簡單線性回歸

1、Shanxi university of Finance and Economics計量經(jīng)濟學(xué)實驗報告科 目：簡單線性回歸模型專 業(yè)：財政金融學(xué)院_姓名：劉世杰學(xué)號：200804020239指導(dǎo)教師：閆新華2011 年 3月 27 日實驗一深圳市地方預(yù)算內(nèi)財政收入與本市生產(chǎn)總值（P64 ）1 .原始數(shù)據(jù):2.散點圖：obsBUDGETGDPobsBUDGETGDP199021.70000171.670019912733000236.6600199242.96000317.3200199367.25000453.U0019947440000634.6700199588.02000842.4800

2、1996131.75001048.U01997142.060012974201998164.39001534.7301999184.21001804.0202000221.92002187.4502001262.49002482.4907F表饑DD從散點圖可以看出預(yù)算內(nèi)財政收入（丫）與生產(chǎn)總值（X ）大體呈 線性相關(guān)關(guān)系，可以建立如下的簡單線性回歸模型：Y = 0 廣 0 2+ 口，3.回歸結(jié)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回歸圖形:5 .模型檢驗：(1 )經(jīng)濟意義的檢驗所估的參數(shù)& = 20.46106, & = 0.084965,說明生產(chǎn)總值每增加121億元，平均來說可導(dǎo)致預(yù)算內(nèi)財政收入增加0.08億元。(2)擬合優(yōu)度和統(tǒng)計的檢驗擬合優(yōu)度的度量：由表3可得，可決系數(shù)為0.977058，

5、說明所 建模型整體上對樣本數(shù)據(jù)擬合較好。對回歸系數(shù)的t檢驗：給定a=0.05，查t分布表，在自由度為 n-2=16 時臨界值為 t 0 025(16)=2.120,因為 t =26.10376 七心 (16)=2.120說明“生產(chǎn)總值”對“預(yù)算內(nèi)財政收入”有顯著影響。6.回歸預(yù)測:(1)若2008年的生產(chǎn)總值8000億元，則預(yù)算內(nèi)財政收入的點a 2 a 2 預(yù)測值為700.1826億元。平均值預(yù)測區(qū)間為Yf = Yf七表5BUDGET與GDP的描述統(tǒng)計結(jié)果700.18262.120 x 27.20621 x/ 1 / 18 + (61236863.24888/ 518256.03099)=70

6、0.1826627.10478即是說當(dāng)2008年生產(chǎn)總值為8000億元時，預(yù)算內(nèi)收入的預(yù)測區(qū)間為(73.07782,1327.28738 )(2)預(yù)測值及標準差的圖形表6實驗二中國國民總收入與最終消費（P65）1.原始數(shù)據(jù):國民總收入（乂）=GNP最終消費（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 .散點圖:從散點圖可以看出最終消費（Y）與國民總收入（X ）大體呈現(xiàn)為 線性可以建立如下的簡單線性回歸模刑1 + 2 X 7，+ 7，察 |土，可. I 12 i i .3.回歸結(jié)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回歸圖形:表45 .模型檢驗：經(jīng)濟意義檢驗所估的參數(shù)& =3044.302, & = 0.530133，說明生產(chǎn)總值每增加

11、1 12億元，平均來說可導(dǎo)致預(yù)算內(nèi)財政收入增加0.53億元。擬合優(yōu)度和統(tǒng)計檢驗擬合優(yōu)度的度量：由表3可得，可決系數(shù)為0.990769，說明所建模型整體上對樣本數(shù)據(jù)擬合較好。對回歸系數(shù)的t檢驗：給定a=0.05，查t分布表，在自由度為n-2=28 時臨界值為一二(28)=2.048,因為 t =54.82088 一二 (28)=2.048說明“國民總收入”對“最終消費”有顯著影響。6.回歸預(yù)測:(1 )若2008年的國民總收入300670億元，則最終消費的點預(yù)X2i測值為162433.2億元。平均值預(yù)測區(qū)間為* =孔七2 &*+氣頃)X2i表5 CONSUME與GNP的描述統(tǒng)計結(jié)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 畝題刎誓2 112992Ef2821898102.1.37E+1152282/即是說當(dāng)208年的、/ 、30總收入為300670時，則最終消費的預(yù)測表6表6區(qū)間為(49441.0761,275425.32382 )(2)預(yù)測值及標準差的圖形Forecast: CONSUMEFActual: CONSUMEForecast sample: 1978 2008Included observations: 30Root Mean Sq