计量学实验报告实验2.docx
实例1中国粮食生产函数依据理论和阅历分析，影响粮食生产（Y）的主要因素有农业化肥施用量（XI）、粮食播种面积（X2）、成 灾面积（X3）、农业机械总动力（X4）和农业劳动力（X5）,其中成灾面积的符号为负，其余均应为正。下表 给出了 19832000中国粮食生产的相关数据，拟建立中国粮食生产函数。年份粮食产量Y （万吨）化肥施用量XI （万千克）播种面积X2 （千公顷）成灾面积X3 （公顷）农业机械总动力X4 （万千瓦）农业劳动力X5 （万人）198338728.01659. 8114047.016209.318022.031645. 1198440731.01739. 8112884.015264.019497. 031685.0198537911.01775.8108845.022705.320913.030351.5198639151.01930. 6110933.023656. 022950.030467. 0198740208.01999.3111268.020392.724836. 030870. 0198839408.02141.5110123.023944. 726575.031455.7198940755.02357. 1112205.024448.728067.032440.5199044624.02590. 3113466.017819.328708.033330.4199143529.02806. 1112314.027814.029389.034186. 3199244264. 02930. 2110560.025894. 730308.034037. 0199345649.03151.9110509.023133.031817.033258.2199444510.03317.9109544.031383.033802.032690.3199546662.03593. 7110060.022267.036118.032334.5199650454.03827. 9112548.021233.038547.032260.4199749417.03980. 7112912.030309.042022. 032434.9199851230.04083. 7113787.025181.045208.032626.4199950839.04124.3113161.026731.048996. 032911.8200046218.04146.4108463.034374.052574.032797.5（1）建立Y对全部解释变量的回归模型，结果如下:Y = -12815.75 + 6.213*X1 + 0.421 *X2 - 0.166*X3 - 0.098*X4 - 0.028*X5VariableCoefficientStd. Errort-StatisticProb.C-12815.7514078.90-0.9102800.3806X16.2125620.7408818.3853730.0000X20.4213800.1269253.3199190.0061X3-0.1662600.059229-2.8070650.0158X4-0.0977700.067647-1.4452990.1740X5-0.0284250.202357-0.1404710.8906R-squared0.982798Mean dependent var44127.11Adjusted R-squared0.975630S.D.dependent var4409.100S.E. of regression688.2984Akaike info criterion16.16752Sum squared resid5685056.Schwarz criterion16.46431Log likelihood-139.5077F-statistic137.1164Durbin-Watson stat1.810512Prob(F-statistic)0.000000从计算结果看，R2较大并接近于1,而且F=137.11>Fo.°5=3.11,故认为粮食生产量与上述全部解释变量间总体线 性相关显著。但是，同时，X4、X5前参数未通过t检验，而且符号的经济意义也不合理，故认为解释变量间 存在多重共线性。为了进一步检验多重共线性，进行下面操作。(2)计算解释变量间的两两相关系数，得到简洁相关系数矩阵如下：XIX2X3X4X5XI1X20.0118231X30. 640175-0.454911X40.960278-0.038480.6895651X50. 545450.1823590.35573530. 4541691从相关分析结果来看，部分解释变量间的确存在相关，尤其XI与X4之间高度相关。为了处理多重共线性, 正确选择解释变量，进行逐步回归，首先选择最优的基本方程。(3)分别做粮食生产量对各个解释变量的回归，得A. Y对XI回归结果:VariableCoefficientStd. Error t-StatisticProb.C30867.311206.36425.587060.0000X14.5761150.39819911.492020.0000R-squared0.891941Mean dependent var44127.11Adjusted R-squared0.885187S.D.dependent var4409.100S.E. of regression1493.984Akaike info criterion17.56072Sum squared resid35711799Schwarz criterion17.65965Log likelihood-156.0465F-statistic132.0666Durbin-Watson stat1.855174Prob(F-statistic)0.000000B. Y对X2回归结果：VariableCoefficientStd. Error t-StatisticProb.C-33822.4168409.15-0.4944140.6277X20.6988800.6132731.1395900.2712R-squared0.075073Mean dependent var44127.11Adjusted R-squared0.017265S.D.dependent var4409.100S.E. of regression4370.873Akaike info criterion19.70775Sum squared resid Log likelihood Durbin-Watson stat3.06E+08-175.3698Schwarz criterion F-statistic0.118043 Prob(F-statistic)19.806681.298665 0.271231C. Y对X3回归结果VariableCoefficientStd. Error t-StatisticProb.C35712.864926.5837.2490120.0000X30.3499780.2022021.7429060.1005R-squared0.159563Mean dependent var44127.11Adjusted R-squared0.107036S.D.dependent var4409.100S.E. of regression4166.457Akaike info criterion19.61196Sum squared resid2.78E+08Schwarz criterion19.71089Log likelihood-174.5076F-statistic3.037721Durbin-Watson stat0.935587Prob(F-statistic)0.100533D. Y对X4回归结果：VariableCoefficientStd. Error t-StatisticProb.C31918.721828.71517.454180.0000X40.3799670.0544486.9785870.0000R-squared0.752707Mean dependent var44127.11Adjusted R-squared0.737252S.D.dependent var4409.100S.E. of regression2260.060Akaike info criterion18.38861Sum squared resid81725964Schwarz criterion18.48754Log likelihood-163.4975F-statistic48.70067Durbin-Watson stat1.109488Prob(F-statistic)0.000003E. Y对X5回归结果：VariableCoefficientStd. Error t-StatisticProb.C-28260.0227240.49-1.0374270.3150X52.2396140.8423522.6587620.0172R-squared0.306429Mean dependent var44127.11Adjusted R-squared0.263081S.D.dependent var4409.100S.E. of regression3784.948Akaike info criterion19.41989Sum squared resid2.29E+08Schwarz criterion19.51882Log likelihood-172.7790F-statistic7.069018Durbin-Watson stat0.357079Prob(F-statistic)0.017160(4)逐步回归,A、Y对XI、X4回归结果:VariableCoefficientStd. Error t-StatisticProb.C31164.921137.21927.404510.0000X16.9259381.3315025.2022970.0001X4-0.2211780.120350-1.8377920.0860R-squared0.911800Mean dependent var44127.11Adjusted R-squared0.900040S.D.dependent var4409.100S.E. of regression1394.000Akaike info criterion17.46875Sum squared resid29148555Schwarz criterion17.61715Log likelihood-154.2188F-statistic77.53409Durbin-Watson stat1.992572Prob(F-statistic)0.000000从HI归结果看，拟合优度虽然提升，但X4的系数不显著，因此，存在共线性，而相比较而言，XI更重要，因 此剔除X4 (从相关分析也有助于这个结论)。B、Y对XI、X5回归结果:Variable Coefficient Std. Error t-Statistic Prob.C24133.84X14.431559X50.22128912406.480.4858830.4057061.9452619.1206250.5454420.07070.00000.5935R-squaredAdjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson statR-squaredAdjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat0.894042 Mean dependent var 0.879914 S.D. dependent var 1527.902 Akaike info criterion35017273 Schwarz criterion-155.8697 F-statistic1.839712 Prob(F-statistic)44127.114409.10017.6521917.8005963.282810.000000拟合优度提升不显著，修正的拟合优度略微下降，且X5系数不显著，因此，剔除X5.C、Y对X1、X3回归结果:Variable Coefficient Std. Error t-Statistic Prob.C35065.01X15.654330X3-0.3045461064.6120.3121990.05645232.9368818.11132-5.3948030.00000.00000.0001R-squaredAdjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson statR-squaredAdjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat0.963248 Mean dependent var0.958348S.D.dependent var899.8443Akaike info criterion12145797 Schwarz criterion -146.3400 F-statistic1.728340 Prob(F-statistic)44127.114409.10016.5933316.74173196.57230.000000从回归结果看，拟合优度提高，X1和X3的系数显著，因此接受X3.D、Y对X1、X2、X3回归结果:Variable Coefficient Std. Error t-Statistic Prob.C-11978.18X15.255935X20.408432X3-0.19460914072.920.2685950.1219740.054533-0.85115119.568283.348522-3.5686370.40900.00000.00480.0031R-squaredAdjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat44127.114409.10016.1161616.31402224.00860.0000000.979593 Mean dependent var0.975220S.D.dependent var694.0715Akaike info criterion6744293. Schwarz criterion-141.0454 F-statistic1.528658 Prob(F-statistic)从回归结果看，拟合优度提高，X1、X2和X3的系数显著，因此接受X2.即，回归方程为：Y = -11978.18057 + 5.255935121*X1 + 0.408432175*X2 - 0.1946087795*X3实例2我们国家1988年T998年的城镇居民人均全年耐用消费品支出、人均全年可支配收入以及耐用消费品价格 指数的统计资料如下表，试建立城镇居民人均全年耐用消费品支出Y关于人均全年可支配收入xl和耐用消费品 价格指数X2的回归模型，并进行回归分析。依据阅历和对经济现实的分析，设定模型为二元线性回归模型，理论形式为：Y = 0/3X +/?2X2 +u ,(1)数据如下表,年份人均全年可支配收入X1 (兀)耐用消费品价格指数X2 (1987)人均耐用消费品支出Y (元)19881181.4115.96137.1619891375.7133.35124.5619901501.2128.21107.9119911700.6124.85102.9619922026.6122.49125.2419932577.4129.86162.4519943496.2139.52217.4319954283140.44253.4219964838.9139.12251.0719975160.3133.35285.8519985425.1126.39327.26（2） Eviews的输出结果（下表）写出回归方程为：EXPENSEY = 158.5398355 + 0.04940379666*INCOMEX1 - 0.911684216TRINDEX2VariableCoefficientStd. Error t-StatisticProb.C158.5398121.80711.3015640.2293INCOMEX10.0494040.00468410.547860.0000PRINDEX2-0.9116840.989546-0.9213160.3838R-squared0.947989Mean dependent var190.4827Adjusted R-squared0.934986S.D.dependent var79.29127S.E. of regression20.21757Akaike info criterion9.077982Sum squared resid3270.001Schwarz criterion9.186499Log likelihood-46.92890F-statistic72.90647Durbin-Watson stat1.035840Prob（F-statistic）0.000007(3)检验从经济意义来看，可支配收入前的系数为0.0494,正的，介于0和1之间，符号、大小与理论符合；价格指数 前的系数为-0.91,大小和符号符合经济理论；从统计角度看，R-squared=0.947989, Adjusted R-squared=0.934986,从多元回归修正的判定系数看，回归方程较好地拟合 了散点，被解释变量的变异中有93%以上可以由方程来解释； 从F统计量的结果来看，F=72.9O647>Foo5(2,8)=4.46,而且F=72.9O647>Fo.oi(2,8)=8.65,可见方程总体来看,无论在0.05还是0.01水平上都显著，即在我们国家城镇居民人均全年耐用消费品支出与人均全年可支配收入和 耐用消费品价格指数之间存在显著的线性关系。这一点结论由F统计量的精确显著性水平Prob=0.000007也可 得到。 t统计量结果来看，可支配收入incomexl的系数，t值=10.54786>t0.05(8)=2.306,系数显著，可支配收入对耐用消费品支出有显著影响，变量x1保留；而对于耐用消费品价格指数prindex2的系数，t值=-0.921316,其肯定 值小于t0.05 (8),可以接受系数为零的原假设，剔除X2。以上结论由Eviews输出结果中系数的精确显著性水 平Prob也可以直接得到。(4)猜测：点猜测和区间猜测若已知2000年，我们国家城镇居民家庭人均可支配收入为5800元，耐用消费品价格指数为135,对2000年我们国家城镇居民家庭人均耐用消费品支出进行猜测。点猜测,将xl=5800, X2=135代入估量方程,EXPENSEY = 158.5398 + 0.0494*5800 - 0.9117*135,得到Y的估量值=321. 9803 （教材中是依据小数点后保留4位数字后的样本回归方程计算得到的，而Eviews 软件的估量值是322. 0045）。（也可可以在Eviews中调整扩大数据范围至2000,再将解释变量的数据输入，再采用Equation窗口下的forecast进行猜测，估量值即保存在EXPENSEYf序列中。）区间猜测 E（Y0）的区间猜测Y的估量值的Y0的方差估量为，= S2X0（XX）T X。已知X2000矩阵为:X 加)。=1 5800 ZUUv L135,则X2000矩阵的转置矩阵为：XI。5800135而解释变量式矩阵为:,11181.4115.96 '11375.7133.3511501.2128.2111700.6124.8512026.6122.4912577.4129.8613496.2139.5214283140.4414838.9139.1215160.3133.35< 15425.1126.39 J11X3X矩阵的转置矩阵为:1.0000001181.400115.96001.0000001375.700133.35001.0000001501.200128.21001.0000001700.600124.85001.0000002026.600122.49001.0000002577.400129.86001.0000003496.200139.52001.0000004283.000140.44001.0000004838.900139.12001.0000005160.300133.35001.0000005425.100126.39003X11因此，Var（匕）= S2Xo（XX）TX° = S2 *X0 *%u砥XX）*X° =155.5708 （其中残差的方差可由输出结果计算得到，其它各项可由矩阵运算得到。）从而得到20Go的标准差估量值为S（3o（x）= J155,57。8 = 12.4728,于是，对于给定的显著性水平。= 0.05 ,计算得到E （Y0）的95%置信区间为：（2。00一心（一 6S（2ooo），Zooo+% （一 %） S（Zooo）=（321,9803 2.306*12.4728,321.9803+2.306*12.4728）2= (293.218,350.7426)同理可计算Y0的猜测区间为Var(b oooZooc0nd + XzoocXXXFXzooobMSZYl + XzooQ汨ye-s&XXXzooo'QSGdBZZl, 从而得到（N颂XX）的标准差估量值为5（%0G 七顿）=J564.3221 = 23.7555,于是，对于给定的显著 性水平a = 0.05,计算得到Y0的95%置信区间为：（2。0%（ 攵）SCzooo 2。），2。+%（ 女）5（右。2。）=（321,9803 2.306*23.7555,321.9803 + 2.306 牛 22二 （267.2001,376.7605）习题1 （数据来源：张晓炯，计量经济学基础，P85,3）题干:经讨论发觉，同学用于购买书籍及课外读物的支出与本人受教育年限和其家庭收入水平有关，对18名同学进行调查的统计资料如下表所示。皿.i rn 数据:同学序号购买书籍及课外读物支出Y （元/年）受教育年限XI （年）家庭月可支配收入X2 （元/月）1450. 54171.22507. 74174.23613.95204.34563.44218.75501.54219.46781. 57240.47541.84273.58611. 15294.891222.110330.210793.27333. 111660.8536612792. 76350.913580.84357.914612. 7535915890.87371.91611219435.3171094. 28523.918125310604. 1问题：（1）试求出同学购买书籍及课外读物的支出Y与受教育年限XI和家庭收入水平X2的估量回归方程： 3。+6/+臣2；（2）对A、夕2的显著性进行t检验;（3）计算R2和R2；（4）假设有一同学的受教育年限Xl = 10年，家庭月可支配收入X2=480元/月，试猜测该同学全年购买书籍及课外读物的支出，并求出相应的猜测区间（二=0.05）。
