第三章 多元线性回归模型(Stata)

#数据198043.0145.17868.928.581991461.4216.178237.14246.81981121.7448.624-37.3862.891992669.68266.381258.83438.57198283.8652.94717.6555.521993739.22346.344293.35336.22198379.4159.34542.5742.4719941175.25467.594574.52499.36198477.3471.7158.1628.919951549.76584.781581.52882.96198589.8589.644-0.5739.5619961967.28678.846529.561355.031986138.25102.02282.950.1719972476.82744.626582.421918.371987223.55119.62562.8379.8319983310.93783.452922.232352.921988270.78149.283133.9776.7619993715.03820.67461743.591910.531989407.97169.092158.8872.3720004180.1894.4222491.271579.821990375.45185.479146.49190.0720014604959.3332516.542007.73对以上数据进行回归分析:Commandvar5regressvar2var3var4var5得到以下结果：SourceSSifMSUmnLer口亡口bs=223f1BJ=5725.35Medel4€323231.2315441077.1Frofc>F=a.OOdCJKesi弧冃丄■45460.7754182^SZ.26&3=C.99^0nlj=0.33呂日Ictal46371€922122DS175.E1祖口tMSE=51.887vse2Coe=.Std.tF>|t1[35%Cqilz.Interval]var3.34fi2口IE.L544：fi9£2.330.Q38.0206732.€697303vae4.5954028.021C13131.490.aco.S2E9S£11.atl®2vaeG.E797595.049507517.77o.aco.7757401.&S2771_cciris■4-21400421.££7250.2D0.044-41.20724&.S2-E21■vb.t4■velttEsavar2Trair2对应的回归表达式为：DEBT=4.31+0.35GDP+1.00DEF+0.88REPAYtttt(0.2)(2.2)(31.5)(17.8)(0.2)(2.2)(31.5)(17.8)R2二0.999,DW二2.1,F二5735.3现在用似然比（LR）统计量检验约束GDP对应的回归系数0等于零是否成立。t1现在不会）三、Wald检验(以表6.2为例进行Wald检验，对输出结果进行检验。)检验过程如下：1.已知数据如表3.2YXIX211103298351541285-61)Y=a+aX+uTOC\o"1-5"\h\zi011i1iY二九+九X+ui022i2iY二B+BX+PX+ui011i22ii(2)回答下列问题：a=B吗？为什么？九二B吗？为什么?1122对上述3个方程进行回归分析，结果分别如下Y—a+aX+ui011i1iCommandregresavar1var2得到结果如下：

SourcessdeMS1-Iumb-eroffub勻F41F31=2D.82Mo-del425.€143E€Ptob>F=0.0115Residual42.43141322223R—sqijared=0.9112AdjR-sqT-ianed.=0.8S17T1口七占147S41195RocitMS3=2..7594varlCoeE.日七日.Err-t1tI[9話Conf.1口七erval]var2e.c1.LSSS2755ECi.0122.S165910.28341_ccns-e.e3_942&26-2..23Ci.112-21.34EL53.748151Y二九+九X+ui022i2iCommandregressvar1varl得到结果如下：S口S口lirasSS：±=MSI-Juinh-er口丘ot^sF'；lr3J=533„7SHc=1£1475n55G2Q€1475.55620-6E匚口b>E=Q.QQQ2Residual2.443793913„81459797R-sijuared.=Q„994SAdjR-squared=Q„9932IDial4784119.5RootMSE=.90255v^rlGoaf-Std.Ee王-tF>lt1[95%Conf.Interval]-1.€68618.□690602a_aoo-1.88829&-1.44883817_34075-4814441afi.02a„aao15„eae5018„87292从上述回归结果可知：&乂0,无乂0。二元回归与分别对X与X所作的一元112212回归，其对应的参数估计不相等，主要原因在于X与X有很强的相关性。12匚qemandcorrelatevar2var3其相关分析结果如下：

-correlatevar2var3■：chg==jvar2var3va.r2丄„000口vac3-0.96791・QQQQ可见，两者的相关系数为0.9679cY二B+BX+PX+ui011i22iiCommandregre&svar1var2var3得到结果如下：SqueccSSd=SqueccSSd=MSMedel47€4223222228-2LGGG7Eies£d.ual12.782aaaaaaTo-tal47S4119-„5Niniitjeiofobg=5F（：2r2）=204„11Prfib>F=a_Da22R-acjuared=□.99^7AdjR-sqxiared=0.9924Raa-tKSE=..gg5（J£vazlCoe=.tF>lt|[35%Ccsnf.var2-1.1777781.11302*6-l.Q€a.401-5_9667433.611187^ar3-1.944444..2693155-7.22a.019-3.103216-.7856732_ccms21.922224.3552585-03a.0373.1830640„66138表3.3列出了某地区家庭人均鸡肉年消费量Y与家庭月平均收入X,鸡肉价格叫，猪肉价格P2与牛肉价格P3的相关数据。年份Y/千X/元P/（元/千克）P2/（元/千克）P3/（元/千克）年份Y/千克X/元P/（元/千克）P2/（元/千克）P3/（元/千克）克19802.783974.225.077.8319924.189113.977.9111.4019812.994133.815.207.9219934.049315.219.5412.4119822.984394.035.407.9219944.0710214.899.4212.7619833.084593.955.537.9219954.0111655.8312.3514.29

19843.124923.735.477.7419964.2713495.7912.9914.3619853.335283.816.378.0219974.4114495.6711.7613.9219863.565603.936.988.0419984.6715756.3713.0916.5519873.646243.786.598.3919995.0617596.1612.9820.3319883.676663.846.458.5520005.0119945.8912.8021.9619893.847174.017.009.3720015.1722586.6414.1022.1619904.047683.867.3210.6120025.2924787.0416.8223.2619914.038433.986.7810.481）求出该地区关于家庭鸡肉消费需求的如下模型：InY二B+PInX+PInP+PInP+PInP+u01213243（2）请分析，鸡肉的家庭消费需求是否受猪肉及牛肉价格的影响。先做回归分析，过程如下：依次生成变量lnvar2lnvar3lnvar4lnvar5lnvar6依次生成变量CommandregretInvar2Invarihivar4InvarS回归结果如下：SourceasizCommandregretInvar2Invarihivar4InvarS回归结果如下：SourceasizMSModel.76L1746€44.190293€-££Elesid.ua1,ai257S21118.□□a754245Total.77475267522.03521504Munnherofobs=23F(4r18)=252,2£Proh%E=Ci.0000El-squaeed=Ci.9S25L.AJR—s<jLiared=Ci.57S£fto-QtMSE=.02747g&ni&i^ateLnva.r2=Log-(v^.ir2)generateInvar3=Log-tva-rS)generateInvar4=Log-(v^ar4)g&n&ratelnvairB=呂)generatelmra_r6=Log-("v^TrC}InvarZCa-ef.Stri...Zrr.tFAltJ[35%Ccjnf.Interval]lnvac3„3452563_082-56474.18a_oai.1717943„518719lnvac4-„5021218„1098305-4.57a_oaa-.7329932--2712504lnwarS.„1468672.09900€1.48a.155-.06113C8.3548711lnvarS„DS71S45„09985220„87a_254-.1225972.2969662-.7215205.2969472-2.46a_024-1-255283ia7657fi所以，回归方程为：InY=—0.7315+0.34631nX-0.50211nP+0.14691nP+0.08721nP123(-2.463)(4.182)(-4.569)(1.483)(0.873)由上述回归结果可以知道，鸡肉消费需求受家庭收入水平和鸡肉价格的影响，而牛肉价格和猪肉价格对鸡肉消费需求的影响并不显著。AIC和SC准则不会算)去掉猪肉价格P2与牛肉价格P3重新进行回归分析。CommandregressInvarfInvar3Invar^得出结果如下：十是目目lnvair2Invar2Lnvav4Source5Sd=MSl-TiunherofoBs22r(2r20>497.28Model75S4SO3242-379740167ProB>F0-口□□口gssidual・01527254120„aa07fi3fi27Q・SQQ3AijR-squared□.9783rental77475287522.035216Q471o-ntMSE.027631Cqbz.Std.Err-t"It1[95%Conf.工口terval]Lrnrar3.4515465..□24554418.99a„aoa.400927_.&n.27C6Lrnrar4--37.27344.OG9104-5_S1a„aoa-.E042671一2411018czons-1.125757„0854201-15_730.000-1.21023S-_34135€AIC和SC准则不会算)

2.某硫酸厂生产的硫酸的透明度指标一直达不到优质要求，经分析透明度低与硫酸中金属杂质的含量太高有关。影响透明度的主要金属杂质是铁、钙、铅、镁等。通过正交试验的方法发现铁是影响硫酸透明度的最主要原因。测量了47组样本值，数据见表3.4。表3.4硫酸透明度y与铁杂质含量x数据序数XY序数XY1311902560502321902660413341802761524351402863345361502964406371203065257391103169308408132742094210033744010428034762511431103579301243803685251348683787161449803889161550503999201652704076201752504110020185360421002019544443110152054544411015215648451222722565046154202358564721020245852硫酸透明度与铁杂质含量的散点图如下:Camtnandscattervar3var2得到以下结果：

所以应该建立非线性回归模型。1.通过线性化的方式估计非线性模型。生成变量：・generaly=(l/v^arSJ-gi&iii&w吕七色x=(L/v^.f25(1)建立倒数模型:Commandregretyy.得到以下结果：-teayJCSoiirceSSdzMSNumh-ezofcsh^B47F.：1,45J142.EC]Model„011670£351.iOllfiTOeaEFnob>Fa.oaacResidual..0026777S545.floaa&i72sR—scjuareda^7fi04AdjR—sqT-ianed7551Total-015348424=6.□口□占合合££：L民口o~t;日国„aaeo4YGoef.Std.Err„tFA|P1[95ftConf.InteEval]-2-372132.1985083-