搜索
第二章简单线性回归模型2.1（1）①首先分析人均寿命与人均GDP的数量关系，用Eviews分析：DependentVariable:YMethod:LeastSquaresDate:12/27/14Time:21:00Sample:122Includedobservations:22VariableCoefficientStd.Errort-StatisticProb.C56.647941.96082028.889920.0000X10.1283600.0272424.7118340.0001R-squared0.526082Meandependentvar62.50000AdjustedR-squared0.502386S.D.dependentvar10.08889S.E.ofregression7.116881Akaikeinfocriterion6.849324Sumsquaredresid1013.000Schwarzcriterion6.948510Loglikelihood-73.34257Hannan-Quinncriter.6.872689F-statistic22.20138Durbin-Watsonstat0.629074Prob(F-statistic)0.000134有上可知，关系式为y=56.64794+0.128360x1②关于人均寿命与成人识字率的关系，用Eviews分析如下：DependentVariable:YMethod:LeastSquaresDate:11/26/14Time:21:10Sample:122Includedobservations:22VariableCoefficientStd.Errort-StatisticProb.C38.794243.53207910.983400.0000X20.3319710.0466567.1153080.0000R-squared0.716825Meandependentvar62.50000AdjustedR-squared0.702666S.D.dependentvar10.08889S.E.ofregression5.501306Akaikeinfocriterion6.334356Sumsquaredresid605.2873Schwarzcriterion6.433542Loglikelihood-67.67792Hannan-Quinncriter.6.357721F-statistic50.62761Durbin-Watsonstat1.846406Prob(F-statistic)0.000001由上可知，关系式为y=38.79424+0.331971x2③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：DependentVariable:YMethod:LeastSquaresDate:11/26/14Time:21:14Sample:122Includedobservations:22VariableCoefficientStd.Errort-StatisticProb.C31.799566.5364344.8649710.0001X30.3872760.0802604.8252850.0001R-squared0.537929Meandependentvar62.50000AdjustedR-squared0.514825S.D.dependentvar10.08889S.E.ofregression7.027364Akaikeinfocriterion6.824009Sumsquaredresid987.6770Schwarzcriterion6.923194Loglikelihood-73.06409Hannan-Quinncriter.6.847374F-statistic23.28338Durbin-Watsonstat0.952555Prob(F-statistic)0.000103由上可知，关系式为y=31.79956+0.387276x3（2）①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（β1）=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。②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（β2）=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。③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（β3）=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）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：DependentVariable:YMethod:LeastSquaresDate:12/03/14Time:17:00Sample(adjusted):133Includedobservations:33afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.X0.1761240.00407243.256390.0000C-154.306339.08196-3.9482740.0004R-squared0.983702Meandependentvar902.5148AdjustedR-squared0.983177S.D.dependentvar1351.009S.E.ofregression175.2325Akaikeinfocriterion13.22880Sumsquaredresid951899.7Schwarzcriterion13.31949Loglikelihood-216.2751Hannan-Quinncriter.13.25931F-statistic1871.115Durbin-Watsonstat0.100021Prob(F-statistic)0.000000②由上可知，模型的参数：斜率系数0.176124，截距为—154.3063③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（β2）=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。④用规范形式写出检验结果如下：Y=0.176124X—154.3063(0.004072)(39.08196)t=(43.25639)（-3.948274）R2=0.983702F=1871.115n=33⑤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，①进行点预测，由上可知Y=0.176124X—154.3063，代入可得：Y=Y=0.176124*32000—154.3063=5481.6617②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-Bera12.6906818.69063Probability0.0017550.000087Sum198014.529782.99SumSq.Dev.1.85E+0958407195Observations3333由上表可知，∑x2=∑（Xi—X）2=δ2x(n—1)=7608.0212x(33—1)=1852223.473(Xf—X)2=(32000—6000.441)2=675977068.2当Xf=32000时，将相关数据代入计算得到：5481.6617—2.0395x175.2325x√1/33+1852223.473/675977068.2≤Yf≤5481.6617+2.0395x175.2325x√1/33+1852223.473/675977068.2即Yf的置信区间为（5481.6617—64.9649,5481.6617+64.9649）(3)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：DependentVariable:LNYMethod:LeastSquaresDate:12/03/14Time:18:00Sample(adjusted):133Includedobservations:33afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.LNX0.9802750.03429628.582680.0000C-1.9182890.268213-7.1521210.0000R-squared0.963442Meandependentvar5.573120AdjustedR-squared0.962263S.D.dependentvar1.684189S.E.ofregression0.327172Akaikeinfocriterion0.662028Sumsquaredresid3.318281Schwarzcriterion0.752726Loglikelihood-8.923468Hannan-Quinncriter.0.692545F-statistic816.9699Durbin-Watsonstat0.096208Prob(F-statistic)0.000000①模型方程为：lnY=0.980275lnX-1.918289②由上可知，模型的参数：斜率系数为0.980275，截距为-1.918289③关于浙江省财政预算收入与全省生产总值的模型，检验其显著性：1）可决系数为0.963442，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（β2）=28.58268t0.025(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。④经济意义：全省生产总值每增长1%，财政预算总收入增长0.980275%2.4（1）对建筑面积与建造单位成本模型，用Eviews分析结果如下：DependentVariable:YMethod:LeastSquaresDate:12/01/14Time:12:40Sample:112Includedobservations:12VariableCoefficientStd.Errort-StatisticProb.X-64.184004.809828-13.344340.0000C1845.47519.2644695.796880.0000R-squared0.946829Meandependentvar1619.333AdjustedR-squared0.941512S.D.dependentvar131.2252S.E.ofregression31.73600Akaikeinfocriterion9.903792Sumsquaredresid10071.74Schwarzcriterion9.984610Loglikelihood-57.42275Hannan-Quinncriter.9.873871F-statistic178.0715Durbin