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+0128360x 1
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+0331971x 2
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+0387276x 3
（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（β 1）4711834>t 0025 (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（β 2）7115308>t 0025 (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（β 3）4825285>t 0025 (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>t 0025 (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） 2
δ2
x(n— 1) 7608021 2
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： lnY0980275lnX1918289②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（β 2） 2858268>t 0025 (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 Y18454756418400X x45 y1556647
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） 2
δ2
x(n— 1) 1989419 2
x (12— 1)435357
(Xf— X)2(45— 3523333 )2095387843
Xf45 时相关数代入计算：
1556647 — 2228x3173600 x√112+435357095387843 ≤
Yf ≤1556647 +2228x3173600 x√ 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+5996865X 2 0524027 X 32265680 X 4
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 4749476 4265020 2922950 4366842 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 X 22281005 LNX 32308481 LNX 4+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 0135474X 2 + 1885348X 3 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 1058454 t（ 15）2131系数显
著 X3 系数应 t 值 1928512 t（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 LNX 2+1760695 LNX 3
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 3777363 1757789 2581229 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 2944186 1006702 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 y TX T 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 0086450E 2 + 396e14
参数：斜率系数 α 0086450截距 396e14
（3）知 β2 α2 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 X1X2X3X4X5 X6 系数应 t 值分： 1254330 0490501 1005377
0951671 0476621 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 X 50054965 X 6+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 4679946 t（12 ）2179 系数显著
均 GDP 年底存款余额显著影响 X6 系数应 t 值 1762581 t
（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 LNGDP t0421791 LNCPI t3111486
（2）
① 该模型决系数 0988051 决系数高 F 检验值 9922582
明显显著 α 005 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 LNGDP t3750670
2）LNY2939295 LNCPI t6854535
3）LNGDP t2511022 LNCPI t2796381
②重线性认识：
单方程拟合效果回系数显著判定系数较高 GDP CPI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 CZZC GDP CZZC SSZE GDP SSZE 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：
0
5000
10000
15000
20000
25000
30000
1000 1500 2000 2500 3000 3500 4000
X
E2
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
∑ e1i
24002499
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
∑ e2i
26918280
3）根 GoldfeldQuanadt 检验 F 统计量：
F∑e2i
2
∑e 1i
2
6918280400249917285
α 005 水分子分母度均 4查分布表界值 F 005 （ 44）639
F17285< F 005 （ 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
0
1000000
2000000
3000000
4000000
5000000
6000000
0 2000 4000 6000 8000 10000
X
E2
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
∑ e1i
21772245
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
∑ e2i
27909670
3）根 GoldfeldQuanadt 检验 F 统计量：
F∑e2i
2 ∑e 1i
2 7909670 177224544631
α 005 水分子分母度均 10 查分布表界值 F 005 （ 1010 ）298
F44631> F 005 （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 nR 20649065 较计算 统计量界值 nR 20649065< 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 w21x 2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 nR 20999322 较计算 统计量界值 nR 20999322< 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 nR 20911022 较计算 统计量界值 nR 20911022< 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：
① GoldfeldQuanadt 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 ∑ e1i
21629301
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
∑ e2i
28453904
3）根 GoldfeldQuanadt 检验 F 统计量：
F∑e2i
2 ∑e 1i
2 8453904 16293015188669
α 005 水分子分母度均 11 查分布表界值 F 005 （ 1111 ）447
F5188669> F 005 （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 nR 21362701 较 计 算 统 计 量 界 值
nR 21362701> 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 nR 22720457 较计算 统计量界值 nR 22720457< 005 （2） 59915 接受原假设该模型消异方差影
响
②权数 w21x 2 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 nR 21452935 较 计 算 统 计 量 界 值
nR 21452935> 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 nR 21172514 较 计 算 统 计 量 界 值
nR 21172514> 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 nR 22068278 较 计 算 统 计 量 界 值
nR 22068278< 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
∑ e1i
27168464
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
∑ e2i
27567157
③根 GoldfeldQuanadt 检验 F 统计量：
F∑e2i
2 ∑e 1i
2 7567157 716846410556176
α 005 水分子分母度均 11 查分布表界值 F 005 （ 1010 ）298
F10556176> F 005 （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 nR 21925463 较 计 算 统 计 量 界 值
nR 21925463> 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 nR 21313158 较 计 算 统 计 量 界 值
nR 21313158> 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
② w11x 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
nR 29236835< 005 （5）110705 接受原假设该模型存异方差
模型消异方差③ w21x 2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
nR 23079235> 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
④ w31sqr(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 nR 21507219> 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：
40
30
20
10
0
10
20
30
40
50
2 4 6 8 10 12 14 16 18
Y Residuals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 dL1180 dU 1401 模型中 DW0574663< d L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 LMTR27425088 p 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 ρ e t 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+0668695X t*
Se(8103546)(0020642)
t(4439737)(3239512)
R20984983 F1049444 DW1830746
式中 Yt*Y t0657352Y t1 X t*X t0657352X t1
广义差分数样容量减少 1 18 查 5 显著水 DW 统计表
知 dL1158d U 1391 模型中 DW1830746 du
差分方程 β 13597761(10657352)1049987 终消费模型：
Yt1049987+0668695X t
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+0669262X t
（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)
R 20969199 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 dL1221 d U1420 模型中 DW1159788< d L显然模
型中相关
(2) 广义差分法处理模型：
1）估计相关系数 ρ e t 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+6653757X t*
Se(1977928)( 0304157)
t(0530679)( 2187605)
R20963751 F4785614DW18222596
式中 Yt*Y t+0012872Y t1 X t*Xt+0012872X t1
广义差分数样容量减少 1 20 查 5 显著水 DW 统计表
知 dL1201d U 1411 模型中 DW18222596 du
差分方程 β 11049645(1+0012872)1036306
终模型：
Yt1036306+6653757X t（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 d L1201d U1411
模型中 DW1590363 d u
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