實驗三多元線性回歸模型的估計和檢驗

1、廉家財經(jīng)大學舉商學院huashang collegeguangdong un1versitv of finances economics實驗報告課程名稱：計量經(jīng)濟學實驗項目： 實驗三 多元線性回歸模型的估計和檢驗實驗類型：綜合性口設計性口 驗證性專業(yè)班別：11本國貿(mào)5班姓 名：學 號：實驗課室：厚德a207指導教師：五立實驗日期： 2014-2-25廣東商學院華商學院教務處制一、實驗項目訓練方案小組合作：是口否小組成員：無實驗目的：掌握多元線性回歸模型估計和檢驗的方法。實驗場地及儀器、設備和材料實驗室：普通配置的計算機，eviews軟件及常用辦公軟件實驗訓練內(nèi)容（包括實驗原理和操作步驟）【實驗

2、步驟】（一）國內(nèi)生產(chǎn)總值的增長模型：分析廣東省國內(nèi)生產(chǎn)總值的增長，根據(jù)廣東數(shù)據(jù)（數(shù) 據(jù)見“表：廣東省宏觀經(jīng)濟數(shù)據(jù)-第三章.xls”文件，各變量的表示按照試驗指導課本上的來表示） 選擇不變價gdp （gdpb）、不變價資本存量（zc）和從業(yè)人員（ry）,把gdpb作 為因變量，zc和ry作為兩個解釋變量進行二元線性回歸分析。要求：按照試驗指導課本f1oo p1o2 ,分別作：1 .作散點圖（gdpb同zc, gdpb同ry）（結(jié)果控制在本頁）gdpb5,5004,0002,0002,0004,0006,0005,0004,5003,5003,0002,500gdpb8,0002 .進行因果關(guān)系檢

3、驗(gdpb同zc, gdpb同ry)(結(jié)果控制在本頁)(1) gdpb同zc的因果分析pairwise granger causality testsdate: 12/01/13 time: 14:39sample: 1978 2005lags: 2null hypothesis:obsf-statisticprob.zc does not granger cause gdpb263.849390.0376gdpb does not granger cause zc19.07482.e-05(2) gdpb同ry的因果分析pairwise granger causality testsdat

4、e: 12/01/13 time: 14:39sample: 1978 2005lags: 3null hypothesis:obsf-statisticprob.ry does not granger cause gdpb252.887440.0641gdpb does not granger cause ry3.463090.0382從因果關(guān)系檢驗看，zc明顯影響gdpb,ry不太明顯，這是可以理解的，計劃經(jīng)濟時期存在著隱性失業(yè)，使 得勞動力的變化對產(chǎn)出的影響不太明顯。3 .作gdpb同zc和ry的多元線性回歸，寫出模型估計的結(jié)果，并分析模型檢驗是均 否通過？（三個檢驗）（結(jié)果控制在本頁）

5、depefloetii variaote gdpb,0imelhad lew曰 squares-p了4dale 1iv29/13 tlrne： im $2/0tswnple w於 2003p14induded observations 絡+444coethclent-sid error-tprati -z0-0 377170-0.003355-45 14265.口.口口口口14r/0j63h*0.042757-8 272o20h0.0qot-o-800.5997-113.7332-7o3ez47.口.叩口口，r-square*gl佻例mean (fe pendent 妒尸1754.112小ad

6、justed0 9的口目爭3 d 啪penctee 驪”1期s.e. 01 regres即on，90um5期皈i短 inio ctfenon10 6003&hsum squared 援虢，sdwarz crttertocbiq 943qq.log likelihood-14.205handao-quinn1u&3 血f statislk.,14736 32-durbin walslat-1日口口 （f-st越詁閡+,o.ooooooha-4所以，由上圖可得， 多元線性回歸方程為gdpb=0.377170*zc+0.353689*ry-800.5997故，估計方程白判定系數(shù) r 2 =0.999

7、085接近1; 參數(shù)顯著性t檢驗值大于2;方程顯著性f檢驗顯 著。4 .將建立的二元回歸模型 （gdpb同zc和ry）同一元回歸模型（gdpb同zc、gdpb 同ry）相比較，分析優(yōu)點。（結(jié)果控制在本頁）(1) gdpb同zc元回歸模型如下(2) gdpb同 ry元回歸模型如下：dependefiri v-ariahiemethod lew蟲 squares dale 111/20/13 tinte. 15.04 sample 1072005 includ&d dbservaiidds 加pi o 點卓eidependent variable gopb*method lea squares-3

8、 dane: 11 網(wǎng)13tim: 1i5:cmsample:. 162005-1 irrclyded o&servaiions. 3b+f宇41宇卓+fcaehfcjenl-sid emant-轂atislk，prob., i3coeftoenhsia. err&thkslilisli白ptdd iqq442b9&0 皿日帕90 46000.q dddq.ry.12.189317-0117735.1b.59523-odoxo25,并 054。s.2ms14.o.oootj.a5519.1374xk.4253-13.73319-o.mxxj.r.squaredi-mean (dependent

9、 ,霞1754 112-0 93006fdean dependem ya(,17m.112.adjusted r-squaredfr泣的方s.d. dte-pendent1 m3 915.adjusted r-square*0 92737!s.d dependem 堀11ba3 912-s.e. of regression*.57302h他si磴 info criteriork1204722.s.e. gt negressiwj53.79d7hmalkelnldcrtenan15.14190.sum squh鉀24?鄧5 0-與gvaq crttmiqfv12 1423&sum, square

10、d lewschwarz crtenofij15.z37m.lag likjelihaadr1rnirw-qtwri g.12 d7b32-log 啪dihdckp-2o0.95mhafinaji-qwinn crflar13.葉麗f-就義宿同,s183l01i1.-qooodd&0/中由于建立的二元回歸模型（gdpb同zc和ry）的調(diào)整的判定系數(shù)為 0.999085 ,故，建立的二元回歸模型（ gdpb同zc和ry）同一元回歸模型（gdpb同zc、gdpb同ry）相比較，其優(yōu)點 是比下面的兩個一元回歸模型有明顯改善。5 .結(jié)合相關(guān)的經(jīng)濟理論，分析估計的二元回歸模型的經(jīng)濟意義。（結(jié)果控制在本頁

11、）由于二元回歸模型 gdpb=0.377170*zc+0.353689*ry-800.5997所以說，模型估計結(jié)果說明，在假定其他變量不變的情況下，當年 gdpb每增加1個單位，zc會增加0.377170 個單位，ry會增加0.353689個單位。（二）宏觀經(jīng)濟模型：根據(jù)廣東數(shù)據(jù)，研究廣東省居民消費行為、固定資產(chǎn)投資行為、 貨物和服務凈出口行為和存貨行為，分別建立居民消費模型、固定資產(chǎn)投資模型、貨 物和服務凈出口模型和存貨增加模型。要求：按照試驗指導課本 &5f1l2,分別作出以下模型，并對需要改進的模型 進行改進。寫出最終估計的模型結(jié)果，并結(jié)合相關(guān)的經(jīng)濟理論，分析模型的經(jīng)濟意義。（數(shù)據(jù)見“表

12、：廣東省宏觀經(jīng)濟數(shù)據(jù)-第三章.x1s”文件，各變量的表示按照試驗指導課本上的來表示。）1.居民消費模型（結(jié)果控制在本頁）9,0008,0007,0006,0005,000b4,0003,0002,0001,000002,0004,0006,0008,00010,000pairwise granger causality testsdate: 12/01/13 time: 15:23sample: 1978 2005lags: 2null hypothesis:obsf-statisticprob.lb does not granger cause xfj267.190100.0042xfj d

13、oes not granger cause lb5.455160.0124從散點圖看，它們具有線性關(guān)系，從因果關(guān)系檢驗看到它們之間似乎具有雙向因果關(guān)系，宏觀經(jīng)濟中確實 如此。進行一元線性回歸如下：dependent variable: xfjmethod: least squaresdate: 12/01/13 time: 15:25sample: 1978 2005included observations: 28coefficientstd. errort-statisticprob.lb0.9867020.01691658.330100.0000c-75.9966259.99073-1.

14、2668060.2165r-squared0.992416mean dependent var2362.277adjusted r-squared0.992125s.d. dependent var2565.722s.e. of regression227.6909akaike info criterion13.76260sum squared resid1347921.schwarz criterion13.85776log likelihood-190.6765hannan-quinn criter.13.79169f-statistic3402.401durbin-watson stat

15、0.701578prob(f-statistic)0.000000所以，由上圖可得，一元線性回 113 方程為xfj=0.986702*lb-75.99662除勞動報酬lb外，企業(yè)盈余yy也會影響居民消費xfj,看散點圖和因果關(guān)系檢驗。7,000 .|：6,000 .5,000 -4,000 y 3,000 -2,000 1,000 -ol02,0004,0006,0008,00010,000xfjpairwise granger causality testsdate: 12/01/13 time: 15:33sample: 1978 2005lags: 1null hypothesis:o

16、bsf-statisticprob.yy does not granger cause xfj274.257200.0501xfj does not granger cause yy0.093580.7623從散點圖看和因果關(guān)系檢驗看應該把 yy引入方程中，進行一元線性回歸如下:dependent variable: xfjmethod: least squaresdate: 12/01/13 time: 15:34sample: 1978 2005included observations: 28coefficientstd. errort-statisticprob.lb0.7408080

17、.03289322.521990.0000yy0.3620750.0464527.7946920.0000c46.9151336.602821.2817350.2117r-squared0.997789mean dependent var2362.277adjusted r-squared0.997612s.d. dependent var2565.722s.e. of regression125.3710akaike info criterion12.60139sum squared resid392946.9schwarz criterion12.74412log likelihood-1

18、73.4194hannan-quinn criter.12.64502f-statistic5641.541durbin-watson stat1.122075prob(f-statistic)0.000000顯然回歸得到改善，引入 yy是正確的，最后得到回歸方程xfj=0.740808*lb+0.362075*yy+46.915132.固定資產(chǎn)投資模型（結(jié)果控制在本頁）進行三元線性回歸如下dependent variable: tzgmethod: least squaresdate: 12/01/13time: 15:38sample: 1978 2005included observat

19、ions: 28coefficientstd. errort-statisticprob.zj1.1118640.2431524.5727160.0001yy0.4316920.0525668.2123520.0000cz0.1432100.4053080.3533380.7269c31.2762527.825171.1240270.2721r-squared0.997573mean dependent var1628.997adjusted r-squared0.997270s.d. dependent var2003.852s.e. of regression104.7010akaike

20、info criterion12.27166sum squared resid263095.1schwarz criterion12.46197log likelihood-167.8032hannan-quinn criter.12.32984f-statistic3288.646durbin-watson stat1.298515prob(f-statistic)0.000000現(xiàn)在分別去掉一個解釋變量進行三個二元回歸如下：(1)dependent variable: tzgmethod: least squaresdate: 12/01/13time: 15:40sample: 1978

21、 2005included observations: 28coefficientstd. errort-statisticprob.zj1.1918780.08699313.700910.0000yy0.4384220.0481299.1093650.0000c33.6561326.520921.2690410.2161r-squared0.997561mean dependent var1628.997adjusted r-squared0.997366s.d. dependent var2003.852s.e. of regression102.8521akaike info crite

22、rion12.20542sum squared resid264463.7schwarz criterion12.34815log likelihood-167.8758hannan-quinn criter.12.24905f-statistic5111.852durbin-watson stat1.370345prob(f-statistic)0.000000dependent variable: tzgmethod: least squaresdate: 12/01/13 time: 15:42sample: 1978 2005included observations: 28coeff

23、icientstd. errort-statisticprob.zj1.0985780.4650212.3624280.0262cz1.3493010.7224791.8676010.0736c-45.6139450.11293-0.9102230.3714r-squared0.990754mean dependent var1628.997adjusted r-squared0.990014s.d. dependent var2003.852s.e. of regression200.2421akaike info criterion13.53789sum squared resid1002

24、422.schwarz criterion13.68062log likelihood-186.5304hannan-quinn criter.13.58152f-statistic1339.431durbin-watson stat0.436795prob(f-statistic)0.000000(3)dependent variable: tzgmethod: least squaresdate: 12/01/13 time: 15:43sample: 1978 2005included observations: 28coefficientstd. errort-statisticpro

25、b.yy0.4300930.0704536.1047090.0000cz1.8692780.1978469.4481350.0000c20.9189337.170150.5627880.5786r-squared0.995459mean dependent var1628.997adjusted r-squared0.995096s.d. dependent var2003.852s.e. of regression140.3301akaike info criterion12.82683sum squared resid492313.8schwarz criterion12.96957log

26、 likelihood-176.5756hannan-quinn criter.12.87047f-statistic2740.226durbin-watson stat0.751924prob(f-statistic)0.000000從上面三個回歸可以結(jié)果看出，只要固定資產(chǎn)折舊zj和財政支出cz其中一個不在方程中，回歸就能得到很好的擬合?，F(xiàn)在暫且取最后一個回歸方程來使用。方程為tzg=0.430093*yy+1.869278*cz+20.918933 .貨物和服務凈流出模型（結(jié)果控制在本頁）gdpdependent variable: ckmethod: least squaresdate:

27、 11/29/13 time: 15:44sample: 1978 2005included observations: 28coefficientstd. errort-statisticprob.gdp0.0993160.00555217.888130.0000c-112.981345.74528-2.4697920.0204r-squared0.924852mean dependent var427.0379adjusted r-squared0.921962s.d. dependent var651.0303s.e. of regression181.8672akaike info c

28、riterion13.31318sum squared resid859967.3schwarz criterion13.40834log likelihood-184.3845hannan-quinn criter.13.34227f-statistic319.9853durbin-watson stat0.959767prob(f-statistic)0.000000從散點圖和因果關(guān)系檢驗看它們具有關(guān)系，進行一元線性回歸如下:dependent variable: ckmethod: least squaresdate: 04/25/14 time: 17:53sample: 1978 2

29、005included observations: 28variablecoefficientstd. errort-statisticprob.gdp0.0993160.00555217.888130.0000c-112.981345.74528-2.4697920.0204r-squared0.924852mean dependent var427.0379adjusted r-squared0.921962s.d. dependent var651.0303s.e. of regression181.8672akaike info criterion13.31318sum squared

30、 resid859967.3schwarz criterion13.40834log likelihood-184.3845hannan-quinn criter.13.34227f-statistic319.9853durbin-watson stat0.959767prob(f-statistic)0.000000所有收集到的統(tǒng)計數(shù)據(jù)中，年利率ll是一個可以考慮引入的因素，引入ll進行二元線性回歸如下:dependent variable: ckmethod: least squaresdate: 04/25/14 time: 17:55sample: 1978 2005included

31、observations: 28variablecoefficientstd. errort-statisticprob.gdp0.0882390.00552515.970670.0000ll-42.6598911.83064-3.6058800.0014c202.217395.250382.1230080.0438r-squared0.950564mean dependent var427.0379adjusted r-squared0.946609s.d. dependent var651.0303s.e. of regression150.4304akaike info criterio

32、n12.96584sum squared resid565732.7schwarz criterion13.10857log likelihood-178.5217hannan-quinn criter.13.00947f-statistic240.3512durbin-watson stat1.504205prob(f-statistic)0.000000最后得到回歸方程ck=0.0882381995057*gdp42.665702172*ll+202.2488405394 .存貨增加模型(結(jié)果控制在本頁)根據(jù)廣東數(shù)據(jù)，建立存貨增加 tzc的二元回歸模型如下：tzc=c+acx+bpsl+u

33、進行估計，結(jié)果為:dependent variable: tzcmethod: least squaresdate: 04/25/14 time: 18:05sample: 1978 2005included observations: 28variablecoefficientstd. errort-statisticprob.cx0.0306330.0047396.4638880.0000psl1.7808060.1988598.9551120.0000c-209.054645.84519-4.5600130.0001r-squared0.952473mean dependent var4

34、24.3629adjusted r-squared0.948671s.d. dependent var392.2360s.e. of regression88.86446akaike info criterion11.91306sum squared resid197422.3schwarz criterion12.05579log likelihood-163.7828hannan-quinn criter.11.95669f-statistic250.5102durbin-watson stat2.164713prob(f-statistic)0.000000故，方程為：tzc=0.0306327182422*cx+1.78080576578*psl209.054640067二、實驗總結(jié)與評價實驗總結(jié)（包括實驗數(shù)據(jù)分析、實驗結(jié)果、實驗過程中出現(xiàn)的問題及解決方法等）t1、多元線性回歸模型是將總體回歸函數(shù)描述為一個被解釋變量與多個解釋變量之間線性關(guān)系的模型。通常多元線性回歸模型可以用矩陣形式表示。2