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国民经济核算是反映国民经济运行状况的有效工具;国民经济核算是宏观经济管理的重要依据;国民经济核算是制定和检验国民经济计划的科学方法;国民经济核算是微观决策的重要依据。国民经济统计工作是整个统计工作的一个重要核心部分,而GNP又是国民经济生产统计中的一个重要目标,GNP是按国民原则计算的国民经济核算中的重要的综合指标,等于国内生产总值与国外净要素之和。虽然GDP是国民经济的最核心指标,但GNP又有其重要意义,比如,联合国根据连续六年的国民生产总值和人均国民生产总值来决定一个国家的会费;世界银行根据人均国民生产总值来决定一个国家所能享受的硬贷款、软贷款等优惠待遇;国际货币基金组织根据国民生产总值、黄金与外汇储备、进出口额、出口额占国民生产总值的比例等因素来决定一个国家在基金的份额,进而决定在基金的投票权、分配特别提款权的份额及向基金借款的份额等等,在这些方面直接影响到我国的经济利益和政治利益。所以,我们从《中国统计年鉴》(1999)上查找到1987--1998年的GNP,并找出一些变量建立多元线形回归模型对GNP进行研究。
我们选择选择人均主要产品产量作为影响GNP变化的变量,人均主要产品产量有粮食,棉花,油料,糖料,茶叶,水果,猪牛羊肉,水产品,布,机制纸及纸板,纱,原煤,原油,发电量,钢,水泥等,经过初步考虑,我们决定选用原煤,粮食和棉花作为建立模型所用的三个变量设为X2,X3,X4,设GNP为Y,数据如下:
Estimation Command:
=====================
LS Y C X2 X3 X4
Estimation Equation:
=====================
Y = C(1) + C(2)*X2 + C(3)*X3 + C(4)*X4
Substituted Coefficients:
=====================
Y = -306717.449 + 142124.3822*X2 + 570.9199106*X3 - 4222.676239*X4
Correlation Matrix
X2 X3 X4
X2 1.000000 0.684966 -0.226024
X3 0.684966 1.000000 -0.167105
X4 -0.226024 -0.167105 1.000000
^
Y=-306717+142124X2+570.9X3-4223X4
(2.738) (2.102)(-0.5073)
R2=0.8316 F=13.17
S=11743 DW=1.426
查表得Fα(r,n-k)=F0.05(4,8)=3.84,tα/2(n-k)=t0.025(8)=2.306,由于F> F0.05(4,8)=3.84,所以拒绝假设H0:β=0,模型在总体上显著。但是通过t值可以看出X3和X4无法通过显著性检验,说明这个模型建立的不是十分理想。我们进而考虑分别建立一个解释变量和两个解释变量的模型,利用Eviews可以得到如下估计结果:
1)对X2
Dependent Variable: Y
Method: Least Squares
Date: 12/13/03 Time: 17:43
Sample: 1987 1998 中国大学排名
Included observations: 12
Variable Coefficient Std. Error t-Statistic Prob.
C -180859.9 42190.69 -4.286725 0.0016
X2 220364.4 42122.47 5.231518 0.0004
R-squared 0.732397 Mean dependent var 38953.65
Adjusted R-squared 0.705637 S.D. dependent var 24406.49
S.E. of regression 13241.81 Akaike info criterion 21.97116
Sum squared resid 1.75E+09 Schwarz criterion 22.05198
Log likelihood -129.8269 F-statistic 27.36878
Durbin-Watson stat 0.716502 Prob(F-statistic) 0.000383
Estimation Command:
=====================
LS Y C X2
Estimation Equation:
=====================
Y = C(1) + C(2)*X2
Substituted Coefficients:
=====================
Y = -180859.8861 + 220364.4473*X2
^
Y=-180860+220364X2 (a)
(5.232)
R2=0.7324 F=27.37
S=13242 DW=0.7165
2)对X3
Dependent Variable: Y
Method: Least Squares
Date: 12/13/03 Time: 15:17
Sample: 1987 1998
Included observations: 12
Variable Coefficient Std. Error t-Statistic Prob.
C -386132.4 97641.28 -3.954602 0.0027
X3 1103.697 253.2660 4.357855 0.0014
R-squared 0.655064 Mean dependent var 38953.65
Adjusted R-squared 0.620571 S.D. dependent var 24406.49
Estimation Command:
=====================
LS Y C X3
Estimation Equation:
=====================
Y = C(1) + C(2)*X3
Substituted Coefficients:
=====================
Y = -386132.4019 + 1103.69677*X3
^
Y=-386132+1104X3 (b)
(4.538)
R2=0.6551 F=18.99
S=15034 DW=0.7165
3)对X4
Dependent Variable: Y
Method: Least Squares
Date: 12/13/03 Time: 15:18
Sample: 1987 1998
Included observations: 12
Variable Coefficient Std. Error t-Statistic Prob.
C 96133.60 64802.43 1.483488 0.1688
X4 -15103.66 17013.62 -0.887740 0.3955
R-squared 0.073051 Mean dependent var 38953.65
Adjusted R-squared -0.019644 S.D. dependent var 24406.49
S.E. of regression 24645.04 Akaike info criterion 23.21355
Sum squared resid 6.07E+09 Schwarz criterion 23.29437
Log likelihood -137.2813 F-statistic 0.788082
Durbin-Watson stat 0.214148 Prob(F-statistic) 0.395531
Estimation Command:
=====================
Estimation Equation:
=====================
Y = C(1) + C(2)*X4
Substituted Coefficients:
=====================
Y = 96133.60497 - 15103.66409*X4
^
Y=96134-15104X4
(-0.8877)
R2=0.07305 F=0.7881
S=24645 DW=0.2141
4)对X2,X3
Dependent Variable: Y
Method: Least Squares
Date: 12/13/03 Time: 15:27
Sample: 1987 1998
Included observations: 12
Variable Coefficient Std. Error t-Statistic Prob.
C -327701.5 75644.37 -4.332134 0.0019
X2 146213.8 49110.47 2.977242 0.0155
X3 573.3049 260.0840 2.204307 0.0550
R-squared 0.826219 Mean dependent var 38953.65
Adjusted R-squared 0.787601 S.D. dependent var 24406.49
S.E. of regression 11248.17 Akaike info criterion 21.70612
Sum squared resid 1.14E+09 Schwarz criterion 21.82734
Log likelihood -127.2367 F-statistic 21.39463
Durbin-Watson stat 1.247999 Prob(F-statistic) 0.000380
Estimation Command:
=====================
LS Y C X2 X3
Estimation Equation:
=====================
Y = C(1) + C(2)*X2 + C(3)*X3
Substituted Coefficients:
=====================
Y = -327701.5357 + 146213.7762*X2 + 573.304887*X3
^
Y=-327701+146214X2+573.3X3 (c)
(2.204)
R2=0.8262 F=21.39 大学排名
S=11248 DW=1.248
5)对X2,X4
Dependent Variable: Y
Method: Least Squares
Date: 12/13/03 Time: 15:31
Sample: 1987 1998
Included observations: 12
Variable Coefficient Std. Error t-Statistic Prob.
C -159025.2 64471.72 -2.466588 0.0358
X2 215651.1 45047.38 4.787206 0.0010
X4 -4525.588 9776.199 -0.462919 0.6544
R-squared 0.738620 Mean dependent var 38953.65
Adjusted R-squared 0.680536 S.D. dependent var 24406.49
S.E. of regression 13794.82 Akaike info criterion 22.11429
Sum squared resid 1.71E+09 Schwarz criterion 22.23552
Log likelihood -129.6858 F-statistic 12.71635
Durbin-Watson stat 0.751053 Prob(F-statistic) 0.002386
Estimation Command:
=====================
LS Y C X2 X4
Estimation Equation:
=====================
Y = C(1) + C(2)*X2 + C(3)*X4
Substituted Coefficients:
=====================
Y = -159025.2067 + 215651.1045*X2 - 4525.587513*X4
^
Y=-159025+215651X2-4526X4
(-0.4629)
R2=0.7386 F=12.72
S=13795 DW=0.7511
6)对X3,X4
Dependent Variable: Y
Method: Least Squares
Date: 12/13/03 Time: 15:43
Sample: 1987 1998
Included observations: 12
Variable Coefficient Std. Error t-Statistic Prob.
C -344553.1 115574.5 -2.981221 0.0154
X3 1072.042 263.3080 4.071439 0.0028
Estimation Command:
=====================
LS Y C X3 X4
Estimation Equation:
=====================
Y = C(1) + C(2)*X3 + C(3)*X4
Substituted Coefficients:
=====================
Y = -344553.0724 + 1072.042485*X3 - 7762.560522*X4
^
Y=-34553+1072X3-7763X4
(-0.7194)
R2=0.6378 F=9.296
S=15410 DW=1.758
查表得F(2,10)=4.10,F0.05(3,9)=3.86,t0.025(10)=2.228, t0.025(9)=2.262。由以上各样本回归方程可以看出X4(人均棉花产量)对Y(GNP)没有显著影响,应该略去。
再比较不含X4的几个方程(a),(b),(c),可以看出,式(a)稍微优于式(b),在式(c)中,
虽然X3没有通过显著性检验,但是相应的t统计量为2.204,很接近临界值t0.025(9)=2.262,且式(c)的可决系数R2明显高于式(a)中的R2,误差项的标准差估计值S明显小于式(a)中的S。因此,最后确定的总体回归模型为
Y=β1+β2X2+β3X3+u
根据刚才的输出结果,样本回归方程为 (转载自http://zw.NSEaC.com科教作文网)
^
Y=-327701+146214X2+573.3X3
(2.977) (2.204)
R2=0.8262 F=21.39
S=11248 DW=1.248
A.多重共线性的检验:由刚才确定总体回归模型在的分析过程可知:R2很大,F=21.39显著大于F0.05(3,9)=3.86,而变量X2对应的偏回归系数t值显著,X3的t值接近显著,所以,这个模型是不存在多重共线性的。
B.异方差性的检验:
对X2,X3
ARCH Test:
F-statistic 0.431993 Probability 0.739434
Obs*R-squared 1.852580 Probability 0.603560
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 12/13/03 Time: 17:55
Sample(adjusted): 1990 1998
Included observations: 9 after adjusting endpoints
Variable Coefficient Std. Error t-Statistic Prob.
C 1.97E+08 1.13E+08 1.748049 0.1409
RESID^2(-1) -0.481687 0.671468 -0.717364 0.5053
RESID^2(-2) -0.138626 0.701171 -0.197706 0.8511
RESID^2(-3) -0.610979 0.667046 -0.915948 0.4017
R-squared 0.205842 Mean dependent var 1.20E+08
Adjusted R-squared -0.270653 S.D. dependent var 1.64E+08
S.E. of regression 1.85E+08 Akaike info criterion 41.21034
Sum squared resid 1.71E+17 Schwarz criterion 41.29800
Log likelihood -181.4465 F-statistic 0.431993
Durbin-Watson stat 1.241293 Prob(F-statistic) 0.739434
从输出的辅助回归函数中得到R2,计算(n-P)R2=(9-3)*0.7282=4.3692,查Χ2分布表,给定α=0.05,自由度为P=3,得临界值Χ20.05(3)=7.815, (n-P)R2=4.3692<Χ20.05(3)=7.815,所以接受H0,表明模型中随机误差项不存在异方差性。从下面的White也可得出相同结果,模型中不存在异方差。
White Heteroskedasticity Test: 中国大学排名
F-statistic 4.688229 Probability 0.037155
Obs*R-squared 8.738234 Probability 0.067986
Test Equation:
Dependent Variable: RESID^2
Method: Least Squares
Date: 12/13/03 Time: 17:56
Sample: 1987 1998
Included observations: 12
Variable Coefficient Std. Error t-Statistic Prob.
C 1.51E+10 1.41E+10 1.068697 0.3207
X2 1.34E+10 8.16E+09 1.636286 0.1458
X2^2 -7.01E+09 3.99E+09 -1.755779 0.1226
X3 -1.18E+08 77269611 -1.523985 0.1713
X3^2 161943.7 99399.14 1.629226 0.1473
R-squared 0.728186 Mean dependent var 94890959
Adjusted R-squared 0.572864 S.D. dependent var 1.48E+08
S.E. of regression 96545494 Akaike info criterion 39.90326
Sum squared resid 6.52E+16 Schwarz criterion 40.10531
Log likelihood -234.4196 F-statistic 4.688229
Durbin-Watson stat 2.218332 Prob(F-statistic) 0.037155
C.自相关性的检验:
从图中可以看出残差et没有呈线形自回归,表明随机误差项不存在自相关性
预测:因为GNP具有非常重要的国民经济统计意义,对它的预测也具有现实意义。首先,可以通过相关部门指定的在预测期内的变量计划生产值来对这一期的GNP数值作出定量的估计;其次还可以在实际统计中,根据已统计出的变量实际生产值来估计当期的GNP将在一个范围内达到多少。这样,根据预测值制定经济发展政策或判断相关经济政策的可行性以及了解已实施的经济政策取得的成果都具有重要意义。 (科教作文网 zw.nseac.com整理)
结束语
至此,我们完成了对国民经济生产总值满足古典假定的多元线性回归模型的建立及分析。进一步强化了所学知识及处理实际应用问题的能力,由于能力有限,如果这份报告中存在缺陷和不足,请老师谅解。