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1、实验三 多元线性回归模型及非线性回归一、多元线性回归模型例题3.2.2建立2006年中国城镇居民人均消费支出的多元线性回归模型。数据：地区2006年消费支出Y :2006年可支配收入X12005年消费支出X2北京14825.4119977.5213244.2天津10548.0514283.099653.3河北7343.4910304.566699.7山西7170.9410027.706342.6内蒙古7666.6110357.996928.6辽宁7987.4910369.617369.3吉林7352.649775.076794.7黑龙江6655.439182.316178.0上海14761.7
2、520667.9113773.4江苏9628.5914084.268621.8浙江13348.5118265.1012253.7安徽7294.739771.056367.7福建9807.7113753.288794.4江西6645.549551.126109.4山东8468.4012192.247457.3河南6685.189810.266038.0湖北7397.329802.656736.6湖南8169.3010504.677505.0广东12432.2216105.5811809.9广西6791.959898.757032.8海南7126.789395.135928.8重庆9398.691
3、1569.748623.3四川7524.819350.116891.3贵州6848.399116.616159.3云南7379.8110069.896996.9西藏6192.578941.088617.1陕西7553.289267.706656.5甘肃6974.218920.596529.2青海6530.119000.356245.3宁夏7205.579177.266404.3新疆6730.018871.276207.51、建立模型Y =。+p X +p X +P0112 22、估计模型（1）录入数据打开 EViews6，点“File” T New” T “Workfile选择 “Unstru
4、ctured/Undated”,在Observations后输入31,如下所示:点“ ok”。在命令行输入：DATA Y X1 X2,回车将数据复制粘贴到Group中的表格中： Group: UNTITLED Workfile: UNTITLED:Untitled I = | 回 lll 豚应何区曲|2| Print MmEeFr能ze Default SortTrarispos Edit+/SEpl+/-14825.41obsYX1X2obsX1X2114325.4119977.5213244.20210543.0514233.099653.30037342.49010304.566699.
5、70047170.94010027.706242.60057666.61010257.996928.60067937.49010369.617369.30077352.6409775.0706794-.700S6655.43091S23106178.000914761.7520667.9113773.40109620.59014034.26S621.S001113343.511S265.1012253.70127294.7309771.0506367.700139007.7101375S.28S794-.400U6645.5409551.1206109.400158468.40012192.2
6、47457.3001666S5.1S09810.2606038.000|1 了Ilf（2）估计回归方程在命令行输入命令：LS Y C X1 X2， 回车X1 X2,或者在主菜单中点“Quick”“Estimate Equation”，在 Specification 中输入 Y C点“确定”。得到如下估计结果: Equation: UNTITLED Workfile: UNTITLED:Untitled | = | 回Vieve Proc | Object) Pint|Nam|F能we |Estimate Forecast I Stats REskhDependent Variable: YMe
7、thod: Least SquaresDate: 09/26/12 Time: 1535Sample: 1 31Included observations: 31Coefficient Std. Error t-Statistic Probc1523586259.0S440.58S1340.5612X10.5592910.0752267.4348360.0000X20.2433S40.1136582.1413650.0411R-squared0.975878Mean dependent var0401.467Adjusted R-squared0.974155S.D. dependent va
8、r2388.455S.E. of regression383.9758Akaike info criterionU.830S0Sum squared resid4128247.Schwarz criterion14.96957Log likelihood-226.87 7 4-Hannan-Quinn criter.14.87604F-statistic566.3870Durbin-Watson stat1.327449Prob(F-statistic)0.000000对照输出的结果，写出回归报告：Y = 152.36 + 0.5593 - X + 0.2434 - Xi1i2i(0.5881
9、) (7.4348)(2.1414)R2 = 0.9759 R2 = 0.9742 F=566.3870D.W.=1.8274做经济意义检验和统计检验: 经济意义检验料的估计值为0.5593, P2的估计值为0.2434，均在0与1之间，符合经济理论和行 为规律（或者说符合合理预期的消费理论，具体介绍见书P329）。 统计检验模型的可决系数为0.9759，模型拟合较好。给定a=0.05，模型的F统计量为566.3870，相伴概率p=0.0000a，表明方程的整体线 性关系显著。给定a=0.05，X对应的t统计量为7.4348,，相伴概率为p=0.00000食品消费支出对总消费支出的弹性，0 p
10、11；P2：食品消费支出对食品的自价格弹性,因为食品是生活必需品，-1 P2 0 , 00.5401, -1-0.2580, -1-0.2280,符合经济理论 和行为规律。P1 + P2 + P3 = 0.540- 0.258 - 0.228 = -0.006，很接近于0，但不为0，需 要进一步检验该条件是否成立。统计检验：R2 = 0.9 7 7 3模型拟合较好。给定a=0.05，F=258.84，相伴概率P=0.0000a，表明线性回归模型整体在5%的 水平上统计显著。变量LnX的t统计量为14.78，相伴概率P=0.0000a，变量LnP的t统计量为-1.41，相伴概率P=0.1766a
11、，表明在5%的0显著性水平下，变量LnX显著，而变量LnP和LnP0不显著。(2)非线性模型的估计对于模型Q = AXP1 PP2P% ,可以直接进行估计： 10在主菜单中点“Quick” “Estimate Equation”，在 Specification 中输入：Q=C(1)*XAC(2)*P1AC(3)*P0AC(4)点“确定”即可。O Equation: UNTITLED Workfile: UNTITLED:Untitled | = | 回 |岫已呼)尸(1|。昨吐|pint|Nani|FEEWE I Estinrirte IlForeca玳|5tatsREsidv IDepend
12、ent Variable: QMethod: Least SquaresDate: 09/26/12 Time: 20:08Sample: 1935 2006Included observations: 22Convergence achieved after 25 iterationsQ=C(1 f XAC2)*P1 AC(3)* P 0 AC(4)VariableCoefficientStd. Errort-StatisticProb.c261.83SS21.3723711.970690.0000C(2)0.5557150.02906719.118740.0000c-0.1901540.1
13、43323-1.3221460.2027C(4)-0.3948610.159291-2.478S660.0233R-squared0.9S3631Mean dependent var1330.000Adjusted R-squared0.9S090SS.D. dependent var365.1392S.E. of regression50.45954Akaike info criterion10.34319Sum squared resid45830.90Schwarz criterion11.04156Log likelihood-115.2751Hannan-Quinn criter.1
14、0.8&992urbin-Watson stat0.672163根据估计结果，写出回归模型：系数的对应关系：Q=C(1)*XAC(2)*P1AC(3)*P0AC(4)Q = AX 吐 P 匕C(1)AC(2)P1C(3)p 2C(4)P 3因此回归方程：Q = 261.83X 0.556P -0.190 P -0.39510（3）约束的检验原假设H0：料+ P2 + P3 = 0备择假设H ： P +。+。N 0 1123I.手工检验方法在约束条件成立的条件下，模型LnQ = P + P LnX + P LnP + P LnP + 1变为:012130LnQ = p + p LnX + p L
15、nP + (p p )LnP + Ji，按系数合并:0121120LnQ = P +P Ln( X / P) + P Ln( P / P) + p010210记模型LnQ = P +P LnX + P LnP + P LnP +i为无约束模型(UM);012130记模型LnQ = 00 +叩点/P ）邛Ln（P / P ） + 1为受约束模型（RM）;估计无约束模型： Equation: UNTITLED Workfile: UNTITLED:Untitled | = | 回|岫丘四 |P(j| CibjEt| |pint|NamdlFe&e| (Estimate Forecast Stats
16、 |ResidsDependent Variable: LNQMethod: Least SquaresDate: 0926/12 Time: 13:15Sample: 19352006Included observations: 22CoefficientStd. Errort-StatisticProb.c5.5319500.09210759.414890.0000LNX0.5399170.03653014.780150.0000LNP1-0.2530120.178186-1.44-79940.1648LNP0-0.2885610.205184-1.4063500.1766R-square
17、d0.977345泠:无约:亍束模型7.493909Adjusted R-squared0.973569S.D. dependent varBa UQQ0.193147S.E. of regression0.031401-? T 的:RSS II；： -3.921001Sum squared resid0.017743Schwarz criterion-3.722630Log likelihood47.13101Hannan-Quinn criter.-3.874271F-statistic258.3448Durbin-Watson stat0.696202Pro b(F-stati stic
18、)0.000000估计受约束模型：LS LnQ C LnX-LnP0 LnP1-LnP0或者：LS LnQ C Log(X/P0) Log(P1/P0) 回车O Equation: UNTITLED Workfile: UNTITLED:Untitled | = | 回 |MiE|oiz|cibjEizt| | Print Name| Freeze | Estimate | Forecast Stats |Resids|Dependent Variable: LNQMethod: Least Squaresate: 09/26/12 Time: 20:26Sample: 19852006Inc
19、luded observations: 22Co efficientStd. Error t-Statistic Prob.C5.5245690.00310066.474810.0000LOG(X/F0)0.5344390.02319323.0S7760.0000LOG(P1/P0-0.2753470.151143-1.S217630.0S4SR-squared0.977296受约束模型；7.493909Adjusted R-squared0.974906二的 RSS0.19(3147S.E. of regression0.030596Akaike info criterion-4-. 00
20、97 41Sum squared resid0.017787Schwarz criterion-3.860963Log likelihood4710715Hannan-Quinn criter.-3.974694F-statistic408.9291Durbin-Watson stat0.695256Prob (F-statistic)0.000000计算检验的统计量：F _ (RSSr RSSu)/(土k? RRSSu /(nL k 1) RRSS r=0.017787； RSS疽0.017748； (无约束模型中解释变量的个数)=3；Kr (受约束模型中解释变量的个数)=2； n=22；F
21、 _ (0.017787 - 0.017748) /(3 - 2) _0.017748/(22 - 3 -1)=0.0396给定a=0.05，查表F005(1,18) _ 4.41, F=0.03964.41,接受原假设，即可以认为: 料+ % + P3 _ 0，消费函数具有零阶齐次性。II.直接检验首先估计无约束回归模型: Equation: UNTITLED Workfile: UNTITLED:Untitled | = | 回MiEw|Poiz|cibjEEt|Print |NamE|F丘 lEstimate I Forecast Stats |ResidsDependent Varia
22、ble: LNQMethod: Least SquaresDate: 0926/12 Time: 20:47Sample: 19352006Included observations: 22CoefTicientStd. Errort-StatisticProb.c5.5319500.09310759.414890.0000LNX0-5399170.02653014.730150.0000LNP1-0.2530120.178186-1 4479940.1648LNPO-0.2885610.205184-1 4063500.1766R-squared0.977345Mean dependent
23、var7.493909Adjusted R-squared0.973569S.D. dependent var0.193147S.E. of regression0.0314-01Akaike info criterion-3.921001Sum squared resid0.017743Schwarz criterion-3.722630Log likelihood47.13101Hannan-Cluinn criter.-3.874271F-statistic253.8 USDurbin-Watson stat0.696202Prob(F-statistic)0.000000在 “Equa
24、tion” 窗口，点击 “View” “Coefficient Tests” “Wald- Coefficient Restrictions”， 在弹出的窗口中输入要检验的约束：C(2)+C(3)+C(4)=0 (即P1 + P2 + P3 _ 0)点“ ok”。 Equation: UNTITLED Workfile: UNTITLED:Untitled | | 回Vw|PQci|gbjEct |Print|Name|Freeze lEstirnate |Forecast|Stats |Resids|Wald TestEquation: UntitledTest StatisticValuedfProbabilityF-statistic0.039034(1.13)0.8455Chi-square0.03903410.8433Null Hypothesis Summary:Normalized Restriction (= 0;ValueStd. Err.C+C-0.0066560.033663Restrictions are linear in coefficients.得到检验的统计量F=0.039084，自由度（1,18）,伴随概率为0.8455。
