简单线性回归

1、Shanxi university of Finance and Economics计量经济学实验报告科 目：简单线性回归模型专 业：财政金融学院_姓名：刘世杰学号：200804020239指导教师：闫新华2011 年 3月 27 日实验一深圳市地方预算内财政收入与本市生产总值（P64 ）1 .原始数据:2.散点图：obsBUDGETGDPobsBUDGETGDP199021.70000171.670019912733000236.6600199242.96000317.3200199367.25000453.U0019947440000634.6700199588.02000842.4800

2、1996131.75001048.U01997142.060012974201998164.39001534.7301999184.21001804.0202000221.92002187.4502001262.49002482.4907F表饥DD从散点图可以看出预算内财政收入（丫）与生产总值（X ）大体呈 线性相关关系，可以建立如下的简单线性回归模型：Y = 0 广 0 2+ 口，3.回归结果:Dependent Variable: BUDGET Method: Least SquaresDate: 0326/11 Time: 03:50Sample: 1990 2007Included o

3、bservations: 13BUDG ET=C(1 )+C *G PVariableCoefficientStd. Error t-StatisticProb.C(1)20.461069.867U02.0735930.0546C0.0349650.00325526.10S760.0000R-squared0.977050Mean dependent var215.9467Adjusted R-squared0.975624S.D. dependent var174.6014S.E. of regression27.26021Akaike info criterion9.552172Sum s

4、quaredesid11839.90Schwarz criterion9.652103Log likelihood-83.97355Hannan-Quinn criter.9.566314F-statistic681 4064Durbin-Watson stat0.932033Prob(F-statistic)0.0000004回归图形:5 .模型检验：(1 )经济意义的检验所估的参数& = 20.46106, & = 0.084965,说明生产总值每增加121亿元，平均来说可导致预算内财政收入增加0.08亿元。(2)拟合优度和统计的检验拟合优度的度量：由表3可得，可决系数为0.977058，

5、说明所 建模型整体上对样本数据拟合较好。对回归系数的t检验：给定a=0.05，查t分布表，在自由度为 n-2=16 时临界值为 t 0 025(16)=2.120,因为 t =26.10376 七心 (16)=2.120说明“生产总值”对“预算内财政收入”有显著影响。6.回归预测:(1)若2008年的生产总值8000亿元，则预算内财政收入的点a 2 a 2 预测值为700.1826亿元。平均值预测区间为Yf = Yf七表5BUDGET与GDP的描述统计结果700.18262.120 x 27.20621 x/ 1 / 18 + (61236863.24888/ 518256.03099)=70

6、0.1826627.10478即是说当2008年生产总值为8000亿元时，预算内收入的预测区间为(73.07782,1327.28738 )(2)预测值及标准差的图形表6实验二中国国民总收入与最终消费（P65）1.原始数据:国民总收入（乂）=GNP最终消费（Y） =CONSUME表1口突 CC3ESUMEIGNP|19732239.1003645.21719792633.7004-062.57919303007.9004545.62419813361.5004-339.4-6119323714.8005330451198341126.4005985.55219344-8463007243.75

7、219855906.3009040.73719366821.80010274.3319877804.60012050.6219889839.50015036.821939111642017000.92199012090.501371832199114091.9021326.20199217203.3026937.28199321899.9035260.02199429241.204-3108.46199536748.2059310.53199643919.5070142.49199748140 6073060.83199851588.208.3024.28199955636.9088479.1

8、5200061516.0093000.45200166878.30103068.2200271691.20119095.7200S77U9.50135174.0200487032.90159586.7200597322.70134083.620061105953213131.720071284U.625U83.22008NA300670.02 .散点图:从散点图可以看出最终消费（Y）与国民总收入（X ）大体呈现为 线性可以建立如下的简单线性回归模刑1 + 2 X 7，+ 7，察 |土，可. I 12 i i .3.回归结果：表3Dependent Variable: CONSUMEMethod

9、: Least Squaresate: 03726/11 Time: 10:14Sample: 1973 2007Included observations: 30CONSUME=C(1 )+C(2)*GNPVariableCoefficientStd. Error t-StatisticProb.C(1)3044.302895.40233.3999270.0020C(2)0.53011S0.00967054.S208S0.0000R-squared0.990769Mean dependent var36584.56Adjusted R-squared0.990440S.D. dependen

10、t var36622.38S.E. of regression3580.396Akaike info criterion19.26395Sum squared resid3.59EHJ8Schwarz criterion1936237Log likelihood-2S7.0343Hannan-Quinn criter.19.29834F-statistic3005.329Durbin-Watson stat0.12S760Prob(F-statistic)0.0000004回归图形:表45 .模型检验：经济意义检验所估的参数& =3044.302, & = 0.530133，说明生产总值每增加

11、1 12亿元，平均来说可导致预算内财政收入增加0.53亿元。拟合优度和统计检验拟合优度的度量：由表3可得，可决系数为0.990769，说明所建模型整体上对样本数据拟合较好。对回归系数的t检验：给定a=0.05，查t分布表，在自由度为n-2=28 时临界值为一二(28)=2.048,因为 t =54.82088 一二 (28)=2.048说明“国民总收入”对“最终消费”有显著影响。6.回归预测:(1 )若2008年的国民总收入300670亿元，则最终消费的点预X2i测值为162433.2亿元。平均值预测区间为* =孔七2 &*+气顷)X2i表5 CONSUME与GNP的描述统计结果Date: 0

12、3/28/11 Time: 16:14 Sample: 1978 2008Mean36584.5663270.07Median19551.6031098.65Maximum128444.6251483.2Minimum2239.1003645.217Std. Dev.36622.8868765.51Skewness0.9271061.200296Kurtcsis27775933.547899Jarque-Bera4.3594627.578800Probability0.1130720.022609CONSUMEGNP162433.2 2.048 x 3580.896 x 必1/30+882619357151097537.371861668.721Sum6 亩题刎誓2 112992Ef2821898102.1.37E+1152282/即是说当208年的、/ 、30总收入为300670时，则最终消费的预测表6表6区间为(49441.0761,275425.32382 )(2)预测值及标准差的图形Forecast: CONSUMEFActual: CONSUMEForecast sample: 1978 2008Included observations: 30Root Mean Sq