復(fù)習(xí)多元線性回歸模型案例

我國農(nóng)民收入影響因素的回歸分析自改革開放以來,雖然中國經(jīng)濟(jì)平均增長速度為9.5但%二元,經(jīng)濟(jì)結(jié)構(gòu)給經(jīng)濟(jì)發(fā)展帶來的問題仍然很突出。農(nóng)村人口占了中國總?cè)丝诘?0%多,農(nóng)業(yè)產(chǎn)業(yè)結(jié)構(gòu)不合理,經(jīng)濟(jì)不發(fā)達(dá),以及農(nóng)民收入增長緩慢等問題勢(shì)必成為我國經(jīng)濟(jì)持續(xù)穩(wěn)定增長的障礙。正確有效地解決好“三農(nóng)”問題是中國經(jīng)濟(jì)走出困境,實(shí)現(xiàn)長期穩(wěn)定增長的關(guān)鍵。其中,農(nóng)民收入增長是核心,也是解決“三農(nóng)”問題的關(guān)鍵。本文力圖應(yīng)用適當(dāng)?shù)亩嘣€性回歸模型,對(duì)有關(guān)農(nóng)民收入的歷史數(shù)據(jù)和現(xiàn)狀進(jìn)行分析,尋找其根源,探討影響農(nóng)民收入的主要因素,并在此基礎(chǔ)上對(duì)如何增加農(nóng)民收入提出相應(yīng)的政策建議。農(nóng)民收入水平的度量，通常采用人均純收入指標(biāo)。影響農(nóng)民收入增長的因素是多方面的，既有結(jié)構(gòu)性矛盾因素，又有體制性障礙因素。但可以歸納為以下幾個(gè)方面：一是農(nóng)產(chǎn)品收購價(jià)格水平。目前農(nóng)業(yè)收入仍是中西部地區(qū)農(nóng)民收入的主要來源。二是農(nóng)業(yè)剩余勞動(dòng)力轉(zhuǎn)移水平。中國的農(nóng)業(yè)目前仍以農(nóng)戶分散經(jīng)營為主，農(nóng)業(yè)比較效益低，盡快地把農(nóng)業(yè)剩余勞動(dòng)力轉(zhuǎn)移出去是有效改善農(nóng)民收入狀況的重要因素。三是城市化、工業(yè)化水平。中國多數(shù)地區(qū)城市化、工業(yè)化水平落后于世界平均水平，這種狀況極大地影響了農(nóng)民收入的增長。四是農(nóng)業(yè)產(chǎn)業(yè)結(jié)構(gòu)狀況。農(nóng)林牧漁業(yè)對(duì)農(nóng)民收入增長貢獻(xiàn)率是不同的。隨著我國“入世”后農(nóng)產(chǎn)品市場(chǎng)的開放和人民生活水平的提高、農(nóng)產(chǎn)品需求市場(chǎng)的改變，農(nóng)業(yè)結(jié)構(gòu)狀況直接影響著農(nóng)民收入的增長。五是農(nóng)業(yè)投入水平。農(nóng)民收入與財(cái)政農(nóng)業(yè)支出、農(nóng)村集體投入、農(nóng)戶個(gè)人投入以及信貸投入都有顯著的正相關(guān)關(guān)系。農(nóng)業(yè)投入是農(nóng)民收入增長的重要保證。但考慮到農(nóng)業(yè)投入主體的多元性，既有國家、集體和農(nóng)戶的投入，又有銀行、企業(yè)和外資的投入，考慮到復(fù)雜性和可行性，所以對(duì)農(nóng)業(yè)投入與農(nóng)民收入，本文暫不作討論。因此，以全國為例，把農(nóng)民收入與各影響因素關(guān)系進(jìn)行線性回歸分析，并建立數(shù)學(xué)模型。一、計(jì)量經(jīng)濟(jì)模型分析（一）、數(shù)據(jù)搜集根據(jù)以上分析，我們?cè)谟绊戅r(nóng)民收入因素中引入個(gè)解釋變量。即：X財(cái)2

政用于農(nóng)業(yè)的支出的比重，X第二、三產(chǎn)業(yè)從業(yè)人數(shù)占全社會(huì)從業(yè)人數(shù)的比重，3TOC\o"1-5"\h\zX非農(nóng)村人口比重，X鄉(xiāng)村從業(yè)人員占農(nóng)村人口的比重，X農(nóng)業(yè)總產(chǎn)值45 6占農(nóng)林牧總產(chǎn)值的比重，X農(nóng)作物播種面積，X農(nóng)村用電量。7 8—年份年可比價(jià)比重比重比重千公頃億千瓦時(shí)資料來源《中國統(tǒng)計(jì)年鑒2006》。TOC\o"1-5"\h\z（二）、計(jì)量經(jīng)濟(jì)學(xué)模型建立我們?cè)O(shè)定模型為下面所示的形式：Y=0+0X+pX+pX+pX+pX+pX+pX+ut1 22 33 44 55 66 77 88t利用Eviews軟件進(jìn)行最小二乘估計(jì)，估計(jì)結(jié)果如下表所示:DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.C-1102.373375.8283-2.9331840.0136X1-6.6353933.781349-1.7547690.1071

X318.229422.066617 8.8208990.0000X42.4300398.370337 0.2903160.7770X5-16.237375.894109 -2.7548470.0187X6-2.1552082.770834 -0.7778190.4531X70.0099620.002328 4.2788100.0013X80.0633890.021276 2.9793480.0125R-squared0.995823Meandependentvar345.5232AdjustedR-squared0.993165S.D.dependentvar139.7117S.E.ofregression11.55028Akaikeinfocriterion8.026857Sumsquaredresid1467.498Schwarzcriterion8.424516Loglikelihood-68.25514F-statistic374.6600Durbin-Watsonstat1.993270Prob（F-statistic）0.000000表1最小二乘估計(jì)結(jié)果回歸分析報(bào)告為：Y=-1102.373-6.6354X+18.2294X+2.4300X-16.2374X-2.1552X+0.0100X+0.0634XSe=（375.83）（3.7813j（2.06661）（8.37034｝（5.8941）（2.7708）（0.00233）（0.02l28）t=（-2.933）（-1.755）（8.82090）（0.20316）（-2.755）（-0.778）（4.27881）（2.9793）R2=0.995823R2=0.993165Df=19DW=1.99327F=374.66、計(jì)量經(jīng)濟(jì)學(xué)檢驗(yàn)(一)、多重共線性的檢驗(yàn)及修正①、檢驗(yàn)多重共線性(a)、直觀法從“表1最小二乘估計(jì)結(jié)果”中可以看出，雖然模型的整體擬合的很好，但是x4x6的t統(tǒng)計(jì)量并不顯著，所以可能存在多重共線性。(b)、相關(guān)系數(shù)矩陣X2X3X4X5X6X7X8X2X3X4X5X6X7X81.000000-0.717662-0.695257-0.7313260.737028-0.332435-0.594699-0.717662-0.695257-0.7313260.737028-0.332435-0.5946991.0000000.9222860.935992-0.9457010.7422510.8838040.9222860.935992-0.9457010.7422510.8838041.0000000.986050-0.9377510.7539280.9746750.9860501.000000-0.9747500.6874390.940436-0.937751-0.9747501.000000-0.603539-0.8874280.7539280.687439-0.6035391.0000000.7427810.9746750.940436-0.8874280.7427811.000000X2X3X4X5X6X7X8X2X3X4X5X6X7X81.000000-0.717662-0.695257-0.7313260.737028-0.332435-0.594699-0.717662-0.695257-0.7313260.737028-0.332435-0.5946991.0000000.9222860.935992-0.9457010.7422510.8838040.9222860.935992-0.9457010.7422510.8838041.0000000.986050-0.9377510.7539280.9746750.9860501.000000-0.9747500.6874390.940436-0.937751-0.9747501.000000-0.603539-0.8874280.7539280.687439-0.6035391.0000000.7427810.9746750.940436-0.8874280.7427811.000000表2相關(guān)系數(shù)矩陣從“表2相關(guān)系數(shù)矩陣”中可以看出，個(gè)個(gè)解釋變量之間的相關(guān)程度較高，所以應(yīng)該存在多重共線性。②、多重共線性的修正—一逐步迭代法

A、A、元回歸DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C820.3133151.8712 5.4013740.0000X2-51.3783616.18923 -3.1736140.0056R-squared0.372041Meandependentvar345.5232AdjustedR-squared0.335102S.D.dependentvar139.7117S.E.ofregression113.9227Akaikeinfocriterion12.40822Sumsquaredresid220632.4Schwarzcriterion12.50763Loglikelihood-115.8781F-statistic10.07183Durbin-Watsonstat0.644400Prob(F-statistic)0.005554 1表3y對(duì)x2的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-525.889164.11333 -8.2024920.0000X319.460311.416043 13.742740.0000R-squared0.917421Meandependentvar345.5232AdjustedR-squared0.912563S.D.dependentvar139.7117S.E.ofregression41.31236Akaikeinfocriterion10.37950Sumsquaredresid29014.09Schwarzcriterion10.47892Loglikelihood-96.60526F-statistic188.8628Durbin-Watsonstat0.598139Prob(F-statistic)0.000000表4y對(duì)x3的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-223.190569.92322 -3.1919370.0053X418.650862.242240 8.3179560.0000R-squared0.802758Meandependentvar345.5232AdjustedR-squared0.791155S.D.dependentvar139.7117S.E.ofregression63.84760Akaikeinfocriterion11.25018Sumsquaredresid69300.77Schwarzcriterion11.34959Loglikelihood-104.8767F-statistic69.18839

Durbin-Watsonstat0.282182Prob(F-statistic)0.000000DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19表5y對(duì)x4的回歸結(jié)果VariableCoefficientStd.Error t-StatisticProb.C-494.1440118.1449 -4.1825260.0006X515.779782.198711 7.1768320.0000R-squared0.751850Meandependentvar345.5232AdjustedR-squared0.737253S.D.dependentvar139.7117S.E.ofregression71.61463Akaikeinfocriterion11.47978Sumsquaredresid87187.14Schwarzcriterion11.57919Loglikelihood-107.0579F-statistic51.50691Durbin-Watsonstat0.318959Prob(F-statistic)0.000002表6y對(duì)x5的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C1288.009143.8088 8.9563950.0000X6-15.523982.351180 -6.6026350.0000R-squared0.719448Meandependentvar345.5232AdjustedR-squared0.702945S.D.dependentvar139.7117S.E.ofregression76.14674Akaikeinfocriterion11.60250Sumsquaredresid98571.54Schwarzcriterion11.70192Loglikelihood-108.2238F-statistic43.59479Durbin-Watsonstat0.395893Prob(F-statistic)0.000004表7y對(duì)x6的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-4417.766681.1678 -6.4855770.0000X70.0315280.004507 6.9949430.0000R-squared0.742148Meandependentvar345.5232AdjustedR-squared0.726980S.D.dependentvar139.7117S.E.ofregression73.00119Akaikeinfocriterion11.51813Sumsquaredresid90595.96Schwarzcriterion11.61754

LoglikelihoodDurbin-Watsonstat-107.42220.572651F-statisticProb(F-statistic)48.929230.000002DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19表8y對(duì)x7的回歸結(jié)果VariableCoefficientStd.Error t-StatisticProb.C140.162528.96616 4.8388350.0002X80.1198270.014543 8.2395030.0000R-squared0.799739Meandependentvar345.5232AdjustedR-squared0.787959S.D.dependentvar139.7117S.E.ofregression64.33424Akaikeinfocriterion11.26536Sumsquaredresid70361.21Schwarzcriterion11.36478Loglikelihood-105.0209F-statistic67.88941Durbin-Watsonstat0.203711Prob(F-statistic)0.000000—1表9y對(duì)x8的回歸結(jié)果綜合比較表3~9的回歸結(jié)果，發(fā)現(xiàn)加入x3的回歸結(jié)果最好。以x3為基礎(chǔ)順次加入其他解釋變量，DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19進(jìn)行二元回歸，具體的回歸結(jié)果如下表10~15所示：VariableCoefficientStd.Error t-StatisticProb.C-754.4481149.1701 -5.0576370.0001X321.788651.932689 11.273750.0000X213.450708.012745 1.6786630.1126R-squared0.929787Meandependentvar345.5232AdjustedR-squared0.921010S.D.dependentvar139.7117S.E.ofregression39.26619Akaikeinfocriterion10.32254Sumsquaredresid24669.34Schwarzcriterion10.47167Loglikelihood-95.06417F-statistic105.9385Durbin-Watsonstat0.595954Prob(F-statistic)0.000000表10加入x2的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-508.678175.73220 -6.7168020.0000

X317.882003.752121 4.7658370.0002X41.7533513.844305 0.4560900.6545R-squared0.918481Meandependentvar345.5232AdjustedR-squared0.908291S.D.dependentvar139.7117S.E.ofregression42.30965Akaikeinfocriterion10.47185Sumsquaredresid28641.71Schwarzcriterion10.62097Loglikelihood-96.48254F-statistic90.13613Durbin-Watsonstat0.596359Prob(F-statistic)0.000000表11加入x4的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-498.155067.21844 -7.4109860.0000X323.975163.967183 6.0433700.0000X5-4.3205663.553466 -1.2158740.2417R-squared0.924405Meandependentvar345.5232AdjustedR-squared0.914956S.D.dependentvar139.7117S.E.ofregression40.74312Akaikeinfocriterion10.39639Sumsquaredresid26560.02Schwarzcriterion10.54551Loglikelihood-95.76570F-statistic97.82772Durbin-Watsonstat0.607882Prob(F-statistic)0.000000表12加入x5的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-1600.965346.9265 -4.6147090.0003X329.937683.534753 8.4695280.0000X69.9801353.184176 3.1342910.0064R-squared0.948835Meandependentvar345.5232AdjustedR-squared0.942440S.D.dependentvar139.7117S.E.ofregression33.51927Akaikeinfocriterion10.00606Sumsquaredresid17976.66Schwarzcriterion10.15518Loglikelihood-92.05754F-statistic148.3576Durbin-Watsonstat1.125188Prob(F-statistic)0.000000表13加入x6的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004

Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-2153.028327.1248 -6.5816730.0000X314.404971.358355 10.604720.0000X70.0122680.002447 5.0140150.0001R-squared0.967884Meandependentvar345.5232AdjustedR-squared0.963869S.D.dependentvar139.7117S.E.ofregression26.55648Akaikeinfocriterion9.540364Sumsquaredresid11283.94Schwarzcriterion9.689485Loglikelihood-87.63345F-statistic241.0961Durbin-Watsonstat0.690413Prob(F-statistic)0.000000表14加入x7的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-400.5635103.0301 -3.8878320.0013X315.542712.916358 5.3294930.0001X80.0292330.019233 1.5199290.1480R-squared0.927840Meandependentvar345.5232AdjustedR-squared0.918820S.D.dependentvar139.7117S.E.ofregression39.80687Akaikeinfocriterion10.34990Sumsquaredresid25353.40Schwarzcriterion10.49902Loglikelihood-95.32401F-statistic102.8643Durbin-Watsonstat0.559772Prob(F-statistic)0.000000表15加入x8的回歸結(jié)果綜合表10?15所示，加入x7的模型的R最大似x3、x7為基礎(chǔ)順次加入其他解釋變量，進(jìn)行三元回歸，具體回歸結(jié)果如下表16~20所示：DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-2133.921340.6965 -6.2634060.0000X314.960232.094645 7.1421340.0000X70.0118430.002786 4.2509080.0007X22.1952436.170403 0.3557700.7270R-squared0.968153Meandependentvar345.5232AdjustedR-squared0.961783S.D.dependentvar139.7117S.E.ofregression27.31242Akaikeinfocriterion9.637224

Sumsquaredresid11189.52Schwarzcriterion9.836053Loglikelihood-87.55363F-statistic151.9988Durbin-Watsonstat0.712258Prob(F-statistic)0.000000表16加入x2的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-2226.420353.4425 -6.2992430.0000X315.667292.443113 6.4128390.0000X70.0127030.002589 4.9063730.0002X4-1.6013622.553294 -0.6271750.5400R-squared0.968705Meandependentvar345.5232AdjustedR-squared0.962445S.D.dependentvar139.7117S.E.ofregression27.07472Akaikeinfocriterion9.619741Sumsquaredresid10995.60Schwarzcriterion9.818571Loglikelihood-87.38754F-statistic154.7677Durbin-Watsonstat0.704178Prob(F-statistic)0.000000表17加入x4的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-2110.381306.2690 -6.8906130.0000X318.601562.617381 7.1069370.0000X70.0121390.002285 5.3116650.0001X5-3.9648782.163262 -1.8328230.0868R-squared0.973760Meandependentvar345.5232AdjustedR-squared0.968512S.D.dependentvar139.7117S.E.ofregression24.79152Akaikeinfocriterion9.443544Sumsquaredresid9219.289Schwarzcriterion9.642373Loglikelihood-85.71367F-statistic185.5507Durbin-Watsonstat0.733972Prob(F-statistic)0.000000表18加入x5的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-2418.859323.7240 -7.4719790.0000

X320.998873.397120 6.1813740.0000X70.0099200.002495 3.9766600.0012X65.3591842.571950 2.0837050.0547R-squared0.975093Meandependentvar345.5232AdjustedR-squared0.970112S.D.dependentvar139.7117S.E.ofregression24.15359Akaikeinfocriterion9.391407Sumsquaredresid8750.940Schwarzcriterion9.590236Loglikelihood-85.21837F-statistic195.7489Durbin-Watsonstat1.084023Prob(F-statistic)0.000000表19加入x6的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-2013.355361.8657 -5.5638180.0001X313.015782.032420 6.4040780.0000X70.0116150.002558 4.5403220.0004X80.0123750.013416 0.9224010.3709R-squared0.969608Meandependentvar345.5232AdjustedR-squared0.963529S.D.dependentvar139.7117S.E.ofregression26.68115Akaikeinfocriterion9.590455Sumsquaredresid10678.26Schwarzcriterion9.789285Loglikelihood-87.10933F-statistic159.5158Durbin-Watsonstat0.672264Prob(F-statistic)0.000000表20加入x8的回歸結(jié)果綜合上述表16?20的回歸結(jié)果所示，其中加入x6的回歸結(jié)果最好，以x3x6x7為基礎(chǔ)一次加入其他解釋變量，作四元回歸估計(jì)，估計(jì)結(jié)果如表21~24所示:DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-2405.108339.7396 -7.0792690.0000X321.268503.699787 5.7485730.0001X65.3105432.665569 1.9922730.0662X70.0096890.002766 3.5033860.0035X21.3026055.655390 0.2303300.8212R-squared0.975187Meandependentvar345.5232AdjustedR-squared0.968098S.D.dependentvar139.7117S.E.ofregression24.95411Akaikeinfocriterion9.492888

Sumsquaredresid8717.904Schwarzcriterion9.741424Loglikelihood-85.18244F-statistic137.5567Durbin-Watsonstat1.082771Prob(F-statistic)0.000000表21加入x2的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-2401.402316.2980 -7.5922150.0000X322.105703.420783 6.4621740.0000X69.0890333.781330 2.4036600.0307X70.0070860.003247 2.1820050.0466X44.4176783.348889 1.3191470.2083R-squared0.977847Meandependentvar345.5232AdjustedR-squared0.971517S.D.dependentvar139.7117S.E.ofregression23.57887Akaikeinfocriterion9.379513Sumsquaredresid7783.481Schwarzcriterion9.628049Loglikelihood-84.10537F-statistic154.4909Durbin-Watsonstat1.580301Prob(F-statistic)0.000000—1表22加入x4的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-2375.188430.7065 -5.5146310.0001X320.834933.657414 5.6966290.0001X64.6291965.252860 0.8812720.3930X70.0102170.003171 3.2219530.0061X5-0.6936924.304485 -0.1611560.8743R-squared0.975139Meandependentvar345.5232AdjustedR-squared0.968036S.D.dependentvar139.7117S.E.ofregression24.97818Akaikeinfocriterion9.494817Sumsquaredresid8734.736Schwarzcriterion9.743353Loglikelihood-85.20076F-statistic137.2849Durbin-Watsonstat1.023211Prob(F-statistic)0.000000 1表23加入x5的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19

VariableCoefficientStd.Error t-StatisticProb.C-2212.242259.5324 -8.5239510.0000X322.066292.662231 8.2886470.0000X69.5956532.380088 4.0316380.0012X70.0061150.002260 2.7059780.0171X80.0369230.011239 3.2853540.0054R-squared0.985936Meandependentvar345.5232AdjustedR-squared0.981918S.D.dependentvar139.7117S.E.ofregression18.78702Akaikeinfocriterion8.925144Sumsquaredresid4941.332Schwarzcriterion9.173681Loglikelihood-79.78887F-statistic245.3639Durbin-Watsonstat2.186293Prob(F-statistic)0.000000—1表24加入x8的回歸結(jié)果綜合表21?24所示的回歸結(jié)果，其中加入x8的回歸結(jié)果最好，以x3x6x7x8為基礎(chǔ)順次加入其他的解釋變量，其回歸結(jié)果如表25~27所示：DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.C-2207.020272.6061-8.0960050.0000X322.174952.9031907.6381330.0000X69.5667312.4800573.8574640.0020X70.0060280.0024512.4589490.0287X80.0368460.0116743.1561950.0076X20.5358114.4226450.1211520.9054R-squared0.985952Meandependentvar345.5232AdjustedR-squared0.980549S.D.dependentvar139.7117S.E.ofregression19.48522Akaikeinfocriterion9.029279Sumsquaredresid4935.759Schwarzcriterion9.327523Loglikelihood-79.77815F-statistic182.4791Durbin-Watsonstat2.180501Prob(F-statistic)0.000000表25加入x2的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Errort-StatisticProb.C-1373.136279.4825-4.9131370.0003X320.093301.92848610.419210.0000X60.4804012.8459720.1688000.8686

X70.0084970.001692 5.0214100.0002X80.0605020.009873 6.1281460.0000X5-11.232922.844094 -3.9495600.0017R-squared0.993607Meandependentvar345.5232AdjustedR-squared0.991148S.D.dependentvar139.7117S.E.ofregression13.14457Akaikeinfocriterion8.241984Sumsquaredresid2246.136Schwarzcriterion8.540228Loglikelihood-72.29885F-statistic404.1009Durbin-Watsonstat1.704834Prob(F-statistic)0.000000表26加入x5的回歸結(jié)果DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-2056.366236.8112 -8.6835690.0000X320.602202.413096 8.5376610.0000X65.2648342.804292 1.8774200.0831X70.0088530.002306 3.8394460.0020X80.0717420.018026 3.9800360.0016X4-9.8612314.279624 -2.3042280.0384R-squared0.990014Meandependentvar345.5232AdjustedR-squared0.986174S.D.dependentvar139.7117S.E.ofregression16.42798Akaikeinfocriterion8.687938Sumsquaredresid3508.420Schwarzcriterion8.986182Loglikelihood-76.53541F-statistic257.7752Durbin-Watsonstat1.965748Prob(F-statistic)0.000000表27加入x4的回歸結(jié)果據(jù)表25~27所示，分別加入x2x4x5后R均有所增加，但是參數(shù)的T檢驗(yàn)均不顯著，所以最終的計(jì)量模型如下表所示：DependentVariable:YMethod:LeastSquaresSample:19862004Includedobservations:19VariableCoefficientStd.Error t-StatisticProb.C-2212.242259.5324 -8.5239510.0000X322.066292.662231 8.2886470.0000X69.5956532.380088 4.0316380.0012X70.0061150.002260 2.7059780.0171X80.0369230.011239 3.2853540.0054R-squared0.985936Meandependentvar345.5232

AdjustedR-squared0.981918S.D.dependentvar139.7117S.E.ofregression18.78702Akaikeinfocriterion8.925144Sumsquaredresid4941.332Schwarzcriterion9.173681Loglikelihood-79.78887F-statistic245.3639Durbin-Watsonstat2.186293Prob（F-statistic）0.000000表28多重共線性修正后的最終模型回歸分析報(bào)告為：Y=-2212.242+22.0663X+9.5956X+0.00612X+0.03692XSe=（259.5324）（2.6622）（2.3801（0.00226/（0.011239）t=（-8.523951）（8.28865）（4.032）（2.70598）（3.285354）R2=0.985936R2=0.981918Df=19DW=2.186293F=245.3639（二）、異方差的檢驗(yàn)A、相關(guān)圖形分析圖1圖圖#圖9從圖中可以看出大部分點(diǎn)落在1、3象限，表明存在正自相關(guān)。從圖中可以看出，隨著t的變化逐次變化，并不頻繁改變符號(hào)，而是正的后面跟著幾個(gè)負(fù)的，表明存在正自相關(guān)。綜上所述，說明模型存在自相關(guān)性。②自相關(guān)的修正——德賓兩步法將廣義方程表示為：Yt=4（1-P）+%X3+^3X6+口4X7+P5X8-P%X3一一P^3X6.1-p^4X7--p^5X8,1+pYt-1+vtt—1 t—1 t—1 t—1將上述式子作為一個(gè)多元模型進(jìn)行普通最小二乘估計(jì)，將Y1的P作為的p估計(jì)值。t—1DependentVariable:YMethod:LeastSquaresSample(adjusted):19872003Includedobservations:17afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.C-2604.5511325.611-1.9647930.0902X37.1311006.6275901.0759720.3176X68.1289833.4627792.3475320.0513X70.0195220.0070682.7620590.0280X8-0.0067280.0718170.0936870.9280X3(1)17.369733.9158844.4357100.0030X6(-1)3.3799903.0459851.1096540.3038X7(-1)-0.0124860.0032633.8268870.0065X8(-1)0.0950230.1146970.8284660.4347Y(-1)-0.2081230.495599 -0.4199420.6871R-squared0.997436Meandependentvar348.9382AdjustedR-squared0.994140S.D.dependentvar132.8918S.E.ofregression10.17327Akaikeinfocriterion7.766572Sumsquaredresid724.4683Schwarzcriterion8.256698Loglikelihood-56.01586F-statistic302.5781Durbin-Watsonstat2.420889Prob(F-statistic)0.000000 1表31廣義方程估計(jì)結(jié)果由上表可知P=-0.208123,下一步使用廣義差分法進(jìn)行修正:令Y=Y令Y=Y-PY,X=X-PX,X=X-PX,X1t t—1 31 3t 3t-1 61 6t 6t-1 71p=B(1-p),p=p,p=p,p=p,p=p;11 1 21 2 31 3 41 4 51 5則模型可表示為：=X7t-PX,X=X-PX;7t-1 81 8t 8t-1Y=p+pX+pX+pX+pX+v1 11 21 31 31 61 41 71 51 81tDependentVariable:Y+Y(-1)*0.208123Method:LeastSquaresSample(adjusted):19872004Includedobservations:18afteradjustingendpointsVariableCoefficientStd.Error t-StatisticProb.C-2681.442307.9863 -8.7063680.0000X3+X3(-1)*0.20812323.587662.433154 9.6942750.0000X6+X6(-1)*0.20812311.094402.238039 4.9571990.0003X7+X7(-1)*0.2081230.0050620.002144 2.3613690.0345X8+X8(-1)*0.2081230.0412480