實驗三 多元回歸模型

實驗三多元回歸模型3.1實驗?zāi)康恼莆斩嘣€性回歸模型的原理，多元線性回歸模型的建立、估計、檢驗及解釋變量的增減的方法，以及相應(yīng)的EViews軟件操作方法。3.2實驗內(nèi)容已知某市糧食年銷售量、常住人口、人均收入、肉、蛋、魚的銷售數(shù)據(jù)，見表3.1。請選擇恰當(dāng)?shù)慕忉屪兞亢颓‘?dāng)?shù)哪Ｐ停⒓Z食年銷售量的回歸模型，并對其進行估計和檢驗。表3.1某市糧食年銷售量、常住人口、人均收入、肉、蛋、魚的銷售數(shù)據(jù)糧食年銷售量Y/常住人口X2/人均收入肉銷售量蛋銷售量魚蝦銷售量年份萬噸萬人X3/元X4/萬噸X5/萬噸X6/萬噸197498.45560.20153.206.531.231.891975100.70603.11190.009.121.302.031976102.80668.05240.308.101.802.711977133.95715.47301.1210.102.093.001978140.13724.27361.0010.932.393.291979143.11736.13420.0011.853.905.241980146.15748.91491.7612.285.136.831981144.60760.32501.0013.505.418.361982148.94774.92529.2015.296.0910.071983158.55785.30552.7218.107.9712.571984169.68795.50771.1619.6110.1815.121985162.14804.80811.8017.2211.7918.251986170.09814.94988.4318.6011.5420.591987178.69828.731094.6523.5311.6823.37下面以第三章中的中國稅收增長的分析案例為示例，說明實驗的步驟，數(shù)據(jù)見表3.2。表3.2中國稅收收入及相關(guān)數(shù)據(jù)年份稅收收入Y國內(nèi)生產(chǎn)總值X2財政支出X3商品零售價格指數(shù)X41978519.283624.11122.09100.71979537.824038.21281.791021980571.74517.81228.831061981629.894862.41138.41102.41982700.025294.71229.98101.91983775.595934.51409.52101.5

1984947.3571711701.02102.819852040.798964.42004.25108.819862090.7310202.22204.9110619872140.3611962.52262.18107.319882390.4714928.32491.21118.519892727.416909.22823.78117.819902821.8618547.93083.59102.119912990.1721617.83386.62102.919923296.9126638.13742.2105.419934255.334634.44642.3113.219945126.8846759.45792.62121.719956038.0458478.16823.72114.819966909.8267884.67937.55106.119978234.0474462.69233.56100.819989262.878345.210798.1897.4199910682.5882067.513187.6797200012581.5189468.115886.598.5200115301.3897314.818902.5899.2200217636.45104790.622053.1598.7200320017.31135822.824649.9599.9200424165.68159878.328486.89102.8200528778.54183217.433930.28100.8200634804.35211923.540422.73101200745621.97249529.949781.35103.83.3實驗步驟3.3.1經(jīng)濟理論分析影響中國稅收收入增長的主要因素可能有：（1） 從宏觀經(jīng)濟看，經(jīng)濟整體增長是稅收增長的基本源泉，表現(xiàn)為正向關(guān)系。（2） 社會經(jīng)濟的發(fā)展和社會保障等都對公共財政提出要求，公共財政的需求對當(dāng)年的稅收收入可能會有一定的影響，表現(xiàn)為正向關(guān)系。（3） 物價水平。中國的稅制結(jié)構(gòu)以流轉(zhuǎn)稅（包括增值稅、消費稅及營業(yè)稅）為主，以現(xiàn)行價格計算的GDP和經(jīng)營者的收入水平都與物價水平有關(guān)，表現(xiàn)為正向關(guān)系。（4） 稅收政策因素。3.3.2建立多元線性回歸模型首先建立散點圖考察Y與X2和X3之間的相關(guān)關(guān)系，如圖3.1和3.2。

Y圖3.1Y建立線性回歸方程如下：模型1：Y=&+&X+&X+&Xt1 221 331 4圖3.20t=1,2,3,,30用EViews進行估計的輸出結(jié)果見圖3.3。圖3.20t=1,2,3,,30DependentVariable:YMethod:LeastSquaresDate:09Z27/11Time:22:39Sample:19782007Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.C-6399.5582132.836 -3.0004920.0059X2-0.0032710.012559 -0.260476□7965X30.8980590.065848 13.650610.0000X457.8317520.06336 2.0824560.0078R-squared0.997046Meandependentvar9153.233AdjustedR-squared0.996705S.D.dependentvar11370.31S.E.ofregression652.7046Akaikeinfocriterion15.92369Sumsquaredresid11076606Schwarzcriterion16.11052Loglikelihood-234.8554F-statistic2924.845Durbin-Watsonstat0.866234Prob(F-statistic)0.000000圖3.3圖3.3中可以看出X2對應(yīng)的p值為0.7965>0.05，應(yīng)當(dāng)要接受P2=0的原假設(shè)，即自變量X2對應(yīng)變量Y沒有顯著的影響。剔除不顯著的X2變量，繼續(xù)建立線性回歸模型。模型2：y=8+pX+pX+u t=1,2,3， ，30t1 23t34t t用EViews進行估計的輸出結(jié)果見圖3.4。DependentVariable:YMethod:LeastSquaresDate:10/09/11Time:22:33Sample:19782007Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.C-6342.6832084.684-3.0425150.0052X30.8819010.00967791.129650.0000X457.1200219.530302.9246870.0069R-squared0.997038Meandependentvar9153.233AdjustedR-squared0.996819S.D.dependentvar11370.31S.E.ofregression641.3386Akaikeinfocriterion15.85963Sumsquaredresid11105511Schwarzcriterion15.99975Loglikelihood-234.8945F-statistic4544.115Durbin-Watsonstat0.867356Prob(F-statistic)0.000000圖3.4對比模型1和模型2的結(jié)果如表3.3。表3.3模型1和模型2的結(jié)果對比表應(yīng)變量截距X2X3X4R2AICSC模型1Y-6399.56-0.003270.89885957.831750.99670515.9236916.110520.00590.79650.0000.0078模型2Y-6342.680.88190157.120020.99681915.8596315.999750.00520.00000.0069從表3.3的對比表可以看出，模型1的擬合優(yōu)度沒有比模型2的有明顯的增加，并且模型1對應(yīng)的AIC和SC兩個指標(biāo)都比模型2的大，即模型1引入變量X2后并沒有使AIC和SC兩個指標(biāo)值變小，說明變量X2可以不用引入了。解釋變量最終選擇X3和X4，即選擇模型2。建立多元線性回歸模型的結(jié)果是：Y=—6342.68+0.882X+57.12Xi 3 4t=(—3.043)(91.123)(2.925)p=(0.0052)(0.0000)(0.0069)R2=0.997F=4544.123.3.3多元線性回歸模型的檢驗(1)經(jīng)濟意義檢驗X3和X4變量的回歸系數(shù)都大于零，同經(jīng)濟理論分析得到的結(jié)論是一致的。說明回歸方程的經(jīng)濟含義是：當(dāng)商品零售價格指數(shù)不變時，財政支出增加1億元，稅收收入將增加0.882億元；當(dāng)財政支出不變時，商品零售價格指數(shù)增加1%，稅收收入將增加57.12億元。(2)統(tǒng)計檢驗三個解釋變量的p值都小于0.05，說明在5%顯著性水平下，都要拒絕系數(shù)為零的原假設(shè)，說明回歸系數(shù)都是顯著的。因為R2=0.997,并且F統(tǒng)計量是一個很大的數(shù)，說明三個解釋變量對被解釋變量Y的聯(lián)合解釋力很強。3.3.4非線性回歸模型的建立對數(shù)據(jù)是絕對數(shù)的變量Y、X2和X3都取對數(shù)，變成相對數(shù)，建立如下非線性回歸模型：模型1：lnY=8+8lnX+8lnX+月X+u t=1,2,3， ，30t1 2 21 3 31 441 t用EViews進行估計的輸出結(jié)果見圖3.5。DependentVariable:LOG(Y)Method:LeastSquaresDate:09/27/11Time:22:48Sample:19782007Includedobservations:30VariableCoefficientStd.Errort-StatisticProb.C-2.7553670.640000-4.3047220.0002LOGtX2)0.4512340.142128 3.1748310.0038LOG(X3)0.6271330.161566 3.8815810.0006X40.0101360.005645 1.7955670.0842R-squared0.987591Meandependentvar8.341376AdjustedR-squared0.986159S.D.dependentvar1.357225S.E.ofregression0.159676Akaikeinfocriterion-0.707778Sumsquaredresid0.662904Schwarzcriterion-0.520952Loglikelihood14.61668F-statistic609.7317Durbin-Watsonstat0.616136F1mb(F-statistic：)0.000000建立非線性回歸模型的結(jié)果是：lnY,=-2.755+0.451lnX