計(jì)量經(jīng)濟(jì)課堂作業(yè)

計(jì)量經(jīng)濟(jì)作業(yè)姓名：齊月學(xué)號(hào)：2009354154班級(jí)：09級(jí)國(guó)貿(mào)經(jīng)濟(jì)2班上課時(shí)間：周三7、8節(jié)；周五7、8節(jié)

計(jì)量經(jīng)濟(jì)第二章作業(yè)10.下表列出了中國(guó)1978-2000年的財(cái)政收入Y和國(guó)內(nèi)生產(chǎn)總值X的統(tǒng)計(jì)資料。要求運(yùn)用EViews軟件：（1）作出散點(diǎn)圖，建立財(cái)政收入隨國(guó)內(nèi)生產(chǎn)總值變化的一元線性回歸模型，并解釋斜率的經(jīng)濟(jì)意義；（2）對(duì)所建立的回歸模型進(jìn)行檢驗(yàn)；（3）若2001年中國(guó)國(guó)內(nèi)生產(chǎn)總值為105709億元，求財(cái)政收入的預(yù)測(cè)值及預(yù)測(cè)區(qū)間。財(cái)政收入和國(guó)內(nèi)生產(chǎn)總值的統(tǒng)計(jì)資料單位：億元年份YX年份YX19781132.263624.119902937.1018547.919791146.384038.219913149.4821617.819801159.934517.819923483.3726638.119811175.794862.419934348.9534634.419821212.335294.719945218.1046759.419831366.955934.519956242.2058478.119841642.867171.019967407.9967884.619852004.828964.419978651.1474462.619862122.0110202.219989875.9578345.219872199.3511962.5199911444.0882067.519882357.2414928.3200013395.2389403.619892664.9016909.2DependentVariable:YMethod:LeastSquaresDate:04/12/11Time:11:26Sample:19782000Includedobservations:23VariableCoefficientStd.Errort-StatisticProb.C556.6477220.89432.5199730.0199X0.1198070.00527322.722980.0000R-squared0.960918Meandependentvar4188.627AdjustedR-squared0.959057S.D.dependentvar3613.700S.E.ofregression731.2086Akaikeinfocriterion16.11022Sumsquaredresid11227988Schwarzcriterion16.20895Loglikelihood-183.2675F-statistic516.3338Durbin-Watsonstat0.347372Prob(F-statistic)0.0000001.通過(guò)已知數(shù)據(jù)得到上面得散點(diǎn)圖，財(cái)政收入隨國(guó)內(nèi)生產(chǎn)總值變化的一元線性回歸方程：?i=556.6477+0.119807Xi（220.8943）（0.005273）t=(2.519973)(22.72298)r2=0.960918F=516.3338=731.2086估計(jì)的解釋變量的系數(shù)為0.119807，說(shuō)明國(guó)內(nèi)生產(chǎn)總值每增加一元，財(cái)政收入將增加0.119807元，符合經(jīng)濟(jì)理論。2.（1）樣本可決系數(shù)r2=0.960918，模擬擬合度較好。（2）系數(shù)的顯著性檢驗(yàn)：給定α=0,05，查t分布表在自由度為n-2=21時(shí)的臨界值為t0.025(21)=2.08因?yàn)閠=2.519973>t0.025(21)=2.08,國(guó)內(nèi)生產(chǎn)總值對(duì)財(cái)政收入有顯著性影響。3．2001年的財(cái)政收入的預(yù)測(cè)值：?01=556.6477+0.119807*105709=13221.3258632001年的財(cái)政收入的預(yù)測(cè)區(qū)間：在1-下，Y01的置信區(qū)間為：Y01即：Y01計(jì)量經(jīng)濟(jì)第三章作業(yè)7.在一項(xiàng)對(duì)某社區(qū)家庭對(duì)某種消費(fèi)品的消費(fèi)需要的調(diào)查中，得到如下的統(tǒng)計(jì)資料。要求用Eviews軟件對(duì)該社區(qū)家庭對(duì)該商品的消費(fèi)需求支出作二元線性回歸分析3）如果商品單價(jià)為35元，家庭月收入為20000元，那么對(duì)其消費(fèi)支出的預(yù)測(cè)是多少？并求出預(yù)測(cè)值的95%的置信區(qū)間序號(hào)消費(fèi)支出Y商品單價(jià)家庭月收入1591.923.5676202654.524.4491203623.632.07106704647.032.46111605674.031434035.30143408724.038.70159609757.139.631800010706.846.6819300DependentVariable:YMethod:LeastSquaresDate:04/17/11Time:21:30Sample:110Includedobservations:10VariableCoefficientStd.Errort-StatisticProb.C626.509340.1301015.611950.0000X1-9.7905703.197843-3.0616170.0183X20.0286180.0058384.9020300.0017R-squared0.902218Meandependentvar670.3300AdjustedR-squared0.874281S.D.dependentvar49.04504S.E.ofregression17.38985Akaikeinfocriterion8.792975Sumsquaredresid2116.847Schwarzcriterion8.883751Loglikelihood-40.96488F-statistic32.29408Durbin-Watsonstat1.650804Prob(F-statistic)0.000292由上表可寫(xiě)如下回歸分析結(jié)果：i=626.5093-9.790570+0.028618t=(15.61195)(-3.061617)(4.902030)R2=0.9022182=0.874281F=32.29408=17.38985=3.197843=0.005838所以2=302.4068830225F檢驗(yàn)：提出檢驗(yàn)的原假設(shè)和備擇假設(shè)：因?yàn)镕=32.29408對(duì)于給定的顯著性水平=0.05，查表得臨界值為：F0，05（2,8）=4.46由于F>4.46，所以拒絕原假設(shè)H0，說(shuō)明回歸方程顯著，即商品單價(jià)、家庭月收入聯(lián)合起來(lái)對(duì)消費(fèi)支出有顯著性線性影響。T檢驗(yàn)：t1=-3.061617t2=4.902030對(duì)于給定的顯著性水平=0.05，查表得臨界值為：t0.025(8)=2.306判斷比較：|t1|=3.061617>2.306,所以否定原假設(shè)H0，顯著不為零，即商品單價(jià)對(duì)消費(fèi)支出有顯著的影響|t2|=4.902030>2.306,所以否定原假設(shè)H0，顯著不為零，即家庭月收入對(duì)消費(fèi)支出有顯著的影響的置信水平是95℅置信區(qū)間是：即：同理的置信水平是95℅置信區(qū)間是如果=35=20000則：X=（1,35,20000）Y0的置信水平是0.95的置信區(qū)間是：0=626.5093-9.790570*35+0.028618*20000=856.19935的置信水平是1-的預(yù)測(cè)區(qū)間為把相應(yīng)的數(shù)據(jù)代入得的置信度為95%的預(yù)測(cè)區(qū)間為（768.2184,943.4604）的置信水平是的預(yù)測(cè)區(qū)間為把相應(yīng)的數(shù)據(jù)代入得的置信度為95%的預(yù)測(cè)區(qū)間為（759.0464，952.6324）計(jì)量經(jīng)濟(jì)第四章作業(yè)3.下表列出了中國(guó)2000年按行業(yè)分的全部制造業(yè)國(guó)有企業(yè)及規(guī)模以上制造業(yè)非國(guó)有企業(yè)的工業(yè)總產(chǎn)值Y，資產(chǎn)合計(jì)K及職工人數(shù)L。設(shè)定模型為：利用上述資料，進(jìn)行回歸分析。對(duì)于上式兩邊取對(duì)數(shù)得：令：=則可將模型轉(zhuǎn)換為二元線性回歸方程模型：序號(hào)工業(yè)總產(chǎn)值/億元資產(chǎn)合計(jì)K/億職工人數(shù)L/萬(wàn)人序號(hào)工業(yè)總產(chǎn)值/億元資產(chǎn)合計(jì)K/億元職工人數(shù)L/萬(wàn)人13722.73078.2211317812.71118.814321442.521684.4367181899.72052.166131752.372742.7784193692.856113.1124041451.291973.8227204732.99228.2522255149.35917.01327212180.232866.658062291.161758.77120222539.762545.639671345.17939.158233046.954787.92228656.77694.9431242192.633255.291639370.18363.4816255364.838129.68244101590.362511.9966264834.685260.214511616.71973.7358277549.587518.7913812617.94516.012828867.91984.5246134429.193785.9161294611.3918626.94218145749.028688.0325430170.3610.9119151781.372798.98331325.531523.1945161243.071808.4433利用Eviews的最小二乘法程序，得到如下輸出結(jié)果：DependentVariable:Y’Method:LeastSquaresDate:04/27/11Time:17:15Sample:131Includedobservations:31VariableCoefficientStd.Errort-StatisticProb.C1.1539940.7276111.5860040.1240X10.6092360.1763783.4541490.0018X20.3607960.2015911.7897410.0843R-squared0.809925Meandependentvar7.493997AdjustedR-squared0.796348S.D.dependentvar0.942960S.E.ofregression0.425538Akaikeinfocriterion1.220839Sumsquaredresid5.070303Schwarzcriterion1.359612Loglikelihood-15.92300F-statistic59.65501Durbin-Watsonstat0.793209Prob(F-statistic)0.000000根據(jù)上述結(jié)果得到估計(jì)的回歸方程為：1.153994+0.609236X1I+0.360796X2It=(1.586004)(3.454149)(1.789741)R2=0.809925F=59.65501DW=0.793209A=e^最終得到估計(jì)的生產(chǎn)函數(shù)為：檢驗(yàn)?zāi)Ｐ停簲M合優(yōu)度檢驗(yàn)：可決系數(shù)R2=0.809925不是太高，修正的可決系數(shù)=0.796348也不是太高，表明模型擬合優(yōu)度還好。F檢驗(yàn)：提出檢驗(yàn)的原假設(shè)和備擇假設(shè)：計(jì)算出F統(tǒng)計(jì)量的值為：F=59.65501對(duì)于給定的顯著性水平α=0.05，查表的臨界值為：F0.05(2,28)=3.34由于F>3.34，所以拒絕原假設(shè)H0，說(shuō)明回歸方程顯著，即資產(chǎn)合計(jì)、職工人數(shù)聯(lián)合起來(lái)對(duì)非國(guó)有企業(yè)的工業(yè)總產(chǎn)值有顯著性線性影響。t檢驗(yàn)：提出檢驗(yàn)的原假設(shè)為：H0:βi=0,(i=1,2)計(jì)算出的t統(tǒng)計(jì)量值為：t1=2.431876t2=3.069616對(duì)于給定的顯著性水平α=0.05，查表得臨界值為：t0.025(28)=2.0484判斷比較：|t1|=2.431876>2.0484,所以否定H0，β1顯著不為零，即認(rèn)為資產(chǎn)合計(jì)對(duì)非國(guó)有企業(yè)的工業(yè)總產(chǎn)值有顯著性影響。|t2|=3.069616>2.0484，所以否定H0，β2顯著不為零，即職工人數(shù)對(duì)非國(guó)有企業(yè)的工業(yè)總產(chǎn)值有顯著性影響。于是在建立模型時(shí)，K、L可以作為解釋變量進(jìn)入模型。計(jì)量經(jīng)濟(jì)第五章作業(yè)6.下表列出了2000年中國(guó)部分省市城鎮(zhèn)居民每個(gè)家庭平均全年可支配收入X和消費(fèi)支出Y的統(tǒng)計(jì)數(shù)據(jù)。1）試用OLS法建立人均消費(fèi)支出與可支配收入的線性模型；2）檢驗(yàn)?zāi)Ｐ褪欠翊嬖诋惙讲睿?）如果模型存在異方差，試采用適當(dāng)?shù)姆椒ü烙?jì)模型參數(shù)。地區(qū)可支配收入消費(fèi)支出地區(qū)可支配收入消費(fèi)支出北京10349.698493.49浙江9279.167020.22天津8140.506121.04山東6489.975022.00河北5661.164348.47河南4766.263830.71山西4724.113941.87湖北5524.544644.5內(nèi)蒙古5129.053927.75湖南6218.735218.79遼寧5357.794356.06廣東9761.578016.91吉林4810.004020.87陜西5124.244276.67黑龍江4912.883824.44甘肅4916.254126.47上海11718.018868.19青海5169.964185.73江蘇6800.235323.18新疆5644.864422.93解：DependentVariable:YMethod:LeastSquaresDate:05/11/11Time:21:53Sample:120Includedobservations:20VariableCoefficientStd.Errort-StatisticProb.C-244.5183218.5042-1.1190560.2778X1.3019420.04020032.386900.0000R-squared0.983129Meandependentvar6524.948AdjustedR-squared0.982192S.D.dependentvar2134.093S.E.ofregression284.7908Akaikeinfocriterion14.23603Sumsquaredresid1459904.Schwarzcriterion14.33560Loglikelihood-140.3603F-statistic1048.912Durbin-Watsonstat1.301563Prob(F-statistic)0.000000估計(jì)結(jié)果為：2）（一）圖形法：（1）生成參差平方序列：（2）判斷：由圖可以看出，殘差平方ei2對(duì)解釋變量X的散點(diǎn)圖主要分布在圖形中橫縱坐標(biāo)的對(duì)角線上，大致看出殘差平方ei2隨X的變動(dòng)呈增大的趨勢(shì)，因此，模型很可能存在異方差。但是否確實(shí)存在異方差還應(yīng)通過(guò)更進(jìn)一步的檢驗(yàn)。（二）Goldfeld-Quanadt檢驗(yàn)（1）對(duì)變量取值排序（按遞增或遞減）。（2）構(gòu)造子樣本區(qū)間，建立回歸模型。在本例中，樣本容量n=20，刪除中間1/4的觀測(cè)值，即6個(gè)觀測(cè)值，余下部分平分得兩個(gè)樣本區(qū)間：1—7和14—20，它們的樣本個(gè)數(shù)均是7個(gè)，即n1=n2=7DependentVariable:YMethod:LeastSquaresDate:05/11/11Time:22:10Sample:17Includedobservations:7VariableCoefficientStd.Errort-StatisticProb.C2622.7171967.0921.3332960.2400X0.5768390.4940241.1676340.2956R-squared0.214253Meandependentvar4918.359AdjustedR-squared0.057103S.D.dependentvar173.3670S.E.ofregression168.3443Akaikeinfocriterion13.32486Sumsquaredresid141699.1Schwarzcriterion13.30940Loglikelihood-44.63700F-statistic1.363369Durbin-Watsonstat2.393931Prob(F-statistic)0.295601DependentVariable:YMethod:LeastSquaresDate:04/15/11Time:21:04Sample:1420Includedobservations:7VariableCoefficientStd.Errort-StatisticProb.C-67.22997873.2455-0.0769890.9416X1.2787640.12221410.463300.0001R-squared0.956325Meandependentvar8895.413AdjustedR-squared0.947589S.D.dependentvar1962.302S.E.ofregression449.2369Akaikeinfocriterion15.28793Sumsquaredresid1009069.Schwarzcriterion15.27248Loglikelihood-51.50777F-statistic109.4807Durbin-Watsonstat1.706289Prob(F-statistic)0.000138（3）求F統(tǒng)計(jì)量值?；诒?和表2中殘差平方和的數(shù)據(jù)，即Sumsquaredresid的值。由表1計(jì)算得到的殘差平方和為，由表2計(jì)算得到的殘差平方和為。根據(jù)Goldfeld-Quanadt檢驗(yàn)，F(xiàn)統(tǒng)計(jì)量為（4）判斷在α=0,05下，式中分子、分母的自由度均為6，查F分布表得臨界值為：因?yàn)镕=7.12>，所以拒絕原假設(shè)，表明模型確實(shí)存在異方差（三）White檢驗(yàn)：輔助函數(shù)為：經(jīng)估計(jì)出現(xiàn)White檢驗(yàn)結(jié)果，見(jiàn)下表：WhiteHeteroskedasticityTest:F-statistic32.96930Probability0.000001Obs*R-squared15.90058Probability0.000353TestEquation:DependentVariable:RESID^2Method:LeastSquaresDate:05/11/11Time:22:55Sample:120Includedobservations:20VariableCoefficientStd.Errort-StatisticProb.C-206224.0136728.8-1.5082710.1498X67.2591648.047771.3998400.1795X^2-0.0023860.003868-0.6168300.5455R-squared0.795029Meandependentvar72995.22AdjustedR-squared0.770915S.D.dependentvar69031.09S.E.ofregression33040.24Akaikeinfocriterion23.78632Sumsquaredresid1.86E+10Schwarzcriterion23.93568Loglikelihood-234.8632F-st