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-squared0.526082Mean dependent var62.50000Adjusted R-squared0.502386S.D. dependent var10.08889S.E. of regression7.116881Akaike info criterion6.849324Sum squared resid1013.000Schwarz criterion6.948510Log likelihood-73.34257Hannan-Quinn criter.6.872689F-statistic22.20138Durbin-Watson stat0.629074Prob(F-statistic)0.000134有上可知，关系式为y=56.64794+0.128360x1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. Errort-StatisticProb.C38.794243.53207910.983400.0000X20.3319710.0466567.1153080.0000R-squared0.716825Mean dependent var62.50000Adjusted 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+0.331971x2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. Errort-StatisticProb.C31.799566.5364344.8649710.0001X30.3872760.0802604.8252850.0001R-squared0.537929Mean dependent var62.50000Adjusted 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+0.387276x3（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（1）=4.711834t0.025(20)=2.086，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（2）=7.115308t0.025(20)=2.086，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）=4.825285t0.025(20)=2.086，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 adjustmentsVariableCoefficientStd. Errort-StatisticProb.X0.1761240.00407243.256390.0000C-154.306339.08196-3.9482740.0004R-squared0.983702Mean dependent var902.5148Adjusted R-squared0.983177S.D. dependent var1351.009S.E. of regression175.2325Akaike info criterion13.22880Sum squared resid951899.7Schwarz criterion13.31949Log likelihood-216.2751Hannan-Quinn criter.13.25931F-statistic1871.115Durbin-Watson stat0.100021Prob(F-statistic)0.000000由上可知，模型的参数：斜率系数0.176124，截距为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（2）=43.25639t0.025(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Y=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：XYMean6000.441902.5148Median2689.280209.3900Maximum27722.314895.410Minimum123.720025.87000Std. 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，x2=（XiX）2=2x(n1)= 7608.0212 x (331)=1852223.473(XfX)2=(320006000.441)2=675977068.2当Xf=32000时，将相关数据代入计算得到：5481.66172.0395x175.2325x1/33+1852223.473/675977068.2Yf5481.6617+2.0395x175.2325x1/33+1852223.473/675977068.2即Yf的置信区间为（5481.661764.9649, 5481.6617+64.964