计量经济学第一次作业-回归方程进行检验及预测

题目：下表俵略）是中国内地2007年各地区税收Y和国内生产总值GDP的统计

资料。要求，以手工和运用Eviews软件操作：

⑴做出散点图，建立税收随国内生产总值变化的一元线性回归方程，并解

释斜率的经济含义；

⑵对所建立的回归方程进行检验；

⑶若2008年某地区国民生产总值为8500亿元，求该地区税收收入的预测值

及预测区间。

解：

用手工方式计算的参数估计值，如下表：

表格1参数估计值

GDP（亿元）Y（亿元）gdPiXgdp：g物y

9353.301435.7C462.17814.65213604.99376507.97

5050.40438.40-3840.73-182.6514751174.72701527.15

13709.50618.304818.37-2.7523216729.87-13273.84

5733.40430.50-3157.73-190.559971232.27601719.93

6091.10347.90-2800.03-273.157840144.51764840.60

11023.50815.702132.37194.654547019.70415056.32

5284.70237.40-3606.43-383.6513006307.091383622.71

7065.00335.00-1826.13-286.053334735.46522372.12

12188.901975.5C3297.771354.4510875314.634466654.30

25741.201894.8C16850.071273.75283925000.3421462700.47

18780.401535.4C9889.27914.3597797744.089042210.01

7364.20401.90-1526.93-219.152331502.42334633.18

9249.10594.00357.97-27.05128145.52-9684.93

5500.30281.90-3390.83-339.1511497699.651150014.98

25965.901308.4C17074.77687.35291547913.7811736263.42

15012.50G25.00G121.373.9537471222.0224149.81

9230.70434.00339.57-187.05115310.63-63519.00

9200.00410.70308.87-210.3595403.27-64973.18

31084.402415.5C22193.271794.45492541419.4539824613.4

5955.70282.70-2935.43-338.358616724.66993215.53

1223.3088.00-7667.83-533.0558795552.594087371.65

4122.50294.50-4768.63-326.5522739792.081557217.83

10505.30629.001614.177.952605558.3312824.87

2741.90211.90-6149.23-409.1537812978.012515985.49

4741.30378.60-4149.83-242.4517221054.221006145.35

342.2011.70-8548.93-609.3573084132.445209329.31

5465.80355.50-3425.33-265.5511732856.88909611.84

2702.40142.10-6188.73-478.9538300327.102964120.17

783.6043.30-8107.53-577.7565731974.694684162.26

889.2058.80-8001.93-562.2564030816.604499121.50

3523.20220.60-5367.93-400.4528814627.462149611.86

由此表可得:

力产登牛=0.071^0=y-^,X=-10.63

因此：Y=-40.6^0.(X7

(1)散点图见下图：

2,500-

2,000-

1,500-

>

1,000-

500-

0-

010,00020,00030,00040,000

GDP

Figure1各地区税收与国民收入的散点图

参数方程见下图:

国Equation:UNTITLEDWorkfile:u国内地2007年各地区税收Y和国民…_曰X

ViewProcObjectPrintNameFreeze|EstimateForecastStatsResids

EstimationCommand：

LSYGDPC

EstimationEquation：

Y=C(1)*GDP+C(2)

SubstitutedCoefficients：

Y=0.0710466236651*GDP-10.6296304208

Figure2一元线性回归方程

检验结果见下图:

l=JEquation:UNTRIEDWorkfile:中国内地2007年各地区税收他国民…_□X

ViewProcObjectPrint|Name|Freeze|EstimateForecastStatsResids

DependentVariables

Method:LeastSquares

Date:03/10/14Time:21:43

Sample(adjusted):131

Includedobservations:31afteradjustments

VariableCoefficientStd.Errort-StatisticProb.

GDP0.0710470.0074079.5912450.0000

C-10629638606992-012350009026

R-squared0.760315Meandependentvar621.0548

AdjustedR-squared0.752050S.D.dependentvar619.5803

S.E.ofregression308.5176Akaikeinfocriterion14.36378

Sumsquaredresid2760310.Schwarzcriterion14.45629

Loglikelihood-220.6385Hannan-Quinncriter.14.39393

F-statistic91.99198Durbin-Watsonstat1.570523

Prob(F-statistic)0.000000

Figure3回归方程检验

斜率的经济学意义：2007年，中国内地各省区GDP增加1亿元，税收就增加

0.0710元。

⑵在5%的显著水平下，自由度为31-2=29的t分布的临界值为2.045。因此从

参数的t检验值看，斜率项显著不为0,但不拒绝截距项为零的假设。另外，拟合

优度R2=0.7603表明，税收的76%的变化也可以由GDP的变化来解释，因此拟合

度情况较好。

Figure4真实值、估计值、残差的曲线图

(=)Equation:UNTITLEDWorkfile:中国内地2007年各地区税收Y和国民…_DX

ViewProcObjectPrint|NameFreezeEstimateForecastStatsResids

obsActualFittedResidualResidualPlot

obsActualFittedResidualResidualPlot•

11435.70653.891781.809I1

2438.400348.18490.2158I

3618.300963.384-345.0841

4430,500396.70933.7909S>1

5347.900422.122-74.2225I《1

6815.700772.55343.1472I》1

7237.400364.830-127.4301/1

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8335.000491.315-156.315

91975.50855,3511120.151

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111535.401323.65211.7461

12401.900512.572-110.6721<

13594.000646.488-52.4877■}1

14281.900380.148-98.24811

151308.401834.16-525.7601

16625.0001055.96-430.9581

17434.000645.180-211.1801

18410,700642,999-232.2991

192415.502197.81217.6881A

20282.700412.503-129.8031<1

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2188.000076.281711.7183，1

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22294,500282.26012.2399/

23629,000735.736-106.7361《1

24211.900184.17327.72691\1

25378,600326.22452.37631,1

2611.700013.6825-1.982521《1

27355,500377.697-22.1970141

28142.100181.367-39.26681<1

2943.300045.0425-1.742501i1

3058.800052.54506.254971«1

31I220,600239.682-19.08181