第二章 一元线性回归模型(Stata)

#中国居民人均消费模型从总体上考察中国居民收入与消费支出的关系。表2.1给出了1990年不变价格测算的中国人均国内生产总值（GDPP）与以居民消费价格指数（1990年为100）所见的人均居民消费支出（CONSP）两组数据。表2.1中国居民人均消费支出与人均GDP（单位：元/人）年份CONSPGDPP年份CONSPGDPP1978395.8000675.10001990797.10001602.3001979437.0000716.90001991861.40001727.2001980464.1000763.70001992966.60001949.8001981501.9000792.400019931048.6002187.9001982533.5000851.100019941108.7002436.1001983572.8000931.400019951213.1002663.7001984635.60001059.20019961322.8002889.1001985716.00001185.20019971380.9003111.9001986746.50001269.60019981460.6003323.1001987788.30001393.60019991564.4003529.3001988836.40001527.00020001690.8003789.7001989779.70001565.9001）建立模型，并分析结果。CommandregressvarZvar32）输出结果为：-regr&ssvar2var3MSNumtafiTorcfegF（：lr21）=22=2859„54Mc>del31-G41G2.4513164162.45Crab，F=a.oana23227„a7€5211106.EIZTA导R—acjuaredAdj&—aquiared=a„9527=a„9524Total31S7399„52221448SL„79«=33.2*65GdbC-Std.Zrr.tPAIt1[95%Gonf.Interval]var3-3861803„007221753.47a.oca-3711619-.4011987ccna201-118914.8840213.51a.aoa1701659232„071S对应的模型表达式为：CONSP=201.107+0.3862GDPP（13.51）（53.47）R2二0.9927,F二2859.23,DW二0.55从回归估计的结果可以看出，拟合度较好，截距项和斜率项系数均通过了t检验。

中国人均消费增加10000元，GDP增加3862元。线性回归模型估计表2.2给出黑龙江省伊春林区1999年16个林业局的年木材采伐量和相应伐木剩余物数据。利用该数据（1）画散点图；（2）进行OLS回归；（3）预测。表2.2年剩余物X和年木材采伐量xt数据林业局名年木材剩余物yt（万m3）t年木材采伐量兀（万m3）乌伊岭26.1361.4东风23.4948.3新青21.9751.8红星11.5335.9五营7.1817.8上甘岭6.8017.0友好18.4355.0翠峦11.6932.7乌马河6.8017.0美溪9.6927.3大丰7.9921.5南岔12.1535.5带岭6.8017.0朗乡17.2050.0桃山9.5030.0双丰5.5213.8合计202.87532.00（1）画散点图Commandscattervarlvar2得散点图OLS估计Commandregressuar1var2得到输出结果如图-regreaavarlvairZSourcaS3drMSMuniberofobs1€F(lr14)L4€.72Model五叮8-37415616E8„3741-56Prob>Fa.aooaR&aidual58-0522097144„1465&255El-gqiiaEsd.a.9129AljR-squaEfida.90€7Tot；"£€€.4264661544.4284311Koqt;HSE2_D363var1Coef-Std.Errt;PA|t|[351%Conf.Interval].4Q4273-S・12-11ana(ia・3226944758655_ccms-.76292791・Z2Q^6-0-62a.542-3・3S16391・S557S3由输出结果可以看出，对应的回归表达式为：y=—0.7629+0.4043xtt(-0.625)(12.11)R2=0.9129,F=146.7166,DW=1.48x=20条件下模型的样本外预测方法首先修改工作文件范围(不会)

表2.3列出了中国1978—2000年的参政收入Y和国内生产总值GDP的统计资料。做出散点图，建立财政收入随国内生产总值变化的一元线性回归方程。表2.3年份财政收入丫GDP年份财政收入丫GDP19781132.2603624.10019902937.10018547.9019791146.3804038.20019913149.48021617.8019801159.9304517.80019923483.37026638.1019811175.7904862.40019934348.95034634.4019821212.3305294.70019945218.10046759.4019831366.9505934.50019956242.20058478.1019841642.8607171.00019967407.99067884.6019852004.8208964.40019978651.14074462.6019862122.01010202.2019989875.95078345.2019872199.35011962.50199911444.0882067.5019882357.24014928.30200013395.2389403.6019892664.90016909.201)做散点图：Commandseatt&rvar2var3得到散点图如下：2)进行回归分析：■Commandregressvar2var3输出结果如下:.regireasweluN■va.ir3SaurceSSMS=23rt丄.亡丄」—Lilu.bJiZiModel2760661731276066173Etc-b3-F=aesidual1122798321534666.145R-3(judre±=a„9五□刁—nQF'Q.^I—LI.J丄ro-tal287294161222130588253.0ctK目亘=731.21r2CoeE-Std.Err_t;F^ltI[9S%Conf.Interval]r3.115S074-005272522.72a.ooo.1088426.1307722czons55€.€477220.S9422.52fl-02097„272&1lOlC-QSS对应的表达式是：Y=556.6+0.12GDP(2.52)(22.72)R2二0.96,F二516.3从上面的结果可以看出，模型的你拟合度较高，各个系数均通过了t检验。财政收入增加10000元，GDP增加1200元。表2.4给出了某国1990—1996年间的CPI指数与S&P500指数。(1)以CPI指数为横轴，S&P500指数为纵轴作图；(2)做回归模型，并解释结果。表2.4年份CPI指数S&P500指数年份CPI指数S&P500指数1990130.7000334.59001994148.2000460.33001991136.20003764000541.64001992140.3000415.74001996159.6000670.83001993144.5000451.41001)作散点图：匚ommandscattervar2var3得散点图如下：

500var360C700500var360C7002）做回归估计：Camiriiandregressvar2varJ得到如下结果：-regreaavar2var3SourceSSdfMSMumbe匚cbs=7IFP5二丫—qno.上；丄r白,—O_L.d-3Mglei547.4276251547.427625ProbaF=0-000333„62369315fi.72533862R-squared=a„3421AdjR-aqiiared—U.3dU□I^tal581-D5731896„8428864MSE=2„5334Cuez.Std„Zee.tF>|t|［号呂童Conf.Interval].□850015.00942199„02o^oaa_06078171092213csong105„08344.4838923.44o„□□□93.55722116.对应的回归表达式为：S&P=—1137.83+11.O8CPI(-6.39)(9.02)回归结果显示，CPI指数与S&P指数正相关，斜率表示当CPI指数变化1个点，会使S&P指数变化11.08个点；截距表示当CPI指数为0是,S&P指数为1137.83，此数据没有明显的经济意义。

表2.5给出了美国30所知名学校的MBA学生1994年基本年薪(ASP),GPA分数(从1—4共四个等级)，GMAT分数，以及每年学费(X)的数据。用双变量回归模型分析GPA分数是否对ASP有影响？用合适的回归模型分析GMAT分数是否与ASP有关？每年的学费与ASP有关吗？如果两变量之间正相关，是否意味着进到最高费用的商业学校是有利的？高学费的商业学校意味着高质量的MBA成绩吗？为什么?表2.5学校ASP/美元GPA分数GMAT分数X/美元Harvard102630.03.400000650.000023894.00Stanford100800.03.300000665.000021189.00Columbian100480.03.300000640.000021400.00Dartmouth95410.003.400000660.000021225.00Wharton89930.003.400000650.000021050.00Northwestern84640.003.300000640.000020634.00Chicago83210.003.300000650.000021656.00MIT80500.003.500000650.000021690.00Virginia74280.003.200000643.000017839.00UCLA74010.003.500000640.000014496.00Berkeley71970.003.200000647.000014361.00Cornell71970.003.200000630.000020400.00NUY70660.003.200000630.000020276.00Duke70490.003.300000623.000021910.00CarnegieMellon59890.003.200000635.000020600.00NorthCarolina69880.003.200000621.000010132.00Michigan67820.003.200000630.000020960.00Texas61890.003.300000625.00008580.000Indiana58520.003.200000615.000014036.00Purdue54720.003.200000581.00009556.000CaseWestern57200.003.100000591.000017600.00Georgetown69830.003.200000619.000019584.00MichiganState41820.003.200000590.000016057.00PennState49120.003.200000580.000011400.00SouthernMethodist60910.003.100000600.000018034.00Tulane44080.003.100000600.000019550.00Illinois47130.003.200000616.000012628.00Lowa41620.003.200000590.00009361.000Minnesota48250.003.200000600.000012618.00Washington44140.003.300000617.000011436.00

以ASP为因变量，GPA为自变量进行回归分析。Ccmmandregressvar1var2结果如下：Satiresssd=MS•色EQfBbS=29-口丿qi—口CSA上G丄f-r/血del合.7520^09-13_752ae-HafrTrobaF=fl.aaasRemn_dua15-23S2e-Ha9-27194010257R—sqtiared.=fl.4174—nOC.RQIstaiS.S912e-^aS2S321115S5Q社口t=varlCoez.Std_Lrr.tF>|t1[95%Ganz.iELtEEVal]vai2109€02.724S19.354.40D.0005S471..22160734.3CJD：na-2873口石.181074.08-3.54□.001-45365^.4-12DS55.9从回归结果可以看出，GPA分数的系数是显著的，对ASP有正的影响。(与Eviews系数结果不一致，仔细核实一下)以ASP为因变量，GMAT为自变量做回归分析。Comman-dregressvar1var3结果如下：S口xizrceS口xizrcess：±zKSHadel€.fi7iae+as1■fi,fi71Qfi+(]SResidual2.32口口古27B593AK4.4Iatal8.S9L2e+32S321115350Mmriber口丘olbs=25F(lr27J=77.£：3F工口b>F=0.OOQO=0.741S匸启日=0.732^EicbQtMSE=9270.1verlCoe=.Std.Zrr-tF>|t|[35%Conf.Interval]VisrS€32.877971.83Q41S.810.0004SE.494178D..2€17_CCELS-326151.44489-2.35-7.270.000-418262.9-234033.9从回归结果可以看出，GMAT分数与ASP是显著正相关的。（与Eviews系数结果不一致，仔细核实一下）（3）以ASP为因变量，X为自变量进行回归分析。Commandregressvar1war4结果如下：-regr&gsvarlva^4SGurcfiSSd=MSNurnh-fiTeib3=itripi\■2S1&.71£L丄.匸7Medel2.7937e-kD912.7927S+-Q9Prcb>F□.0001Eieaidiial5.197€e-b0927152502393R—sqijared□.4213AdjR—sqT-ianed□.4005TotalS.S512e-b05321115350Rao-tMSE13S75varlCoen.Std.Err„t?>l11[95%Conf.Interval]Viax42.542010・572S2Q84.4-4a.aa叮1„3«70973.71S93S_c；cns25025・7fi10255□.□2235^2.5SS4fiQfi7.33从回归结果可以看出，每年的学费与ASP显著正相关。学费高，ASP就高;但学费仅解释了ASP变化的一部分，明显还有其他因素影响着ASP。（与Eviews系数结果不一致，仔细核实一下）（5）以GPA为因变量，X为自变量进行回归分析。匚ominandregress.var2var4结果如下：

.Tregrasavar-Sitel莒S口uccisSSMSNuint-ecc=口匕目29FClrZ7）Mcniel..0287104641.028710464E匚口b>FD.LD99Reaidual.2837033&327.010507533R-aqriared□.□919AdjR-squarel□„Q583IiJtal..3124128G228.011157628HSE.10251var2Coe£_Std.Err.tF>ltl[95%Conf.Interva1]Viax46.SSe-Ofi屯.23s-1・65口.iia-1.fiSe-Ofi-aaaaiB?_cons3„130499„075767241„32□„aaa2-9750373_2859fi从回归结果可以看出，尽管高学费的商业学校与高质量的MBA成绩略有正相关性，但学费对G