第二章 一元線性回歸模型(Stata)

#中國(guó)居民人均消費(fèi)模型從總體上考察中國(guó)居民收入與消費(fèi)支出的關(guān)系。表2.1給出了1990年不變價(jià)格測(cè)算的中國(guó)人均國(guó)內(nèi)生產(chǎn)總值（GDPP）與以居民消費(fèi)價(jià)格指數(shù)（1990年為100）所見的人均居民消費(fèi)支出（CONSP）兩組數(shù)據(jù)。表2.1中國(guó)居民人均消費(fèi)支出與人均GDP（單位：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，并分析結(jié)果。CommandregressvarZvar32）輸出結(jié)果為：-regr&ssvar2var3MSNumtafiTorcfegF（：lr21）=22=2859?54Mc>del31-G41G2.4513164162.45Crab，F(xiàn)=a.oana23227?a7€5211106.EIZTA導(dǎo)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對(duì)應(yīng)的模型表達(dá)式為：CONSP=201.107+0.3862GDPP（13.51）（53.47）R2二0.9927,F二2859.23,DW二0.55從回歸估計(jì)的結(jié)果可以看出，擬合度較好，截距項(xiàng)和斜率項(xiàng)系數(shù)均通過了t檢驗(yàn)。

中國(guó)人均消費(fèi)增加10000元，GDP增加3862元。線性回歸模型估計(jì)表2.2給出黑龍江省伊春林區(qū)1999年16個(gè)林業(yè)局的年木材采伐量和相應(yīng)伐木剩余物數(shù)據(jù)。利用該數(shù)據(jù)（1）畫散點(diǎn)圖；（2）進(jìn)行OLS回歸；（3）預(yù)測(cè)。表2.2年剩余物X和年木材采伐量xt數(shù)據(jù)林業(yè)局名年木材剩余物yt（萬m3）t年木材采伐量兀（萬m3）烏伊嶺26.1361.4東風(fēng)23.4948.3新青21.9751.8紅星11.5335.9五營(yíng)7.1817.8上甘嶺6.8017.0友好18.4355.0翠巒11.6932.7烏馬河6.8017.0美溪9.6927.3大豐7.9921.5南岔12.1535.5帶嶺6.8017.0朗鄉(xiāng)17.2050.0桃山9.5030.0雙豐5.5213.8合計(jì)202.87532.00（1）畫散點(diǎn)圖Commandscattervarlvar2得散點(diǎn)圖OLS估計(jì)Commandregressuar1var2得到輸出結(jié)果如圖-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由輸出結(jié)果可以看出，對(duì)應(yīng)的回歸表達(dá)式為：y=—0.7629+0.4043xtt(-0.625)(12.11)R2=0.9129,F=146.7166,DW=1.48x=20條件下模型的樣本外預(yù)測(cè)方法首先修改工作文件范圍(不會(huì))

表2.3列出了中國(guó)1978—2000年的參政收入Y和國(guó)內(nèi)生產(chǎn)總值GDP的統(tǒng)計(jì)資料。做出散點(diǎn)圖，建立財(cái)政收入隨國(guó)內(nèi)生產(chǎn)總值變化的一元線性回歸方程。表2.3年份財(cái)政收入丫GDP年份財(cái)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)做散點(diǎn)圖：Commandseatt&rvar2var3得到散點(diǎn)圖如下：2)進(jìn)行回歸分析：■Commandregressvar2var3輸出結(jié)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目亙=731.21r2CoeE-Std.Err_t;F^ltI[9S%Conf.Interval]r3.115S074-005272522.72a.ooo.1088426.1307722czons55€.€477220.S9422.52fl-02097?272&1lOlC-QSS對(duì)應(yīng)的表達(dá)式是：Y=556.6+0.12GDP(2.52)(22.72)R2二0.96,F二516.3從上面的結(jié)果可以看出，模型的你擬合度較高，各個(gè)系數(shù)均通過了t檢驗(yàn)。財(cái)政收入增加10000元，GDP增加1200元。表2.4給出了某國(guó)1990—1996年間的CPI指數(shù)與S&P500指數(shù)。(1)以CPI指數(shù)為橫軸，S&P500指數(shù)為縱軸作圖；(2)做回歸模型，并解釋結(jié)果。表2.4年份CPI指數(shù)S&P500指數(shù)年份CPI指數(shù)S&P500指數(shù)1990130.7000334.59001994148.2000460.33001991136.20003764000541.64001992140.3000415.74001996159.6000670.83001993144.5000451.41001)作散點(diǎn)圖：匚ommandscattervar2var3得散點(diǎn)圖如下：

500var360C700500var360C7002）做回歸估計(jì)：Camiriiandregressvar2varJ得到如下結(jié)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|［號(hào)呂童Conf.Interval].□850015.00942199?02o^oaa_06078171092213csong105?08344.4838923.44o?□□□93.55722116.對(duì)應(yīng)的回歸表達(dá)式為：S&P=—1137.83+11.O8CPI(-6.39)(9.02)回歸結(jié)果顯示，CPI指數(shù)與S&P指數(shù)正相關(guān)，斜率表示當(dāng)CPI指數(shù)變化1個(gè)點(diǎn)，會(huì)使S&P指數(shù)變化11.08個(gè)點(diǎn)；截距表示當(dāng)CPI指數(shù)為0是,S&P指數(shù)為1137.83，此數(shù)據(jù)沒有明顯的經(jīng)濟(jì)意義。

表2.5給出了美國(guó)30所知名學(xué)校的MBA學(xué)生1994年基本年薪(ASP),GPA分?jǐn)?shù)(從1—4共四個(gè)等級(jí))，GMAT分?jǐn)?shù)，以及每年學(xué)費(fèi)(X)的數(shù)據(jù)。用雙變量回歸模型分析GPA分?jǐn)?shù)是否對(duì)ASP有影響？用合適的回歸模型分析GMAT分?jǐn)?shù)是否與ASP有關(guān)？每年的學(xué)費(fèi)與ASP有關(guān)嗎？如果兩變量之間正相關(guān)，是否意味著進(jìn)到最高費(fèi)用的商業(yè)學(xué)校是有利的？高學(xué)費(fèi)的商業(yè)學(xué)校意味著高質(zhì)量的MBA成績(jī)嗎？為什么?表2.5學(xué)校ASP/美元GPA分?jǐn)?shù)GMAT分?jǐn)?shù)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為因變量，GPA為自變量進(jìn)行回歸分析。Ccmmandregressvar1var2結(jié)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從回歸結(jié)果可以看出，GPA分?jǐn)?shù)的系數(shù)是顯著的，對(duì)ASP有正的影響。(與Eviews系數(shù)結(jié)果不一致，仔細(xì)核實(shí)一下)以ASP為因變量，GMAT為自變量做回歸分析。Comman-dregressvar1var3結(jié)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匸啟日=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從回歸結(jié)果可以看出，GMAT分?jǐn)?shù)與ASP是顯著正相關(guān)的。（與Eviews系數(shù)結(jié)果不一致，仔細(xì)核實(shí)一下）（3）以ASP為因變量，X為自變量進(jìn)行回歸分析。Commandregressvar1war4結(jié)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從回歸結(jié)果可以看出，每年的學(xué)費(fèi)與ASP顯著正相關(guān)。學(xué)費(fèi)高，ASP就高;但學(xué)費(fèi)僅解釋了ASP變化的一部分，明顯還有其他因素影響著ASP。（與Eviews系數(shù)結(jié)果不一致，仔細(xì)核實(shí)一下）（5）以GPA為因變量，X為自變量進(jìn)行回歸分析。匚ominandregress.var2var4結(jié)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從回歸結(jié)果可以看出，盡管高學(xué)費(fèi)的商業(yè)學(xué)校與高質(zhì)量的MBA成績(jī)略有正相關(guān)性，但學(xué)費(fèi)對(duì)G