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1、第五章课后答案5.1(1)因为f(Xi)=X22i所以取川21=，用W2i乘给定模型两端，得X2i工一心JX2iX2iX2i X2i上述模型的随机误差项的方差为一固定常数，即Ui 12Var( 一)rVar(Ui)=二X2iX2i(2)根据加权最小二乘法，可得修正异方差后的参数估计式为& =Y -2X 2 -? 3X 3 * *2 *?v 为 W、x Wi y x Max2.* 2.,一.*2一 ，一.*2*W2ix2iI .一W2ix3i - W2ix2ix3i2(乙W2iyi xi)(乙W2i为/(乙W2i Yijtxi乙W i x i x222*i.W2ix2i】W2ix3i-W2ix2
2、iX3i其中5.2(D.二.W2i X 2- W2i W i2X i 3-W2i WiY2- W4ix2i =*X2i - X2*x3 = X3 - X3* *y= iY- yln(u) = ln(ln(1 YY311X 2u = ln(u) 1又 E Eln(u) =0.E()=Eln( u) 1 =Eln( u) 1 =1Eln( N) = Pi In 耳=lnn NiP =0二口 NiP =1E(N) = 口叶=1不能推导出口 BP =1所以E (N) =1时，不一定有E (ln N) =0(3)对方程进行差分得：lnYi-lnYi-1 = MnX 3 )+(ln-ln )则有：E(ln
3、i Tni4) =05.3(1)该模型样本回归估计式的书写形式为:Y = 11.44213599 + 0.6267829962*X (3.629253)(0.019872)t= 3.15275231.54097_ 2- 2R 0. 94 49 1 1 R =0. 94 39 6 1 S.E.=9.158900DW=1.597946F=994.8326(2)首先，用Goldfeld-Quandt法进行检验。a. 将样本X按递增顺序排序，去掉中间1/4的样本，再分为两个部分的 样本，即 n1 = n2 = 22。b.分别对两个部分的样本求最小二乘估计，得到两个部分的残差平方 和，即 e2 = 62
4、4.3004 e2 = 2495.840求F统计量为F=2495.840=TT =3 9978工2 624.3004给定a =0.05,查F分布表，得临界值为F0.05(20,20) =2.12。c.比较临界值与F统计量值，有F =4.1390%05(20,20)=2.12,说明该模型 的随机误差项存在异方差。其次，用White法进行检验。具体结果见下表White Heteroskedasticity Test:F-statistic6.105557Probability0.003958Obs*R-squared10.58597Probability0.005027给定a =0.05,在自由度
5、为2下查卡方分布表，得72 = 5.9915o比较临界值与卡方统计量值，即口片=10.864072=5.9915,同样说明模型中的 随机误差项存在异方差。(2)用权数W=1/|e|,作加权最小二乘估计，得如下结果Dependent Variable: YMethod: Least SquaresDate: 05/28/07 Time: 00:20Sample: 1 60Included observations: 60Weighting series: 1/RVariableCoefficie ntStd. Errort-StatisticProb.C27.500006.09E-084.52E
6、+080.0000X0.5000007.16E-106.98E+080.0000Weighted StatisticsR-squared1.000000Mean dependent70.0196var4Adjusted1.000000S.D. dependent379.890R-squaredvar9S.E. of regression8.44E-10Akaike info-38.916criterion22Sum squared4.13E-17Schwarz criterion-38.846resid41Log likelihood1169.487F-statistic4.88E+17Dur
7、bin-Watson0.786091Prob(F-statistic)0.00000stat0UnweightedStatisticsR-squared0.883132Mean dependent119.666var7Adjusted0.881117S.D. dependent38.6898R-squaredvar4S.E. of regression13.34005Sum squared10321.5resid0Durbin-Watson0.377804statWhite检验:White Heteroskedastidty Test:F-statistic2.357523Probabilit
8、y0.103822Obs*R-squared4.584017Probability20.101063Test Equation:Dependent Variable: STD_RESIDA2Method: Least SquaresDate: 05/28/07 Time: 00:27Sample: 1 60Included observations: 60VariableCoefficieStd. Error t-StatisticProb.ntC3.86E-191.73E-19 2.2337560.0294X3.21E-212.16E-21 1.4895320.1419XA2-7.59E-2
9、46.18E-24 -1.2296410.2239R-squared0.076400Mean dependent6.88E-1var9Adjusted0.043993S.D. dependent1.56E-1R-squaredvar9S.E. of regression1.52E-19Sum squared1.32E-3resid6F-statistic2.357523Durbin-Watson1.19153stat1Prob(F-statistic)0.1038225.4令Y表示农业总产值，X1-X5分别表示农业劳动力、灌溉面积、化肥用量、户 均固定资产和农机动力。建立模型：Y = 01X1
10、2X23X34X45X回归结果如下：Y?= 4.717198 0.039615X1-0.036895X2 0.263256X3 0.013463X4 0.025469X5 ”(0.516910)(1.452697) ( -0.474813) (0.479104) (2.712997) (1.625993)R2 =0.974539 R2=0.953321 DW=1.969898 F=45.93047从回归结果可以看出，模型的R2和R2值都较高，F统计量也显著。但是除X4的系数显著之外，其他系数均不显著，模型可能存在多重共线性。 计算各解释变量的相关系数。相关系数矩阵X1X2X3X4X5X11.0
11、000000.8518670.9631730.4569130.892506X20.8518671.0000000.8435410.5493900.856933X30.9631730.8435411.0000000.5830480.924806X40.4569130.5493900.5830481.0000000.543765X50.8925060.8569330.9248060.5437651.000000由相关系数矩阵可以看出，解释变量之间的相关系数较高，存在多重共线性。采用逐步回归的办法，来解决多重共线性问题。分别做 Y对XI、X2、X3、X4、X5的一元回归，结果如下表所示：一元回归结果
12、变量参数估计值t统计量R2R2X10.0840788.0976510.8676760.854443X20.4567675.0993710.7222500.694475X31.52641011.621320.9310610.924167X40.0352772.9913260.4722410.419465X50.0782698.1979290.8704760.857524其中加入X3的方程R2最大，以X3为基础，顺次加入其他变量逐步回归，结果 如下：加入新变量的回归结果（一）变量X3, X1X3, X2X3, X4X3, X5X10.002636(0.089770)X20.0669090.7899
13、58X31.481909(2.8792931.360291 5.456584 1.352291 9.776764 1.115680(3.355936)X40.0096912.159071X50.023552(1.335921)R2 0.9158160.9212040.9444920.929684经比较，新加入X4的方程R2 =0.944492 ,改进最大。且从经济意义来看，户均固定资产对农业总产值有影响，因此保留 X4,再加入其他变量逐步回归，结果 如下：加入新变量的回归结果（二）变量X3, X4 X1X10.035438(1.365712)X2X3, X4 X20.047486 (1.487193)X3, X4 ,X5X30.696651(1.399128)1.241502 (5.528062)0.951924(3.375236X40.012887(2.638461) 0.009296 (1.984375) 0.009594 (2.31
