15）2131系数显著
（3）
①（1）式中济意义：工业增加1亿元出口货物总额增加0135474亿元民币汇率增加1出口货物总额增加1885348亿元
②（2）式中济意义：工业增加额增加1出口货物总额增加1564221民币汇率增加1出口货物总额增加1760695
33
（1）家庭书刊消费家庭月均收入户受教育年数计量模型Eviews分析结果：
Dependent Variable Y
Method Least Squares
Date 120114 Time 2030
Sample 1 18
Included observations 18
Variable
Coefficient
Std Error
tStatistic
Prob
X
0086450
0029363
2944186
00101
T
5237031
5202167
1006702
00000
C
5001638
4946026
1011244
03279
Rsquared
0951235
Mean dependent var
7551222
Adjusted Rsquared
0944732
SD dependent var
2587206
SE of regression
6082273
Akaike info criterion
1120482
Sum squared resid
5549107
Schwarz criterion
1135321
Log likelihood
9784334
HannanQuinn criter
1122528
Fstatistic
1462974
DurbinWatson stat
2605783
Prob(Fstatistic)
0000000
①模型：Y 0086450X + 5237031T5001638
②模型进行检验：
1）决系数0951235修正决系数0944732说明模型样拟合较
2）F检验F5397364> F（215）477回方程显著
3）t检验t统计量分29441861006702均t（15）2131系数显著
③济意义：家庭月均收入增加1元家庭书刊年消费支出增加0086450元户受教育年数增加1年家庭书刊年消费支出增加5237031元
（2）Eviews分析：
①
Dependent Variable Y
Method Least Squares
Date 120114 Time 2230
Sample 1 18
Included observations 18
Variable
Coefficient
Std Error
tStatistic
Prob
T
6301676
4548581
1385416
00000
C
1158171
5802290
0199606
08443
Rsquared
0923054
Mean dependent var
7551222
Adjusted Rsquared
0918245
SD dependent var
2587206
SE of regression
7397565
Akaike info criterion
1154979
Sum squared resid
8755836
Schwarz criterion
1164872
Log likelihood
1019481
HannanQuinn criter
1156343
Fstatistic
1919377
DurbinWatson stat
2134043
Prob(Fstatistic)
0000000
②
Dependent Variable X
Method Least Squares
Date 120114 Time 2234
Sample 1 18
Included observations 18
Variable
Coefficient
Std Error
tStatistic
Prob
T
1231516
3184150
3867644
00014
C
4445888
4061786
1094565
02899
Rsquared
0483182
Mean dependent var
1942933
Adjusted Rsquared
0450881
SD dependent var
6988325
SE of regression
5178529
Akaike info criterion
1544170
Sum squared resid
4290746
Schwarz criterion
1554063
Log likelihood
1369753
HannanQuinn criter
1545534
Fstatistic
1495867
DurbinWatson stat
1052251
Prob(Fstatistic)
0001364
分yTXT元回
模型分：
Y 6301676T 1158171
X 1231516T + 4445888
（3）残差进行模型分析Eviews分析结果：
Dependent Variable E1
Method Least Squares
Date 120314 Time 2039
Sample 1 18
Included observations 18
Variable
Coefficient
Std Error
tStatistic
Prob
E2
0086450
0028431
3040742
00078
C
396E14
1388083
285E15
10000
Rsquared
0366239
Mean dependent var
230E14
Adjusted Rsquared
0326629
SD dependent var
7176693
SE of regression
5889136
Akaike info criterion
1109370
Sum squared resid
5549107
Schwarz criterion
1119264
Log likelihood
9784334
HannanQuinn criter
1110735
Fstatistic
9246111
DurbinWatson stat
2605783
Prob(Fstatistic)
0007788
模型：
E1 0086450E2 + 396e14
参数：斜率系数α0086450截距396e14
（3）知β2α2系数样回系数解释变量残差系数样变化规律致
36
（1）预期符号X1X2X3X4X5符号正X6符号负
（2）根Eviews分析数：
Dependent Variable Y
Method Least Squares
Date 120414 Time 1324
Sample 1994 2011
Included observations 18
Variable
Coefficient
Std Error
tStatistic
Prob
X2
0001382
0001102
1254330
02336
X3
0001942
0003960
0490501
06326
X4
3579090
3559949
1005377
03346
X5
0004791
0005034
0951671
03600
X6
0045542
0095552
0476621
06422
C
1377732
1573366
0875659
03984
Rsquared
0994869
Mean dependent var
1276667
Adjusted Rsquared
0992731
SD dependent var
9746631
SE of regression
0830963
Akaike info criterion
2728738
Sum squared resid
8285993
Schwarz criterion
3025529
Log likelihood
1855865
HannanQuinn criter
2769662
Fstatistic
4653617
DurbinWatson stat
1553294
Prob(Fstatistic)
0000000
①预期相符
②评价：
1） 决系数0994869数相认拟合程度
2） F检验F4653617>F（512）389回方程显著
3） T检验X1X2X3X4X5X6 系数应t值分：12543300490501100537709516710476621均t（12）2179系数显著
（3）根Eviews分析数：
Dependent Variable Y
Method Least Squares
Date 120314 Time 1112
Sample 1994 2011
Included observations 18
Variable
Coefficient
Std Error
tStatistic
Prob
X5
0001032
220E05
4679946
00000
X6
0054965
0031184
1762581
00983
C
4205481
3335602
1260786
02266
Rsquared
0993601
Mean dependent var
1276667
Adjusted Rsquared
0992748
SD dependent var
9746631
SE of regression
0830018
Akaike info criterion
2616274
Sum squared resid
1033396
Schwarz criterion
2764669
Log likelihood
2054646
HannanQuinn criter
2636736
Fstatistic
1164567
DurbinWatson stat
1341880
Prob(Fstatistic)
0000000
①模型方程：
Y0001032 X50054965 X6+4205481
②评价：
1） 决系数0993601数相认拟合程度
2） F检验F1164567>F（512）389回方程显著
3） T检验X5 系数应t值4679946t（12）2179系数显著均GDP年底存款余额显著影响 X6 系数应t值1762581t（12）2179系数显著
43
（1）根Eviews分析数：
Dependent Variable LNY
Method Least Squares
Date 120514 Time 1139
Sample 1985 2011
Included observations 27
Variable
Coefficient
Std Error
tStatistic
Prob
LNGDP
1338533
0088610
1510582
00000
LNCPI
0421791
0233295
1807975
00832
C
3111486
0463010
6720126
00000
Rsquared
0988051
Mean dependent var
9484710
Adjusted Rsquared
0987055
SD dependent var
1425517
SE of regression
0162189
Akaike info criterion
0695670
Sum squared resid
0631326
Schwarz criterion
0551689
Log likelihood
1239155
HannanQuinn criter
0652857
Fstatistic
9922582
DurbinWatson stat
0522613
Prob(Fstatistic)
0000000
模型方程：
LNY1338533 LNGDPt0421791 LNCPIt3111486
（2）
① 该模型决系数0988051决系数高F检验值9922582
明显显著α005时t（24）2064LNCPI系数显著存重线性
②相关系数矩阵：
LNY
LNGDP
LNCPI
LNY
1000000
0993189
0935116
LNGDP
0993189
1000000
0953740
LNCPI
0935116
0953740
1000000
LNGDP LNCPI间相关系数高证实确实存重线性
（3）Eviews：
a）
Dependent Variable LNY
Method Least Squares
Date 120314 Time 1441
Sample 1985 2011
Included observations 27
Variable
Coefficient
Std Error
tStatistic
Prob
LNGDP
1185739
0027822
4261933
00000
C
3750670
0312255
1201156
00000
Rsquared
0986423
Mean dependent var
9484710
Adjusted Rsquared
0985880
SD dependent var
1425517
SE of regression
0169389
Akaike info criterion
0642056
Sum squared resid
0717312
Schwarz criterion
0546068
Log likelihood
1066776
HannanQuinn criter
0613514
Fstatistic
1816407
DurbinWatson stat
0471111
Prob(Fstatistic)
0000000
b)
Dependent Variable LNY
Method Least Squares
Date 120314 Time 1441
Sample 1985 2011
Included observations 27
Variable
Coefficient
Std Error
tStatistic
Prob
LNCPI
2939295
0222756
1319511
00000
C
6854535
1242243
5517871
00000
Rsquared
0874442
Mean dependent var
9484710
Adjusted Rsquared
0869419
SD dependent var
1425517
SE of regression
0515124
Akaike info criterion
1582368
Sum squared resid
6633810
Schwarz criterion
1678356
Log likelihood
1936196
HannanQuinn criter
1610910
Fstatistic
1741108
DurbinWatson stat
0137042
Prob(Fstatistic)
0000000
c)
Dependent Variable LNGDP
Method Least Squares
Date 120514 Time 1111
Sample 1985 2011
Included observations 27
Variable
Coefficient
Std Error
tStatistic
Prob
LNCPI
2511022
0158302
1586227
00000
C
2796381
0882798
3167634
00040
Rsquared
0909621
Mean dependent var
1116214
Adjusted Rsquared
0906005
SD dependent var
1194029
SE of regression
0366072
Akaike info criterion
0899213
Sum squared resid
3350216
Schwarz criterion
0995201
Log likelihood
1013938
HannanQuinn criter
0927755
Fstatistic
2516117
DurbinWatson stat
0099623
Prob(Fstatistic)
0000000
①回方程分
1）LNY1185739 LNGDPt3750670
2）LNY2939295 LNCPIt6854535
3）LNGDPt2511022 LNCPIt2796381
②重线性认识：
单方程拟合效果回系数显著判定系数较高GDPCPI进口显著单影响两变量时引入模型时影响方发生改变通相关系数分析发现
（4）建议：果仅仅作预测意种重线性果进行结构分析应该引起注意
44
（1）设计理模型Eviews分析：
Dependent Variable CZSR
Method Least Squares
Date 120314 Time 1140
Sample 1985 2011
Included observations 27
Variable
Coefficient
Std Error
tStatistic
Prob
CZZC
0090114
0044367
2031129
00540
GDP
0025334
0005069
4998036
00000
SSZE
1176894
0062162
1893271
00000
C
2218540
1306532
1698038
01030
Rsquared
0999857
Mean dependent var
2257256
Adjusted Rsquared
0999838
SD dependent var
2773949
SE of regression
3530540
Akaike info criterion
1470707
Sum squared resid
2866884
Schwarz criterion
1489905
Log likelihood
1945455
HannanQuinn criter
1476416
Fstatistic
5349393
DurbinWatson stat
1458128
Prob(Fstatistic)
0000000
回结果见决系数0999857校正决系数0999838模型拟合F统计量5349393说明α005水回方程回方程整体显著t检验结果表明国生产总值财政收入影响显著回系数符号负实际符合知该方程存重线性
（2）相关系数矩阵：
CZSR
CZZC
GDP
SSZE
CZSR
1000000
0998729
0992838
0999832
CZZC
0998729
1000000
0992536
0998575
GDP
0992838
0992536
1000000
0994370
SSZE
0999832
0998575
0994370
1000000
表知CZZCGDPCZZCSSZEGDPSSZE间相关系数非常高说明确实存重线性
（3）做辅助回
解释变量
决系数
方差扩子
CZZC
0997168
353
GDP
0988833
90
SSZE
0997862
468
方差扩子均10存严重重线性通分析两两解释变量间相关性高
（4）解决方式：分作出财政收入财政支出国生产总值税收总额间元回
52
（1）
①图形法检验
绘制e2散点图Eviews分析：
图知模型存异方差
② GoldfeldQuanadt检验
1）定义区间17时软件分析：
Dependent Variable Y
Method Least Squares
Date 121014 Time 1452
Sample 1 7
Included observations 7
Variable
Coefficient
Std Error
tStatistic
Prob
T
3520664
4901492
7182843
00020
X
0109949
0061965
1774380
01507
C
7712588
8232844
0936807
04019
Rsquared
0943099
Mean dependent var
5656857
Adjusted Rsquared
0914649
SD dependent var
1082755
SE of regression
3163265
Akaike info criterion
1004378
Sum squared resid
4002499
Schwarz criterion
1002060
Log likelihood
3215324
HannanQuinn criter
9757267
Fstatistic
3314880
DurbinWatson stat
1426262
Prob(Fstatistic)
0003238
∑e1i24002499
2）定义区间1218时软件分析：
Dependent Variable Y
Method Least Squares
Date 121014 Time 1350
Sample 12 18
Included observations 7
Variable
Coefficient
Std Error
tStatistic
Prob
T
5240588
6923378
7569409
00016
X
0068689
0053763
1277635
02705
C
8789265
7992542
0109968
09177
Rsquared
0984688
Mean dependent var
8876143
Adjusted Rsquared
0977032
SD dependent var
2744148
SE of regression
4158810
Akaike info criterion
1059103
Sum squared resid
6918280
Schwarz criterion
1056785
Log likelihood
3406861
HannanQuinn criter
1030451
Fstatistic
1286166
DurbinWatson stat
2390329
Prob(Fstatistic)
0000234
∑e2i26918280
3）根GoldfeldQuanadt检验F统计量：
F∑e2i2 ∑e1i2 6918280400249917285
α005水分子分母度均4查分布表界值F005（44）639F17285< F005（44）639接受原假设检验表明模型存异方差
（2）存异方差估计参数方法：
①模型进行变换
②加权二法进行计算出模型方程进行相关检验
③模型进行数变换进行分析
（3）评价：
33结相信机扰动项间存异方差回方程显著
53
(1)Eviews软件分析：
Dependent Variable Y
Method Least Squares
Date 121014 Time 1600
Sample 1 31
Included observations 31
Variable
Coefficient
Std Error
tStatistic
Prob
X
1244281
0079032
1574411
00000
C
2424488
2911940
0832602
04119
Rsquared
0895260
Mean dependent var
4443526
Adjusted Rsquared
0891649
SD dependent var
1972072
SE of regression
6491426
Akaike info criterion
1585152
Sum squared resid
12220196
Schwarz criterion
1594404
Log likelihood
2436986
HannanQuinn criter
1588168
Fstatistic
2478769
DurbinWatson stat
1078581
Prob(Fstatistic)
0000000
表知2007年国农村居民家庭均消费支出（x）均纯收入（y）模型：
Y1244281X+2424488
（2）
①图形法检验
图知模型存异方差
②GoldfeldQuanadt检验
1）定义区间112时软件分析：
Dependent Variable Y1
Method Least Squares
Date 121014 Time 1134
Sample 1 12
Included observations 12
Variable
Coefficient
Std Error
tStatistic
Prob
X1
1485296
0500386
2968297
00141
C
5505492
1220063
0451247
06614
Rsquared
0468390
Mean dependent var
3052950
Adjusted Rsquared
0415229
SD dependent var
5505148
SE of regression
4209803
Akaike info criterion
1507406
Sum squared resid
1772245
Schwarz criterion
1515488
Log likelihood
8844437
HannanQuinn criter
1504414
Fstatistic
8810789
DurbinWatson stat
2354167
Prob(Fstatistic)
0014087
∑e1i21772245
2）定义区间2031时软件分析：
Dependent Variable Y1
Method Least Squares
Date 121014 Time 1636
Sample 20 31
Included observations 12
Variable
Coefficient
Std Error
tStatistic
Prob
X1
1086940
0148863
7301623
00000
C
1173307
7332520
1600141
01407
Rsquared
0842056
Mean dependent var
6188329
Adjusted Rsquared
0826262
SD dependent var
2133692
SE of regression
8893633
Akaike info criterion
1656990
Sum squared resid
7909670
Schwarz criterion
1665072
Log likelihood
9741940
HannanQuinn criter
1653998
Fstatistic
5331370
DurbinWatson stat
2339767
Prob(Fstatistic)
0000026
∑e2i27909670
3）根GoldfeldQuanadt检验F统计量：
F∑e2i2 ∑e1i2 7909670 177224544631
α005水分子分母度均10查分布表界值F005（1010）298F44631> F005（1010）298拒绝原假设检验表明模型存异方差
（3）
1）采WLS法估计程中
①权数w11X建立回：
Dependent Variable Y
Method Least Squares
Date 120914 Time 1113
Sample 1 31
Included observations 31
Weighting series W1
Variable
Coefficient
Std Error
tStatistic
Prob
X
1425859
0119104
1197157
00000
C
3348131
3443523
0972298
03389
Weighted Statistics
Rsquared
0831707
Mean dependent var
3946082
Adjusted Rsquared
0825904
SD dependent var
5361907
SE of regression
5366796
Akaike info criterion
1547102
Sum squared resid
8352726
Schwarz criterion
1556354
Log likelihood
2378008
HannanQuinn criter
1550118
Fstatistic
1433184
DurbinWatson stat
1369081
Prob(Fstatistic)
0000000
Unweighted Statistics
Rsquared
0875855
Mean dependent var
4443526
Adjusted Rsquared
0871574
SD dependent var
1972072
SE of regression
7067236
Sum squared resid
14484289
DurbinWatson stat
1532908
模型进行White检验：
Heteroskedasticity Test White
Fstatistic
0299395
Prob F(228)
07436
Obs*Rsquared
0649065
Prob ChiSquare(2)
07229
Scaled explained SS
1798067
Prob ChiSquare(2)
04070
Test Equation
Dependent Variable WGT_RESID^2
Method Least Squares
Date 121014 Time 2113
Sample 1 31
Included observations 31
Collinear test regressors dropped from specification
Variable
Coefficient
Std Error
tStatistic
Prob
C
6192789
1045682
0059222
09532
WGT^2
5939279
1173622
0506064
06168
X*WGT^2
2824407
7479780
0377606
07086
Rsquared
0020938
Mean dependent var
2694428
Adjusted Rsquared
0048995
SD dependent var
6891665
SE of regression
7058476
Akaike info criterion
2986395
Sum squared resid
140E+13
Schwarz criterion
3000273
Log likelihood
4598913
HannanQuinn criter
2990919
Fstatistic
0299395
DurbinWatson stat
1922336
Prob(Fstatistic)
0743610
知nR20649065较计算统计量界值nR20649065<005（2）59915接受原假设该模型消异方差
估计结果：
Y1425859X3348131
t（1197157）（0972298）
R20875855 F1433184 DW1369081
②权数w21x2回分析：
Dependent Variable Y
Method Least Squares
Date 120914 Time 2108
Sample 1 31
Included observations 31
Weighting series W2
Variable
Coefficient
Std Error
tStatistic
Prob
X
1557040
0145392
1070922
00000
C
6931946
3764760
1841272
00758
Weighted Statistics
Rsquared
0798173
Mean dependent var
3635028
Adjusted Rsquared
0791214
SD dependent var
1029830
SE of regression
4668513
Akaike info criterion
1519224
Sum squared resid
6320554
Schwarz criterion
1528475
Log likelihood
2334797
HannanQuinn criter
1522240
Fstatistic
1146875
DurbinWatson stat
1562975
Prob(Fstatistic)
0000000
Unweighted Statistics
Rsquared
0834850
Mean dependent var
4443526
Adjusted Rsquared
0829156
SD dependent var
1972072
SE of regression
8151229
Sum squared resid
19268334
DurbinWatson stat
1678365
模型进行White检验：
Heteroskedasticity Test White
Fstatistic
0299790
Prob F(327)
08252
Obs*Rsquared
0999322
Prob ChiSquare(3)
08014
Scaled explained SS
1789507
Prob ChiSquare(3)
06172
Test Equation
Dependent Variable WGT_RESID^2
Method Least Squares
Date 121014 Time 2129
Sample 1 31
Included observations 31
Variable
Coefficient
Std Error
tStatistic
Prob
C
1116618
5498557
0203075
08406
WGT^2
4262202
2240181
0190262
08505
X^2*WGT^2
0194888
0516395
0377402
07088
X*WGT^2
5832151
2082820
0280012
07816
Rsquared
0032236
Mean dependent var
2038888
Adjusted Rsquared
0075293
SD dependent var
4192820
SE of regression
4347801
Akaike info criterion
2892298
Sum squared resid
510E+12
Schwarz criterion
2910801
Log likelihood
4443062
HannanQuinn criter
2898330
Fstatistic
0299790
DurbinWatson stat
1835854
Prob(Fstatistic)
0825233
知nR20999322较计算统计量界值nR20999322<005（2）59915接受原假设该模型消异方差
估计结果：
Y1557040X6931946
t（1070922）（1841272）
R20798173 F1146875 DW1562975
③权数w31sqr（x）回分析：
Dependent Variable Y
Method Least Squares
Date 120914 Time 2135
Sample 1 31
Included observations 31
Weighting series W3
Variable
Coefficient
Std Error
tStatistic
Prob
X
1330130
0098345
1352507
00000
C
4740242
3131154
0151390
08807
Weighted Statistics
Rsquared
0863161
Mean dependent var
4164118
Adjusted Rsquared
0858442
SD dependent var
9912079
SE of regression
5869555
Akaike info criterion
1565012
Sum squared resid
9990985
Schwarz criterion
1574263
Log likelihood
2405768
HannanQuinn criter
1568027
Fstatistic
1829276
DurbinWatson stat
1237664
Prob(Fstatistic)
0000000
Unweighted Statistics
Rsquared
0890999
Mean dependent var
4443526
Adjusted Rsquared
0887240
SD dependent var
1972072
SE of regression
6622171
Sum squared resid
12717412
DurbinWatson stat
1314859
模型进行White检验：
Heteroskedasticity Test White
Fstatistic
0423886
Prob F(228)
06586
Obs*Rsquared
0911022
Prob ChiSquare(2)
06341
Scaled explained SS
2768332
Prob ChiSquare(2)
02505
Test Equation
Dependent Variable WGT_RESID^2
Method Least Squares
Date 120914 Time 2036
Sample 1 31
Included observations 31
Collinear test regressors dropped from specification
Variable
Coefficient
Std Error
tStatistic
Prob
C
1212308
2141958
0565981
05759
WGT^2
7156730
1301839
0549740
05869
X^2*WGT^2
0015194
0082276
0184677
08548
Rsquared
0029388
Mean dependent var
3222898
Adjusted Rsquared
0039942
SD dependent var
8633567
SE of regression
8804298
Akaike info criterion
3030597
Sum squared resid
217E+13
Schwarz criterion
3044475
Log likelihood
4667426
HannanQuinn criter
3035121
Fstatistic
0423886
DurbinWatson stat
1887426
Prob(Fstatistic)
0658628
知nR20911022较计算统计量界值nR20911022<005（2）59915接受原假设该模型消异方差
估计结果：
Y1330130X4740242
t（1352507）（0151390）
R20863161 F1829276 DW1237664
检验发现权数w1效果综知修改结果：
Y1425859X3348131
t（1197157）（0972298）
R20875855 F1433184 DW1369081
56
(1)
a)Eviews模型分析：
Dependent Variable Y
Method Least Squares
Date 121014 Time 2016
Sample 1978 2011
Included observations 34
Variable
Coefficient
Std Error
tStatistic
Prob
X
0746241
0019120
3903027
00000
C
9255422
4280529
2162215
00382
Rsquared
0979426
Mean dependent var
1295802
Adjusted Rsquared
0978783
SD dependent var
1188791
SE of regression
1731597
Akaike info criterion
1320333
Sum squared resid
9594972
Schwarz criterion
1329311
Log likelihood
2224566
HannanQuinn criter
1323395
Fstatistic
1523362
DurbinWatson stat
1534491
Prob(Fstatistic)
0000000
回模型：
Y0746241 X+9255422
b)检验否存异方差：
①GoldfeldQuanadt检验：
1）定义区间113时软件分析：
Dependent Variable Y
Method Least Squares
Date 121114 Time 1147
Sample 1 13
Included observations 13
Variable
Coefficient
Std Error
tStatistic
Prob
X
0967839
0026879
3600771
00000
C
1886861
8963780
2104984
00591
Rsquared
0991587
Mean dependent var
2801377
Adjusted Rsquared
0990823
SD dependent var
1270409
SE of regression
1217039
Akaike info criterion
7976527
Sum squared resid
1629301
Schwarz criterion
8063442
Log likelihood
4984742
HannanQuinn criter
7958662
Fstatistic
1296555
DurbinWatson stat
1071505
Prob(Fstatistic)
0000000
∑e1i21629301
2）定义区间113时软件分析：
Dependent Variable Y
Method Least Squares
Date 121114 Time 1221
Sample 22 34
Included observations 13
Variable
Coefficient
Std Error
tStatistic
Prob
X
0719567
0058312
1233998
00000
C
1793950
2028764
0884258
03955
Rsquared
0932629
Mean dependent var
2496127
Adjusted Rsquared
0926504
SD dependent var
1022591
SE of regression
2772250
Akaike info criterion
1422817
Sum squared resid
8453904
Schwarz criterion
1431509
Log likelihood
9048313
HannanQuinn criter
1421031
Fstatistic
1522752
DurbinWatson stat
1658418
Prob(Fstatistic)
0000000
∑e2i28453904
3）根GoldfeldQuanadt检验F统计量：
F∑e2i2 ∑e1i2 8453904 16293015188669
α005水分子分母度均11查分布表界值F005（1111）447F5188669> F005（1111）447拒绝原假设检验表明模型存异方差
②White检验
EViews软件分析：
Heteroskedasticity Test White
Fstatistic
1036759
Prob F(231)
00004
Obs*Rsquared
1362701
Prob ChiSquare(2)
00011
Scaled explained SS
7613635
Prob ChiSquare(2)
00000
Test Equation
Dependent Variable RESID^2
Method Least Squares
Date 121114 Time 1256
Sample 1 34
Included observations 34
Variable
Coefficient
Std Error
tStatistic
Prob
C
1158111
2611711
0443430
06605
X
2769901
2786540
0994029
03279
X^2
0012230
0005156
2371861
00241
Rsquared
0400795
Mean dependent var
2822051
Adjusted Rsquared
0362136
SD dependent var
1017389
SE of regression
8125515
Akaike info criterion
2553267
Sum squared resid
205E+11
Schwarz criterion
2566735
Log likelihood
4310554
HannanQuinn criter
2557860
Fstatistic
1036759
DurbinWatson stat
3021651
Prob(Fstatistic)
0000357
图中出nR21362701较计算统计量界值nR21362701>005（2）59915拒绝原假设拒绝备择假设表明模型存异方差
两种方法检验模型存异方差
c)修正模型
1）加权二法修正异方差现象步骤：
①权数w11x时软件分析：
Dependent Variable Y
Method Least Squares
Date 121114 Time 1322
Sample 1 34
Included observations 34
Weighting series W1
Variable
Coefficient
Std Error
tStatistic
Prob
X
0821013
0016866
4867993
00000
C
1769318
6283256
2815926
00083
Weighted Statistics
Rsquared
0986676
Mean dependent var
4578505
Adjusted Rsquared
0986260
SD dependent var
4170384
SE of regression
3791285
Akaike info criterion
1016548
Sum squared resid
4599629
Schwarz criterion
1025527
Log likelihood
1708132
HannanQuinn criter
1019610
Fstatistic
2369735
DurbinWatson stat
0605852
Prob(Fstatistic)
0000000
Unweighted Statistics
Rsquared
0968070
Mean dependent var
1295802
Adjusted Rsquared
0967072
SD dependent var
1188791
SE of regression
2157175
Sum squared resid
1489089
DurbinWatson stat
1079107
方程模型：
Y0821013X1769318
t（4867993）（2815926）
R20986676 F2369735 DW0605852
模型进行White检验：
Heteroskedasticity Test White
Fstatistic
1348072
Prob F(231)
02745
Obs*Rsquared
2720457
Prob ChiSquare(2)
02566
Scaled explained SS
1221901
Prob ChiSquare(2)
05428
Test Equation
Dependent Variable WGT_RESID^2
Method Least Squares
Date 121114 Time 1120
Sample 1 34
Included observations 34
Collinear test regressors dropped from specification
Variable
Coefficient
Std Error
tStatistic
Prob
C
1678870
4165417
4030498
00003
WGT^2
3213071
1876175
0171257
08651
X*WGT^2
0484040
1279449
0378319
07078
Rsquared
0080013
Mean dependent var
1352832
Adjusted Rsquared
0020659
SD dependent var
1382825
SE of regression
1368467
Akaike info criterion
1736487
Sum squared resid
58053732
Schwarz criterion
1749955
Log likelihood
2922027
HannanQuinn criter
1741080
Fstatistic
1348072
DurbinWatson stat
1199640
Prob(Fstatistic)
0274545
图中出nR22720457较计算统计量界值
nR22720457<005（2）59915接受原假设该模型消异方差影响
②权数w21x2时软件分析：
Dependent Variable Y
Method Least Squares
Date 121114 Time 1327
Sample 1 34
Included observations 34
Weighting series W2
Variable
Coefficient
Std Error
tStatistic
Prob
X
0852193
0020150
4229335
00000
C
8890886
3604301
2466744
00192
Weighted Statistics
Rsquared
0982425
Mean dependent var
2302433
Adjusted Rsquared
0981875
SD dependent var
2471718
SE of regression
1620273
Akaike info criterion
8465259
Sum squared resid
8400912
Schwarz criterion
8555045
Log likelihood
1419094
HannanQuinn criter
8495879
Fstatistic
1788728
DurbinWatson stat
0604647
Prob(Fstatistic)
0000000
Unweighted Statistics
Rsquared
0954142
Mean dependent var
1295802
Adjusted Rsquared
0952709
SD dependent var
1188791
SE of regression
2585207
Sum squared resid
2138654
DurbinWatson stat
0781788
方程模型：
Y0852193X+8890886
t（4229335）（2466744）
R20982425 F1788728 DW0604647
White检验模型：
Heteroskedasticity Test White
Fstatistic
7462185
Prob F(330)
00007
Obs*Rsquared
1452935
Prob ChiSquare(3)
00023
Scaled explained SS
1940139
Prob ChiSquare(3)
00002
Test Equation
Dependent Variable WGT_RESID^2
Method Least Squares
Date 121114 Time 1119
Sample 1 34
Included observations 34
Variable
Coefficient
Std Error
tStatistic
Prob
C
7684700
8576169
0089605
09292
WGT^2
6420016
9611160
0667975
05093
X^2*WGT^2
0006306
0003431
1838317
00759
X*WGT^2
1247222
1163558
1071903
02923
Rsquared
0427334
Mean dependent var
2470857
Adjusted Rsquared
0370067
SD dependent var
4354791
SE of regression
3456323
Akaike info criterion
1463876
Sum squared resid
3583851
Schwarz criterion
1481833
Log likelihood
2448589
HannanQuinn criter
1470000
Fstatistic
7462185
DurbinWatson stat
1586012
Prob(Fstatistic)
0000712
图中出nR21452935较计算统计量界值nR21452935>005（2）59915拒绝原假设拒绝备择假设表明模型存异方差模型未消异方差
③权数w31sqr(x)时软件分析：
Dependent Variable Y
Method Least Squares
Date 121114 Time 1321
Sample 1 34
Included observations 34
Weighting series W3
Variable
Coefficient
Std Error
tStatistic
Prob
X
0778551
0015677
4966347
00000
C
4045770
1457528
2775775
00091
Weighted Statistics
Rsquared
0987192
Mean dependent var
7763266
Adjusted Rsquared
0986792
SD dependent var
3673152
SE of regression
7919828
Akaike info criterion
1163881
Sum squared resid
2007158
Schwarz criterion
1172859
Log likelihood
1958597
HannanQuinn criter
1166943
Fstatistic
2466460
DurbinWatson stat
1178340
Prob(Fstatistic)
0000000
Unweighted Statistics
Rsquared
0977590
Mean dependent var
1295802
Adjusted Rsquared
0976890
SD dependent var
1188791
SE of regression
1807210
Sum squared resid
1045123
DurbinWatson stat
1460832
方程模型：
Y0778551X+4045770
t（4966347）（2775775）
R20986792 F2466460 DW1178340
模型进行White检验：
Heteroskedasticity Test White
Fstatistic
8158958
Prob F(231)
00014
Obs*Rsquared
1172514
Prob ChiSquare(2)
00028
Scaled explained SS
2808353
Prob ChiSquare(2)
00000
Test Equation
Dependent Variable WGT_RESID^2
Method Least Squares
Date 121014 Time 1323
Sample 1 34
Included observations 34
Collinear test regressors dropped from specification
Variable
Coefficient
Std Error
tStatistic
Prob
C
7585186
5311263
1428132
01633
WGT^2
2468369
1996041
1236632
02255
X^2*WGT^2
0009139
0002481
3684177
00009
Rsquared
0344857
Mean dependent var
5903405
Adjusted Rsquared
0302590
SD dependent var
1393464
SE of regression
1163697
Akaike info criterion
2164586
Sum squared resid
420E+09
Schwarz criterion
2178054
Log likelihood
3649796
HannanQuinn criter
2169179
Fstatistic
8158958
DurbinWatson stat
2344068
Prob(Fstatistic)
0001423
图中出nR21172514较计算统计量界值nR21172514>005（2）59915拒绝原假设拒绝备择假设表明模型存异方差模型未消异方差
综述加权二法w1效果模型：
方程模型：
Y0821013X1769318
t（4867993）（2815926）
R20986676 F2369735 DW0605852
2）数模型法
软件分析：
Dependent Variable LNY
Method Least Squares
Date 121114 Time 0954
Sample 1 34
Included observations 34
Variable
Coefficient
Std Error
tStatistic
Prob
LNX
0946887
0011228
8433549
00000
C
0201861
0077905
2591100
00143
Rsquared
0995521
Mean dependent var
6687779
Adjusted Rsquared
0995381
SD dependent var
1067124
SE of regression
0072525
Akaike info criterion
2352753
Sum squared resid
0168315
Schwarz criterion
2262967
Log likelihood
4199680
HannanQuinn criter
2322134
Fstatistic
7112475
DurbinWatson stat
0812150
Prob(Fstatistic)
0000000
模型：
LnY0946887 LNX+0201861
模型进行White检验：
Heteroskedasticity Test White
Fstatistic
1003964
Prob F(231)
03780
Obs*Rsquared
2068278
Prob ChiSquare(2)
03555
Scaled explained SS
1469638
Prob ChiSquare(2)
04796
Test Equation
Dependent Variable RESID^2
Method Least Squares
Date 121114 Time 0955
Sample 1 34
Included observations 34
Variable
Coefficient
Std Error
tStatistic
Prob
C
0039547
0046759
0845753
04042
LNX
0011601
0014012
0827969
04140
LNX^2
0000932
0001028
0906774
03715
Rsquared
0060832
Mean dependent var
0004950
Adjusted Rsquared
0000240
SD dependent var
0006365
SE of regression
0006364
Akaike info criterion
7192271
Sum squared resid
0001255
Schwarz criterion
7057592
Log likelihood
1252686
HannanQuinn criter
7146342
Fstatistic
1003964
DurbinWatson stat
2022904
Prob(Fstatistic)
0378027
图中出nR22068278较计算统计量界值nR22068278<005（2）59915接受原假设模型消异方差
综合两种方法改进模型：
LnY0946887 LNX+0201861
(2)
1）考虑价格素首先软件三者关系进行分析：
Dependent Variable Y
Method Least Squares
Date 121214 Time 1926
Sample 1 34
Included observations 34
Variable
Coefficient
Std Error
tStatistic
Prob
X
0741684
0019905
3726095
00000
P
0235025
0271701
0865012
03937
C
4341715
7122946
0609539
05466
Rsquared
0979911
Mean dependent var
1295802
Adjusted Rsquared
0978615
SD dependent var
1188791
SE of regression
1738449
Akaike info criterion
1323830
Sum squared resid
9368837
Schwarz criterion
1337298
Log likelihood
2220511
HannanQuinn criter
1328423
Fstatistic
7560627
DurbinWatson stat
1681521
Prob(Fstatistic)
0000000
1）GoldfeldQuanadt检验：
①样113时进行回分析：
Dependent Variable P
Method Least Squares
Date 121414 Time 1926
Sample 1 13
Included observations 13
Variable
Coefficient
Std Error
tStatistic
Prob
X
0170484
0203868
0836247
04225
Y
0458660
0209755
2186646
00536
C
5950496
7385841
8056627
00000
Rsquared
0956255
Mean dependent var
1353231
Adjusted Rsquared
0947506
SD dependent var
3695380
SE of regression
8466678
Akaike info criterion
7309328
Sum squared resid
7168464
Schwarz criterion
7439701
Log likelihood
4451063
HannanQuinn criter
7282530
Fstatistic
1092993
DurbinWatson stat
0637181
Prob(Fstatistic)
0000000
∑e1i27168464
②样2234时做回分析：
Dependent Variable Y
Method Least Squares
Date 121414 Time2039
Sample 22 34
Included observations 13
Variable
Coefficient
Std Error
tStatistic
Prob
X
0641197
0092678
6918569
00000
P
1206222
1114278
1082514
03044
C
7956887
6038605
1317670
02170
Rsquared
0939696
Mean dependent var
2496127
Adjusted Rsquared
0927635
SD dependent var
1022591
SE of regression
2750847
Akaike info criterion
1427121
Sum squared resid
7567157
Schwarz criterion
1440158
Log likelihood
8976286
HannanQuinn criter
1424441
Fstatistic
7791291
DurbinWatson stat
1128778
Prob(Fstatistic)
0000001
∑e2i27567157
③根GoldfeldQuanadt检验F统计量：
F∑e2i2 ∑e1i2 7567157 716846410556176
α005水分子分母度均11查分布表界值F005（1010）298F10556176> F005（1010）298拒绝原假设检验表明模型存异方差
2）White检验软件分析结果：
Heteroskedasticity Test White
Fstatistic
7312529
Prob F(528)
00002
Obs*Rsquared
1925463
Prob ChiSquare(5)
00017
Scaled explained SS
1193072
Prob ChiSquare(5)
00000
Test Equation
Dependent Variable RESID^2
Method Least Squares
Date 121214 Time 1931
Sample 1 34
Included observations 34
Variable
Coefficient
Std Error
tStatistic
Prob
C
7954108
1126473
0706107
04860
X
2094964
6390400
3278298
00028
X^2
0024133
0010712
2252841
00323
X*P
0235137
0106647
2204822
00358
P
1175326
1156253
1016495
03181
P^2
1637366
2600020
0629751
05340
Rsquared
0566313
Mean dependent var
2755540
Adjusted Rsquared
0488869
SD dependent var
1079909
SE of regression
7720644
Akaike info criterion
2550514
Sum squared resid
167E+11
Schwarz criterion
2577450
Log likelihood
4275874
HannanQuinn criter
2559700
Fstatistic
7312529
DurbinWatson stat
2787044
Prob(Fstatistic)
0000171
图中出nR21925463较计算统计量界值nR21925463>005（5）110705拒绝原假设拒绝备择假设表明模型存异方差
2）修正
①建立数模型软件分析：
Dependent Variable LNY
Method Least Squares
Date 121214 Time 1924
Sample 1 34
Included observations 34
Variable
Coefficient
Std Error
tStatistic
Prob
LNX
0939605
0013645
6886088
00000
LNP
0026821
0028454
0942609
03532
C
0108230
0126322
0856784
03981
Rsquared
0995646
Mean dependent var
6687779
Adjusted Rsquared
0995365
SD dependent var
1067124
SE of regression
0072652
Akaike info criterion
2322188
Sum squared resid
0163625
Schwarz criterion
2187509
Log likelihood
4247720
HannanQuinn criter
2276259
Fstatistic
3544292
DurbinWatson stat
0930109
Prob(Fstatistic)
0000000
模型进行White检验：
Heteroskedasticity Test White
Fstatistic
3523832
Prob F(528)
00135
Obs*Rsquared
1313158
Prob ChiSquare(5)
00222
Scaled explained SS
1214373
Prob ChiSquare(5)
00329
Test Equation
Dependent Variable RESID^2
Method Least Squares
Date 121214 Time 1924
Sample 1 34
Included observations 34
Variable
Coefficient
Std Error
tStatistic
Prob
C
0422872
0273746
1544759
01336
LNX
0080712
0031833
2535502
00171
LNX^2
0003917
0003037
1289564
02078
LNX*LNP
0004955
0005136
0964765
03429
LNP
0254992
0129858
1963631
00596
LNP^2
0026470
0012675
2088390
00460
Rsquared
0386223
Mean dependent var
0004813
Adjusted Rsquared
0276620
SD dependent var
0007286
SE of regression
0006197
Akaike info criterion
7170690
Sum squared resid
0001075
Schwarz criterion
6901332
Log likelihood
1279017
HannanQuinn criter
7078831
Fstatistic
3523832
DurbinWatson stat
2264261
Prob(Fstatistic)
0013502
图中出nR21313158较计算统计量界值nR21313158>005（5）110705拒绝原假设拒绝备择假设表明模型存异方差模型没消异方差
②w11x时软件分析：
Dependent Variable Y
Method Least Squares
Date 121314 Time 1849
Sample 1 34
Included observations 34
Weighting series W1
Variable
Coefficient
Std Error
tStatistic
Prob
X
0723218
0022965
3149212
00000
P
0719506
0141085
5099795
00000
C
4472084
1311268
3410502
00018
Weighted Statistics
Rsquared
0992755
Mean dependent var
4578505
Adjusted Rsquared
0992287
SD dependent var
4170384
SE of regression
2840494
Akaike info criterion
9615100
Sum squared resid
2501205
Schwarz criterion
9749779
Log likelihood
1604567
HannanQuinn criter
9661030
Fstatistic
2123843
DurbinWatson stat
1298389
Prob(Fstatistic)
0000000
Unweighted Statistics
Rsquared
0977704
Mean dependent var
1295802
Adjusted Rsquared
0976266
SD dependent var
1188791
SE of regression
1831446
Sum squared resid
1039800
DurbinWatson stat
1740795
模型：
Y0723218X+0719506p4472084
模型进行White检验：
Heteroskedasticity Test White
Fstatistic
2088840
Prob F(528)
00966
Obs*Rsquared
9236835
Prob ChiSquare(5)
01000
Scaled explained SS
2550696
Prob ChiSquare(5)
00001
Test Equation
Dependent Variable WGT_RESID^2
Method Least Squares
Date 121414 Time 1957
Sample 1 34
Included observations 34
Collinear test regressors dropped from specification
Variable
Coefficient
Std Error
tStatistic
Prob
C
3861793
1068806
3613183
00012
WGT^2
3260199
4309988
0756429
04557
X*WGT^2
1372241
8453473
1623287
01157
X*P*WGT^2
0151725
0061588
2463567
00202
P^2*WGT^2
0431162
0278315
1549186
01326
P*WGT^2
7613221
7340636
1037134
03085
Rsquared
0271672
Mean dependent var
7356486
Adjusted Rsquared
0141613
SD dependent var
1924655
SE of regression
1783177
Akaike info criterion
1796897
Sum squared resid
89032169
Schwarz criterion
1823832
Log likelihood
2994724
HannanQuinn criter
1806082
Fstatistic
2088840
DurbinWatson stat
2336495
Prob(Fstatistic)
0096616
nR29236835<005（5）110705接受原假设该模型存异方差模型消异方差
③w21x2软件分析：
Dependent Variable Y
Method Least Squares
Date 121514 Time 2002
Sample 1 34
Included observations 34
Weighting series W2
Variable
Coefficient
Std Error
tStatistic
Prob
X
0639012
0039216
1629477
00000
P
1200751
0206023
5828234
00000
C
8185973
1577499
5189209
00000
Weighted Statistics
Rsquared
0991614
Mean dependent var
2302433
Adjusted Rsquared
0991073
SD dependent var
2471718
SE of regression
1137136
Akaike info criterion
7784170
Sum squared resid
4008543
Schwarz criterion
7918849
Log likelihood
1293309
HannanQuinn criter
7830100
Fstatistic
1832775
DurbinWatson stat
1167961
Prob(Fstatistic)
0000000
Unweighted Statistics
Rsquared
0956816
Mean dependent var
1295802
Adjusted Rsquared
0954030
SD dependent var
1188791
SE of regression
2548849
Sum squared resid
2013955
DurbinWatson stat
1002870
模型：
Y0639012X+1200751p8185973
该模型进行White检验：
Heteroskedasticity Test White
Fstatistic
4319853
Prob F(627)
00000
Obs*Rsquared
3079235
Prob ChiSquare(6)
00000
Scaled explained SS
4742430
Prob ChiSquare(6)
00000
Test Equation
Dependent Variable WGT_RESID^2
Method Least Squares
Date 121414 Time 1920
Sample 1 34
Included observations 34
Variable
Coefficient
Std Error
tStatistic
Prob
C
2751002
2012556
1366919
01829
WGT^2
1245193
8372352
1487268
01485
X^2*WGT^2
0007732
0005450
1418649
01674
X*WGT^2
7948582
4884597
1627275
01153
X*P*WGT^2
0111755
0064061
1744525
00924
P^2*WGT^2
0184342
0164562
1120199
02725
P*WGT^2
3127017
2356724
0132685
08954
Rsquared
0905657
Mean dependent var
1178983
Adjusted Rsquared
0884692
SD dependent var
2303570
SE of regression
7822224
Akaike info criterion
1173823
Sum squared resid
1652054
Schwarz criterion
1205248
Log likelihood
1925498
HannanQuinn criter
1184539
Fstatistic
4319853
DurbinWatson stat
1794799
Prob(Fstatistic)
0000000
nR23079235>005（5）110705拒绝原假设拒绝备择假设表明模型存异方差模型没消异方差
④w31sqr(x)时软件分析：
Dependent Variable Y
Method Least Squares
Date 121414 Time 1906
Sample 1 34
Included observations 34
Weighting series W3
Variable
Coefficient
Std Error
tStatistic
Prob
X
0744661
0019825
3756252
00000
P
0451861
0179971
2510739
00175
C
1349643
2537768
0531823
05986
Weighted Statistics
Rsquared
0989356
Mean dependent var
7763266
Adjusted Rsquared
0988670
SD dependent var
3673152
SE of regression
7335237
Akaike info criterion
1151252
Sum squared resid
1667977
Schwarz criterion
1164720
Log likelihood
1927129
HannanQuinn criter
1155845
Fstatistic
1440783
DurbinWatson stat
1599590
Prob(Fstatistic)
0000000
Unweighted Statistics
Rsquared
0979407
Mean dependent var
1295802
Adjusted Rsquared
0978079
SD dependent var
1188791
SE of regression
1760098
Sum squared resid
9603626
DurbinWatson stat
1761225
模型：
Y0744661X+0451861p1349643
模型进行White检验：
Heteroskedasticity Test White
Fstatistic
4459272
Prob F(528)
00041
Obs*Rsquared
1507219
Prob ChiSquare(5)
00101
Scaled explained SS
7239077
Prob ChiSquare(5)
00000
Test Equation
Dependent Variable WGT_RESID^2
Method Least Squares
Date 121414 Time 1908
Sample 1 34
Included observations 34
Collinear test regressors dropped from specification
Variable
Coefficient
Std Error
tStatistic
Prob
C
6116322
2753193
2221538
00346
WGT^2
2825198
1735039
1628320
01147
X^2*WGT^2
0001093
0006624
0164950
08702
X*P*WGT^2
0235836
0077110
3058447
00049
P^2*WGT^2
1236884
0644872
1918030
00654
P*WGT^2
5033080
2625884
1916718
00655
Rsquared
0443300
Mean dependent var
4905814
Adjusted Rsquared
0343889
SD dependent var
1692697
SE of regression
1371096
Akaike info criterion
2204856
Sum squared resid
526E+09
Schwarz criterion
2231792
Log likelihood
3688256
HannanQuinn criter
2214042
Fstatistic
4459272
DurbinWatson stat
2450171
Prob(Fstatistic)
0004103
nR21507219>005（5）110705拒绝原假设拒绝备择假设表明模型存异方差模型没消异方差
综述修改模型：
Y Y0723218X+0719506p4472084
t(3149212) (5099705) (3410502)
R20992755 F2123843 DW1298389
(3)体会：模型采取数模型法者加权二法具异方差性模型进行改进消异方差模型度导致改进方法改进模型进行进步检验行
61
(1)建立居民收入消费模型Eviews分析结果：
Dependent Variable Y
Method Least Squares
Date 122014 Time 1422
Sample 1 19
Included observations 19
Variable
Coefficient
Std Error
tStatistic
Prob
X
0690488
0012877
5362068
00000
C
7993004
1239919
6446390
00000
Rsquared
0994122
Mean dependent var
7002747
Adjusted Rsquared
0993776
SD dependent var
2464491
SE of regression
1944245
Akaike info criterion
8872095
Sum squared resid
6426149
Schwarz criterion
8971510
Log likelihood
8228490
HannanQuinn criter
8888920
Fstatistic
2875178
DurbinWatson stat
0574663
Prob(Fstatistic)
0000000
模型：
Y0690488X+7993004
Se(0012877)(1239919)
t(5362068)(6446390)
R20994122 F2875178 DW0574663
（2）
1）检验模型中存问题
①做出残差图：
残差变动系统模式连续正连续负表明残差项存阶相关
②该回方程决系数较高回系数均显著样量19解释变量模型5显著水查DW统计表知dL1180dU1401模型中DW0574663< dL显然模型中相关
③模型进行BG检验Eviews分析结果：
BreuschGodfrey Serial Correlation LM Test
Fstatistic
4811108
Prob F(215)
00243
Obs*Rsquared
7425088
Prob ChiSquare(2)
00244
Test Equation
Dependent Variable RESID
Method Least Squares
Date 122014 Time 1503
Sample 1 19
Included observations 19
Presample missing value lagged residuals set to zero
Variable
Coefficient
Std Error
tStatistic
Prob
X
0003275
0010787
0303586
07656
C
1929546
1035593
0186323
08547
RESID(1)
0608886
0292707
2080189
00551
RESID(2)
0089988
0291120
0309110
07615
Rsquared
0390794
Mean dependent var
165E13
Adjusted Rsquared
0268953
SD dependent var
1889466
SE of regression
1615518
Akaike info criterion
8587023
Sum squared resid
3914848
Schwarz criterion
8785852
Log likelihood
7757671
HannanQuinn criter
8620672
Fstatistic
3207406
DurbinWatson stat
1570723
Prob(Fstatistic)
0053468
表显示LMTR27425088p值00244表明存相关
2）模型进行处理：
①采取广义差分法
a)估计相关系数ρet进行滞期回EViews分析结果：
Dependent Variable E
Method Least Squares
Date 122014 Time 1504
Sample (adjusted) 2 19
Included observations 18 after adjustments
Variable
Coefficient
Std Error
tStatistic
Prob
E(1)
0657352
0177626
3700759
00018
Rsquared
0440747
Mean dependent var
1717433
Adjusted Rsquared
0440747
SD dependent var
1785134
SE of regression
1334980
Akaike info criterion
8074833
Sum squared resid
3029692
Schwarz criterion
8124298
Log likelihood
7167349
HannanQuinn criter
8081653
DurbinWatson stat
1634573
知ρ0657352
b)原模型进行广义差分回Eviews进行分析结果：
Dependent Variable Y0657352*Y(1)
Method Least Squares
Date 122014 Time 1504
Sample (adjusted) 2 19
Included observations 18 after adjustments
Variable
Coefficient
Std Error
tStatistic
Prob
C
3597761
8103546
4439737
00004
X0657352*X(1)
0668695
0020642
3239512
00000
Rsquared
0984983
Mean dependent var
2781002
Adjusted Rsquared
0984044
SD dependent var
1051781
SE of regression
1328570
Akaike info criterion
8115693
Sum squared resid
2824158
Schwarz criterion
8214623
Log likelihood
7104124
HannanQuinn criter
8129334
Fstatistic
1049444
DurbinWatson stat
1830746
Prob(Fstatistic)
0000000
图知回方程：
Yt*3597761+0668695Xt*
Se(8103546)(0020642)
t(4439737)(3239512)
R20984983 F1049444 DW1830746
式中Yt*Yt0657352Yt1 Xt*Xt0657352Xt1
广义差分数样容量减少118查5显著水DW统计表知dL1158dU1391模型中DW1830746du
终消费模型：
Yt1049987+0668695Xt
②科克伦奥克特迭代法EVIews分析结果：
Dependent Variable Y
Method Least Squares
Date 122014 Time 1515
Sample (adjusted) 2 19
Included observations 18 after adjustments
Convergence achieved after 5 iterations
Variable
Coefficient
Std Error
tStatistic
Prob
C
1040449
2387618
4357687
00006
X
0669262
0020831
3212757
00000
AR(1)
0630015
0164218
3836462
00016
Rsquared
0997097
Mean dependent var
7191867
Adjusted Rsquared
0996710
SD dependent var
2389866
SE of regression
1370843
Akaike info criterion
8224910
Sum squared resid
2818814
Schwarz criterion
8373306
Log likelihood
7102419
HannanQuinn criter
8245372
Fstatistic
2575896
DurbinWatson stat
1787878
Prob(Fstatistic)
0000000
Inverted AR Roots
63
方程：
Yt1040449+0669262Xt
（3）济意义：均实际收入增加1元均说均时间消费支出增加0669262元
64
（1）
1）针数模型Eviews分析结果：
Dependent Variable LNY
Method Least Squares
Date 122714 Time 1613
Sample 1980 2000
Included observations 21
Variable
Coefficient
Std Error
tStatistic
Prob
LNX
0951090
0038897
2445123
00000
C
2171041
0241025
9007529
00000
Rsquared
0969199
Mean dependent var
8039307
Adjusted Rsquared
0967578
SD dependent var
0565486
SE of regression
0101822
Akaike info criterion
1640785
Sum squared resid
0196987
Schwarz criterion
1541307
Log likelihood
1922825
HannanQuinn criter
1619196
Fstatistic
5978626
DurbinWatson stat
1159788
Prob(Fstatistic)
0000000
模型：
lnY0951090lnX+2171041
se(0038897) (0241025)
t(2445123) (9007529)
R20969199 F5978626 DW1159788
2）检验模型相关性
该回方程决系数较高回系数均显著样量21解释变量模型5显著水查DW统计表知dL1221dU1420模型中DW1159788< dL显然模型中相关
(2)广义差分法处理模型：
1）估计相关系数ρet进行滞期回EViews分析结果：
Dependent Variable E
Method Least Squares
Date 122714 Time 1618
Sample (adjusted) 1982 2000
Included observations 19 after adjustments
Variable
Coefficient
Std Error
tStatistic
Prob
E(1)
0012872
0280581
0045878
09639
Rsquared
0000073
Mean dependent var
2556737
Adjusted Rsquared
0000073
SD dependent var
3977924
SE of regression
3977778
Akaike info criterion
1486086
Sum squared resid
2848090
Schwarz criterion
1491057
Log likelihood
1401782
HannanQuinn criter
1486927
DurbinWatson stat
1700254
知ρ0012872
2）原模型进行广义差分回Eviews进行分析结果：
Dependent Variable Y+0012872*Y(1)
Method Least Squares
Date 122714 Time 2106
Sample (adjusted) 1981 2000
Included observations 20 after adjustments
Variable
Coefficient
Std Error
tStatistic
Prob
C
1049645
1977928
0530679
06021
X+0012872*X(1)
6653757
0304157
2187605
00000
Rsquared
0963751
Mean dependent var
3753934
Adjusted Rsquared
0961737
SD dependent var
2045606
SE of regression
4001404
Akaike info criterion
1491615
Sum squared resid
2882022
Schwarz criterion
1501572
Log likelihood
1471615
HannanQuinn criter
1493559
Fstatistic
4785614
DurbinWatson stat
1822259
Prob(Fstatistic)
0000000
图知回方程：
Yt*1049645+6653757Xt*
Se(1977928)( 0304157)
t(0530679)( 2187605)
R20963751 F4785614DW18222596
式中Yt*Yt+0012872Yt1 Xt*Xt+0012872Xt1
广义差分数样容量减少120查5显著水DW统计表知dL1201dU1411模型中DW18222596du
终模型：
Yt1036306+6653757Xt
（3）模型Eviews分析结果：
Dependent Variable LNY1
Method Least Squares
Date 122714 Time 2216
Sample (adjusted) 1981 2000
Included observations 20 after adjustments
Variable
Coefficient
Std Error
tStatistic
Prob
LNX1
0442224
0066024
6697901
00000
C
0054047
0013322
4056896
00007
Rsquared
0713658
Mean dependent var
0091592
Adjusted Rsquared
0697750
SD dependent var
0098311
SE of regression
0054049
Akaike info criterion
2903219
Sum squared resid
0052583
Schwarz criterion
2803646
Log likelihood
3103219
HannanQuinn criter
2883781
Fstatistic
4486188
DurbinWatson stat
1590363
Prob(Fstatistic)
0000003
题目知模型样容量20查5显著水DW统计表知dL1201dU1411模型中DW1590363du
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