t检验到底是大于t检验临界值表接受原假设还是小于t检验临界值表
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时间：2016-06-18 07:35
t检验中，t值的大小代表什么？表示两组数据的相似度大小的参数？？？有具体的参考文献吗？_百度知道
t检验中，t值的大小代表什么？表示两组数据的相似度大小的参数？？？有具体的参考文献吗？
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是不能拒绝原假设的 显著性水平为1-0; 概率0，反之接受，也就是接受原假设.05 <，那么t值是没用的，如果你没法知道临界值，则拒绝原假设.073.95 = 0。t值大于critical value。t值的用处在于你知道critical value也就是临界值的条件下才行
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出门在外也不愁计量经济学(庞皓)第三版课后答案05_计量经济学课后答案-牛bb文章网
计量经济学(庞皓)第三版课后答案05 计量经济学课后答案
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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： Dependent Variable: Y Method: Least Squares Date: 12/27/14 Time: 21:00 Sample: 1 22 Included observations: 22Variable Coefficient Std. Error t-Statistic Prob. C 56.820 28.0 X1 0....0001 R-squared 0.526082 Mean dependent var 62.50000Adjusted R-squared 0.502386 S.D. dependent var 10.08889 S.E. of regression 7.116881 Akaike info criterion 6.849324 Sum squared resid
Schwarz criterion 6.948510 Log likelihood -73.34257 Hannan-Quinn criter. 6.872689 F-statistic 22.20138 Durbin-Watson stat 0.629074 Prob(F-statistic) 0.000134有上可知，关系式为y=56.360x1②关于人均寿命与成人识字率的关系，用Eviews分析如下： Dependent Variable: Y Method: Least Squares Date: 11/26/14 Time: 21:10 Sample: 1 22 Included observations: 22Variable Coefficient Std. Error t-Statistic Prob. C 38.079 10.0 X2 0....0000 R-squared 0.716825 Mean dependent var 62.50000Adjusted R-squared 0.702666 S.D. dependent var 10.08889 S.E. of regression 5.501306 Akaike info criterion 6.334356 Sum squared resid 605.2873 Schwarz criterion 6.433542 Log likelihood -67.67792 Hannan-Quinn criter. 6.357721 F-statistic 50.62761 Durbin-Watson stat 1.846406 Prob(F-statistic) 0.000001由上可知，关系式为y=38.971x2③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: Y Method: Least Squares Date: 11/26/14 Time: 21:14 Sample: 1 22 Included observations: 22Variable Coefficient Std. Error t-Statistic Prob. C 31.434 4......0001 R-squared 0.537929 Mean dependent var 62.50000Adjusted R-squared 0.514825 S.D. dependent var 10.08889 S.E. of regression 7.027364 Akaike info criterion 6.824009 Sum squared resid 987.6770 Schwarz criterion 6.923194 Log likelihood -73.06409 Hannan-Quinn criter. 6.847374 F-statistic 23.28338 Durbin-Watson stat 0.952555 Prob(F-statistic) 0.000103由上可知，关系式为y=31.276x3（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..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..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..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： Dependent Variable: Y Method: Least Squares Date: 12/03/14 Time: 17:00 Sample (adjusted): 1 33Included observations: 33 after adjustmentsVariable Coefficient Std. Error t-Statistic X 0...25639 C -154.96 -3.948274 R-squared 0.983702 Mean dependent varAdjusted R-squared 0.983177 S.D. dependent var S.E. of regression 175.2325 Akaike info criterion Sum squared resid
Schwarz criterion Log likelihood -216.2751 Hannan-Quinn criter. F-statistic
Durbin-Watson stat Prob(F-statistic) 0.000000Prob. 0.4 902.9 13.49 13.021②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）=43.2(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=0.983702 F= n=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=0.00―154.17②进行区间预测：∑x2=∑（Xi―X）2=δ2x(n―1)=
x (33―1)= (Xf―X)2=(32000― = 当Xf=32000时，将相关数据代入计算得到：―2.5x√1/33+/≤ Yf≤.5x√1/33+/ 即Yf的置信区间为（―64..9）(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： Dependent Variable: LNY Method: Least Squares Date: 12/03/14 Time: 18:00 Sample (adjusted): 1 33 Included observations: 33 after adjustmentsVariable Coefficient Std. Error t-Statistic Prob. LNX 0...0 C -1....0000 R-squared 0.963442 Mean dependent var 5.573120Adjusted R-squared 0.962263 S.D. dependent var 1.684189 S.E. of regression 0.327172 Akaike info criterion 0.662028 Sum squared resid 3.318281 Schwarz criterion 0.752726 Log likelihood -8.923468 Hannan-Quinn criter. 0.692545 F-statistic 816.9699 Durbin-Watson stat 0.096208 Prob(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）=28.5(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..4（1）对建筑面积与建造单位成本模型，用Eviews分析结果如下： Dependent Variable: Y Method: Least Squares Date: 12/01/14 Time: 12:40 Sample: 1 12 Included observations: 12Variable Coefficient Std. Error t-Statistic Prob. X -64.828 -13.0 C .88 0.0000 R-squared 0.946829 Mean dependent var Adjusted R-squared 0.941512 S.D. dependent var 131.2252 S.E. of regression 31.73600 Akaike info criterion 9.903792 Sum squared resid 10071.74 Schwarz criterion 9.984610 Log likelihood -57.42275 Hannan-Quinn criter. 9.873871 F-statistic 178.0715 Durbin-Watson stat 1.172407 Prob(F-statistic) 0.000000由上可得：建筑面积与建造成本的回归方程为：Y=.18400X（2）经济意义：建筑面积每增加1万平方米，建筑单位成本每平方米减少64.18400元。（3）①首先进行点预测，由Y=.18400X得，当x=4.5，y=②再进行区间估计：计量经济学(庞皓)第三版课后答案05_计量经济学课后答案由上表可知，∑x2=∑（Xi―X）2=δ2x(n―1)= 1.9894192 x (12―1)=43.5357(Xf―X)2=(4.5― 3.=0.当Xf=4.5时，将相关数据代入计算得到：.228x31.73600x√1/12+43.87843≤Yf≤.228x31.73600x√1/12+43.87843即Yf的置信区间为（8..647+478.1231）3.1（1）①对百户拥有家用汽车量计量经济模型，用Eviews分析结果如下：Dependent Variable: YMethod: Least SquaresDate: 11/25/14 Time: 12:38Sample: 1 31Included observations: 31Variable Coefficient Std. Error t-Statistic Prob.X2 5....0002X3 -0....0069X4 -2....0002C 246.00 4..0001R-squared 0.666062 Mean dependent var 16.77355Adjusted R-squared 0.628957 S.D. dependent var 8.252535S.E. of regression 5.026889 Akaike info criterion 6.187394Sum squared resid 682.2795 Schwarz criterion 6.372424Log likelihood -91.90460 Hannan-Quinn criter. 6.247709F-statistic 17.95108 Durbin-Watson stat 1.147253Prob(F-statistic) 0.000001②得到模型得：Y=246.865X2- 0.-2.③对模型进行检验：1） 可决系数是0.666062，修正的可决系数为0.628957，说明模型对样本拟合较好2） F检验，F=17.95108&F（3,27）=3.65，回归方程显著。3）t检验，t统计量分别为4..265020，-2.922950，-4.366842，均大于 t（27）=2.0518，所以这些系数都是显著的。④依据：1） 可决系数越大，说明拟合程度越好2） F的值与临界值比较，若大于临界值，则否定原假设，回归方程是显著的；若小于临界值，则接受原假设，回归方程不显著。3） t的值与临界值比较，若大于临界值，则否定原假设，系数都是显著的；若小于临界值，则接受原假设，系数不显著。（2）经济意义：人均ＧＤＰ增加１万元，百户拥有家用汽车增加5.996865辆，城镇人口比重增加１个百分点，百户拥有家用汽车减少0.524027辆，交通工具消费价格指数每上升１，百户拥有家用汽车减少2.265680辆。（3）用EViews分析得：Dependent Variable: YMethod: Least SquaresDate: 12/08/14 Time: 17:28Sample: 1 31Included observations: 31 Variable Coefficient Std. Error t-Statistic Prob. X2 5....0000LNX3 -22.820 -3..0023LNX4 -230.91 -4..0001C .974 0.0000 R-squared 0.691952 Mean dependent var 16.77355Adjusted R-squared 0.657725 S.D. dependent var 8.252535S.E. of regression 4.828088 Akaike info criterion 6.106692Sum squared resid 629.3818 Schwarz criterion 6.291723Log likelihood -90.65373 Hannan-Quinn criter. 6.167008F-statistic 20.21624 Durbin-Watson stat 1.150090Prob(F-statistic) 0.000000 模型方程为：Y=5.-22.81005 LNX3-230.8481 LNX4+此分析得出的可决系数为0..666062，拟合程度得到了提高，可这样改进。3.2（１）对出口货物总额计量经济模型，用Eviews分析结果如下：：Dependent Variable: YMethod: Least SquaresDate: 12/01/14 Time: 20:25Sample: Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob. X2 0...0X3 18.181 1..0729C -8.216 -2..0520 R-squared 0.985838 Mean dependent var Adjusted R-squared 0.983950 S.D. dependent var S.E. of regression 730.6306 Akaike info criterion 16.17670Sum squared resid 8007316. Schwarz criterion 16.32510Log likelihood -142.5903 Hannan-Quinn criter. 16.19717F-statistic 522.0976 Durbin-Watson stat 1.173432Prob(F-statistic) 0.000000 ①由上可知，模型为：Y = 0. + 18.85348X3 - 18231.58②对模型进行检验：1）可决系数是0.985838，修正的可决系数为0.983950，说明模型对样本拟合较好2）F检验，F=522.0976&F（2,15）=4.77，回归方程显著3）t检验，t统计量分别为X2的系数对应t值为10.58454，大于t（15）=2.131，系数是显著的，X3的系数对应t值为1.928512，小于t（15）=2.131，说明此系数是不显著的。（2）对于对数模型，用Eviews分析结果如下：Dependent Variable: LNYMethod: Least SquaresDate: 12/01/14 Time: 20:25Sample: Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob. LNX2 1...0LNX3 1....0209C -20.487 -3..0018 R-squared 0.986295 Mean dependent var 8.400112Adjusted R-squared 0.984467 S.D. dependent var 0.941530S.E. of regression 0.117343 Akaike info criterion -1.296424Sum squared resid 0.206540 Schwarz criterion -1.148029Log likelihood 14.66782 Hannan-Quinn criter. -1.275962F-statistic 539.7364 Durbin-Watson stat 0.686656Prob(F-statistic) 0.000000 ①由上可知，模型为：LNY=-20.221 LNX2+1.760695 LNX3②对模型进行检验：1）可决系数是0.986295，修正的可决系数为0.984467，说明模型对样本拟合较好。2）F检验，F=539.7364& F（2,15）=4.77，回归方程显著。3）t检验，t统计量分别为-3..5229，均大于t（15）=2.131，所以这些系数都是显著的。（3）①（1）式中的经济意义：工业增加1亿元，出口货物总额增加0.135474亿元，人民币汇率增加1，出口货物总额增加18.85348亿元。②（2）式中的经济意义：工业增加额每增加1%，出口货物总额增加1.564221%，人民币汇率每增加1%，出口货物总额增加1.760695%3.3（1）对家庭书刊消费对家庭月平均收入和户主受教育年数计量模型，由Eviews分析结果如下：Dependent Variable: YMethod: Least SquaresDate: 12/01/14 Time: 20:30Sample: 1 18Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob. X 0....0101T 52.167 10.0C -50.26 -1..3279 R-squared 0.951235 Mean dependent var 755.1222Adjusted R-squared 0.944732 S.D. dependent var 258.7206S.E. of regression 60.82273 Akaike info criterion 11.20482Sum squared resid 55491.07 Schwarz criterionLog likelihood -97.84334 Hannan-Quinn criter.F-statistic 146.2974 Durbin-Watson statProb(F-statistic) 0.000000①模型为：Y = 0.086450X + 52.33811.28 2.605783②对模型进行检验：1）可决系数是0.951235，修正的可决系数为0.944732，说明模型对样本拟合较好。2）F检验，F=539.7364& F（2,15）=4.77，回归方程显著。3）t检验，t统计量分别为2..06702，均大于t（15）=2.131，所以这些系数都是显著的。③经济意义：家庭月平均收入增加1元，家庭书刊年消费支出增加0.086450元，户主受教育年数增加1年，家庭书刊年消费支出增加52.37031元。（2）用Eviews分析：①Dependent Variable: YMethod: Least SquaresDate: 12/01/14 Time: 22:30Sample: 1 18Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob. T 63.581 13.0C -11.90 -0..8443 R-squared 0.923054 Mean dependent var 755.1222Adjusted R-squared 0.918245 S.D. dependent var 258.7206S.E. of regression 73.97565 Akaike info criterion 11.54979Sum squared resid 87558.36 Schwarz criterion 11.64872Log likelihood -101.9481 Hannan-Quinn criter. 11.56343F-statistic 191.9377 Durbin-Watson stat 2.134043Prob(F-statistic) 0.000000 ②Dependent Variable: XMethod: Least SquaresDate: 12/01/14 Time: 22:34Sample: 1 18Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob.计量经济学(庞皓)第三版课后答案05_计量经济学课后答案T 123.50 3..0014C 444.6 1..2899 R-squared 0.483182 Mean dependent var Adjusted R-squared 0.450881 S.D. dependent var 698.8325S.E. of regression 517.8529 Akaike info criterion 15.44170Sum squared resid 4290746. Schwarz criterion 15.54063Log likelihood -136.9753 Hannan-Quinn criter. 15.45534F-statistic 14.95867 Durbin-Watson stat 1.052251Prob(F-statistic) 0.001364 以上分别是y与T，X与T的一元回归模型分别是：Y = 63.01676T - 11.58171X = 123.1516T + 444.5888（3）对残差进行模型分析，用Eviews分析结果如下：Dependent Variable: E1Method: Least SquaresDate: 12/03/14 Time: 20:39Sample: 1 18Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob. E2 0....0078C 3.96E-14 13.E-15 1.0000 R-squared 0.366239 Mean dependent var 2.30E-14Adjusted R-squared 0.326629 S.D. dependent var 71.76693S.E. of regression 58.89136 Akaike info criterion 11.09370Sum squared resid 55491.07 Schwarz criterion 11.19264Log likelihood -97.84334 Hannan-Quinn criter. 11.10735F-statistic 9.246111 Durbin-Watson stat 2.605783Prob(F-statistic) 0.007788 模型为：E1 = 0. + 3.96e-14参数：斜率系数α为0.086450，截距为3.96e-14（3）由上可知，β2与α2的系数是一样的。回归系数与被解释变量的残差系数是一样的，它们的变化规律是一致的。3.6（1）预期的符号是X1，X2,X3,X4,X5的符号为正，X6的符号为负（2）根据Eviews分析得到数据如下：Dependent Variable: YMethod: Least SquaresDate: 12/04/14 Time: 13:24Sample: Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob. X2 0....2336X3 0....6326X4 -3....3346X5 0....3600X6 0....6422C -13.66 -0..3984 R-squared 0.994869 Mean dependent var 12.76667Adjusted R-squared 0.992731 S.D. dependent var 9.746631S.E. of regression 0.830963 Akaike info criterion 2.728738Sum squared resid 8.285993 Schwarz criterion 3.025529Log likelihood -18.55865 Hannan-Quinn criter. 2.769662F-statistic 465.3617 Durbin-Watson stat 1.553294Prob(F-statistic) 0.000000 ①与预期不相符。②评价：1） 可决系数为0.994869，数据相当大，可以认为拟合程度很好。2） F检验，F=465.3617&F（5.12）=3,89，回归方程显著3） T检验，X1，X2,X3,X4,X5，X6 系数对应的t值分别为：1..490501，-1.005377，0..476621，均小于t（12）=2.179，所以所得系数都是不显著的。（3）根据Eviews分析得到数据如下：Dependent Variable: YMethod: Least SquaresDate: 12/03/14 Time: 11:12Sample: Included observations: 18Variable Coefficient Std. Error t-StatisticX5 0..20E-05 46.79946X6 -0...762581C 4...260786 Prob. 0.3 0.2266R-squared 0.993601 Mean dependent var 12.76667Adjusted R-squared 0.992748 S.D. dependent var 9.746631S.E. of regression 0.830018 Akaike info criterion 2.616274Sum squared resid 10.33396 Schwarz criterion 2.764669Log likelihood -20.54646 Hannan-Quinn criter. 2.636736F-statistic
Durbin-Watson stat 1.341880Prob(F-statistic) 0.000000 ①得到模型的方程为：Y=0.-0.+4.205481②评价：1） 可决系数为0.993601，数据相当大，可以认为拟合程度很好。2） F检验，F=&F（5.12）=3,89，回归方程显著3） T检验，X5 系数对应的t值为46.79946，大于t（12）=2.179，所以系数是显著的，即人均GDP对年底存款余额有显著影响。 X6 系数对应的t值为-1.762581，小于t（12）=2.179，所以系数是不显著的。4.3（1）根据Eviews分析得到数据如下：Dependent Variable: LNYMethod: Least SquaresDate: 12/05/14 Time: 11:39Sample: Included observations: 27 Variable Coefficient Std. Error t-Statistic Prob. LNGDP 1...0LNCPI -0....0832C -3....0000 R-squared 0.988051 Mean dependent var 9.484710Adjusted R-squared 0.987055 S.D. dependent var 1.425517S.E. of regression 0.162189 Akaike info criterion -0.695670Sum squared resid 0.631326 Schwarz criterion -0.551689Log likelihood 12.39155 Hannan-Quinn criter. -0.652857F-statistic 992.2582 Durbin-Watson stat 0.522613Prob(F-statistic) 0.000000 得到的模型方程为：LNY=1.338533 LNGDPt-0.421791 LNCPIt-3.111486（2）① 该模型的可决系数为0.988051，可决系数很高，F检验值为992.2582，明显显著。但当α=0.05时，t（24）=2.064，LNCPI的系数不显著，可能存在多重共线性。 ②得到相关系数矩阵如下：LNGDP， LNCPI之间的相关系数很高，证实确实存在多重共线性。（3）由Eviews得：a）Dependent Variable: LNYMethod: Least SquaresDate: 12/03/14 Time: 14:41Sample: Included observations: 27Variable Coefficient Std. Error t-Statistic Prob. LNGDP 1...0C -3...0 R-squared 0.986423 Mean dependent var 9.484710 Adjusted R-squared 0.985880 S.D. dependent var 1.425517 S.E. of regression 0.169389 Akaike info criterion -0.642056 Sum squared resid 0.717312 Schwarz criterion -0.546068 Log likelihood 10.66776 Hannan-Quinn criter. -0.613514 F-statistic
Durbin-Watson stat 0.471111 Prob(F-statistic) 0.000000 b)Dependent Variable: LNY Method: Least Squares Date: 12/03/14 Time: 14:41 Sample:
Included observations: 27 Variable Coefficient Std. Error t-Statistic Prob. LNCPI 2...0C -6....0000 R-squared 0.874442 Mean dependent var 9.484710 Adjusted R-squared 0.869419 S.D. dependent var 1.425517 S.E. of regression 0.515124 Akaike info criterion 1.582368 Sum squared resid 6.633810 Schwarz criterion 1.678356 Log likelihood -19.36196 Hannan-Quinn criter. 1.610910 F-statistic 174.1108 Durbin-Watson stat 0.137042 Prob(F-statistic) 0.000000 c)Dependent Variable: LNGDP Method: Least Squares Date: 12/05/14 Time: 11:11 Sample:
Included observations: 27 Variable Coefficient Std. Error t-Statistic Prob. LNCPI 2...0C -2....0040 R-squared 0.909621 Mean dependent var 11.16214 Adjusted R-squared 0.906005 S.D. dependent var 1.194029计量经济学(庞皓)第三版课后答案05_计量经济学课后答案S.E. of regression 0.366072 Akaike info criterion 0.899213 Sum squared resid 3.350216 Schwarz criterion 0.995201 Log likelihood -10.13938 Hannan-Quinn criter. 0.927755 F-statistic 251.6117 Durbin-Watson stat 0.099623 Prob(F-statistic) 0.000000①得到的回归方程分别为1）LNY=1.185739 LNGDPt-3.）LNY=2.939295 LNCPIt-6.）LNGDPt=2.511022 LNCPIt-2.796381②对多重共线性的认识：单方程拟合效果都很好，回归系数显著，判定系数较高，GDP和CPI对进口的显著的单一影响，在这两个变量同时引入模型时影响方向发生了改变，这只有通过相关系数的分析才能发现。（4）建议：如果仅仅是作预测，可以不在意这种多重共线性，但如果是进行结构分析，还是应该引起注意的。4.4（1）按照设计的理论模型，由Eviews分析得：Dependent Variable: CZSR Method: Least Squares Date: 12/03/14 Time: 11:40 Sample:
Included observations: 27Variable Coefficient Std. Error t-Statistic CZZC 0...031129 GDP -0...998036 SSZE 1...93271 C -221.2 -1.698038 R-squared 0.999857 Mean dependent varAdjusted R-squared 0.999838 S.D. dependent var S.E. of regression 353.0540 Akaike info criterion Sum squared resid 2866884. Schwarz criterion Log likelihood -194.5455 Hannan-Quinn criter. F-statistic 53493.93 Durbin-Watson stat Prob(F-statistic) 0.000000Prob. 0.0 0.0 39.49 14.05 14.128从回归结果可见，可决系数为0.999857，校正的可决系数为0.999838，模型拟合的很好。F的统计量为53493.93，说明在α=0.05,水平下，回归方程回归方程整体上是显著的。但是t检验结果表明，国内生产总值对财政收入的影响显著，但回归系数的符号为负，与实际不符合。由此可得知，该方程可能存在多重共线性。（2）得到相关系数矩阵如下：由上表可知，CZZC与GDP，CZZC与SSZE，GDP与SSZE之间的相关系数都非常高，说明确实存在多重共线性。方差扩大因子均大于10，存在严重多重共线性。并且通过以上分析，两两被解释变量之间相关性都很高。（4）解决方式：分别作出财政收入与财政支出、国内生产总值、税收总额之间的一元回归。5.2（1）①用图形法检验绘制e2的散点图，用Eviews分析如下：由上图可知，模型可能存在异方差，② Goldfeld-Quanadt检验1）定义区间为1-7时，由软件分析得： Dependent Variable: Y Method: Least Squares Date: 12/10/14 Time: 14:52 Sample: 1 7 Included observations: 7Variable Coefficient Std. Error t-Statistic T 35.492 7.182843 X 0...774380 C 77.44 0.936807 R-squared 0.943099 Mean dependent varAdjusted R-squared 0.914649 S.D. dependent var S.E. of regression 31.63265 Akaike info criterion Sum squared resid
Schwarz criterion Log likelihood -32.15324 Hannan-Quinn criter. F-statistic 33.14880 Durbin-Watson stat Prob(F-statistic) 0.0032382得∑e1i=2）定义区间为12-18时，由软件分析得：Prob. 0.7 0.7 108.78 10.267 1.426262Dependent Variable: Y Method: Least Squares Date: 12/10/14 Time: 13:50 Sample: 12 18 Included observations: 7Variable Coefficient Std. Error t-Statistic Prob. T 52.378 7..0016 X 0....2705 C -8..9968 0.9177 R-squared 0.984688 Mean dependent var 887.6143Adjusted R-squared 0.977032 S.D. dependent var 274.4148 S.E. of regression 41.58810 Akaike info criterion 10.59103 Sum squared resid
Schwarz criterion 10.56785 Log likelihood -34.06861 Hannan-Quinn criter. 10.30451 F-statistic 128.6166 Durbin-Watson stat 2.390329 Prob(F-statistic) 0.0002342 得∑e2i=3）根据Goldfeld-Quanadt检验，F统计量为： F=∑e2i2 /∑e1i2 =2.499=1.7285在α=0.05水平下，分子分母的自由度均为4，查分布表得临界值F0.05（4,4）=6.39，因为F=1.7285& F0.05（4,4）=6.39，所以接受原假设，此检验表明模型不存在异方差。（2）存在异方差，估计参数的方法： ①可以对模型进行变换②使用加权最小二乘法进行计算，得出模型方程，并对其进行相关检验 ③对模型进行对数变换，进行分析（3）评价：3.3所得结论是可以相信的，随机扰动项之间不存在异方差。回归方程是显著的。计量经济学(庞皓)第三版课后答案05_计量经济学课后答案5.3(1)由Eviews软件分析得：Dependent Variable: YMethod: Least SquaresDate: 12/10/14 Time: 16:00Sample: 1 31Included observations: 31 Variable Coefficient Std. Error t-Statistic Prob. X 1...0C 242.0 0..4119 R-squared 0.895260 Mean dependent var Adjusted R-squared 0.891649 S.D. dependent var S.E. of regression 649.1426 Akaike info criterion 15.85152Sum squared resid
Schwarz criterion 15.94404Log likelihood -243.6986 Hannan-Quinn criter. 15.88168F-statistic 247.8769 Durbin-Watson stat 1.078581Prob(F-statistic) 0.000000 由上表可知，2007年我国农村居民家庭人均消费支出（x）对人均纯收入（y）的模型为： Y=1.2.4488（2）①由图形法检验由上图可知，模型可能存在异方差。②Goldfeld-Quanadt检验1）定义区间为1-12时，由软件分析得：Dependent Variable: Y1Method: Least SquaresDate: 12/10/14 Time: 11:34Sample: 1 12Included observations: 12 Variable Coefficient Std. Error t-Statistic Prob. X1 1....0141C -550.3 -0..6614 R-squared 0.468390 Mean dependent var Adjusted R-squared 0.415229 S.D. dependent var 550.5148 S.E. of regression 420.9803 Akaike info criterion 15.07406 Sum squared resid 1772245. Schwarz criterion 15.15488 Log likelihood -88.44437 Hannan-Quinn criter. 15.04414 F-statistic 8.810789 Durbin-Watson stat 2.354167 Prob(F-statistic) 0. 得∑e1i=1772245.2）定义区间为20-31时，由软件分析得：Dependent Variable: Y1Method: Least SquaresDate: 12/10/14 Time: 16:36Sample: 20 31Included observations: 12 Variable Coefficient Std. Error t-Statistic Prob. X1 1....0000C .141 0.1407 R-squared 0.842056 Mean dependent var Adjusted R-squared 0.826262 S.D. dependent var
S.E. of regression 889.3633 Akaike info criterion 16.56990 Sum squared resid 7909670. Schwarz criterion 16.65072 Log likelihood -97.41940 Hannan-Quinn criter. 16.53998 F-statistic 53.31370 Durbin-Watson stat 2.339767 Prob(F-statistic) 0. 得∑e2i=7909670.3）根据Goldfeld-Quanadt检验，F统计量为：F=∑e2i2 /∑e1i2 =7909670./ .4631在α=0.05水平下，分子分母的自由度均为10，查分布表得临界值F0.05（10,10）=2.98，因为F=4.4631& F0.05（10,10）=2.98，所以拒绝原假设，此检验表明模型存在异方差。（3）1）采用WLS法估计过程中，①用权数w1=1/X,建立回归得：Dependent Variable: YMethod: Least SquaresDate: 12/09/14 Time: 11:13Sample: 1 31Included observations: 31Weighting series: W1 Variable Coefficient Std. Error t-Statistic Prob. X 1...0C -334.3 -0..3389 Weighted Statistics R-squared 0.831707 Mean dependent var Adjusted R-squared 0.825904 S.D. dependent var 536.1907 S.E. of regression 536.6796 Akaike info criterion 15.47102 Sum squared resid 8352726. Schwarz criterion 15.56354 Log likelihood -237.8008 Hannan-Quinn criter. 15.50118 F-statistic 143.3184 Durbin-Watson stat 1.369081 Prob(F-statistic) 0.000000 Unweighted Statistics R-squared 0.875855 Mean dependent var Adjusted R-squared 0.871574 S.D. dependent var
S.E. of regression 706.7236 Sum squared resid
Durbin-Watson stat 1.532908对此模型进行White检验得：Heteroskedasticity Test: White F-statistic 0.299395 Prob. F(2,28) 0.7436Obs*R-squared 0.649065 Prob. Chi-Square(2) 0.7229 Scaled explained SS 1.798067 Prob. Chi-Square(2) 0.4070Test Equation:Dependent Variable: WGT_RESID^2Method: Least SquaresDate: 12/10/14 Time: 21:13Sample: 1 31Included observations: 31Collinear test regressors dropped from specification Variable Coefficient Std. Error t-Statistic Prob. C 222 0.9532WGT^2 - 1173622. -0..6168X*WGT^2 282.0 0..7086 R-squared 0.020938 Mean dependent var Adjusted R-squared -0.048995 S.D. dependent var
S.E. of regression
Akaike info criterion 29.86395 Sum squared resid 1.40E+13 Schwarz criterion 30.00273 Log likelihood -459.8913 Hannan-Quinn criter. 29.90919 F-statistic 0.299395 Durbin-Watson stat 1.922336 Prob(F-statistic) 0.743610从上可知，nR2=0.649065，比较计算的统计量的临界值，因为nR2=0.649065&（2）=5.9915，所以接受原假设，该模型消除了异方差。估计结果为：Y=1.4.8131t=（11.97157）（-0.972298）R2=0.875855 F=143.3184 DW=1.369081②用权数w2=1/x2,用回归分析得：Dependent Variable: YMethod: Least SquaresDate: 12/09/14 Time: 21:08Sample: 1 31Included observations: 31Weighting series: W2Variable Coefficient Std. Error t-StatisticX 1...70922C -693.0 -1.841272Weighted StatisticsR-squared 0.798173 Mean dependent varAdjusted R-squared 0.791214 S.D. dependent varS.E. of regression 466.8513 Akaike info criterionSum squared resid 6320554. Schwarz criterionLog likelihood -233.4797 Hannan-Quinn criter.F-statistic 114.6875 Durbin-Watson stat 0.05 Prob. 0.8 9.830 15.75 15.975Prob(F-statistic) 0.000000 Unweighted Statistics R-squared 0.834850 Mean dependent var Adjusted R-squared 0.829156 S.D. dependent var
S.E. of regression 815.1229 Sum squared resid
Durbin-Watson stat 1.678365对此模型进行White检验得：Heteroskedasticity Test: White F-statistic 0.299790 Prob. F(3,27) 0.8252Obs*R-squared 0.999322 Prob. Chi-Square(3) 0.8014 Scaled explained SS 1.789507 Prob. Chi-Square(3) 0.6172Test Equation:Dependent Variable: WGT_RESID^2Method: Least SquaresDate: 12/10/14 Time: 21:29Sample: 1 31Included observations: 31 Variable Coefficient Std. Error t-Statistic Prob. C -
-0..8406WGT^2
..8505X^2*WGT^2 0....7088X*WGT^2 -583.0 -0..7816 R-squared 0.032236 Mean dependent var Adjusted R-squared -0.075293 S.D. dependent var
S.E. of regression
Akaike info criterion 28.92298 Sum squared resid 5.10E+12 Schwarz criterion 29.10801 Log likelihood -444.3062 Hannan-Quinn criter. 28.98330 F-statistic 0.299790 Durbin-Watson stat 1.835854 Prob(F-statistic) 0.825233从上可知，nR2=0.999322，比较计算的统计量的临界值，因为nR2=0.999322&（2）=5.9915，所以接受原假设，该模型消除了异方差。估计结果为：Y=1.3.1946t=（10.70922）（-1.841272）R2=0.798173 F=114.6875 DW=1..05计量经济学(庞皓)第三版课后答案05_计量经济学课后答案③用权数w3=1/sqr（x）,用回归分析得：Dependent Variable: YMethod: Least SquaresDate: 12/09/14 Time: 21:35Sample: 1 31Included observations: 31Weighting series: W3 Variable Coefficient Std. Error t-Statistic Prob. X 1...0C -47.54 -0..8807 Weighted Statistics R-squared 0.863161 Mean dependent var Adjusted R-squared 0.858442 S.D. dependent var 991.2079 S.E. of regression 586.9555 Akaike info criterion 15.65012 Sum squared resid 9990985. Schwarz criterion 15.74263 Log likelihood -240.5768 Hannan-Quinn criter. 15.68027 F-statistic 182.9276 Durbin-Watson stat 1.237664 Prob(F-statistic) 0.000000 Unweighted Statistics R-squared 0.890999 Mean dependent var Adjusted R-squared 0.887240 S.D. dependent var
S.E. of regression 662.2171 Sum squared resid
Durbin-Watson stat 1.314859对此模型进行White检验得：Heteroskedasticity Test: White F-statistic 0.423886 Prob. F(2,28) 0.6586Obs*R-squared 0.911022 Prob. Chi-Square(2) 0.6341 Scaled explained SS 2.768332 Prob. Chi-Square(2) 0.2505Test Equation:Dependent Variable: WGT_RESID^2Method: Least SquaresDate: 12/09/14 Time: 20:36Sample: 1 31Included observations: 31Collinear test regressors dropped from specificationVariable Coefficient Std. Error t-StatisticC 4981WGT^2 - 1301839. -0.549740X^2*WGT^2 -0...184677R-squared 0.029388 Mean dependent varAdjusted R-squared -0.039942 S.D. dependent varS.E. of regression
Akaike info criterionSum squared resid 2.17E+13 Schwarz criterionLog likelihood -466.7426 Hannan-Quinn criter.F-statistic 0.423886 Durbin-Watson statProb(F-statistic) 0.658628Prob. 0.9 0..8
30.75 30.426估计结果为：Y=1..40242t=（13.52507）（-0.151390）R2=0.863161 F=182.9276 DW=1.237664经过检验发现，用权数w1的效果最好，所以综上可知，即修改后的结果为： Y=1.4.8131t=（11.97157）（-0.972298）R2=0.875855 F=143.3184 DW=1.3690815.6(1)a)用Eviews模型分析得：Dependent Variable: YMethod: Least SquaresDate: 12/10/14 Time: 20:16Sample: Included observations: 34Variable Coefficient Std. Error t-StatisticX 0...03027C 92.29 2.162215R-squared 0.979426 Mean dependent varAdjusted R-squared 0.978783 S.D. dependent varS.E. of regression 173.1597 Akaike info criterionSum squared resid
Schwarz criterionLog likelihood -222.4566 Hannan-Quinn criter.F-statistic
Durbin-Watson statProb(F-statistic) 0.000000得回归模型为：Y=0.746241 X+92.55422b)检验是否存在异方差：①用Goldfeld-Quanadt检验如下：1）当定义区间为1-13时，由软件分析得：Dependent Variable: YMethod: Least SquaresDate: 12/11/14 Time: 11:47Sample: 1 13Included observations: 13Variable Coefficient Std. Error t-StatisticX 0...00771C -18.780 -2.104984R-squared 0.991587 Mean dependent varAdjusted R-squared 0.990823 S.D. dependent varS.E. of regression 12.17039 Akaike info criterionSum squared resid
Schwarz criterionLog likelihood -49.84742 Hannan-Quinn criter.F-statistic
Durbin-Watson statProb(F-statistic) 0.000000Prob. 0.2 8.791 13.11 13.491 Prob. 0.1 280.9 7....071505得∑e1i2=2）当定义区间为1-13时，由软件分析得：Dependent Variable: Y Method: Least Squares Date: 12/11/14 Time: 12:21 Sample: 22 34 Included observations: 13 Variable Coefficient Std. Error t-Statistic Prob. X 0...0C 179.4 0..3955 R-squared 0.932629 Mean dependent var
Adjusted R-squared 0.926504 S.D. dependent var
S.E. of regression 277.2250 Akaike info criterion 14.22817 Sum squared resid
Schwarz criterion 14.31509 Log likelihood -90.48313 Hannan-Quinn criter. 14.21031 F-statistic 152.2752 Durbin-Watson stat 1.658418 Prob(F-statistic) 0. 得∑e2i=3）根据Goldfeld-Quanadt检验，F统计量为：F=∑e2i2 /∑e1i2 =/ .8669在α=0.05水平下，分子分母的自由度均为11，查分布表得临界值F0.05（11,11）=4.47，因为F=518.8669& F0.05（11,11）=4.47，所以拒绝原假设，此检验表明模型存在异方差。②White检验用EViews软件分析得：Heteroskedasticity Test: White F-statistic 10.36759 Prob. F(2,31) 0.0004 Obs*R-squared 13.62701 Prob. Chi-Square(2) 0.0011 Scaled explained SS 76.13635 Prob. Chi-Square(2) 0.0000Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 12/11/14 Time: 12:56 Sample: 1 34 Included observations: 34Variable Coefficient Std. Error t-StatisticC 17.11 0.443430 X -27.40 -0.994029 X^2 0...371861 R-squared 0.400795 Mean dependent var Adjusted R-squared 0.362136 S.D. dependent var S.E. of regression 81255.15 Akaike info criterion Sum squared resid 2.05E+11 Schwarz criterion Log likelihood -431.0554 Hannan-Quinn criter. F-statistic 10.36759 Durbin-Watson stat Prob(F-statistic) 0.000357从上图中可以看出，nR2=13.62701，比较计算的nR2=13.62701&异方差。用以上两种方法，可以检验模型是存在异方差的。c)修正模型1）用加权二乘法修正异方差现象步骤如下：①当权数w1=1/x时，用软件分析得：Dependent Variable: Y Method: Least Squares Date: 12/11/14 Time: 13:22 Sample: 1 34 Included observations: 34 Weighting series: W1Variable Coefficient Std. Error t-Statistic X 0...67993C 17.256 2.815926 Weighted StatisticsR-squared 0.986676 Mean dependent var Adjusted R-squared 0.986260 S.D. dependent var S.E. of regression 37.91285 Akaike info criterion Sum squared resid 45996.29 Schwarz criterionLog likelihood -170.8132 Hannan-Quinn criter. Prob. 0.9 0..51
25.35 25.651统计量的临界值，因为0.05（2）=5.9915，所以拒绝原假设，不拒绝备择假设，表明模型存在 Prob. 0.3 457.84 10.27 10.19610计量经济学(庞皓)第三版课后答案05_计量经济学课后答案F-statistic
Durbin-Watson stat 0.605852Prob(F-statistic) 0.000000 Unweighted Statistics R-squared 0.968070 Mean dependent var Adjusted R-squared 0.967072 S.D. dependent var S.E. of regression 215.7175 Sum squared resid 1489089.Durbin-Watson stat 1.079107 得方程模型为：Y=0..69318t=（48.67993）（2.815926）R2=0.986676 F= DW=0.605852对此模型进行White检验如下：Heteroskedasticity Test: White F-statistic 1.348072 Prob. F(2,31) 0.2745Obs*R-squared 2.720457 Prob. Chi-Square(2) 0.2566Scaled explained SS 1.221901 Prob. Chi-Square(2) 0.5428Test Equation:Dependent Variable: WGT_RESID^2Method: Least SquaresDate: 12/11/14 Time: 11:20Sample: 1 34Included observations: 34Collinear test regressors dropped from specification Variable Coefficient Std. Error t-Statistic Prob. C .498 0.0003WGT^2 -32.75 -0..8651X*WGT^2 -0....7078 R-squared 0.080013 Mean dependent var Adjusted R-squared 0.020659 S.D. dependent var S.E. of regression
Akaike info criterion 17.36487Sum squared resid
Schwarz criterion 17.49955Log likelihood -292.2027 Hannan-Quinn criter. 17.41080F-statistic 1.348072 Durbin-Watson stat 1.199640Prob(F-statistic) 0.2745452从上图中可以看出，nR=2.720457，比较计算的统计量的临界值，因为nR2=2.720457&响。0.05（2）=5.9915，所以接受原假设，即该模型消除了异方差的影②当权数w2=1/x2时，用软件分析得：Dependent Variable: YMethod: Least SquaresDate: 12/11/14 Time: 13:27Sample: 1 34Included observations: 34Weighting series: W2Variable Coefficient Std. Error t-StatisticX 0...29335C 8...466744Weighted StatisticsR-squared 0.982425 Mean dependent varAdjusted R-squared 0.981875 S.D. dependent varS.E. of regression 16.20273 Akaike info criterionSum squared resid
Schwarz criterionLog likelihood -141.9094 Hannan-Quinn criter.F-statistic
Durbin-Watson statProb(F-statistic) 0.000000Unweighted StatisticsR-squared 0.954142 Mean dependent varAdjusted R-squared 0.952709 S.D. dependent varS.E. of regression 258.5207 Sum squared residDurbin-Watson stat 0.781788得方程模型为：Y=0..890886t=（42.29335）（2.466744）R2=0.982425 F= DW=0.604647用White检验模型得：Heteroskedasticity Test: WhiteF-statistic 7.462185 Prob. F(3,30)Obs*R-squared 14.52935 Prob. Chi-Square(3)Scaled explained SS 19.40139 Prob. Chi-Square(3)Prob. 0.2 230.8 8....5.802 7 0.2Test Equation:Dependent Variable: WGT_RESID^2Method: Least SquaresDate: 12/11/14 Time: 11:19Sample: 1 34Included observations: 34Variable Coefficient Std. Error t-StatisticC -7..7605WGT^2 64.60 0.667975X^2*WGT^2 0...838317X*WGT^2 -1...071903R-squared 0.427334 Mean dependent varAdjusted R-squared 0.370067 S.D. dependent varS.E. of regression 345.6323 Akaike info criterionSum squared resid 3583851. Schwarz criterionLog likelihood -244.8589 Hannan-Quinn criter.F-statistic 7.462185 Durbin-Watson statProb(F-statistic) 0.000712从上图中可以看出，nR2=14.52935，比较计算的nR2=14.52935& Prob. 0.3 0.3 247.1 14.33 14.012统计量的临界值，因为0.05（2）=5.9915，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差。此模型并未消除异方差。③当权数w3=1/sqr(x)时，用软件分析得：Dependent Variable: YMethod: Least SquaresDate: 12/11/14 Time: 13:21Sample: 1 34Included observations: 34Weighting series: W3Variable Coefficient Std. Error t-Statistic Prob.X 0...0C 40.28 2..0091Weighted StatisticsR-squared 0.987192 Mean dependent var 776.3266Adjusted R-squared 0.986792 S.D. dependent varS.E. of regression 79.19828 Akaike info criterionSum squared resid
Schwarz criterionLog likelihood -195.8597 Hannan-Quinn criter.F-statistic
Durbin-Watson statProb(F-statistic) 0.000000Unweighted StatisticsR-squared 0.977590 Mean dependent varAdjusted R-squared 0.976890 S.D. dependent varS.E. of regression 180.7210 Sum squared residDurbin-Watson stat 1.460832得方程模型为：Y=0..45770t=（49.66347）（2.775775）R2=0.986792 F= DW=1.178340对所得模型进行White检验：Heteroskedasticity Test: WhiteF-statistic 8.158958 Prob. F(2,31)Obs*R-squared 11.72514 Prob. Chi-Square(2)Scaled explained SS 28.08353 Prob. Chi-Square(2)Test Equation:Dependent Variable: WGT_RESID^2Method: Least SquaresDate: 12/10/14 Time: 13:23Sample: 1 34Included observations: 34Collinear test regressors dropped from specification Variable Coefficient Std. Error t-StatisticC -1.263 -1.428132WGT^2 6.041 1.236632X^2*WGT^2 0...684177R-squared 0.344857 Mean dependent varAdjusted R-squared 0.302590 S.D. dependent varS.E. of regression 11636.97 Akaike info criterionSum squared resid 4.20E+09 Schwarz criterionLog likelihood -364.9796 Hannan-Quinn criter. 367.81 11.43 1.5.802 4 0.0 Prob. 0.5 0.5 .54 21.69179F-statistic 8.158958 Durbin-Watson statProb(F-statistic) 0.001423从上图中可以看出，nR2=11.72514，比较计算的nR2=11.068统计量的临界值，因为0.05（2）=5.9915，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差。此模型并未消除异方差。综上所述，用加权二乘法w1的效果最好，所以模型为：得方程模型为：Y=0..69318t=（48.67993）（2.815926）R2=0.986676 F= DW=0.6058522）用对数模型法用软件分析得：Dependent Variable: LNY Method: Least SquaresDate: 12/11/14 Time: 09:54Sample: 1 34Included observations: 34Variable Coefficient Std. Error t-Statistic Prob.LNX 0...0C 0....0143R-squared 0.995521 Mean dependent var 6.687779Adjusted R-squared 0.995381 S.D. dependent var 1.067124S.E. of regression 0.072525 Akaike info criterion -2.352753Sum squared resid 0.168315 Schwarz criterion -2.262967Log likelihood 41.99680 Hannan-Quinn criter. -2.322134F-statistic
Durbin-Watson stat 0.812150Prob(F-statistic) 0.000000得到模型为：LnY=0.946887 LNX+0.201861对此模型进行White检验得：Heteroskedasticity Test: WhiteF-statistic 1.003964 Prob. F(2,31) 0.3780Obs*R-squared 2.068278 Prob. Chi-Square(2) 0.3555Scaled explained SS 1.469638 Prob. Chi-Square(2) 0.4796计量经济学(庞皓)第三版课后答案05_计量经济学课后答案Test Equation:Dependent Variable: RESID^2Method: Least SquaresDate: 12/11/14 Time: 09:55Sample: 1 34Included observations: 34 Variable Coefficient Std. Error t-Statistic Prob.C 0....4042 LNX -0....4140LNX^2 0....3715 R-squared 0.060832 Mean dependent var 0.004950Adjusted R-squared 0.000240 S.D. dependent var 0.006365S.E. of regression 0.006364 Akaike info criterion -7.192271Sum squared resid 0.001255 Schwarz criterion -7.057592Log likelihood 125.2686 Hannan-Quinn criter. -7.146342F-statistic 1.003964 Durbin-Watson stat 2.022904Prob(F-statistic) 0.378027从上图中可以看出，nR2=2.068278，比较计算的统计量的临界值，nR2=2..05（2）=5.9915，所以接受原假设，此模型消除了异方差。综合两种方法，改进后的模型最好为：LnY=0.946887 LNX+0.201861(2)1）考虑价格因素，首先用软件三者关系进行分析如下：Dependent Variable: YMethod: Least SquaresDate: 12/12/14 Time: 19:26Sample: 1 34Included observations: 34Variable Coefficient Std. Error t-Statistic Prob.X 0...0P 0....3937C 43.46 0..5466R-squared 0.979911 Mean dependent var
为因Adjusted R-squared 0.978615 S.D. dependent varS.E. of regression 173.8449 Akaike info criterionSum squared resid
Schwarz criterionLog likelihood -222.0511 Hannan-Quinn criter.F-statistic 756.0627 Durbin-Watson statProb(F-statistic) 0.0000001）用Goldfeld-Quanadt检验如下：①当样本为1-13时，进行回归分析：Dependent Variable: PMethod: Least SquaresDate: 12/14/14 Time: 19:26Sample: 1 13Included observations: 13Variable Coefficient Std. Error t-StatisticX -0...836247Y 0...186646C 59.841 8.056627R-squared 0.956255 Mean dependent varAdjusted R-squared 0.947506 S.D. dependent varS.E. of regression 8.466678 Akaike info criterionSum squared resid 716.8464 Schwarz criterionLog likelihood -44.51063 Hannan-Quinn criter.F-statistic 109.2993 Durbin-Watson statProb(F-statistic) 0.0000002 得∑e1i=716.8464②当样本为22-34时，做回归分析得：Dependent Variable: YMethod: Least SquaresDate: 12/14/14 Time:20:39Sample: 22 34Included observations: 13Variable Coefficient Std. Error t-StatisticX 0...918569P -1...082514C 795.5 1.317670.98 13.521 Prob. 0.6 0.1 36.328 7...637181 Prob. 0.4 0.2170R-squared 0.939696 Mean dependent var Adjusted R-squared 0.927635 S.D. dependent var S.E. of regression 275.0847 Akaike info criterion 14.27121Sum squared resid
Schwarz criterion 14.40158Log likelihood -89.76286 Hannan-Quinn criter. 14.24441F-statistic 77.91291 Durbin-Watson stat 1.128778Prob(F-statistic) 0. 得∑e2i=③根据Goldfeld-Quanadt检验，F统计量为：F=∑e2i2 /∑e1i2 =/ 716.76在α=0.05水平下，分子分母的自由度均为11，查分布表得临界值F0.05（10,10）=2.98，因为F=& F0.05（10,10）=2.98，所以拒绝原假设，此检验表明模型存在异方差。2）用White检验，软件分析结果为：Heteroskedasticity Test: WhiteF-statistic 7.312529 Prob. F(5,28)Obs*R-squared 19.25463 Prob. Chi-Square(5)Scaled explained SS 119.3072 Prob. Chi-Square(5)Test Equation:Dependent Variable: RESID^2Method: Least SquaresDate: 12/12/14 Time: 19:31Sample: 1 34Included observations: 34Variable Coefficient Std. Error t-StatisticC 647.3 0.706107X 209.00 3.278298X^2 -0...252841X*P -0...204822P -6.253 -1.016495P^2 1...629751R-squared 0.566313 Mean dependent varAdjusted R-squared 0.488869 S.D. dependent varS.E. of regression 77206.44 Akaike info criterionSum squared resid 1.67E+11 Schwarz criterionLog likelihood -427.5874 Hannan-Quinn criter.F-statistic 7.312529 Durbin-Watson statProb(F-statistic) 0..7 0.0000 Prob. 0.8 0.8 0.0 990.9 25.50 25.044从上图中可以看出，nR2=19.25463，比较计算的nR2=19.25463&统计量的临界值，因为0.05（5）=11.0705，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差。2）修正①建立对数模型，用软件分析如下：Dependent Variable: LNYMethod: Least SquaresDate: 12/12/14 Time: 19:24Sample: 1 34Included observations: 34Variable Coefficient Std. Error t-Statistic Prob.LNX 0...0LNP 0....3532C 0....3981R-squared 0.995646 Mean dependent var 6.687779Adjusted R-squared 0.995365 S.D. dependent var 1.067124S.E. of regression 0.072652 Akaike info criterion -2.322188Sum squared resid 0.163625 Schwarz criterion -2.187509Log likelihood 42.47720 Hannan-Quinn criter. -2.276259F-statistic
Durbin-Watson stat 0.930109Prob(F-statistic) 0.000000对此模型进行White检验：Heteroskedasticity Test: WhiteF-statistic 3.523832 Prob. F(5,28) 0.0135Obs*R-squared 13.13158 Prob. Chi-Square(5) 0.0222Scaled explained SS 12.14373 Prob. Chi-Square(5) 0.0329Test Equation:Dependent Variable: RESID^2Method: Least SquaresDate: 12/12/14 Time: 19:24Sample: 1 34Included observations: 34Variable Coefficient Std. Error t-Statistic Prob.C 0....1336LNX 0....0171LNX^2 -0....2078LNX*LNP -0....3429LNP -0....0596LNP^2 0....0460 R-squared 0.386223 Mean dependent var 0.004813Adjusted R-squared 0.276620 S.D. dependent var 0.007286S.E. of regression 0.006197 Akaike info criterion -7.170690Sum squared resid 0.001075 Schwarz criterion -6.901332Log likelihood 127.9017 Hannan-Quinn criter. -7.078831F-statistic 3.523832 Durbin-Watson stat 2.264261Prob(F-statistic) 0.0135022从上图中可以看出，nR=13.13158，比较计算的统计量的临界值，因为nR2=13.（5）=11.0705，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差，所以此模型没有消除异方差。②当w1=1/x时，用软件分析如下：Dependent Variable: YMethod: Least SquaresDate: 12/13/14 Time: 18:49Sample: 1 34Included observations: 34Weighting series: W1Variable Coefficient Std. Error t-StatisticX 0...49212P 0...099795C -44.68 -3.410502Weighted StatisticsR-squared 0.992755 Mean dependent varAdjusted R-squared 0.992287 S.D. dependent varS.E. of regression 28.40494 Akaike info criterionSum squared resid 25012.05 Schwarz criterionLog likelihood -160.4567 Hannan-Quinn criter.F-statistic
Durbin-Watson statProb(F-statistic) 0.000000Unweighted Statistics Prob. 0.0 0.5 41.100 9...298389计量经济学(庞皓)第三版课后答案05_计量经济学课后答案R-squared 0.977704 Mean dependent var Adjusted R-squared 0.976266 S.D. dependent var
S.E. of regression 183.1446 Sum squared resid 1039800. Durbin-Watson stat 1.740795所得模型为：Y=0...72084对此模型进行White检验得： Heteroskedasticity Test: WhiteF-statistic 2.088840 Prob. F(5,28) 0.0966Obs*R-squared 9.236835 Prob. Chi-Square(5) 0.1000 Scaled explained SS 25.50696 Prob. Chi-Square(5) 0.0001Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 12/14/14 Time: 19:57 Sample: 1 34 Included observations: 34 Collinear test regressors dropped from specificationVariable Coefficient Std. Error t-Statistic Prob. C 8.806 3..0012 WGT^2 9.988 0..4557 X*WGT^2 13.473 1..1157 X*P*WGT^2 -0....0202 P^2*WGT^2 0....1326 P*WGT^2 -76.36 -1..3085R-squared 0.271672 Mean dependent var 735.6486Adjusted R-squared 0.141613 S.D. dependent var
S.E. of regression
Akaike info criterion 17.96897 Sum squared resid
Schwarz criterion 18.23832 Log likelihood -299.4724 Hannan-Quinn criter. 18.06082 F-statistic 2.088840 Durbin-Watson stat 2.336495 Prob(F-statistic) 0.0966162因为nR=9..05（5）=11.0705，所以接受原假设。该模型不存在异方差，所以此模型消除了异方差。③当w2=1/x2，用软件分析得： Dependent Variable: Y Method: Least Squares Date: 12/15/14 Time: 20:02 Sample: 1 34 Included observations: 34 Weighting series: W2Variable Coefficient Std. Error t-Statistic X 0...29477 P 1...828234 C -81.99 -5.189209 Weighted Statistics R-squared 0.991614 Mean dependent varAdjusted R-squared 0.991073 S.D. dependent var S.E. of regression 11.37136 Akaike info criterion Sum squared resid
Schwarz criterion Log likelihood -129.3309 Hannan-Quinn criter. F-statistic
Durbin-Watson stat Prob(F-statistic) 0.000000Unweighted Statistics R-squared 0.956816 Mean dependent varAdjusted R-squared 0.954030 S.D. dependent var S.E. of regression 254.8849 Sum squared resid Durbin-Watson stat 1.002870所得模型为：Y=0...85973对该模型进行White检验得： Heteroskedasticity Test: WhiteF-statistic 43.19853 Prob. F(6,27)Obs*R-squared 30.79235 Prob. Chi-Square(6) Scaled explained SS 47.42430 Prob. Chi-Square(6)Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 12/14/14 Time: 19:20Prob. 0.0 0.3 247.170 7...1679618.791 2013955.0.0 0.0000Sample: 1 34 Included observations: 34Variable Coefficient Std. Error t-Statistic Prob. C 27.56 1..1829 WGT^2 -.268 0.1485 X^2*WGT^2 0....1674 X*WGT^2 7....1153 X*P*WGT^2 -0....0924 P^2*WGT^2 0....2725 P*WGT^2 -3..5685 0.8954R-squared 0.905657 Mean dependent var 117.8983Adjusted R-squared 0.884692 S.D. dependent var 230.3570 S.E. of regression 78.22224 Akaike info criterion 11.73823 Sum squared resid
Schwarz criterion 12.05248 Log likelihood -192.5498 Hannan-Quinn criter. 11.84539 F-statistic 43.19853 Durbin-Watson stat 1.794799 Prob(F-statistic) 0.000000因为nR2=30.（5）=11.0705，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差，所以此模型没有消除异方差。④当w3=1/sqr(x)时，用软件分析得： Dependent Variable: Y Method: Least Squares Date: 12/14/14 Time: 19:06 Sample: 1 34 Included observations: 34 Weighting series: W3Variable Coefficient Std. Error t-Statistic X 0...56252 P 0...510739 C -13.68 -0.531823 Weighted Statistics R-squared 0.989356 Mean dependent varAdjusted R-squared 0.988670 S.D. dependent var S.E. of regression 73.35237 Akaike info criterion Sum squared resid
Schwarz criterion Log likelihood -192.7129 Hannan-Quinn criter.Prob. 0.5 0.6 367.52 11.45F-statisticProb(F-statistic)R-squared Adjusted R-squared S.E. of regression Durbin-Watson stat所得模型为： Durbin-Watson stat 0.000000Unweighted Statistics 0.979407 Mean dependent var 0.978079 S.D. dependent var 176.0098 Sum squared resid 1.7612251.5995908.791 Y=0...49643对所得模型进行White检验得： Heteroskedasticity Test: WhiteF-statistic 4.459272 Prob. F(5,28)Obs*R-squared 15.07219 Prob. Chi-Square(5) Scaled explained SS 72.39077 Prob. Chi-Square(5)Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 12/14/14 Time: 19:08 Sample: 1 34 Included observations: 34 Collinear test regressors dropped from specificationVariable Coefficient Std. Error t-Statistic C 31.93 2.221538 WGT^2 50.39 1.628320 X^2*WGT^2 -0...164950 X*P*WGT^2 -0...058447 P^2*WGT^2 1...918030 P*WGT^2 -503.4 -1.916718R-squared 0.443300 Mean dependent varAdjusted R-squared 0.343889 S.D. dependent var S.E. of regression 13710.96 Akaike info criterion Sum squared resid 5.26E+09 Schwarz criterion Log likelihood -368.8256 Hannan-Quinn criter. F-statistic 4.459272 Durbin-Watson stat Prob(F-statistic) 0.0041030.1 0.0000 Prob. 0.7 0.9 0.5 26.97 22.92 22.171因为nR2=15.07219&0.05（5）=11.0705，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差，所以此模型没有消除异方差。综上所述，修改后的模型为：Y= Y=0...72084 t=(31.49212) (5.099705) (-3.410502) R2=0.992755 F= DW=1.298389(3)体会：对于不同的模型，可采取对数模型法或者加权二乘法对具有异方差性的模型进行改进，从而消除异方差。但对于不同的模型，自由度的不同，可能导致改进的方法不同，所以要对改进的模型进行进一步的检验才行。计量经济学(庞皓)第三版课后答案05_计量经济学课后答案6.1(1)建立居民收入-消费模型，用Eviews分析结果如下：Dependent Variable: YMethod: Least SquaresDate: 12/20/14 Time: 14:22Sample: 1 19Included observations: 19Variable Coefficient Std. Error t-StatisticX 0...62068C 79.19 6.446390R-squared 0.994122 Mean dependent varAdjusted R-squared 0.993776 S.D. dependent varS.E. of regression 19.44245 Akaike info criterionSum squared resid
Schwarz criterionLog likelihood -82.28490 Hannan-Quinn criter.F-statistic
Durbin-Watson statProb(F-statistic) 0.000000Prob. 0.0 700.1 8....574663残差的变动有系统模式，连续为正和连续为负，表明残差项存在一阶自相关。②该回归方程可决系数较高，回归系数均显著。对样本量为19，一个解释变量的模型，5%的显著水平，查DW统计表可知，dL=1.180，dU=1.401，模型中DW=0.574663,& dL,显然模型中有自相关。③对模型进行BG检验，用Eviews分析结果如下：Breusch-Godfrey Serial Correlation LM Test:F-statistic 4.811108 Prob. F(2,15) 0.0243Obs*R-squared 7.425088 Prob. Chi-Square(2) 0.0244Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 12/20/14 Time: 15:03Sample: 1 19Included observations: 19 Presample missing value lagged residuals set to zero.Variable Coefficient Std. Error t-Statistic Prob.X -0....7656C 1..323 0.8547RESID(-1) 0....0551RESID(-2) 0....7615R-squared 0.390794 Mean dependent var -1.65E-13Adjusted R-squared 0.268953 S.D. dependent var 18.89466S.E. of regression 16.15518 Akaike info criterion 8.587023Sum squared resid
Schwarz criterion 8.785852Log likelihood -77.57671 Hannan-Quinn criter. 8.620672F-statistic 3.207406 Durbin-Watson stat 1.570723Prob(F-statistic) 0.053468 如上表显示，LM=TR2=7.425088，其p值为0.0244，表明存在自相关。2）对模型进行处理：①采取广义差分法a)为估计自相关系数ρ。对et进行滞后一期的自回归，用EViews分析结果如下： Dependent Variable: EMethod: Least SquaresDate: 12/20/14 Time: 15:04Sample (adjusted): 2 19Included observations: 18 after adjustmentsVariable Coefficient Std. Error t-StatisticE(-1) 0...700759R-squared 0.440747 Mean dependent varAdjusted R-squared 0.440747 S.D. dependent varS.E. of regression 13.34980 Akaike info criterionSum squared resid
Schwarz criterionLog likelihood -71.67349 Hannan-Quinn criter.Durbin-Watson stat 1.634573由上可知，ρ=0.657352 Prob. 0.433 17.833 8..081653 b)对原模型进行广义差分回归，用Eviews进行分析所得结果如下：Dependent Variable: Y-0.657352*Y(-1)Method: Least SquaresDate: 12/20/14 Time: 15:04 Sample (adjusted): 2 19Included observations: 18 after adjustmentsVariable Coefficient Std. Error t-Statistic Prob.C 35.546 4..0004 X-0.657352*X(-1) 0...0R-squared 0.984983 Mean dependent var 278.1002Adjusted R-squared 0.984044 S.D. dependent var 105.1781S.E. of regression 13.28570 Akaike info criterion 8.115693Sum squared resid
Schwarz criterion 8.214623Log likelihood -71.04124 Hannan-Quinn criter. 8.129334F-statistic
Durbin-Watson stat 1.830746 Prob(F-statistic) 0.000000 由上图可知回归方程为：Yt*=35.695Xt*Se=(8..020642)t=(4..39512)R2=0.984983 F= DW=1.830746式中，Yt*=Yt-0.657352Yt-1, Xt*=Xt-0.657352Xt-1由于使用了广义差分数据，样本容量减少了1个，为18个。查5%显著水平的DW统计表可知，dL=1.158,dU=1.391模型中DW=1,830746，du&DW&4- dU，说明在5%的显著水平下广义差分模型中已无自相关。可决系数R2，t，F统计量也均达到理想水平。由差分方程，β1=35.9.4.9987由此最终的消费模型为：Yt=104.695Xt②用科克伦-奥克特迭代法，用EVIews分析结果如下：Dependent Variable: YMethod: Least SquaresDate: 12/20/14 Time: 15:15Sample (adjusted): 2 19Included observations: 18 after adjustmentsConvergence achieved after 5 iterationsVariable Coefficient Std. Error t-StatisticC 104.18 4.357687X 0...12757AR(1) 0...836462R-squared 0.997097 Mean dependent varAdjusted R-squared 0.996710 S.D. dependent varS.E. of regression 13.70843 Akaike info criterionSum squared resid
Schwarz criterionLog likelihood -71.02419 Hannan-Quinn criter.F-statistic
Durbin-Watson statProb(F-statistic) 0.000000Inverted AR Roots .63所得方程为：Yt=104.262XtProb. 0.0 0.7 238.910 8...787878（3）经济意义：人均实际收入每增加1元，平均说来人均时间消费支出将增加0.669262元。6.4（1）1）针对对数模型，用Eviews分析结果如下：Dependent Variable: LNYMethod: Least SquaresDate: 12/27/14 Time: 16:13Sample: Included observations: 21 Variable Coefficient Std. Error t-Statistic Prob. LNX 0...0C 2....0000 R-squared 0.969199 Mean dependent var 8.039307Adjusted R-squared 0.967578 S.D. dependent var 0.565486S.E. of regression 0.101822 Akaike info criterion -1.640785Sum squared resid 0.196987 Schwarz criterion -1.541307Log likelihood 19.22825 Hannan-Quinn criter. -1.619196F-statistic 597.8626 Durbin-Watson stat 1.159788Prob(F-statistic) 0.000000 所得模型为：lnY=0,951090lnX+2.171041se=(0.038897) (0.241025)t=(24.45123) (9.007529)R2=0.969199 F=597.8626 DW=1.1597882）检验模型的自相关性该回归方程可决系数较高，回归系数均显著。对样本量为21，一个解释变量的模型，5%的显著水平，查DW统计表可知，dL=1.221，dU=1.420，模型中DW=1.159788& dL,显然模型中有自相关。(2)用广义差分法处理模型：1）为估计自相关系数ρ。对et进行滞后一期的自回归，用EViews分析结果如下： Dependent Variable: EMethod: Least SquaresDate: 12/27/14 Time: 16:18Sample (adjusted): Included observations: 19 after adjustments计量经济学(庞皓)第三版课后答案05_计量经济学课后答案Variable Coefficient Std. Error t-Statistic Prob. E(-1) -0....9639 R-squared 0.000073 Mean dependent var -2.556737Adjusted R-squared 0.000073 S.D. dependent var 397.7924S.E. of regression 397.7778 Akaike info criterion 14.86086Sum squared resid 2848090. Schwarz criterion 14.91057Log likelihood -140.1782 Hannan-Quinn criter. 14.86927Durbin-Watson stat 1.700254 由上可知，ρ=-0.0128722）对原模型进行广义差分回归，用Eviews进行分析所得结果如下：Dependent Variable: Y+0.012872*Y(-1)Method: Least SquaresDate: 12/27/14 Time: 21:06 Sample (adjusted): Included observations: 20 after adjustmentsVariable Coefficient Std. Error t-Statistic Prob.C -104.8 -0..6021 X+0.012872*X(-1) 6...0R-squared 0.963751 Mean dependent var Adjusted R-squared 0.961737 S.D. dependent var S.E. of regression 400.1404 Akaike info criterion 14.91615Sum squared resid 2882022. Schwarz criterion 15.01572Log likelihood -147.1615 Hannan-Quinn criter. 14.93559F-statistic 478.5614 Durbin-Watson stat 1.822259 Prob(F-statistic) 0.000000 由上图可知回归方程为：Yt*=-104.757Xt*Se=(197.7928)( 0.304157)t=(-0.530679)( 21.87605)R2=0.963751 F=478.5614DW=1.8222596式中，Yt*=Yt+0.012872Yt-1, Xt*=Xt+0.012872Xt-1由于使用了广义差分数据，样本容量减少了1个，为20个。查5%显著水平的DW统计表可知，dL=1.201,dU=1.411模型中DW=1.8222596，du&DW&4- dU，说明在5%的显著水平下广义差分模型中已无自相关。可决系数R2，t，F统计量也均达到理想水平。 由差分方程，β1=-104..012872)=-103.6306由此最终的模型为：Yt=-103.757Xt（3）对于此模型，用Eviews分析结果如下：Dependent Variable: LNY1 Method: Least Squares Date: 12/27/14 Time: 22:16 Sample (adjusted):
Included observations: 20 after adjustments Variable Coefficient Std. Error t-Statistic Prob. LNX1 0....0000C 0....0007 R-squared 0.713658 Mean dependent var 0.091592Adjusted R-squared 0.697750 S.D. dependent var 0.098311 S.E. of regression 0.054049 Akaike info criterion -2.903219 Sum squared resid 0.052583 Schwarz criterion -2.803646 Log likelihood 31.03219 Hannan-Quinn criter. -2.883781 F-statistic 44.86188 Durbin-Watson stat 1.590363 Prob(F-statistic) 0.000003 由题目可知，此模型样本容量为20，查5%显著水平的DW统计表可知，dL=1.201,dU=1.411模型中DW=1.590363，du&DW&4- dU，说明在5%的显著水平此模型中无自相关。可决系数R2，t，F统计量也均达到理想水平欢迎您转载分享：
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t检验中，t值的大小代表什么？表示两组数据的相似度大小的参数？？？有具体的参考文献吗？
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是不能拒绝原假设的 显著性水平为1-0; 概率0，反之接受，也就是接受原假设.05 <，那么t值是没用的，如果你没法知道临界值，则拒绝原假设.073.95 = 0。t值大于critical value。t值的用处在于你知道critical value也就是临界值的条件下才行
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出门在外也不愁计量经济学(庞皓)第三版课后答案05_计量经济学课后答案-牛bb文章网
计量经济学(庞皓)第三版课后答案05 计量经济学课后答案
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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： Dependent Variable: Y Method: Least Squares Date: 12/27/14 Time: 21:00 Sample: 1 22 Included observations: 22Variable Coefficient Std. Error t-Statistic Prob. C 56.820 28.0 X1 0....0001 R-squared 0.526082 Mean dependent var 62.50000Adjusted R-squared 0.502386 S.D. dependent var 10.08889 S.E. of regression 7.116881 Akaike info criterion 6.849324 Sum squared resid
Schwarz criterion 6.948510 Log likelihood -73.34257 Hannan-Quinn criter. 6.872689 F-statistic 22.20138 Durbin-Watson stat 0.629074 Prob(F-statistic) 0.000134有上可知，关系式为y=56.360x1②关于人均寿命与成人识字率的关系，用Eviews分析如下： Dependent Variable: Y Method: Least Squares Date: 11/26/14 Time: 21:10 Sample: 1 22 Included observations: 22Variable Coefficient Std. Error t-Statistic Prob. C 38.079 10.0 X2 0....0000 R-squared 0.716825 Mean dependent var 62.50000Adjusted R-squared 0.702666 S.D. dependent var 10.08889 S.E. of regression 5.501306 Akaike info criterion 6.334356 Sum squared resid 605.2873 Schwarz criterion 6.433542 Log likelihood -67.67792 Hannan-Quinn criter. 6.357721 F-statistic 50.62761 Durbin-Watson stat 1.846406 Prob(F-statistic) 0.000001由上可知，关系式为y=38.971x2③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: Y Method: Least Squares Date: 11/26/14 Time: 21:14 Sample: 1 22 Included observations: 22Variable Coefficient Std. Error t-Statistic Prob. C 31.434 4......0001 R-squared 0.537929 Mean dependent var 62.50000Adjusted R-squared 0.514825 S.D. dependent var 10.08889 S.E. of regression 7.027364 Akaike info criterion 6.824009 Sum squared resid 987.6770 Schwarz criterion 6.923194 Log likelihood -73.06409 Hannan-Quinn criter. 6.847374 F-statistic 23.28338 Durbin-Watson stat 0.952555 Prob(F-statistic) 0.000103由上可知，关系式为y=31.276x3（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..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..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..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： Dependent Variable: Y Method: Least Squares Date: 12/03/14 Time: 17:00 Sample (adjusted): 1 33Included observations: 33 after adjustmentsVariable Coefficient Std. Error t-Statistic X 0...25639 C -154.96 -3.948274 R-squared 0.983702 Mean dependent varAdjusted R-squared 0.983177 S.D. dependent var S.E. of regression 175.2325 Akaike info criterion Sum squared resid
Schwarz criterion Log likelihood -216.2751 Hannan-Quinn criter. F-statistic
Durbin-Watson stat Prob(F-statistic) 0.000000Prob. 0.4 902.9 13.49 13.021②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）=43.2(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=0.983702 F= n=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=0.00―154.17②进行区间预测：∑x2=∑（Xi―X）2=δ2x(n―1)=
x (33―1)= (Xf―X)2=(32000― = 当Xf=32000时，将相关数据代入计算得到：―2.5x√1/33+/≤ Yf≤.5x√1/33+/ 即Yf的置信区间为（―64..9）(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： Dependent Variable: LNY Method: Least Squares Date: 12/03/14 Time: 18:00 Sample (adjusted): 1 33 Included observations: 33 after adjustmentsVariable Coefficient Std. Error t-Statistic Prob. LNX 0...0 C -1....0000 R-squared 0.963442 Mean dependent var 5.573120Adjusted R-squared 0.962263 S.D. dependent var 1.684189 S.E. of regression 0.327172 Akaike info criterion 0.662028 Sum squared resid 3.318281 Schwarz criterion 0.752726 Log likelihood -8.923468 Hannan-Quinn criter. 0.692545 F-statistic 816.9699 Durbin-Watson stat 0.096208 Prob(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）=28.5(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..4（1）对建筑面积与建造单位成本模型，用Eviews分析结果如下： Dependent Variable: Y Method: Least Squares Date: 12/01/14 Time: 12:40 Sample: 1 12 Included observations: 12Variable Coefficient Std. Error t-Statistic Prob. X -64.828 -13.0 C .88 0.0000 R-squared 0.946829 Mean dependent var Adjusted R-squared 0.941512 S.D. dependent var 131.2252 S.E. of regression 31.73600 Akaike info criterion 9.903792 Sum squared resid 10071.74 Schwarz criterion 9.984610 Log likelihood -57.42275 Hannan-Quinn criter. 9.873871 F-statistic 178.0715 Durbin-Watson stat 1.172407 Prob(F-statistic) 0.000000由上可得：建筑面积与建造成本的回归方程为：Y=.18400X（2）经济意义：建筑面积每增加1万平方米，建筑单位成本每平方米减少64.18400元。（3）①首先进行点预测，由Y=.18400X得，当x=4.5，y=②再进行区间估计：计量经济学(庞皓)第三版课后答案05_计量经济学课后答案由上表可知，∑x2=∑（Xi―X）2=δ2x(n―1)= 1.9894192 x (12―1)=43.5357(Xf―X)2=(4.5― 3.=0.当Xf=4.5时，将相关数据代入计算得到：.228x31.73600x√1/12+43.87843≤Yf≤.228x31.73600x√1/12+43.87843即Yf的置信区间为（8..647+478.1231）3.1（1）①对百户拥有家用汽车量计量经济模型，用Eviews分析结果如下：Dependent Variable: YMethod: Least SquaresDate: 11/25/14 Time: 12:38Sample: 1 31Included observations: 31Variable Coefficient Std. Error t-Statistic Prob.X2 5....0002X3 -0....0069X4 -2....0002C 246.00 4..0001R-squared 0.666062 Mean dependent var 16.77355Adjusted R-squared 0.628957 S.D. dependent var 8.252535S.E. of regression 5.026889 Akaike info criterion 6.187394Sum squared resid 682.2795 Schwarz criterion 6.372424Log likelihood -91.90460 Hannan-Quinn criter. 6.247709F-statistic 17.95108 Durbin-Watson stat 1.147253Prob(F-statistic) 0.000001②得到模型得：Y=246.865X2- 0.-2.③对模型进行检验：1） 可决系数是0.666062，修正的可决系数为0.628957，说明模型对样本拟合较好2） F检验，F=17.95108&F（3,27）=3.65，回归方程显著。3）t检验，t统计量分别为4..265020，-2.922950，-4.366842，均大于 t（27）=2.0518，所以这些系数都是显著的。④依据：1） 可决系数越大，说明拟合程度越好2） F的值与临界值比较，若大于临界值，则否定原假设，回归方程是显著的；若小于临界值，则接受原假设，回归方程不显著。3） t的值与临界值比较，若大于临界值，则否定原假设，系数都是显著的；若小于临界值，则接受原假设，系数不显著。（2）经济意义：人均ＧＤＰ增加１万元，百户拥有家用汽车增加5.996865辆，城镇人口比重增加１个百分点，百户拥有家用汽车减少0.524027辆，交通工具消费价格指数每上升１，百户拥有家用汽车减少2.265680辆。（3）用EViews分析得：Dependent Variable: YMethod: Least SquaresDate: 12/08/14 Time: 17:28Sample: 1 31Included observations: 31 Variable Coefficient Std. Error t-Statistic Prob. X2 5....0000LNX3 -22.820 -3..0023LNX4 -230.91 -4..0001C .974 0.0000 R-squared 0.691952 Mean dependent var 16.77355Adjusted R-squared 0.657725 S.D. dependent var 8.252535S.E. of regression 4.828088 Akaike info criterion 6.106692Sum squared resid 629.3818 Schwarz criterion 6.291723Log likelihood -90.65373 Hannan-Quinn criter. 6.167008F-statistic 20.21624 Durbin-Watson stat 1.150090Prob(F-statistic) 0.000000 模型方程为：Y=5.-22.81005 LNX3-230.8481 LNX4+此分析得出的可决系数为0..666062，拟合程度得到了提高，可这样改进。3.2（１）对出口货物总额计量经济模型，用Eviews分析结果如下：：Dependent Variable: YMethod: Least SquaresDate: 12/01/14 Time: 20:25Sample: Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob. X2 0...0X3 18.181 1..0729C -8.216 -2..0520 R-squared 0.985838 Mean dependent var Adjusted R-squared 0.983950 S.D. dependent var S.E. of regression 730.6306 Akaike info criterion 16.17670Sum squared resid 8007316. Schwarz criterion 16.32510Log likelihood -142.5903 Hannan-Quinn criter. 16.19717F-statistic 522.0976 Durbin-Watson stat 1.173432Prob(F-statistic) 0.000000 ①由上可知，模型为：Y = 0. + 18.85348X3 - 18231.58②对模型进行检验：1）可决系数是0.985838，修正的可决系数为0.983950，说明模型对样本拟合较好2）F检验，F=522.0976&F（2,15）=4.77，回归方程显著3）t检验，t统计量分别为X2的系数对应t值为10.58454，大于t（15）=2.131，系数是显著的，X3的系数对应t值为1.928512，小于t（15）=2.131，说明此系数是不显著的。（2）对于对数模型，用Eviews分析结果如下：Dependent Variable: LNYMethod: Least SquaresDate: 12/01/14 Time: 20:25Sample: Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob. LNX2 1...0LNX3 1....0209C -20.487 -3..0018 R-squared 0.986295 Mean dependent var 8.400112Adjusted R-squared 0.984467 S.D. dependent var 0.941530S.E. of regression 0.117343 Akaike info criterion -1.296424Sum squared resid 0.206540 Schwarz criterion -1.148029Log likelihood 14.66782 Hannan-Quinn criter. -1.275962F-statistic 539.7364 Durbin-Watson stat 0.686656Prob(F-statistic) 0.000000 ①由上可知，模型为：LNY=-20.221 LNX2+1.760695 LNX3②对模型进行检验：1）可决系数是0.986295，修正的可决系数为0.984467，说明模型对样本拟合较好。2）F检验，F=539.7364& F（2,15）=4.77，回归方程显著。3）t检验，t统计量分别为-3..5229，均大于t（15）=2.131，所以这些系数都是显著的。（3）①（1）式中的经济意义：工业增加1亿元，出口货物总额增加0.135474亿元，人民币汇率增加1，出口货物总额增加18.85348亿元。②（2）式中的经济意义：工业增加额每增加1%，出口货物总额增加1.564221%，人民币汇率每增加1%，出口货物总额增加1.760695%3.3（1）对家庭书刊消费对家庭月平均收入和户主受教育年数计量模型，由Eviews分析结果如下：Dependent Variable: YMethod: Least SquaresDate: 12/01/14 Time: 20:30Sample: 1 18Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob. X 0....0101T 52.167 10.0C -50.26 -1..3279 R-squared 0.951235 Mean dependent var 755.1222Adjusted R-squared 0.944732 S.D. dependent var 258.7206S.E. of regression 60.82273 Akaike info criterion 11.20482Sum squared resid 55491.07 Schwarz criterionLog likelihood -97.84334 Hannan-Quinn criter.F-statistic 146.2974 Durbin-Watson statProb(F-statistic) 0.000000①模型为：Y = 0.086450X + 52.33811.28 2.605783②对模型进行检验：1）可决系数是0.951235，修正的可决系数为0.944732，说明模型对样本拟合较好。2）F检验，F=539.7364& F（2,15）=4.77，回归方程显著。3）t检验，t统计量分别为2..06702，均大于t（15）=2.131，所以这些系数都是显著的。③经济意义：家庭月平均收入增加1元，家庭书刊年消费支出增加0.086450元，户主受教育年数增加1年，家庭书刊年消费支出增加52.37031元。（2）用Eviews分析：①Dependent Variable: YMethod: Least SquaresDate: 12/01/14 Time: 22:30Sample: 1 18Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob. T 63.581 13.0C -11.90 -0..8443 R-squared 0.923054 Mean dependent var 755.1222Adjusted R-squared 0.918245 S.D. dependent var 258.7206S.E. of regression 73.97565 Akaike info criterion 11.54979Sum squared resid 87558.36 Schwarz criterion 11.64872Log likelihood -101.9481 Hannan-Quinn criter. 11.56343F-statistic 191.9377 Durbin-Watson stat 2.134043Prob(F-statistic) 0.000000 ②Dependent Variable: XMethod: Least SquaresDate: 12/01/14 Time: 22:34Sample: 1 18Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob.计量经济学(庞皓)第三版课后答案05_计量经济学课后答案T 123.50 3..0014C 444.6 1..2899 R-squared 0.483182 Mean dependent var Adjusted R-squared 0.450881 S.D. dependent var 698.8325S.E. of regression 517.8529 Akaike info criterion 15.44170Sum squared resid 4290746. Schwarz criterion 15.54063Log likelihood -136.9753 Hannan-Quinn criter. 15.45534F-statistic 14.95867 Durbin-Watson stat 1.052251Prob(F-statistic) 0.001364 以上分别是y与T，X与T的一元回归模型分别是：Y = 63.01676T - 11.58171X = 123.1516T + 444.5888（3）对残差进行模型分析，用Eviews分析结果如下：Dependent Variable: E1Method: Least SquaresDate: 12/03/14 Time: 20:39Sample: 1 18Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob. E2 0....0078C 3.96E-14 13.E-15 1.0000 R-squared 0.366239 Mean dependent var 2.30E-14Adjusted R-squared 0.326629 S.D. dependent var 71.76693S.E. of regression 58.89136 Akaike info criterion 11.09370Sum squared resid 55491.07 Schwarz criterion 11.19264Log likelihood -97.84334 Hannan-Quinn criter. 11.10735F-statistic 9.246111 Durbin-Watson stat 2.605783Prob(F-statistic) 0.007788 模型为：E1 = 0. + 3.96e-14参数：斜率系数α为0.086450，截距为3.96e-14（3）由上可知，β2与α2的系数是一样的。回归系数与被解释变量的残差系数是一样的，它们的变化规律是一致的。3.6（1）预期的符号是X1，X2,X3,X4,X5的符号为正，X6的符号为负（2）根据Eviews分析得到数据如下：Dependent Variable: YMethod: Least SquaresDate: 12/04/14 Time: 13:24Sample: Included observations: 18 Variable Coefficient Std. Error t-Statistic Prob. X2 0....2336X3 0....6326X4 -3....3346X5 0....3600X6 0....6422C -13.66 -0..3984 R-squared 0.994869 Mean dependent var 12.76667Adjusted R-squared 0.992731 S.D. dependent var 9.746631S.E. of regression 0.830963 Akaike info criterion 2.728738Sum squared resid 8.285993 Schwarz criterion 3.025529Log likelihood -18.55865 Hannan-Quinn criter. 2.769662F-statistic 465.3617 Durbin-Watson stat 1.553294Prob(F-statistic) 0.000000 ①与预期不相符。②评价：1） 可决系数为0.994869，数据相当大，可以认为拟合程度很好。2） F检验，F=465.3617&F（5.12）=3,89，回归方程显著3） T检验，X1，X2,X3,X4,X5，X6 系数对应的t值分别为：1..490501，-1.005377，0..476621，均小于t（12）=2.179，所以所得系数都是不显著的。（3）根据Eviews分析得到数据如下：Dependent Variable: YMethod: Least SquaresDate: 12/03/14 Time: 11:12Sample: Included observations: 18Variable Coefficient Std. Error t-StatisticX5 0..20E-05 46.79946X6 -0...762581C 4...260786 Prob. 0.3 0.2266R-squared 0.993601 Mean dependent var 12.76667Adjusted R-squared 0.992748 S.D. dependent var 9.746631S.E. of regression 0.830018 Akaike info criterion 2.616274Sum squared resid 10.33396 Schwarz criterion 2.764669Log likelihood -20.54646 Hannan-Quinn criter. 2.636736F-statistic
Durbin-Watson stat 1.341880Prob(F-statistic) 0.000000 ①得到模型的方程为：Y=0.-0.+4.205481②评价：1） 可决系数为0.993601，数据相当大，可以认为拟合程度很好。2） F检验，F=&F（5.12）=3,89，回归方程显著3） T检验，X5 系数对应的t值为46.79946，大于t（12）=2.179，所以系数是显著的，即人均GDP对年底存款余额有显著影响。 X6 系数对应的t值为-1.762581，小于t（12）=2.179，所以系数是不显著的。4.3（1）根据Eviews分析得到数据如下：Dependent Variable: LNYMethod: Least SquaresDate: 12/05/14 Time: 11:39Sample: Included observations: 27 Variable Coefficient Std. Error t-Statistic Prob. LNGDP 1...0LNCPI -0....0832C -3....0000 R-squared 0.988051 Mean dependent var 9.484710Adjusted R-squared 0.987055 S.D. dependent var 1.425517S.E. of regression 0.162189 Akaike info criterion -0.695670Sum squared resid 0.631326 Schwarz criterion -0.551689Log likelihood 12.39155 Hannan-Quinn criter. -0.652857F-statistic 992.2582 Durbin-Watson stat 0.522613Prob(F-statistic) 0.000000 得到的模型方程为：LNY=1.338533 LNGDPt-0.421791 LNCPIt-3.111486（2）① 该模型的可决系数为0.988051，可决系数很高，F检验值为992.2582，明显显著。但当α=0.05时，t（24）=2.064，LNCPI的系数不显著，可能存在多重共线性。 ②得到相关系数矩阵如下：LNGDP， LNCPI之间的相关系数很高，证实确实存在多重共线性。（3）由Eviews得：a）Dependent Variable: LNYMethod: Least SquaresDate: 12/03/14 Time: 14:41Sample: Included observations: 27Variable Coefficient Std. Error t-Statistic Prob. LNGDP 1...0C -3...0 R-squared 0.986423 Mean dependent var 9.484710 Adjusted R-squared 0.985880 S.D. dependent var 1.425517 S.E. of regression 0.169389 Akaike info criterion -0.642056 Sum squared resid 0.717312 Schwarz criterion -0.546068 Log likelihood 10.66776 Hannan-Quinn criter. -0.613514 F-statistic
Durbin-Watson stat 0.471111 Prob(F-statistic) 0.000000 b)Dependent Variable: LNY Method: Least Squares Date: 12/03/14 Time: 14:41 Sample:
Included observations: 27 Variable Coefficient Std. Error t-Statistic Prob. LNCPI 2...0C -6....0000 R-squared 0.874442 Mean dependent var 9.484710 Adjusted R-squared 0.869419 S.D. dependent var 1.425517 S.E. of regression 0.515124 Akaike info criterion 1.582368 Sum squared resid 6.633810 Schwarz criterion 1.678356 Log likelihood -19.36196 Hannan-Quinn criter. 1.610910 F-statistic 174.1108 Durbin-Watson stat 0.137042 Prob(F-statistic) 0.000000 c)Dependent Variable: LNGDP Method: Least Squares Date: 12/05/14 Time: 11:11 Sample:
Included observations: 27 Variable Coefficient Std. Error t-Statistic Prob. LNCPI 2...0C -2....0040 R-squared 0.909621 Mean dependent var 11.16214 Adjusted R-squared 0.906005 S.D. dependent var 1.194029计量经济学(庞皓)第三版课后答案05_计量经济学课后答案S.E. of regression 0.366072 Akaike info criterion 0.899213 Sum squared resid 3.350216 Schwarz criterion 0.995201 Log likelihood -10.13938 Hannan-Quinn criter. 0.927755 F-statistic 251.6117 Durbin-Watson stat 0.099623 Prob(F-statistic) 0.000000①得到的回归方程分别为1）LNY=1.185739 LNGDPt-3.）LNY=2.939295 LNCPIt-6.）LNGDPt=2.511022 LNCPIt-2.796381②对多重共线性的认识：单方程拟合效果都很好，回归系数显著，判定系数较高，GDP和CPI对进口的显著的单一影响，在这两个变量同时引入模型时影响方向发生了改变，这只有通过相关系数的分析才能发现。（4）建议：如果仅仅是作预测，可以不在意这种多重共线性，但如果是进行结构分析，还是应该引起注意的。4.4（1）按照设计的理论模型，由Eviews分析得：Dependent Variable: CZSR Method: Least Squares Date: 12/03/14 Time: 11:40 Sample:
Included observations: 27Variable Coefficient Std. Error t-Statistic CZZC 0...031129 GDP -0...998036 SSZE 1...93271 C -221.2 -1.698038 R-squared 0.999857 Mean dependent varAdjusted R-squared 0.999838 S.D. dependent var S.E. of regression 353.0540 Akaike info criterion Sum squared resid 2866884. Schwarz criterion Log likelihood -194.5455 Hannan-Quinn criter. F-statistic 53493.93 Durbin-Watson stat Prob(F-statistic) 0.000000Prob. 0.0 0.0 39.49 14.05 14.128从回归结果可见，可决系数为0.999857，校正的可决系数为0.999838，模型拟合的很好。F的统计量为53493.93，说明在α=0.05,水平下，回归方程回归方程整体上是显著的。但是t检验结果表明，国内生产总值对财政收入的影响显著，但回归系数的符号为负，与实际不符合。由此可得知，该方程可能存在多重共线性。（2）得到相关系数矩阵如下：由上表可知，CZZC与GDP，CZZC与SSZE，GDP与SSZE之间的相关系数都非常高，说明确实存在多重共线性。方差扩大因子均大于10，存在严重多重共线性。并且通过以上分析，两两被解释变量之间相关性都很高。（4）解决方式：分别作出财政收入与财政支出、国内生产总值、税收总额之间的一元回归。5.2（1）①用图形法检验绘制e2的散点图，用Eviews分析如下：由上图可知，模型可能存在异方差，② Goldfeld-Quanadt检验1）定义区间为1-7时，由软件分析得： Dependent Variable: Y Method: Least Squares Date: 12/10/14 Time: 14:52 Sample: 1 7 Included observations: 7Variable Coefficient Std. Error t-Statistic T 35.492 7.182843 X 0...774380 C 77.44 0.936807 R-squared 0.943099 Mean dependent varAdjusted R-squared 0.914649 S.D. dependent var S.E. of regression 31.63265 Akaike info criterion Sum squared resid
Schwarz criterion Log likelihood -32.15324 Hannan-Quinn criter. F-statistic 33.14880 Durbin-Watson stat Prob(F-statistic) 0.0032382得∑e1i=2）定义区间为12-18时，由软件分析得：Prob. 0.7 0.7 108.78 10.267 1.426262Dependent Variable: Y Method: Least Squares Date: 12/10/14 Time: 13:50 Sample: 12 18 Included observations: 7Variable Coefficient Std. Error t-Statistic Prob. T 52.378 7..0016 X 0....2705 C -8..9968 0.9177 R-squared 0.984688 Mean dependent var 887.6143Adjusted R-squared 0.977032 S.D. dependent var 274.4148 S.E. of regression 41.58810 Akaike info criterion 10.59103 Sum squared resid
Schwarz criterion 10.56785 Log likelihood -34.06861 Hannan-Quinn criter. 10.30451 F-statistic 128.6166 Durbin-Watson stat 2.390329 Prob(F-statistic) 0.0002342 得∑e2i=3）根据Goldfeld-Quanadt检验，F统计量为： F=∑e2i2 /∑e1i2 =2.499=1.7285在α=0.05水平下，分子分母的自由度均为4，查分布表得临界值F0.05（4,4）=6.39，因为F=1.7285& F0.05（4,4）=6.39，所以接受原假设，此检验表明模型不存在异方差。（2）存在异方差，估计参数的方法： ①可以对模型进行变换②使用加权最小二乘法进行计算，得出模型方程，并对其进行相关检验 ③对模型进行对数变换，进行分析（3）评价：3.3所得结论是可以相信的，随机扰动项之间不存在异方差。回归方程是显著的。计量经济学(庞皓)第三版课后答案05_计量经济学课后答案5.3(1)由Eviews软件分析得：Dependent Variable: YMethod: Least SquaresDate: 12/10/14 Time: 16:00Sample: 1 31Included observations: 31 Variable Coefficient Std. Error t-Statistic Prob. X 1...0C 242.0 0..4119 R-squared 0.895260 Mean dependent var Adjusted R-squared 0.891649 S.D. dependent var S.E. of regression 649.1426 Akaike info criterion 15.85152Sum squared resid
Schwarz criterion 15.94404Log likelihood -243.6986 Hannan-Quinn criter. 15.88168F-statistic 247.8769 Durbin-Watson stat 1.078581Prob(F-statistic) 0.000000 由上表可知，2007年我国农村居民家庭人均消费支出（x）对人均纯收入（y）的模型为： Y=1.2.4488（2）①由图形法检验由上图可知，模型可能存在异方差。②Goldfeld-Quanadt检验1）定义区间为1-12时，由软件分析得：Dependent Variable: Y1Method: Least SquaresDate: 12/10/14 Time: 11:34Sample: 1 12Included observations: 12 Variable Coefficient Std. Error t-Statistic Prob. X1 1....0141C -550.3 -0..6614 R-squared 0.468390 Mean dependent var Adjusted R-squared 0.415229 S.D. dependent var 550.5148 S.E. of regression 420.9803 Akaike info criterion 15.07406 Sum squared resid 1772245. Schwarz criterion 15.15488 Log likelihood -88.44437 Hannan-Quinn criter. 15.04414 F-statistic 8.810789 Durbin-Watson stat 2.354167 Prob(F-statistic) 0. 得∑e1i=1772245.2）定义区间为20-31时，由软件分析得：Dependent Variable: Y1Method: Least SquaresDate: 12/10/14 Time: 16:36Sample: 20 31Included observations: 12 Variable Coefficient Std. Error t-Statistic Prob. X1 1....0000C .141 0.1407 R-squared 0.842056 Mean dependent var Adjusted R-squared 0.826262 S.D. dependent var
S.E. of regression 889.3633 Akaike info criterion 16.56990 Sum squared resid 7909670. Schwarz criterion 16.65072 Log likelihood -97.41940 Hannan-Quinn criter. 16.53998 F-statistic 53.31370 Durbin-Watson stat 2.339767 Prob(F-statistic) 0. 得∑e2i=7909670.3）根据Goldfeld-Quanadt检验，F统计量为：F=∑e2i2 /∑e1i2 =7909670./ .4631在α=0.05水平下，分子分母的自由度均为10，查分布表得临界值F0.05（10,10）=2.98，因为F=4.4631& F0.05（10,10）=2.98，所以拒绝原假设，此检验表明模型存在异方差。（3）1）采用WLS法估计过程中，①用权数w1=1/X,建立回归得：Dependent Variable: YMethod: Least SquaresDate: 12/09/14 Time: 11:13Sample: 1 31Included observations: 31Weighting series: W1 Variable Coefficient Std. Error t-Statistic Prob. X 1...0C -334.3 -0..3389 Weighted Statistics R-squared 0.831707 Mean dependent var Adjusted R-squared 0.825904 S.D. dependent var 536.1907 S.E. of regression 536.6796 Akaike info criterion 15.47102 Sum squared resid 8352726. Schwarz criterion 15.56354 Log likelihood -237.8008 Hannan-Quinn criter. 15.50118 F-statistic 143.3184 Durbin-Watson stat 1.369081 Prob(F-statistic) 0.000000 Unweighted Statistics R-squared 0.875855 Mean dependent var Adjusted R-squared 0.871574 S.D. dependent var
S.E. of regression 706.7236 Sum squared resid
Durbin-Watson stat 1.532908对此模型进行White检验得：Heteroskedasticity Test: White F-statistic 0.299395 Prob. F(2,28) 0.7436Obs*R-squared 0.649065 Prob. Chi-Square(2) 0.7229 Scaled explained SS 1.798067 Prob. Chi-Square(2) 0.4070Test Equation:Dependent Variable: WGT_RESID^2Method: Least SquaresDate: 12/10/14 Time: 21:13Sample: 1 31Included observations: 31Collinear test regressors dropped from specification Variable Coefficient Std. Error t-Statistic Prob. C 222 0.9532WGT^2 - 1173622. -0..6168X*WGT^2 282.0 0..7086 R-squared 0.020938 Mean dependent var Adjusted R-squared -0.048995 S.D. dependent var
S.E. of regression
Akaike info criterion 29.86395 Sum squared resid 1.40E+13 Schwarz criterion 30.00273 Log likelihood -459.8913 Hannan-Quinn criter. 29.90919 F-statistic 0.299395 Durbin-Watson stat 1.922336 Prob(F-statistic) 0.743610从上可知，nR2=0.649065，比较计算的统计量的临界值，因为nR2=0.649065&（2）=5.9915，所以接受原假设，该模型消除了异方差。估计结果为：Y=1.4.8131t=（11.97157）（-0.972298）R2=0.875855 F=143.3184 DW=1.369081②用权数w2=1/x2,用回归分析得：Dependent Variable: YMethod: Least SquaresDate: 12/09/14 Time: 21:08Sample: 1 31Included observations: 31Weighting series: W2Variable Coefficient Std. Error t-StatisticX 1...70922C -693.0 -1.841272Weighted StatisticsR-squared 0.798173 Mean dependent varAdjusted R-squared 0.791214 S.D. dependent varS.E. of regression 466.8513 Akaike info criterionSum squared resid 6320554. Schwarz criterionLog likelihood -233.4797 Hannan-Quinn criter.F-statistic 114.6875 Durbin-Watson stat 0.05 Prob. 0.8 9.830 15.75 15.975Prob(F-statistic) 0.000000 Unweighted Statistics R-squared 0.834850 Mean dependent var Adjusted R-squared 0.829156 S.D. dependent var
S.E. of regression 815.1229 Sum squared resid
Durbin-Watson stat 1.678365对此模型进行White检验得：Heteroskedasticity Test: White F-statistic 0.299790 Prob. F(3,27) 0.8252Obs*R-squared 0.999322 Prob. Chi-Square(3) 0.8014 Scaled explained SS 1.789507 Prob. Chi-Square(3) 0.6172Test Equation:Dependent Variable: WGT_RESID^2Method: Least SquaresDate: 12/10/14 Time: 21:29Sample: 1 31Included observations: 31 Variable Coefficient Std. Error t-Statistic Prob. C -
-0..8406WGT^2
..8505X^2*WGT^2 0....7088X*WGT^2 -583.0 -0..7816 R-squared 0.032236 Mean dependent var Adjusted R-squared -0.075293 S.D. dependent var
S.E. of regression
Akaike info criterion 28.92298 Sum squared resid 5.10E+12 Schwarz criterion 29.10801 Log likelihood -444.3062 Hannan-Quinn criter. 28.98330 F-statistic 0.299790 Durbin-Watson stat 1.835854 Prob(F-statistic) 0.825233从上可知，nR2=0.999322，比较计算的统计量的临界值，因为nR2=0.999322&（2）=5.9915，所以接受原假设，该模型消除了异方差。估计结果为：Y=1.3.1946t=（10.70922）（-1.841272）R2=0.798173 F=114.6875 DW=1..05计量经济学(庞皓)第三版课后答案05_计量经济学课后答案③用权数w3=1/sqr（x）,用回归分析得：Dependent Variable: YMethod: Least SquaresDate: 12/09/14 Time: 21:35Sample: 1 31Included observations: 31Weighting series: W3 Variable Coefficient Std. Error t-Statistic Prob. X 1...0C -47.54 -0..8807 Weighted Statistics R-squared 0.863161 Mean dependent var Adjusted R-squared 0.858442 S.D. dependent var 991.2079 S.E. of regression 586.9555 Akaike info criterion 15.65012 Sum squared resid 9990985. Schwarz criterion 15.74263 Log likelihood -240.5768 Hannan-Quinn criter. 15.68027 F-statistic 182.9276 Durbin-Watson stat 1.237664 Prob(F-statistic) 0.000000 Unweighted Statistics R-squared 0.890999 Mean dependent var Adjusted R-squared 0.887240 S.D. dependent var
S.E. of regression 662.2171 Sum squared resid
Durbin-Watson stat 1.314859对此模型进行White检验得：Heteroskedasticity Test: White F-statistic 0.423886 Prob. F(2,28) 0.6586Obs*R-squared 0.911022 Prob. Chi-Square(2) 0.6341 Scaled explained SS 2.768332 Prob. Chi-Square(2) 0.2505Test Equation:Dependent Variable: WGT_RESID^2Method: Least SquaresDate: 12/09/14 Time: 20:36Sample: 1 31Included observations: 31Collinear test regressors dropped from specificationVariable Coefficient Std. Error t-StatisticC 4981WGT^2 - 1301839. -0.549740X^2*WGT^2 -0...184677R-squared 0.029388 Mean dependent varAdjusted R-squared -0.039942 S.D. dependent varS.E. of regression
Akaike info criterionSum squared resid 2.17E+13 Schwarz criterionLog likelihood -466.7426 Hannan-Quinn criter.F-statistic 0.423886 Durbin-Watson statProb(F-statistic) 0.658628Prob. 0.9 0..8
30.75 30.426估计结果为：Y=1..40242t=（13.52507）（-0.151390）R2=0.863161 F=182.9276 DW=1.237664经过检验发现，用权数w1的效果最好，所以综上可知，即修改后的结果为： Y=1.4.8131t=（11.97157）（-0.972298）R2=0.875855 F=143.3184 DW=1.3690815.6(1)a)用Eviews模型分析得：Dependent Variable: YMethod: Least SquaresDate: 12/10/14 Time: 20:16Sample: Included observations: 34Variable Coefficient Std. Error t-StatisticX 0...03027C 92.29 2.162215R-squared 0.979426 Mean dependent varAdjusted R-squared 0.978783 S.D. dependent varS.E. of regression 173.1597 Akaike info criterionSum squared resid
Schwarz criterionLog likelihood -222.4566 Hannan-Quinn criter.F-statistic
Durbin-Watson statProb(F-statistic) 0.000000得回归模型为：Y=0.746241 X+92.55422b)检验是否存在异方差：①用Goldfeld-Quanadt检验如下：1）当定义区间为1-13时，由软件分析得：Dependent Variable: YMethod: Least SquaresDate: 12/11/14 Time: 11:47Sample: 1 13Included observations: 13Variable Coefficient Std. Error t-StatisticX 0...00771C -18.780 -2.104984R-squared 0.991587 Mean dependent varAdjusted R-squared 0.990823 S.D. dependent varS.E. of regression 12.17039 Akaike info criterionSum squared resid
Schwarz criterionLog likelihood -49.84742 Hannan-Quinn criter.F-statistic
Durbin-Watson statProb(F-statistic) 0.000000Prob. 0.2 8.791 13.11 13.491 Prob. 0.1 280.9 7....071505得∑e1i2=2）当定义区间为1-13时，由软件分析得：Dependent Variable: Y Method: Least Squares Date: 12/11/14 Time: 12:21 Sample: 22 34 Included observations: 13 Variable Coefficient Std. Error t-Statistic Prob. X 0...0C 179.4 0..3955 R-squared 0.932629 Mean dependent var
Adjusted R-squared 0.926504 S.D. dependent var
S.E. of regression 277.2250 Akaike info criterion 14.22817 Sum squared resid
Schwarz criterion 14.31509 Log likelihood -90.48313 Hannan-Quinn criter. 14.21031 F-statistic 152.2752 Durbin-Watson stat 1.658418 Prob(F-statistic) 0. 得∑e2i=3）根据Goldfeld-Quanadt检验，F统计量为：F=∑e2i2 /∑e1i2 =/ .8669在α=0.05水平下，分子分母的自由度均为11，查分布表得临界值F0.05（11,11）=4.47，因为F=518.8669& F0.05（11,11）=4.47，所以拒绝原假设，此检验表明模型存在异方差。②White检验用EViews软件分析得：Heteroskedasticity Test: White F-statistic 10.36759 Prob. F(2,31) 0.0004 Obs*R-squared 13.62701 Prob. Chi-Square(2) 0.0011 Scaled explained SS 76.13635 Prob. Chi-Square(2) 0.0000Test Equation: Dependent Variable: RESID^2 Method: Least Squares Date: 12/11/14 Time: 12:56 Sample: 1 34 Included observations: 34Variable Coefficient Std. Error t-StatisticC 17.11 0.443430 X -27.40 -0.994029 X^2 0...371861 R-squared 0.400795 Mean dependent var Adjusted R-squared 0.362136 S.D. dependent var S.E. of regression 81255.15 Akaike info criterion Sum squared resid 2.05E+11 Schwarz criterion Log likelihood -431.0554 Hannan-Quinn criter. F-statistic 10.36759 Durbin-Watson stat Prob(F-statistic) 0.000357从上图中可以看出，nR2=13.62701，比较计算的nR2=13.62701&异方差。用以上两种方法，可以检验模型是存在异方差的。c)修正模型1）用加权二乘法修正异方差现象步骤如下：①当权数w1=1/x时，用软件分析得：Dependent Variable: Y Method: Least Squares Date: 12/11/14 Time: 13:22 Sample: 1 34 Included observations: 34 Weighting series: W1Variable Coefficient Std. Error t-Statistic X 0...67993C 17.256 2.815926 Weighted StatisticsR-squared 0.986676 Mean dependent var Adjusted R-squared 0.986260 S.D. dependent var S.E. of regression 37.91285 Akaike info criterion Sum squared resid 45996.29 Schwarz criterionLog likelihood -170.8132 Hannan-Quinn criter. Prob. 0.9 0..51
25.35 25.651统计量的临界值，因为0.05（2）=5.9915，所以拒绝原假设，不拒绝备择假设，表明模型存在 Prob. 0.3 457.84 10.27 10.19610计量经济学(庞皓)第三版课后答案05_计量经济学课后答案F-statistic
Durbin-Watson stat 0.605852Prob(F-statistic) 0.000000 Unweighted Statistics R-squared 0.968070 Mean dependent var Adjusted R-squared 0.967072 S.D. dependent var S.E. of regression 215.7175 Sum squared resid 1489089.Durbin-Watson stat 1.079107 得方程模型为：Y=0..69318t=（48.67993）（2.815926）R2=0.986676 F= DW=0.605852对此模型进行White检验如下：Heteroskedasticity Test: White F-statistic 1.348072 Prob. F(2,31) 0.2745Obs*R-squared 2.720457 Prob. Chi-Square(2) 0.2566Scaled explained SS 1.221901 Prob. Chi-Square(2) 0.5428Test Equation:Dependent Variable: WGT_RESID^2Method: Least SquaresDate: 12/11/14 Time: 11:20Sample: 1 34Included observations: 34Collinear test regressors dropped from specification Variable Coefficient Std. Error t-Statistic Prob. C .498 0.0003WGT^2 -32.75 -0..8651X*WGT^2 -0....7078 R-squared 0.080013 Mean dependent var Adjusted R-squared 0.020659 S.D. dependent var S.E. of regression
Akaike info criterion 17.36487Sum squared resid
Schwarz criterion 17.49955Log likelihood -292.2027 Hannan-Quinn criter. 17.41080F-statistic 1.348072 Durbin-Watson stat 1.199640Prob(F-statistic) 0.2745452从上图中可以看出，nR=2.720457，比较计算的统计量的临界值，因为nR2=2.720457&响。0.05（2）=5.9915，所以接受原假设，即该模型消除了异方差的影②当权数w2=1/x2时，用软件分析得：Dependent Variable: YMethod: Least SquaresDate: 12/11/14 Time: 13:27Sample: 1 34Included observations: 34Weighting series: W2Variable Coefficient Std. Error t-StatisticX 0...29335C 8...466744Weighted StatisticsR-squared 0.982425 Mean dependent varAdjusted R-squared 0.981875 S.D. dependent varS.E. of regression 16.20273 Akaike info criterionSum squared resid
Schwarz criterionLog likelihood -141.9094 Hannan-Quinn criter.F-statistic
Durbin-Watson statProb(F-statistic) 0.000000Unweighted StatisticsR-squared 0.954142 Mean dependent varAdjusted R-squared 0.952709 S.D. dependent varS.E. of regression 258.5207 Sum squared residDurbin-Watson stat 0.781788得方程模型为：Y=0..890886t=（42.29335）（2.466744）R2=0.982425 F= DW=0.604647用White检验模型得：Heteroskedasticity Test: WhiteF-statistic 7.462185 Prob. F(3,30)Obs*R-squared 14.52935 Prob. Chi-Square(3)Scaled explained SS 19.40139 Prob. Chi-Square(3)Prob. 0.2 230.8 8....5.802 7 0.2Test Equation:Dependent Variable: WGT_RESID^2Method: Least SquaresDate: 12/11/14 Time: 11:19Sample: 1 34Included observations: 34Variable Coefficient Std. Error t-StatisticC -7..7605WGT^2 64.60 0.667975X^2*WGT^2 0...838317X*WGT^2 -1...071903R-squared 0.427334 Mean dependent varAdjusted R-squared 0.370067 S.D. dependent varS.E. of regression 345.6323 Akaike info criterionSum squared resid 3583851. Schwarz criterionLog likelihood -244.8589 Hannan-Quinn criter.F-statistic 7.462185 Durbin-Watson statProb(F-statistic) 0.000712从上图中可以看出，nR2=14.52935，比较计算的nR2=14.52935& Prob. 0.3 0.3 247.1 14.33 14.012统计量的临界值，因为0.05（2）=5.9915，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差。此模型并未消除异方差。③当权数w3=1/sqr(x)时，用软件分析得：Dependent Variable: YMethod: Least SquaresDate: 12/11/14 Time: 13:21Sample: 1 34Included observations: 34Weighting series: W3Variable Coefficient Std. Error t-Statistic Prob.X 0...0C 40.28 2..0091Weighted StatisticsR-squared 0.987192 Mean dependent var 776.3266Adjusted R-squared 0.986792 S.D. dependent varS.E. of regression 79.19828 Akaike info criterionSum squared resid
Schwarz criterionLog likelihood -195.8597 Hannan-Quinn criter.F-statistic
Durbin-Watson statProb(F-statistic) 0.000000Unweighted StatisticsR-squared 0.977590 Mean dependent varAdjusted R-squared 0.976890 S.D. dependent varS.E. of regression 180.7210 Sum squared residDurbin-Watson stat 1.460832得方程模型为：Y=0..45770t=（49.66347）（2.775775）R2=0.986792 F= DW=1.178340对所得模型进行White检验：Heteroskedasticity Test: WhiteF-statistic 8.158958 Prob. F(2,31)Obs*R-squared 11.72514 Prob. Chi-Square(2)Scaled explained SS 28.08353 Prob. Chi-Square(2)Test Equation:Dependent Variable: WGT_RESID^2Method: Least SquaresDate: 12/10/14 Time: 13:23Sample: 1 34Included observations: 34Collinear test regressors dropped from specification Variable Coefficient Std. Error t-StatisticC -1.263 -1.428132WGT^2 6.041 1.236632X^2*WGT^2 0...684177R-squared 0.344857 Mean dependent varAdjusted R-squared 0.302590 S.D. dependent varS.E. of regression 11636.97 Akaike info criterionSum squared resid 4.20E+09 Schwarz criterionLog likelihood -364.9796 Hannan-Quinn criter. 367.81 11.43 1.5.802 4 0.0 Prob. 0.5 0.5 .54 21.69179F-statistic 8.158958 Durbin-Watson statProb(F-statistic) 0.001423从上图中可以看出，nR2=11.72514，比较计算的nR2=11.068统计量的临界值，因为0.05（2）=5.9915，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差。此模型并未消除异方差。综上所述，用加权二乘法w1的效果最好，所以模型为：得方程模型为：Y=0..69318t=（48.67993）（2.815926）R2=0.986676 F= DW=0.6058522）用对数模型法用软件分析得：Dependent Variable: LNY Method: Least SquaresDate: 12/11/14 Time: 09:54Sample: 1 34Included observations: 34Variable Coefficient Std. Error t-Statistic Prob.LNX 0...0C 0....0143R-squared 0.995521 Mean dependent var 6.687779Adjusted R-squared 0.995381 S.D. dependent var 1.067124S.E. of regression 0.072525 Akaike info criterion -2.352753Sum squared resid 0.168315 Schwarz criterion -2.262967Log likelihood 41.99680 Hannan-Quinn criter. -2.322134F-statistic
Durbin-Watson stat 0.812150Prob(F-statistic) 0.000000得到模型为：LnY=0.946887 LNX+0.201861对此模型进行White检验得：Heteroskedasticity Test: WhiteF-statistic 1.003964 Prob. F(2,31) 0.3780Obs*R-squared 2.068278 Prob. Chi-Square(2) 0.3555Scaled explained SS 1.469638 Prob. Chi-Square(2) 0.4796计量经济学(庞皓)第三版课后答案05_计量经济学课后答案Test Equation:Dependent Variable: RESID^2Method: Least SquaresDate: 12/11/14 Time: 09:55Sample: 1 34Included observations: 34 Variable Coefficient Std. Error t-Statistic Prob.C 0....4042 LNX -0....4140LNX^2 0....3715 R-squared 0.060832 Mean dependent var 0.004950Adjusted R-squared 0.000240 S.D. dependent var 0.006365S.E. of regression 0.006364 Akaike info criterion -7.192271Sum squared resid 0.001255 Schwarz criterion -7.057592Log likelihood 125.2686 Hannan-Quinn criter. -7.146342F-statistic 1.003964 Durbin-Watson stat 2.022904Prob(F-statistic) 0.378027从上图中可以看出，nR2=2.068278，比较计算的统计量的临界值，nR2=2..05（2）=5.9915，所以接受原假设，此模型消除了异方差。综合两种方法，改进后的模型最好为：LnY=0.946887 LNX+0.201861(2)1）考虑价格因素，首先用软件三者关系进行分析如下：Dependent Variable: YMethod: Least SquaresDate: 12/12/14 Time: 19:26Sample: 1 34Included observations: 34Variable Coefficient Std. Error t-Statistic Prob.X 0...0P 0....3937C 43.46 0..5466R-squared 0.979911 Mean dependent var
为因Adjusted R-squared 0.978615 S.D. dependent varS.E. of regression 173.8449 Akaike info criterionSum squared resid
Schwarz criterionLog likelihood -222.0511 Hannan-Quinn criter.F-statistic 756.0627 Durbin-Watson statProb(F-statistic) 0.0000001）用Goldfeld-Quanadt检验如下：①当样本为1-13时，进行回归分析：Dependent Variable: PMethod: Least SquaresDate: 12/14/14 Time: 19:26Sample: 1 13Included observations: 13Variable Coefficient Std. Error t-StatisticX -0...836247Y 0...186646C 59.841 8.056627R-squared 0.956255 Mean dependent varAdjusted R-squared 0.947506 S.D. dependent varS.E. of regression 8.466678 Akaike info criterionSum squared resid 716.8464 Schwarz criterionLog likelihood -44.51063 Hannan-Quinn criter.F-statistic 109.2993 Durbin-Watson statProb(F-statistic) 0.0000002 得∑e1i=716.8464②当样本为22-34时，做回归分析得：Dependent Variable: YMethod: Least SquaresDate: 12/14/14 Time:20:39Sample: 22 34Included observations: 13Variable Coefficient Std. Error t-StatisticX 0...918569P -1...082514C 795.5 1.317670.98 13.521 Prob. 0.6 0.1 36.328 7...637181 Prob. 0.4 0.2170R-squared 0.939696 Mean dependent var Adjusted R-squared 0.927635 S.D. dependent var S.E. of regression 275.0847 Akaike info criterion 14.27121Sum squared resid
Schwarz criterion 14.40158Log likelihood -89.76286 Hannan-Quinn criter. 14.24441F-statistic 77.91291 Durbin-Watson stat 1.128778Prob(F-statistic) 0. 得∑e2i=③根据Goldfeld-Quanadt检验，F统计量为：F=∑e2i2 /∑e1i2 =/ 716.76在α=0.05水平下，分子分母的自由度均为11，查分布表得临界值F0.05（10,10）=2.98，因为F=& F0.05（10,10）=2.98，所以拒绝原假设，此检验表明模型存在异方差。2）用White检验，软件分析结果为：Heteroskedasticity Test: WhiteF-statistic 7.312529 Prob. F(5,28)Obs*R-squared 19.25463 Prob. Chi-Square(5)Scaled explained SS 119.3072 Prob. Chi-Square(5)Test Equation:Dependent Variable: RESID^2Method: Least SquaresDate: 12/12/14 Time: 19:31Sample: 1 34Included observations: 34Variable Coefficient Std. Error t-StatisticC 647.3 0.706107X 209.00 3.278298X^2 -0...252841X*P -0...204822P -6.253 -1.016495P^2 1...629751R-squared 0.566313 Mean dependent varAdjusted R-squared 0.488869 S.D. dependent varS.E. of regression 77206.44 Akaike info criterionSum squared resid 1.67E+11 Schwarz criterionLog likelihood -427.5874 Hannan-Quinn criter.F-statistic 7.312529 Durbin-Watson statProb(F-statistic) 0..7 0.0000 Prob. 0.8 0.8 0.0 990.9 25.50 25.044从上图中可以看出，nR2=19.25463，比较计算的nR2=19.25463&统计量的临界值，因为0.05（5）=11.0705，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差。2）修正①建立对数模型，用软件分析如下：Dependent Variable: LNYMethod: Least SquaresDate: 12/12/14 Time: 19:24Sample: 1 34Included observations: 34Variable Coefficient Std. Error t-Statistic Prob.LNX 0...0LNP 0....3532C 0....3981R-squared 0.995646 Mean dependent var 6.687779Adjusted R-squared 0.995365 S.D. dependent var 1.067124S.E. of regression 0.072652 Akaike info criterion -2.322188Sum squared resid 0.163625 Schwarz criterion -2.187509Log likelihood 42.47720 Hannan-Quinn criter. -2.276259F-statistic
Durbin-Watson stat 0.930109Prob(F-statistic) 0.000000对此模型进行White检验：Heteroskedasticity Test: WhiteF-statistic 3.523832 Prob. F(5,28) 0.0135Obs*R-squared 13.13158 Prob. Chi-Square(5) 0.0222Scaled explained SS 12.14373 Prob. Chi-Square(5) 0.0329Test Equation:Dependent Variable: RESID^2Method: Least SquaresDate: 12/12/14 Time: 19:24Sample: 1 34Included observations: 34Variable Coefficient Std. Error t-Statistic Prob.C 0....1336LNX 0....0171LNX^2 -0....2078LNX*LNP -0....3429LNP -0....0596LNP^2 0....0460 R-squared 0.386223 Mean dependent var 0.004813Adjusted R-squared 0.276620 S.D. dependent var 0.007286S.E. of regression 0.006197 Akaike info criterion -7.170690Sum squared resid 0.001075 Schwarz criterion -6.901332Log likelihood 127.9017 Hannan-Quinn criter. -7.078831F-statistic 3.523832 Durbin-Watson stat 2.264261Prob(F-statistic) 0.0135022从上图中可以看出，nR=13.13158，比较计算的统计量的临界值，因为nR2=13.（5）=11.0705，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差，所以此模型没有消除异方差。②当w1=1/x时，用软件分析如下：Dependent Variable: YMethod: Least SquaresDate: 12/13/14 Time: 18:49Sample: 1 34Included observations: 34Weighting series: W1Variable Coefficient Std. Error t-StatisticX 0...49212P 0...099795C -44.68 -3.410502Weighted StatisticsR-squared 0.992755 Mean dependent varAdjusted R-squared 0.992287 S.D. dependent varS.E. of regression 28.40494 Akaike info criterionSum squared resid 25012.05 Schwarz criterionLog likelihood -160.4567 Hannan-Quinn criter.F-statistic
Durbin-Watson statProb(F-statistic) 0.000000Unweighted Statistics Prob. 0.0 0.5 41.100 9...298389计量经济学(庞皓)第三版课后答案05_计量经济学课后答案R-squared 0.977704 Mean dependent var Adjusted R-squared 0.976266 S.D. dependent var
S.E. of regression 183.1446 Sum squared resid 1039800. Durbin-Watson stat 1.740795所得模型为：Y=0...72084对此模型进行White检验得： Heteroskedasticity Test: WhiteF-statistic 2.088840 Prob. F(5,28) 0.0966Obs*R-squared 9.236835 Prob. Chi-Square(5) 0.1000 Scaled explained SS 25.50696 Prob. Chi-Square(5) 0.0001Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 12/14/14 Time: 19:57 Sample: 1 34 Included observations: 34 Collinear test regressors dropped from specificationVariable Coefficient Std. Error t-Statistic Prob. C 8.806 3..0012 WGT^2 9.988 0..4557 X*WGT^2 13.473 1..1157 X*P*WGT^2 -0....0202 P^2*WGT^2 0....1326 P*WGT^2 -76.36 -1..3085R-squared 0.271672 Mean dependent var 735.6486Adjusted R-squared 0.141613 S.D. dependent var
S.E. of regression
Akaike info criterion 17.96897 Sum squared resid
Schwarz criterion 18.23832 Log likelihood -299.4724 Hannan-Quinn criter. 18.06082 F-statistic 2.088840 Durbin-Watson stat 2.336495 Prob(F-statistic) 0.0966162因为nR=9..05（5）=11.0705，所以接受原假设。该模型不存在异方差，所以此模型消除了异方差。③当w2=1/x2，用软件分析得： Dependent Variable: Y Method: Least Squares Date: 12/15/14 Time: 20:02 Sample: 1 34 Included observations: 34 Weighting series: W2Variable Coefficient Std. Error t-Statistic X 0...29477 P 1...828234 C -81.99 -5.189209 Weighted Statistics R-squared 0.991614 Mean dependent varAdjusted R-squared 0.991073 S.D. dependent var S.E. of regression 11.37136 Akaike info criterion Sum squared resid
Schwarz criterion Log likelihood -129.3309 Hannan-Quinn criter. F-statistic
Durbin-Watson stat Prob(F-statistic) 0.000000Unweighted Statistics R-squared 0.956816 Mean dependent varAdjusted R-squared 0.954030 S.D. dependent var S.E. of regression 254.8849 Sum squared resid Durbin-Watson stat 1.002870所得模型为：Y=0...85973对该模型进行White检验得： Heteroskedasticity Test: WhiteF-statistic 43.19853 Prob. F(6,27)Obs*R-squared 30.79235 Prob. Chi-Square(6) Scaled explained SS 47.42430 Prob. Chi-Square(6)Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 12/14/14 Time: 19:20Prob. 0.0 0.3 247.170 7...1679618.791 2013955.0.0 0.0000Sample: 1 34 Included observations: 34Variable Coefficient Std. Error t-Statistic Prob. C 27.56 1..1829 WGT^2 -.268 0.1485 X^2*WGT^2 0....1674 X*WGT^2 7....1153 X*P*WGT^2 -0....0924 P^2*WGT^2 0....2725 P*WGT^2 -3..5685 0.8954R-squared 0.905657 Mean dependent var 117.8983Adjusted R-squared 0.884692 S.D. dependent var 230.3570 S.E. of regression 78.22224 Akaike info criterion 11.73823 Sum squared resid
Schwarz criterion 12.05248 Log likelihood -192.5498 Hannan-Quinn criter. 11.84539 F-statistic 43.19853 Durbin-Watson stat 1.794799 Prob(F-statistic) 0.000000因为nR2=30.（5）=11.0705，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差，所以此模型没有消除异方差。④当w3=1/sqr(x)时，用软件分析得： Dependent Variable: Y Method: Least Squares Date: 12/14/14 Time: 19:06 Sample: 1 34 Included observations: 34 Weighting series: W3Variable Coefficient Std. Error t-Statistic X 0...56252 P 0...510739 C -13.68 -0.531823 Weighted Statistics R-squared 0.989356 Mean dependent varAdjusted R-squared 0.988670 S.D. dependent var S.E. of regression 73.35237 Akaike info criterion Sum squared resid
Schwarz criterion Log likelihood -192.7129 Hannan-Quinn criter.Prob. 0.5 0.6 367.52 11.45F-statisticProb(F-statistic)R-squared Adjusted R-squared S.E. of regression Durbin-Watson stat所得模型为： Durbin-Watson stat 0.000000Unweighted Statistics 0.979407 Mean dependent var 0.978079 S.D. dependent var 176.0098 Sum squared resid 1.7612251.5995908.791 Y=0...49643对所得模型进行White检验得： Heteroskedasticity Test: WhiteF-statistic 4.459272 Prob. F(5,28)Obs*R-squared 15.07219 Prob. Chi-Square(5) Scaled explained SS 72.39077 Prob. Chi-Square(5)Test Equation: Dependent Variable: WGT_RESID^2 Method: Least Squares Date: 12/14/14 Time: 19:08 Sample: 1 34 Included observations: 34 Collinear test regressors dropped from specificationVariable Coefficient Std. Error t-Statistic C 31.93 2.221538 WGT^2 50.39 1.628320 X^2*WGT^2 -0...164950 X*P*WGT^2 -0...058447 P^2*WGT^2 1...918030 P*WGT^2 -503.4 -1.916718R-squared 0.443300 Mean dependent varAdjusted R-squared 0.343889 S.D. dependent var S.E. of regression 13710.96 Akaike info criterion Sum squared resid 5.26E+09 Schwarz criterion Log likelihood -368.8256 Hannan-Quinn criter. F-statistic 4.459272 Durbin-Watson stat Prob(F-statistic) 0.0041030.1 0.0000 Prob. 0.7 0.9 0.5 26.97 22.92 22.171因为nR2=15.07219&0.05（5）=11.0705，所以拒绝原假设，不拒绝备择假设，表明模型存在异方差，所以此模型没有消除异方差。综上所述，修改后的模型为：Y= Y=0...72084 t=(31.49212) (5.099705) (-3.410502) R2=0.992755 F= DW=1.298389(3)体会：对于不同的模型，可采取对数模型法或者加权二乘法对具有异方差性的模型进行改进，从而消除异方差。但对于不同的模型，自由度的不同，可能导致改进的方法不同，所以要对改进的模型进行进一步的检验才行。计量经济学(庞皓)第三版课后答案05_计量经济学课后答案6.1(1)建立居民收入-消费模型，用Eviews分析结果如下：Dependent Variable: YMethod: Least SquaresDate: 12/20/14 Time: 14:22Sample: 1 19Included observations: 19Variable Coefficient Std. Error t-StatisticX 0...62068C 79.19 6.446390R-squared 0.994122 Mean dependent varAdjusted R-squared 0.993776 S.D. dependent varS.E. of regression 19.44245 Akaike info criterionSum squared resid
Schwarz criterionLog likelihood -82.28490 Hannan-Quinn criter.F-statistic
Durbin-Watson statProb(F-statistic) 0.000000Prob. 0.0 700.1 8....574663残差的变动有系统模式，连续为正和连续为负，表明残差项存在一阶自相关。②该回归方程可决系数较高，回归系数均显著。对样本量为19，一个解释变量的模型，5%的显著水平，查DW统计表可知，dL=1.180，dU=1.401，模型中DW=0.574663,& dL,显然模型中有自相关。③对模型进行BG检验，用Eviews分析结果如下：Breusch-Godfrey Serial Correlation LM Test:F-statistic 4.811108 Prob. F(2,15) 0.0243Obs*R-squared 7.425088 Prob. Chi-Square(2) 0.0244Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 12/20/14 Time: 15:03Sample: 1 19Included observations: 19 Presample missing value lagged residuals set to zero.Variable Coefficient Std. Error t-Statistic Prob.X -0....7656C 1..323 0.8547RESID(-1) 0....0551RESID(-2) 0....7615R-squared 0.390794 Mean dependent var -1.65E-13Adjusted R-squared 0.268953 S.D. dependent var 18.89466S.E. of regression 16.15518 Akaike info criterion 8.587023Sum squared resid
Schwarz criterion 8.785852Log likelihood -77.57671 Hannan-Quinn criter. 8.620672F-statistic 3.207406 Durbin-Watson stat 1.570723Prob(F-statistic) 0.053468 如上表显示，LM=TR2=7.425088，其p值为0.0244，表明存在自相关。2）对模型进行处理：①采取广义差分法a)为估计自相关系数ρ。对et进行滞后一期的自回归，用EViews分析结果如下： Dependent Variable: EMethod: Least SquaresDate: 12/20/14 Time: 15:04Sample (adjusted): 2 19Included observations: 18 after adjustmentsVariable Coefficient Std. Error t-StatisticE(-1) 0...700759R-squared 0.440747 Mean dependent varAdjusted R-squared 0.440747 S.D. dependent varS.E. of regression 13.34980 Akaike info criterionSum squared resid
Schwarz criterionLog likelihood -71.67349 Hannan-Quinn criter.Durbin-Watson stat 1.634573由上可知，ρ=0.657352 Prob. 0.433 17.833 8..081653 b)对原模型进行广义差分回归，用Eviews进行分析所得结果如下：Dependent Variable: Y-0.657352*Y(-1)Method: Least SquaresDate: 12/20/14 Time: 15:04 Sample (adjusted): 2 19Included observations: 18 after adjustmentsVariable Coefficient Std. Error t-Statistic Prob.C 35.546 4..0004 X-0.657352*X(-1) 0...0R-squared 0.984983 Mean dependent var 278.1002Adjusted R-squared 0.984044 S.D. dependent var 105.1781S.E. of regression 13.28570 Akaike info criterion 8.115693Sum squared resid
Schwarz criterion 8.214623Log likelihood -71.04124 Hannan-Quinn criter. 8.129334F-statistic
Durbin-Watson stat 1.830746 Prob(F-statistic) 0.000000 由上图可知回归方程为：Yt*=35.695Xt*Se=(8..020642)t=(4..39512)R2=0.984983 F= DW=1.830746式中，Yt*=Yt-0.657352Yt-1, Xt*=Xt-0.657352Xt-1由于使用了广义差分数据，样本容量减少了1个，为18个。查5%显著水平的DW统计表可知，dL=1.158,dU=1.391模型中DW=1,830746，du&DW&4- dU，说明在5%的显著水平下广义差分模型中已无自相关。可决系数R2，t，F统计量也均达到理想水平。由差分方程，β1=35.9.4.9987由此最终的消费模型为：Yt=104.695Xt②用科克伦-奥克特迭代法，用EVIews分析结果如下：Dependent Variable: YMethod: Least SquaresDate: 12/20/14 Time: 15:15Sample (adjusted): 2 19Included observations: 18 after adjustmentsConvergence achieved after 5 iterationsVariable Coefficient Std. Error t-StatisticC 104.18 4.357687X 0...12757AR(1) 0...836462R-squared 0.997097 Mean dependent varAdjusted R-squared 0.996710 S.D. dependent varS.E. of regression 13.70843 Akaike info criterionSum squared resid
Schwarz criterionLog likelihood -71.02419 Hannan-Quinn criter.F-statistic
Durbin-Watson statProb(F-statistic) 0.000000Inverted AR Roots .63所得方程为：Yt=104.262XtProb. 0.0 0.7 238.910 8...787878（3）经济意义：人均实际收入每增加1元，平均说来人均时间消费支出将增加0.669262元。6.4（1）1）针对对数模型，用Eviews分析结果如下：Dependent Variable: LNYMethod: Least SquaresDate: 12/27/14 Time: 16:13Sample: Included observations: 21 Variable Coefficient Std. Error t-Statistic Prob. LNX 0...0C 2....0000 R-squared 0.969199 Mean dependent var 8.039307Adjusted R-squared 0.967578 S.D. dependent var 0.565486S.E. of regression 0.101822 Akaike info criterion -1.640785Sum squared resid 0.196987 Schwarz criterion -1.541307Log likelihood 19.22825 Hannan-Quinn criter. -1.619196F-statistic 597.8626 Durbin-Watson stat 1.159788Prob(F-statistic) 0.000000 所得模型为：lnY=0,951090lnX+2.171041se=(0.038897) (0.241025)t=(24.45123) (9.007529)R2=0.969199 F=597.8626 DW=1.1597882）检验模型的自相关性该回归方程可决系数较高，回归系数均显著。对样本量为21，一个解释变量的模型，5%的显著水平，查DW统计表可知，dL=1.221，dU=1.420，模型中DW=1.159788& dL,显然模型中有自相关。(2)用广义差分法处理模型：1）为估计自相关系数ρ。对et进行滞后一期的自回归，用EViews分析结果如下： Dependent Variable: EMethod: Least SquaresDate: 12/27/14 Time: 16:18Sample (adjusted): Included observations: 19 after adjustments计量经济学(庞皓)第三版课后答案05_计量经济学课后答案Variable Coefficient Std. Error t-Statistic Prob. E(-1) -0....9639 R-squared 0.000073 Mean dependent var -2.556737Adjusted R-squared 0.000073 S.D. dependent var 397.7924S.E. of regression 397.7778 Akaike info criterion 14.86086Sum squared resid 2848090. Schwarz criterion 14.91057Log likelihood -140.1782 Hannan-Quinn criter. 14.86927Durbin-Watson stat 1.700254 由上可知，ρ=-0.0128722）对原模型进行广义差分回归，用Eviews进行分析所得结果如下：Dependent Variable: Y+0.012872*Y(-1)Method: Least SquaresDate: 12/27/14 Time: 21:06 Sample (adjusted): Included observations: 20 after adjustmentsVariable Coefficient Std. Error t-Statistic Prob.C -104.8 -0..6021 X+0.012872*X(-1) 6...0R-squared 0.963751 Mean dependent var Adjusted R-squared 0.961737 S.D. dependent var S.E. of regression 400.1404 Akaike info criterion 14.91615Sum squared resid 2882022. Schwarz criterion 15.01572Log likelihood -147.1615 Hannan-Quinn criter. 14.93559F-statistic 478.5614 Durbin-Watson stat 1.822259 Prob(F-statistic) 0.000000 由上图可知回归方程为：Yt*=-104.757Xt*Se=(197.7928)( 0.304157)t=(-0.530679)( 21.87605)R2=0.963751 F=478.5614DW=1.8222596式中，Yt*=Yt+0.012872Yt-1, Xt*=Xt+0.012872Xt-1由于使用了广义差分数据，样本容量减少了1个，为20个。查5%显著水平的DW统计表可知，dL=1.201,dU=1.411模型中DW=1.8222596，du&DW&4- dU，说明在5%的显著水平下广义差分模型中已无自相关。可决系数R2，t，F统计量也均达到理想水平。 由差分方程，β1=-104..012872)=-103.6306由此最终的模型为：Yt=-103.757Xt（3）对于此模型，用Eviews分析结果如下：Dependent Variable: LNY1 Method: Least Squares Date: 12/27/14 Time: 22:16 Sample (adjusted):
Included observations: 20 after adjustments Variable Coefficient Std. Error t-Statistic Prob. LNX1 0....0000C 0....0007 R-squared 0.713658 Mean dependent var 0.091592Adjusted R-squared 0.697750 S.D. dependent var 0.098311 S.E. of regression 0.054049 Akaike info criterion -2.903219 Sum squared resid 0.052583 Schwarz criterion -2.803646 Log likelihood 31.03219 Hannan-Quinn criter. -2.883781 F-statistic 44.86188 Durbin-Watson stat 1.590363 Prob(F-statistic) 0.000003 由题目可知，此模型样本容量为20，查5%显著水平的DW统计表可知，dL=1.201,dU=1.411模型中DW=1.590363，du&DW&4- dU，说明在5%的显著水平此模型中无自相关。可决系数R2，t，F统计量也均达到理想水平欢迎您转载分享：
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