resid Log -79.196 F-statistic 0.539likelihoo73 021 d
Durbin-Wa1.59284 Prob(F-statist0.592tson stat 5 ic) 965 结果还是显示无异方差。故可以认为不存在异方差。 （2）去掉智利的数据之后再来回归：
Dependent Variable: Y Method: Least Squares
Date: 05/15/03 Time: 17:16 Sample(adjusted): 1 19
Included observations: 19 after adjusting endpoints Variable CoefficStd. t-StatiProb.ient Error stic X 0.221480.5550.398660.6954 568 3 1
C 6.738082.3842.825350.011
2 860 8 7 R-squared 0.00926 Mean dependent 7.6362 var 842
Adjusted -0.0490 S.D. dependent 3.310R-squared 16 var 457 S.E. of 3.39061 Akaike info 5.379regressio9 criterion 203 n Sum 195.437 Schwarz 5.478squared 1 criterion 618 resid Log -49.102 F-statistic 0.158likelihoo43 932 d
Durbin-Wa2.61990 Prob(F-statist0.695tson stat 2 ic) 105 结果是回归中斜率系数不显著。可决系数非常低。F检验没有通过。不过这时候再来分析一下残差。做ARCH检验：
ARCH Test: F-statist0.63824 Probability 0.604ic 9 727 Obs*R-squ2.20168 Probability 0.531ared 9 616 Test Equation:
Dependent Variable: RESID^2 Method: Least Squares
Date: 05/15/03 Time: 17:20 Sample(adjusted): 4 19
Included observations: 16 after adjusting endpoints Variable CoefficStd. t-StatiProb.ient Error stic C 12.26196.9751.757790.1040 750 0 2
RESID^2(-0.186870.2930.637560.535
1) 5 106 8 7 RESID^2(--0.34730.279-1.24050.238
2) 16 965 70 5 RESID^2(--0.02060.305-0.06760.947
3) 63 449 48 2 R-squared 0.13760 Mean dependent 10.026 var 876
Adjusted -0.0779 S.D. dependent 13.54R-squared 93 var 799 S.E. of 14.0664 Akaike info 8.337regressio0 criterion 773 n Sum 2374.36 Schwarz 8.530squared 3 criterion 920 resid Log -62.702 F-statistic 0.638likelihoo18 249 d
Durbin-Wa1.87281 Prob(F-statist0.604tson stat 9 ic) 727 仍然显示有无方差存在。做White检验来验证： White Heteroskedasticity Test: F-statist0.23185 Probability 0.795ic 4 680 Obs*R-squ0.53514 Probability 0.765ared 4 235 Test Equation:
Dependent Variable: RESID^2 Method: Least Squares
Date: 05/15/03 Time: 17:22 Sample: 1 19
Included observations: 19 Variable
C X X^2 R-squared Adjusted R-squared S.E. of regression Sum 2724.77 Schwarz 8.268squared 9 criterion 492 resid Log -74.134 F-statistic 0.231likelihoo02 854 d
Durbin-Wa1.77979 Prob(F-statist0.795tson stat 8 ic) 680 结果还是表明无异方差存在。 8. 解答：用Y，X2，X3，X4，X5，X6分别代表农业总产值、农用化肥量、农田水利、农业劳动力、户均固定资产以及农机动力。 （1）建立我国北方地区农业产出线性模型：
Y??1??2X2??3X3??4X4??5X5??6X6?uCoefficient 10.24930
1.15220
6
-0.2517
34 0.028165
-0.0933
14 13.0498
5 Std. t-StatiError stic 20.830.49187712 7 8.8390.13034454 8 0.873-0.2881604 56 Mean dependent var
S.D. dependent var
Akaike info criterion Prob.
0.6295 0.897
9 0.776
9 10.28616 12.48054 8.119370
（8.1）
对（8.1）式回归，结果如下：
Dependent Variable: Y Method: Least Squares
Date: 05/15/03 Time: 21:58 Sample: 1 12
Included observations: 12 Variable CoefficStd. ient Error X2 0.039610.0276 270
X3 -0.03680.077
96 704
X4 0.263230.549
9 474
t-Statistic 1.452738 -0.4748
23 0.47907
6 Prob. 0.1965 0.651
7 0.648
8
X5 X6 C R-squared Adjusted R-squared S.E. of regression Sum 1663.31 Schwarz 9.011squared 3 criterion 991 resid Log -46.617 F-statistic 45.93likelihoo22 115 d
Durbin-Wa1.96991 Prob(F-statist0.000tson stat 6 ic) 105 从回归结果可以看出存在明显的多重共线性。先来修正共线性。作相关系数矩阵如下： Y X2 X3 X4 X5 X6 Y 1.00 0.93 0.84 0.96 0.68 0.93
0000 1484 9853 4915 7198 2993
X 0.93 1.00 0.85 0.96 0.45 0.892 1484 0000 1861 3168 6890 2501 X 0.84 0.85 1.00 0.84 0.54 0.853 9853 1861 0000 3541 9390 6933 X 0.96 0.96 0.84 1.00 0.58 0.924 4915 3168 3541 0000 3048 4806 X 0.68 0.45 0.54 0.58 1.00 0.545 7198 6890 9390 3048 0000 3765 X 0.93 0.89 0.85 0.92 0.54 1.006 2993 2501 6933 4806 3765 0000 从表中知道，Y与上面各个变量都具有较强的相关性。在各个解释变量之间，X2与X3、X4、X6，X3与X4、X6，X4与X6，X5与各个变量的相关性不是很强，而X6同各个变量（除了X5）都比较强。所以我们在原模型中去掉X4、X3、X6，再回归，看看结果如何：
Dependent Variable: Y Method: Least Squares
Date: 05/15/03 Time: 23:07 Sample: 1 12
0.01346
4
0.02546
9
4.71630
2 0.974539
0.95332
2
16.6498
9 0.0042.71303963 0 0.0151.62602663 1 9.1250.51681757 2 Mean dependent var
S.D. dependent var
Akaike info criterion 0.035
0 0.155
1 0.623
8 96.62750 77.06446 8.769537
Included observations: 12 Variable Coefficient X2 0.070443
X5 0.01697
3
C 12.2652
2 R-squared 0.954159
Adjusted 0.94397R-squared 2 S.E. of 18.2413regressio4 n Sum 2994.71squared 7 resid Log -50.145likelihoo45 d
Durbin-Wa2.51889tson stat 6 从回归结果看，效果良好。现在就以
Std. t-StatiError stic 0.0079.72703242 6 0.0044.12091119 8 8.1821.49898325 9 Mean dependent var
S.D. dependent var
Akaike info criterion Schwarz criterion F-statistic
Prob. 0.0000 0.002
6 0.168
1 96.62750 77.06446 8.857576 8.978802 93.66521 0.000001 Prob(F-statistic) Y??1??2X2??5X5?u为基本模型。
（2）检查有无异方差。
同时做ARCH检验和White检验。结果如下： ARCH Test: F-statisti0.437211 Probability c
Obs*R-squa0.509612 Probability red Test Equation:
Dependent Variable: RESID^2 Method: Least Squares
Date: 05/15/03 Time: 23:15 Sample(adjusted): 2 12
Included observations: 11 after adjusting endpoints Variable CoefficieStd. t-Statistnt Error ic C 328.1191 176.351.860514 0.525036 0.4753
07 Prob. 0.0957