中国储蓄存款总额（Y，亿元）与GDP（元）数据如下表。

解：一、估计一元线性回归模型Y i=0β^+1β^GDP t+e t由经济理论知，储蓄存款总额受GDP影响，当GDP增加时，储蓄存款总额也随着增加，他们之间具有正向的同步变动趋势。

储蓄存款总额除受GDP影响之外，还受到其他一些变量的影响及随机因素的影响，将其他变量及随机因素的影响均并到随机变量U中，根据X与Y的样本数据，作X与Y之间的散点图可以看出，他们的变化趋势是线性的，由此建立中国储蓄存款总额Y与GDP之间的一员线性回归模型。

Y i=β0+β1X1i+u i由表1-1中样本观测数据，样本回归模型为Y i=0β^+1β^GDP t+ℯt用Eviews软件估计结果：Dependent Variable: YMethod: Least SquaresDate: 12/14/14 Time: 10:41Sample: 1978 2012Included observations: 35Coefficient Std. Error t-Statistic Prob.C -7304.294 1561.216 -4.678592 0.0000GDP 0.762529 0.008698 87.66252 0.0000R-squared 0.995724 Mean dependent var 78882.56Adjusted R-squared 0.995595 S.D. dependent var 108096.8 S.E. of regression 7174.769 Akaike info criterion 20.64997 Sum squared resid 1.70E+09 Schwarz criterion 20.73885 Log likelihood -359.3745 Hannan-Quinn criter. 20.68065 F-statistic 7684.717 Durbin-Watson stat 1.224720Prob(F-statistic)0.000000即样本回归方程为：tY ^=−7304.294+0.762529gdp-4.678592 87.66252 r 2=0.995724二、对估计结果做结构分析 （1）对回归方程的结构分析1β^=0.762529是样本回归方程的斜率，他表示GDP 的边际 增长率，说明GDP 每增加1元，将有0.762529用于储蓄；0β^=-7304.294是样本回归方程的截距，他表示不受GDP 影响的自发性储蓄增长。

0β^和1β^的符号和大小，均符合经济理论及目前国家的实际情况。

（2）统计检验r 2=0.995724，说明总离差平方和的99.6%被样本回归直线解释，仅有0.4%未被解释，因此，样本回归直线对样本点的拟合优度是很高的。

给出显著性水平α=0.05，查自由度v=35-2=33的t 分布表，得临界值t 0.052(33)=2.03，|t 0|=4.678592＞2.03，故回归系数均显著不为零，回归模型中应摆放常数项，GDP 对Y 有显著影响。

从以上的评价可以看出，此模型是比较好的。

三、假设gdp 2013=568845.0，对2013年国民储蓄总额进行预测给出gdp 2013=568845.0，可以得到Y f2013=568845图1-2四、对异方差进行检验用怀特检验法进行异方差检验：Heteroskedasticity Test: WhiteF-statistic 0.081308 Prob. F(3,28) 0.9696 Obs*R-squared 0.276363 Prob. Chi-Square(3) 0.9644 Scaled explained SS 0.882741 Prob. Chi-Square(3) 0.8296Test Equation:Dependent Variable: RESID^2Method: Least SquaresDate: 12/14/14 Time: 14:54Sample: 1981 2012Included observations: 32Coefficient Std. Error t-Statistic Prob.C 38523385 20655638 1.865030 0.0727E(-1)^2 -0.042001 0.172609 -0.243333 0.8095 E(-1)*E(-2) -0.409631 0.859096 -0.476816 0.6372E(-2)^2 0.094082 0.282003 0.333620 0.7412R-squared 0.008636 Mean dependent var 36993700 Adjusted R-squared -0.097581 S.D. dependent var 1.01E+08 S.E. of regression 1.06E+08 Akaike info criterion 39.91526 Sum squared resid 3.16E+17 Schwarz criterion 40.09848 Log likelihood -634.6442 Hannan-Quinn criter. 39.97599 F-statistic 0.081308 Durbin-Watson stat 1.876393 Prob(F-statistic) 0.969643提出假设：H0：αi=0， i=1,2H1：α1，α2中至少有一个不等于零Heteroskedasticity Test: WhiteF-statistic 0.081308 Prob. F(3,28) 0.9696 Obs*R-squared 0.276363 Prob. Chi-Square(3) 0.9644 Scaled explained SS 0.882741 Prob. Chi-Square(3) 0.8296Test Equation:Dependent Variable: RESID^2Method: Least SquaresDate: 12/14/14 Time: 14:54Sample: 1981 2012Included observations: 32Coefficient Std. Error t-Statistic Prob.C 38523385 20655638 1.865030 0.0727E(-1)^2 -0.042001 0.172609 -0.243333 0.8095E(-1)*E(-2) -0.409631 0.859096 -0.476816 0.6372E(-2)^2 0.094082 0.282003 0.333620 0.7412R-squared 0.008636 Mean dependent var 36993700Adjusted R-squared -0.097581 S.D. dependent var 1.01E+08S.E. of regression 1.06E+08 Akaike info criterion 39.91526Sum squared resid 3.16E+17 Schwarz criterion 40.09848Log likelihood -634.6442 Hannan-Quinn criter. 39.97599F-statistic 0.081308 Durbin-Watson stat 1.876393Prob(F-statistic) 0.969643WT（g）=T R2=0.276363当H0成立时服从自由度为g的χ2分布，其中g=（k+1）（k+2）-1=22给定显著性水平α，查临界值χα2(g)=5.991WT（g）＜χα2(g)则H0成立，那么原模型不存在不存在异方差。

五、自相关检验检验误差项u t是否存在自相关：已知DW=1.224720，若给定α=0.05，查表，D L==1.40，D u=1.52。

因为DW=1.22＜1.40，依据判别规则，认为误差项u t存在严重的正自相关。

残差序列见图1-3。

图1-3e t=1.187e t−1-0.479e t−2+v tDependent Variable: EMethod: Least SquaresDate: 12/14/14 Time: 14:46Sample (adjusted): 1981 2012Included observations: 32 after adjustmentsCoefficient Std. Error t-Statistic Prob.E(-1) 0.187118 0.182095 1.027581 0.3124E(-2) -0.479147 0.188696 -2.539257 0.0165R-squared 0.181787 Mean dependent var -181.2631 Adjusted R-squared 0.154513 S.D. dependent var 6831.637 S.E. of regression 6281.715 Akaike info criterion 20.38914 Sum squared resid 1.18E+09 Schwarz criterion 20.48074 Log likelihood -324.2262 Hannan-Quinn criter. 20.41950 Durbin-Watson stat 1.385678一阶广义差分：Dependent Variable: GDYMethod: Least SquaresDate: 12/15/14 Time: 22:03Sample (adjusted): 1979 2012Included observations: 34 after adjustmentsCoefficient Std. Error t-Statistic Prob.C -4804.899 1508.843 -3.184493 0.0032GDGDP 0.767232 0.012561 61.07998 0.0000R-squared 0.991496 Mean dependent var 54110.50 Adjusted R-squared 0.991230 S.D. dependent var 72242.89 S.E. of regression 6765.480 Akaike info criterion 20.53408 Sum squared resid 1.46E+09 Schwarz criterion 20.62386 Log likelihood -347.0793 Hannan-Quinn criter. 20.56470 F-statistic 3730.764 Durbin-Watson stat 1.690568 Prob(F-statistic) 0.000000二阶广义差分：e=residls e e(-1) e(-2)Dependent Variable: EMethod: Least SquaresDate: 12/15/14 Time: 22:13Sample (adjusted): 1981 2012Included observations: 32 after adjustmentsCoefficient Std. Error t-Statistic Prob.E(-1) 0.187118 0.182095 1.027581 0.3124E(-2) -0.479147 0.188696 -2.539257 0.0165R-squared 0.181787 Mean dependent var -181.2631 Adjusted R-squared 0.154513 S.D. dependent var 6831.637 S.E. of regression 6281.715 Akaike info criterion 20.38914 Sum squared resid 1.18E+09 Schwarz criterion 20.48074 Log likelihood -324.2262 Hannan-Quinn criter. 20.41950 Durbin-Watson stat 1.385678Dependent Variable: GDYMethod: Least SquaresDate: 12/15/14 Time: 22:23Sample (adjusted): 1980 2012Included observations: 33 after adjustmentsCoefficient Std. Error t-Statistic Prob.C -9855.152 1630.151 -6.045546 0.0000GDGDP 0.763513 0.007365 103.6741 0.0000R-squared 0.997124 Mean dependent var 99555.96 Adjusted R-squared 0.997031 S.D. dependent var 130994.4 S.E. of regression 7137.270 Akaike info criterion 20.64274 Sum squared resid 1.58E+09 Schwarz criterion 20.73344 Log likelihood -338.6052 Hannan-Quinn criter. 20.67326 F-statistic 10748.31 Durbin-Watson stat 0.915423 Prob(F-statistic) 0.000000六、多重共线性由于只有一个解释变量，所以不存在解释变量之间的共线性。