實驗五回歸分析SAS進程

1、實驗五回歸分析SAS進程（2）實驗?zāi)康模? .會對實際問題成立有效的多元回歸模型，能對回歸模型進行殘差分析；2 .把握SAS輸出結(jié)果用于判別回歸方程優(yōu)良性的不同統(tǒng)計量，能對回歸模型進行 運用，對實際問題進行預(yù)測或操縱.實驗要求:編寫程序，結(jié)果分析.實驗內(nèi)容：1.誤差的正態(tài)性查驗有幾種方式，何時以為誤差項服從正態(tài)散布？答：1.學(xué)生化殘差2.殘差正態(tài)性的頻率查驗3.殘差的正態(tài)QQ圖查驗判定假設(shè)散點，大致在一條直線上之一力仇）一力相關(guān)系數(shù)：戶一-廠一V 1-1/-I以為彳（i = l,2,來自正態(tài)散布，同意誤差正態(tài)性查驗.2 .回歸方程的選取的窮舉法中，評判回歸方程優(yōu)良性的準(zhǔn)那么有哪些？依照準(zhǔn)那 么

2、何時方程最優(yōu)？答：1）修正的復(fù)相關(guān)系數(shù)準(zhǔn)那么或均方殘差準(zhǔn)那么（心（p）或MS1紇準(zhǔn)那么）2） g準(zhǔn)那么3）預(yù)測平方和準(zhǔn)那么（PRE%,準(zhǔn)那么）擬合所有可能的-1個回歸方程，畫出C?圖：（p,Cp）,在圖當(dāng)選取最接近參考 直線Cp= p的點所對應(yīng)的回歸方程為最優(yōu)方程.3 .簡述慢慢回歸方式的思想和步驟.大體思想：逐個引入自變量成立回歸方程，每次引入對丫阻礙最顯著的自變量，并對方程 中舊變量逐個進行查驗,把變成不顯著的變量逐個從方程中剔除掉,最終取得的方程中，既不 漏掉對丫顯著阻礙的變量，又不包括對丫阻礙不顯著的變量.添加或刪除某個自變量的準(zhǔn)那 么是用殘差平方和的相對減少或增加來衡量.步驟：（1）

3、修正的復(fù)相關(guān)系數(shù)準(zhǔn)那么、C”準(zhǔn)那么選擇模型（2）預(yù)測平方和準(zhǔn)那么選擇PRESSp最優(yōu)回歸方程（3）最優(yōu)模型的擬合查驗4 .做（選作）注意：能夠選課外綜合題目。程序:data examp2_6; input xl x2 y; cards;70656372818366758075797676697574858671647880747277818280808087 run;proc reg data= examp2_6;model y=xl-x2;output out=a p=predict r=resid h=h student=r;run;data b;set a;drop xl-x2;run;

4、proc print data=b;run;proc capability graphics noprint data=a; /* 對數(shù)據(jù)集 a 挪用 capability進程，高分辨圖，不打印輸出*/qqplot r/normal;/*作student數(shù)據(jù)的正態(tài)QQ圖*/run;goptions reset=all;/*將圖形的設(shè)置恢復(fù)為默許狀態(tài)*/proc gplot data=a;/*對數(shù)據(jù)集a作出畫高分辨的散點圖或曲線圖*/plot resid*predict; /*畫縱坐標(biāo)為殘差、橫坐標(biāo)為yi散點圖*/symbol v=dot i=none; /*散點表示符號圓點，不畫連線*/run

5、;/*此處至Quit是計算學(xué)生化殘差對應(yīng)的標(biāo)準(zhǔn)正態(tài)散布的分位數(shù)*/proc sort data=a;by r;/*按r排序*/proc iml;/*挪用iml矩陣分析模塊，計算數(shù)據(jù)*/use a;/*打開數(shù)據(jù)集a */read all varr into rr; /*讀入集a中變量r （學(xué)生化殘差）各觀測值到矩陣rr中*/do i=l to 31;/*此循環(huán)計算*/qi=probit （/;q=QObsypredictresi drh110.34.83775.462341.496490.11583210.34.55395.746151.602950.14721310.24.81705.3830

6、21.528460.17686416.415.87410.525880.139670.05919518.819.8690-1.06901-0.293680.12066619.721.0183-1.31833-0.369620.15575715.616.1927-0.59269-0.162280.11480818.219.2459-1.04595-0.276660.05148922.621.41301.186980.320900.092011019.920.1876-0.28758-0.075930.0479?1124.222.01542.184600.584770.073831221.021.

7、4685-0.46846-0.123690.048091321.421.4685-0.06846-0.OISOS0.048091421.320.50620.793850.212370.072761519.123.9541-4.85411-1.274690.037651622.227.8522-5.65220-1.482750.035671733.831.58402.216030.612500.131311827.433.8065-6.40648-1.783240.143461925.730.6010-4.90098-1.306850.066662024.928.6970-3.79704-1.1

8、013?0.211242134.534.38820.111820.029330.035812231.736.0083-4.30832-1.135960.045422336.335.38530.914740.241760.049952438.341.7690-3.46900-0.948030.111432542.644.8777-2.27770-0.608210.069312655.450.94294.457131.202600.088422755.752.22383.476250.941880.096032858.353.42854.871491.327570.106422951.553.89

9、93-2.39933-0.655110.109833051.053.8993-2.89933-0.791630.10983317?.O68.51538.484702.486140,22706SAS系統(tǒng)2008年08月01日 星期五 下午06時18分33秒2-Rnp-saa PV7 二 cvpes-10正態(tài)分位數(shù)4 GRAPHl WORJOGSKxGPlOT0：|五 00Residual*2艾里：R旬單統(tǒng)計里受里N均值標(biāo)準(zhǔn)差總和最小值最大宜R310.010311.036800.31962-1.783242.486140310.671720.62292-20.82318-2.272750.1624

10、3Pearson相關(guān)天數(shù), N = 3 當(dāng) HO： Rho=0 時，Prob >rlRQR1.000000.94091<.0001Q0.940911.00000<0001pY XI9X2YAYYa -1Y(A) = |，2*° A SS可為Z)SS旦人Z)5SZ;Za,) AInk 2 = 0lambdaO0.31200g車og月01日£ObsXIX2Z18.3703.4210728.6653.4210738.8633.40100410.5724.45205510.7814.78410610.8834.30105711.0664.33393811.0754

11、.70396911.1805.254511011.2754.926541111.3795.436251211.4765.063651311.4765.112281411.7695.100191512.0754.823501612.9745.207691712.9856.381521813.3865.776231913.7715.599252013.8645.513162114.0786.442762214.2806.192372314.5746.596412416.0726.761082516.3777.085992617.3817.971832717.5827-390532817.9808.

12、150352318.0807.721283018.0807.688223120.6879-17501SS£(A;Za) = (Z'A> )T (I - H)ZU) 55£(A;ZU) 2yO.31 _55£(2;Za>) A = 0.31 2 = 0.31 Z Z =Z X1,X”X?,X4 Z = X/7 +w031-Z = X/3 + s Z = XJ3 + s2008號08月OlE星電五下午06時18分33秒$The REC ProcXire枇 de I： HDDGL1Dependent Variable： ZMnber of fteer

13、vat ions? Read rnber of Cbzervat ions UsedVarisbeInterceptKIK?Parar»>?terEet irrdteStandard Errort ValuePr > |tl-2.948800.61162-6.6?<.0001fl.419400.0156526.80<.00010.040510.007715.26<.0001rroFieler 1st irr©tesAnjlys is of /oirionccSourceDF3un of Squaresfe?n SquareF Vain?Pr &

14、gt; FModalErrorCorroded Total2283064.651441.4800866.0314732,275720.95286SID.81<.0001Root M5E Depen5=rit Coeff VerMean0.223915.787083.872B2R-SquareAdj R-Sq0.37TB0.3780Z XPX7 £”a = l,2,31)Z正態(tài)分位數(shù)-enp-s3H psz'LuaprusPredicted Vilg of 2Z z R2 = 0.9776 Z Z = -2.84830+0.41940X, +0.04051X2 Z =仄+

15、儀/3?X/8Pearson Correlation Coefficients, N = 31Prob > |rI under HO： Rho=0RRQQRR1.000000.96990<.0001QQ0.96990<.”011.00000Parameter EstimatesVariableDFPa rameter EstimateStandard Errort VluePr > IIIIntercept1162.8759025.775656.32<.0001xl1-1.210320.30145-4.010.0007x21-0.665910.82100-0.81

16、0.4274z31-8.6130312.24125-0.700.4902Analysis of VarianceSourceDFSum ofSquaresMean SquareF ValuePr > FMode 134133.633221377.8777413.01<.0001Error192011.58417105.87285CorrectedTotal226145.21739Root MSE10.28845R-Square0.6727DependentMean61.34783Adj R-Sq0.6210Coeff Var16.77232Parameter EstimatesVa

17、riableDFParameter EstimateSUnda rd Errort ValuePr > ItlIntercept1162.8759025.775656.32<.0001xl1-1.210320.30145-4.010.0007x21-0.G65910.82100-0.810.4274x31-8.6130312.24125-0.700.4302Obsypredictresidrh14848.5888-0.5888-0.061500.1341825768.8628-11.8828-1.283030.1925536663.55102.44900.246820.070124

18、7068.44961.5504Q.172310.2352458984.84964.15040.452040.2037863642,6336-6.6336-0.781140.31S8374659.7986-13.7988-1.383010.0597785455.7768-1.7768-0.189980.17375g2633.6754-7.6754-0.917300.33870107776,39400.60600.063410141913.85811.549790.24478126754.867912.13211.214370-05728134761.3103-14.31

19、03-1.584700.22977145167.9538-16.8539-1.710280.07185155743.821513.17851.545200.31298166669.4430-3.4430-0.354040.1036217?964.112114.88791.628920.20905188880.78037.21970.7578202187-12.2187-1.238770.07809204941.67587.32410.811580.23078217?73.33963.68040.387620.15772n5246.02165.97840.665550.

20、23787236057.72702.27300.227750.05918正西分位效GRAPH! WDRK.GSEG.CAPAK11Prodictod Valufl o* ,Pearson 相關(guān)系數(shù)，N = 23 , 當(dāng) HO: Rho=0 時，Prob > lr|RQR1.000000.96428<.0001Q0.964281.00000<.0001pY X1,X?,X3CpR；(p)2002年呢月01日星期五下午The REG ProcedureModel： NODEL1D&pendent Variable： 2C(p) Select ion MethodNumbe

21、r of Observations Read23Number of Observations Used23Number inModelC(p)R-SquareVariables in Model22.79670.6579xl x222.95180.6553xl x334.00000.B717xl x2 x316.53750.5587xl214.88530.4491乂2 x3115,05870.4115x311G.09640.3936乂 2R，P)R：(P)£Cp2002年呢月01日星期五下午The REQ ProcedureModel： MODEL1Dependent Variabl

22、e! zC(p) SeIect ion MethodNumber of Observations Read23Number of Observations Used23Number in Modelc(p)R-SquareVariables in Model22.78670.6578xl x222.95180.6553xl x334.00000.6717xl x2 x316.53750.5587xl214.88530.4491x2 x3115.05870.4115x3116.09640.3936x2Cp£ PRESSp=£d；(p)2003年08月01口星期立|、二MEAN

23、S PROCEDURE分析麥里：press Residual without Current Observation未校平方和1.8820041MEANS PROCEDURE分析受里：press Residual without Current Observation未校平方和2.4935484MEANS PROCEDURE分析變里：press Residual without Current Observation未檢平方和1.6531882MEANS PROCEDURE分析變里：press Residual without Current Observation未校平方和1.5890749

24、2008年08月01日星期五7MEANS PROCEDURE分析麥里：press Residual without Current Observation未校平方和2.8511881MEANS PROCEDURE分析愛里：press Residual without Current Observ&t ion未校平方和1.8059710Z =+ 自乂 + £200街08月01 m星期五F午OS時12分秒19Ihe REG PrccedjreModel： M0DEL1fependant Variable： 7Number of Observotions Read23Number

25、of Observations Used23Analysis of VarisncoSourceDFSurn of SquaresMeanSquareF ValuePr > FModel22.235811.1179019.23<.0001Error201.162440.05912CorrectedTotal228.83825iFbot MSE0.24108R-Square0.6579Dspcncfent 杷0n4.72242Adj R-$qB.G23?Cueff Ver5.10511Psrariter Eel i m?.tecVariableCFParanctcrEst imate

26、Standard Errort ValueFr > It IIntercept17.391450.5911212.50<.0001xl1-0.026990.00C88-3.930.9008z21-0.031510.01303-2.410.0256爐=0.6579 內(nèi)當(dāng)天 zZ = 739145-0.0269咯-0.0315% A = 0/ = 1x,(i<z：<5-i)r = A)+A +£ 8”=SSRXJMSE(Xk)“)=P(6(1,23 2)之耳)ZUUH耳U&月UI 口 壬即工The REG ProcedureModel： MODEL1dep

27、endent Variable: z3 Qu22Number of Observations ReadNumber of Observations UsedStepwise Selection： StepStatstics for Entry DF = 1,21VariableToleranceMode 1 R-SquareF ValuePr > Fx11.0000000.558726.59<0001x21.0000000.393613.630.0014x31.0000000.411514.680.0010and C(p) = 6.5375Variable xl Entered:

28、R-Square = 0.5587下21”.SSR(X J-=26.59F pX| p p = 0.0001<a£ =0.101 M Y = J3()+F Fq= i)/? = O.OOOl <aD =0,101 Z = Bo + 自吊 +£ Z 二/。+ 自吊 +£Ana lysis of VarianceSourceDFSum ofSquaresMean SquareF ValuePr > FMode 111.898721.8987228.59<.0001Error211.499530.07141Corrected Total223.3

29、982555(%) = 1.89872SS瓦X )=1.49953) = 0.07141 Z=/o+同M+eVariablePa rameterEsti mateStandardErrorType II SSF ValuePr > FIntercept6.086590.2722535.80742501.46<-0001xl-0.034690.006731.8987226.59<.0001Bounds on condition number： 1, 1y = 4+4X+& A = XJ = 2XX2yX3Y = j3()+PkXk+fiX1+h g c e 萬斤SS&a

30、mp;X/X）心成立以：& =。（八123"月“（M）",23 - 3）P不 S-乂)丁=p(F(l, 20) > 月)伏= 2,3) X2 F . MSE5,占> p p = 0.0258 <a£ =0.10 乂？ x( XX2Y = p.y+pxX+p2X2+sStepwise Select ion： Step 2SUt ist ics for Entry DF = 1,20VariableToleranceModel R-SquareF ValuePr > Fx20.7822760.65795.800.0258x30.7523

31、000.65535.600.02S2Variable x2Entered! R-Square = 0.6579and C(p)=2.7967X,一尸=區(qū)=,_SSR(占_r： _XltX2F 1 MSE(XX。1' MSE(XX：) - p；r；p)=尸(尸(1,20)之百)p = P(F(1,20) > F) X3 F Fi -5-80P=0.0258<aD =0.10 x、,X2 X1,X?Y =d+4X1+dX?+8, A = XX2y 1 = 3Analysis of VarianceSum ofMeanSourceDFSquaresSquareF ValuePr

32、> F1.117900.0581219.23<.00012 o222.235811.162443.39825Mode IErrorCorrected TotalVariableParameter EstimateStandardErrorType II SSF ValuePr > FIntercept7.391450.591129.08751156.35<0001Xi-0.026980.006860.8983815.460.0008x2-0.031510.013080.337035.800.0258Bounds on condition number： 1.2783,

33、5.1133Statistics： for Removal DF 二 1,20VariablePartialR-SquareModel R-SquareF ValuePr > Fxl0.26440.393615.460.0008x20.08920.55875.800.0258XX2第三步，第二步選擇模型y=&+gX+&X2+£, a=x,x2, 1=3,3進：對不在模型中的自變量X3,逐個添加到此模型中，擬合相應(yīng)模型丫 =鳳+4乂4+力乂+&*2+&假設(shè)”0% ；瓦=0 (左= 1,2),計算各自偏x統(tǒng)計量3)= 5S/?(XJXpX2) F(1 234),相應(yīng)的 ：3)= P(F(1,19) &g