第二章简单线性回归模型.docx

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1、第二章简单线性回归模型2.1(1)首先分析人均寿命与人均GDP的数量关系，用Eviews分析:Dependent Variable: YMethod: Least SquaresDate: 12/23/15 Time: 14:37Sample: 1 22Included observations: 22VariableCoefficientStd. Errort-StatisticProb.C56.647941.96082028.889920.0000X10.1283600.0272424.7118340.0001R-squaredAdjusted R-squaredS.E. of regre

2、ssionSum squared residLog likelihoodF-statistic62.5000010,088896.8493246.9485106.8726890.6290740.526082 Mean dependent var0.502386 S.D. dependent var7.116881 Akaike info criterion1013.000 Schwarz criterion-73.34257 Hannan-Quinn criter.22.20138 Durbin-Watson statProb(F-statistic)0.000134有上可知，关系式为y=56

3、.64794+0.128360xi关于人均寿命与成人识字率的关系，用Eviews分析如下:Dependent Variable: YMethod: Least SquaresDate: 12/23/15 Time: 15:01Sample: 1 22Included observations: 22VariableCoefficientStd. Error t-StatisticProb.c38.794243.53207910.983400.0000X20.3319710.0466567.1153080.0000R-squared0.716825Mean dependent var62.500

4、00Adjusted R-squared0.702666S.D.dependent var10.08889S.E. of regression5.501306Akaike info criterion6.334356Sum squared resid605.2873Schwarz criterion6.433542Log likelihood-67.67792Hannan-Quinn criter.6.357721F-statistic50.62761Durbin-Watson stat1.846406Prob(F-statistic)0.000001由上可知，关系式为y=38.79424+0

5、.331971X2关于人均寿命与一岁儿童疫苗接种率的关系，用Eviews分析如下:Dependent Variable: YMethod: Least SquaresDate: 12/23/14 Time: 15:20Sample: 1 22Included observations: 22VariableCoefficientStd. Error t-StatisticProb.C31.799566.5364344.8649710.0001X30.3872760.0802604.8252850.0001R-squared0.537929Mean dependent var62.50000Ad

6、justed R-squared0.514825S.D.dependent var10.08889S.E. of regression7.027364Akaike info criterion6.824009Sum squared resid987.6770Schwarz criterion6.923194Log likelihood-73.06409Hannan-Quinn criter.6.847374F-statistic23.28338Durbin-Watson stat0.952555Prob(F-statistic)0.000103由上可知，关系式为y=31,79956+0.387

7、276x3（2）关于人均寿命与人均GDP模型，由上可知，可决系数为0.526082,说明所建模型整体上对样本数据拟合较好。对于回归系数的t检验：t （ M）=4.711834too25（2O）=2.O86,对斜率系数的显著性检验表明，人均GDP对人均寿命有显著影响。关于人均寿命与成人识字率模型，由上可知，可决系数为0.716825,说明所建模型整体上对样本数据拟合较好。对于回归系数的t检验：t （Bz） =7.1153O8to.o25（2O）=2.O86,对斜率系数的显著性检验表明，成人识字率对人均寿命有显著影响。关于人均寿命与一岁儿童疫苗的模型，由上可知，可决系数为0.537929,说明所建

8、模型整体上对样本数据拟合较好。对于回归系数的t检验：t （ 3）=4.825285to.o25（2O）=2.O86,对斜率系数的显著性检验表明，一岁儿童疫苗接种率对人均寿命有显著影响。2.2(1)对于浙江省预算收入与全省生产总值的模型，用Eviews分析结果如下:Dependent Variable: YMethod: Least SquaresDate: 12/23/15 Time: 17:46Sample (adjusted): 1 33Included observations: 33 after adjustmentsVariable Coefficient Std. Error t-

9、Statistic Prob.X0.1761240.00407243.256390.0000C-154.306339.08196 -3.9482740.0004R-squaredAdjusted R-squaredS.E. of regressionSum squared residLog likelihoodF-statistic902.51481351.00913,2288013.3194913.259310.1000210.983702 Mean dependent var0.983177 S.D. dependent var175.2325 Akaike info criterion9

10、51899.7 Schwarz criterion-216.2751 Hannan-Quinn criter.1871.115 Durbin-Watson statProb(F-statistic)0.000000由上可知，模型的参数：斜率系数0.176124,截距为一154.3063关于浙江省财政预算收入与全省生产总值的模型，检验模型的显著性：1)可决系数为0.983702,说明所建模型整体上对样本数据拟合较好。2)对于回归系数的t检验：t ( B2) =43.25639to.O25(31 )=2.0395,对斜率系数的显著性检验表明，全省生产总值对财政预算总收入有显著影响。用规范形式写出检

11、验结果如下：Y=0.176124X154,3063(0.004072)(39.08196)t= (43.25639)(-3.948274)R2=0.983702 F=1871.115 n=33经济意义是：全省生产总值每增加1亿元，财政预算总收入增加0.176124亿元。(2)当 x=32000 时，进行点预测，由上可知丫=0.176124X154.3063,代入可得：Y= Y=0.176124*32000154.3063=5481.6617进行区间预测：先由Eviews分析:XYMean6000.441902.5148Median2689.280209.3900Maximum27722.314

12、895.410Minimum123.720025.87000Std. Dev.7608.0211351.009Skewness1.4325191.663108Kurtosis4.0105154.590432Jarque-Bera12.6906818.69063Probability0.0017550.000087Sum198014.529782.99Sum Sq. Dev.1.85E+0958407195Observations3333由上表可知，=W (Xi-X) 2=62x(n-l)= 7608.0212 x (33-1)=1852223.473(Xf-X产=(32000- 6000.44

13、1尸=675977068.2当Xf=32000时，将相关数据代入计算得到：5481.6617-2.0395xl75.2325xVl/33+1852223.473/675977068.2Yf5481.6617+2.0395xl75.2325xVl/33+1852223.473/675977068.2即 Yf 的置信区间为(5481.6617-64.9649, 5481.6617+64.9649)对于浙江省预算收入对数与全省生产总值对数的模型，由Eviews分析结果如下:Dependent Variable: LNYMethod: Least SquaresDate: 12/23/15 Time:

14、 18:04Sample (adjusted): 1 33Included observations: 33 after adjustmentsVariableCoefficientStd. Errort-StatisticProb.LNX0.9802750.03429628.582680.0000C-1.9182890.268213-7.1521210.0000R-squaredAdjusted R-squaredS.E. of regressionSum squared residLog likelihoodF-statistic0.963442 Mean dependent var0.962263 S.D. dependent var0.327172 Akaike info criterion3.318281 Schwarz criterionProb(F-statistic)0.0000005.5731201.6841890.6620280.7527260.6925450.096208-8.92