SAS實(shí)驗(yàn) 相關(guān)與回歸分析

%紡財俺乂曙學(xué)生實(shí)驗(yàn)報告學(xué)生實(shí)驗(yàn)報告學(xué)生姓名學(xué)號同組人實(shí)驗(yàn)項(xiàng)目相關(guān)與回歸分析必修 操作性實(shí)驗(yàn)實(shí)驗(yàn)地點(diǎn)0505實(shí)驗(yàn)儀器臺號指導(dǎo)教師重成武實(shí)驗(yàn)日期及節(jié)次一、實(shí)驗(yàn)?zāi)康募耙螅?、目的學(xué)會和掌握參數(shù)估計(jì)與假設(shè)檢驗(yàn)2、內(nèi)容及要求學(xué)會用SAS作總體均值、方差估計(jì)，以及單樣本均值、方差比例檢驗(yàn)，雙樣本均值、方差、比例的比較和配對樣本均值比較檢驗(yàn)等操作二、儀器用具：儀器名稱規(guī)格/型號數(shù)量備注計(jì)算機(jī)1SAS軟件1三、實(shí)驗(yàn)方法與步驟:步驟一、運(yùn)行SAS軟件，新建各題要用到的數(shù)據(jù)集；步驟二、新建數(shù)據(jù)集后，輸入analyst命令或在點(diǎn)擊解決方案—分析—分析家進(jìn)入分析員應(yīng)用環(huán)境；步驟三、在分析員應(yīng)用環(huán)境打開新建的數(shù)據(jù)集；步驟四、再根據(jù)各題要求，點(diǎn)擊統(tǒng)計(jì)選項(xiàng)來分析。四、實(shí)驗(yàn)結(jié)果與數(shù)據(jù)處理:1.下面是某地一年級的12位女生的體重(kg)和肺活量(L)的數(shù)據(jù)試求肺活量對體重的回歸方程。體重4242464646505050525258肺活量2.552.22.752.42.82.813.413.13.462.853.5對肺活量和體重進(jìn)行相關(guān)分析。繪制體重與肺活量的散點(diǎn)圖，計(jì)算其相關(guān)系數(shù)。并對輸出結(jié)果進(jìn)行解釋。將數(shù)據(jù)保存至EXCEL文件，導(dǎo)入數(shù)據(jù)，得到數(shù)據(jù)集；在INSIGHT環(huán)境中調(diào)入數(shù)據(jù)，繪制體重與肺活量的散點(diǎn)圖，如圖所示。P3.5-■■■IJ1■m2.0-■Fl■■■n■ar2.5-■■n■455055 v/eight在INSIGHT環(huán)境中利用多元進(jìn)行分析，得出體重與肺活量的相關(guān)系數(shù)。山 :山 :puInionary:weight頓型方程?1卑買里筑計(jì)里里N均值:最小值最天值pulmonaryi12I2.3025i0.414412.2000i3.5000?lieight i12s49.3333!5.2800i42.0000i58.0000?pulmonaryight桐天系數(shù)擔(dān)陣pulmonaryi 1.OODOi0.7485weight[0.749B:1.0000“單變量統(tǒng)計(jì)量”中提供了每個變量的5個統(tǒng)計(jì)量，分別為數(shù)量、均值、標(biāo)準(zhǔn)差、最小值和最大值。相關(guān)系數(shù)舉證”中則提供了變量間的相關(guān)系數(shù)，體重（weight）和肺活量（pulmonary）的相關(guān)系數(shù)為0.7495（2）判斷體重和肺活量兩變量的關(guān)系，擬合肺活量對體重的方程，對回歸系數(shù)進(jìn)行解釋和對回歸系數(shù)進(jìn)行檢驗(yàn)，繪制殘差圖。①用insight視圖下的分析來擬合肺活量對體重的方程；對回歸系數(shù)進(jìn)行解釋和對回歸系數(shù)進(jìn)行檢驗(yàn):抵臺廠總0.2878抵臺廠總0.2878i檢左R平方0.5G170.5179上表提供模型擬合的匯總度量，肺活量的均值是2.9025，模型的R2=0.5617,說明肺活量變異的大約56%可以由體重來說明?！纉 方差分析平萬相均方!F細(xì)計(jì)里!Pr>F1!1.06121.061212.82丫0.005010:0.82800.082811=1.8892」源?…「自田建了平萬和III荽檢驗(yàn)■hF">T”””罰上1卜筑計(jì)里ici：iloi ii i.u6i21.0612i12-82Li.OObO±j 蜃埶店計(jì)值估計(jì)值標(biāo)準(zhǔn)誤差iT績計(jì)里iPr>|t| 苔差 i方差底脹因子WIF）I「itercept0.000410.014915.069E-04i0.99961 1 0COL0ii0.0588i0.0164i3.58e0.0050i 1.0000i 1.0000從方差分析表中可以看到，P值小于，所以拒絕原假設(shè)接受備擇假設(shè)，所以這一模型擬合數(shù)據(jù)較好。繪制殘差圖：■TOC\o"1-5"\h\zRQ.4- --0.2-—■\o"CurrentDocument"U? ? ?aa.o- L1-.2- ■?B—■1-.4- ?GEM.Ed.Ud.ZS.4z P_COL1_1對體重為57kg的女生的肺活量進(jìn)行估計(jì)，打開數(shù)據(jù)集直接在weight(體重)最下方輸入57，得到預(yù)測值。所以體重為57kg的女生的肺活量的估計(jì)值是3.3535。斗區(qū)間型區(qū)間型甌間型weightpuImoriaFyRpulnonaryPpu1monary■1422.550.07892.4711■2422.20-0.27112.4711■3462.750.04362.7064■4482.40-0.30642.70S4■5462.800.09362.7064■e502.SI-0.13172.3417■7503.410.46832.3417■8503.100.15832.S417■9523.460.40063.0594■10522.$5-0.20943.0594■11583.500.08773.4123■1?583.00-0.4123■13573.3535■ 并求出肺活量期望值的95%的可信區(qū)間。........狐蓋信區(qū)囘估計(jì)值2.3025!2.63320.4144i0.2936Hfi0.1717?0.D8G2""3"'"i'6580.70360.4951由上圖表可知，肺活量期望值的95%的區(qū)間為［2.6392,3.1658］。

2、利用dst.fitness數(shù)據(jù)集，擬合多元線性方程(以O(shè)XYGEN變量為因變量)。擬合多元線性方程的方程。用編程擬合多元線性回歸，編程如下：Procregdata=dst.fitness;ModelOXYGEN=ageweightruntimerstpulserunpulsemaxpulsegroup;run;提交這一程序后可得到如下的輸出：Modlel:MODEL1BEpendentUnriab1OKVGEN OxysEncon^unptionSourceDFSunofSourceDFSunofSquaresMeanSqyareF<Jalue網(wǎng)口u177SS.04EE6143.1H3S119.33EErrsr￡31^3.37E^5ECTetal306S1.3BIS4RootHSEEa371R=squareDapMeflnH7a37sei fldiR-sqQ.BQ1S5.DQ51BfinslysissfU?riinGeProb>FO.OAOIPBraneterE孚ti常日屯巳生Uariab1耳DFParameterEstimateStundurdErirsrTfsrHO：PairiiMeter=DPreb>IT]INTERCEP11?l.9EH1H713?BS73BS30〒?33E■OOtHRGE1"O-ESDl-HS0?1BSB913H=1.EE4.ElSOUEIGHT10.058S01BO■1?ES9?FEI1RUHTIHE1-S?6B09310-3SE9H1E0-7-001.000jRSTPULSE1?0?001BE30.0G13333H-0.034.9765RUHPULSE1-0.37E7E56-lE3H0glH-3.0￡?■ODB1HRHPULSE：1O.30S3GHo.ineHiHiGs&.175.OHQBGROUP1=0.?73GlZ0?9907i3?H-0.074血.snmUafiAbleUariablleOFL<beIINTERCEP 1 InterceptRGE 1 flgEinWEIGHT 1 inRUHTIHE 1 +0廣im1.5niIlesRSTPULSE： 1 Heartrate MhiIe restingRUHPULSE： t Heartrate MhiIs rulingHRHPULSE：1MaximumheartGROUP 1ExperiMentaIg產(chǎn)oup這一輸出與簡單線性回歸的輸出時完全相仿的，只是進(jìn)入回歸的自變量有7個。從參數(shù)的估計(jì)值容易得到擬合的回歸為：OXYGEN=-0.21043AGE-0.073700WEIGHT-2.680931RUNTIME-0.001829RSTPULSE-0.372725RUNPULSE+0.305364MAXPULSE-0.073612GROUP+101.824147判斷方程是否存在共線性和異方差？如果方程存在共線性，怎樣用逐步回歸法進(jìn)行變量篩選擬合回歸方程(保留模式的顯著性水平為0.15)。從參數(shù)估計(jì)檢驗(yàn)部分可以看出，變量AGE、WEIGHT、RSTPULSE和GROUP的回歸系數(shù)，不能拒絕它們?yōu)?的原假設(shè)。在這里須小心地看待這些檢驗(yàn)，因?yàn)樗鼈兌际窃谄渌兞考尤牖貧w的前提下進(jìn)行顯著性檢驗(yàn)的，完全可能因?yàn)樽宰兞块g存在較強(qiáng)的相關(guān)而掩蓋它們對回歸的貢獻(xiàn)，所以在剔除不顯著的回歸變量時必須逐個進(jìn)行。

①用編程方法判斷方程是否存在共線性Procregdata二dst.fitness;ModelOXYGEN二ageweightruntimerstpulserunpulsemaxpulsegroup/collinvif;run;②提交這一程序后可得到如下的輸出:ParameterEstiriatesVariableLabelDFFaranet已「EstimftteStandardErrortValuePr>111/arianceInflationInterceptIntErcept1101.S2415ia.AS7397.99■CODLilnliCEAgeinyears1-0.21014l：la1f：E：2!=!-E2Cl：la2l!jl：l4.00i95i'.'EICHTWeightinkg1-0.073700-058B0-1.260.22111.27D46RUN!IMEMinat口「i」n1?Hmi1ds1-2.86D990.38294"7.00<■00011.60647RSTFULSEHeartrate'ivni1crestingHeartralewhi1匚running1-0.001990.06139h：i.O80.97661.38026RLNFULSE1h：i.372730.12340-3.0￡0.00616.53fl1lH剛PULSEMaxirrumheartrate10.305380-14041Z.17i：i.04ii28.83D77GROUPExperimeritb.Igroup1-0.073610.39076-i：i.O70.34143.65302C@IIiirneariOUgino^fis?CDnditi0nu§rPirspUarPropUai^FriBipUarPrapu>ai廣Pl-opUairPrepNuiMiberE1g&HiUB1Uh!1n日已m1NTEKCEPAGE凰1匡1GHTRUNTIMERSTPULSERUNPULSEi7B5SliBa?0doci0?MM叭”陽0.0003Q?gg己0?H.551GH0?OOCQQ?OOQQi0-6007Q.OOOS0■cm30?0QOQ30?OSEOB19m呂耳BUSCl?OOlSi0?CO3TOK0fe1HI30fl?0003q0aOOQ02：ET亠百岳iB百110a￡|i91l￡0.820HI&.￡138R???l15?.0065峠3H+C9T?1?s0Ci3B0‘帕白0?iBBSeOM弭心壬”5??005HB37.S4SSI9直???3H03Q■13B44.4Q15勺?01GBe.?4G070.OQOTSSB#垃3尬0?T9￡&0?EQSQi0.0IOEfl-.QlTSB0?0OO1??0310□d.00017730?1目目呂0?D*1呂BO?0EM1o.cmit0-01130?口BSEU?rPrep PrepbomberMREPULSE0B009^?.E5560B009^?.E556ci?oioets0?OCiTII0?01220bHISS9?.E5N3D?04353 D?WTH Q?1>D10S D?0070G iDadOllT *3北0 0?9BHS由檢測結(jié)果可知,方差膨脹因子最大只有8.83077,并沒有超過10，這表明不由檢測結(jié)果可知,存在共線性問題。用編程的方法做逐步回歸法進(jìn)行變量篩選擬合回歸方程。Procregdata=dst.fitness;ModelOXYGEN=ageweightruntimerstpulserunpulsemaxpulsegroup/selection=stepwise;run;提交這一程序后可得到如下的輸出：呂tu口'A'ise；~；eIection：W；t七口1RUNTIMEH=RUNTIMEH=S?=|LjaLr^i：i?7494^.nd匸江尸》=11■日400AnaI專昌IbofVarienceSumofMeanSnurcE□F巳口Liare3呂口uareFVaIue Pr>FMade11ESZ.SDDIDB3￡.3DDI□34.LH <.DUDIError23218.481447?53SS4CorrectetdTotal3QSEI.3SI54ParaiiietergtandardVar1ah1eEstirri&tao—II￡5FVa1uePi->FIntesrc：ept日上.421778B0553i：i34斗已?S&654457B05 <.0001RUNTIME一9?910580?98113892.9001094.LH<aiJLHJlt'o'-jndson匸口ndiEionnumber: 1

已phise￡已丨曰二ti□「!:Step2VarisibleAGEEntered：R-Square=0.7642andC(p)=10.6825AnaIysisofVarianceModeIModeIErrorCo廠廠已匸:te：匚ITotal650.66573325.3328745.33<.0001200.715017.16842851.38154SumufMeanSourceDFSquaresSquareFValuePr>FParameter ：ttanda-rdVariab1&E：±ti「陽上eErrorTypeIISSFViluePr>FIntere已pt88.462295.372641943.41071271.11<.0001AGE-Q.15J370.055117.75563143C.1267RUNTIME-3.203950.35877571.6775179.75Boundsonconditi□nriurnber：1.0369,4.1473St&P1.1.1i：-：eEeIection:E+ep-3AnaIysisuf'v1arianeeSourceDFSumofSquaresMeanSqjafEFValueFr>FModel3e30.5508e230.1836238.64<.0001Error27160.830695.95669CorrectedTotal3D851.38154VariableParameterEat1mateStandardErrorTypeIISSFValuePr>FIntereept111.71SO610.235087C9.69014113.14<.0001AGE-0.256400.0962342.288677.100.0129RUNTIME-2.825380.35828370.4352962.13<.0001RUNPULSE-0.130910.0505939.885126.700.0154Boundsonconditionnumber!1.3548,11-597：?tepVi1iseSeI匸匚tiun:E：tep4VariableMAXFULSEEntered:F：-Square二0?S368andC(p：：'二3.t：984AnaIys：isofVa.rianceSuurceDFSumofSqua.resMeanSqua.reFValueF'r>FMode1712.45153178.11Z8833.33■C.nnn1Error26138.930025.34346Correct已匚1Total30851.38154VariablePararnet^rEw：tImait昭StandardError1r/peIISSFValuePr>FIntercept98.1478911.78569370.5737369.35<.0001AOE-0.197730.0956422.042314.270.0498RUNTIME-2.767580.34054352.9357066.15<.ooaiRUNPULSE-0.348110.1175046.900898.730.0064MAXPULSE0.270510.1336221.900G74.10i：i.0533Boundsonconditionnurnbe^8.4182,76.851Surnnftr：/ofStepwiseSelectionVariableStepEntered^arableHenovedLabeNumberPartialModelYarsInVariableStepEntered^arableHenovedLabeNumberPartialModelYarsInR-SquareR-Squarec?FValuePrJFnurn[meAGE$ HUNPULSE4 NflKPULSEMin.torun1.5mlesAgeinyearsHeartratewhilerumirgMaxinunheartrate11.^34(I.[1209 0.7B420.D468 0.BI11.i4JiH.JI<.uu2.43〔雷卩b.iilia.!i1.1h43.E9044.1)0.0533在輸出報告中，提供了進(jìn)入回歸變量逐次改變后回歸方差分析和擬合的信息。在報告的最后，利用逐步回歸法挑選，變量RUNTIME、AGE、RUNPULSE和MAXPULSE四個變量進(jìn)入回歸。所有進(jìn)入回歸的變量在0.15的水平下是顯著的。（3）檢驗(yàn)樣本中是否存在強(qiáng)影響點(diǎn)。①用編程的方法作回歸CookD診斷：Procregdata=dir.fitness;ModelOXYGEN=ageweightruntimerstpulserunpulsemaxpulsegroup/r;run;②提交這一程序后可得到如下的輸出:OutputStatisticsobsUBpendentVariableFredict曰dValueStdErrorMeanPredictResidualStdErrorResidual12-H-458/89012345s71l.'H901?■!?:>4567Ou30111111111112obsUBpendentVariableFredict曰dValueStdErrorMeanPredictResidualStdErrorResidual12-H-458/89012345s71l.'H901?■!?:>4567Ou30111111111112222□!■222-sllL23Ou39.401046.09B045.441054.625045.118039.203045.730050.54E048.673047.3213047.461050.541037.388044.754047,273051.85E049.158040.83604e.G75046.774050.388044.603045.313054.297059.571049.8740W.811045.681043.031099.4420GO.056039_S1504G.G69448.783054.8585U.G247S6.fl?0045.431550.901448.689646.531645-5612IS.565137.420745.635847.23484G-S3i：i950.779946.345819J13847-04U47-566744.619518.319656.195156-643351J79B43.09S645.019443.123540.285956.01511-27730-S7361.35500JG941.43361.Z0331.40341JM84UM66flJIJOO1.15431.536G1.D^220.91201-U1E：1.27730-S56T0JE701-22101.56480,93701.D7851.23051.35381.?E221.16291.18161.D5481.190513623D.1820-3.3420-0.2JS35D.493339300.358