二次回歸與RSREG課件

正交旋轉(zhuǎn)二次回歸設(shè)計(jì)與RsReg第七節(jié)響應(yīng)面分析當(dāng)試驗(yàn)中考察的指標(biāo)宜于用多元二次回歸方程來擬合因素與指標(biāo)的函數(shù)關(guān)系，就可以分析回歸方程所反應(yīng)的曲面形狀，如果得到的曲面是凸面(像山丘)或凹面(像山谷)這類簡單曲面，那么預(yù)測(cè)的最佳指標(biāo)值(極大值或極小值)可以從所估計(jì)的曲面上獲得；如果曲面很復(fù)雜，或者預(yù)測(cè)的最佳點(diǎn)遠(yuǎn)離所考察因素的試驗(yàn)范圍，那么可以通過嶺嵴分析來確定重新進(jìn)行試驗(yàn)的方向.這就是應(yīng)用較廣，頗有實(shí)用價(jià)值的響應(yīng)面分析法(ResponseSurfaceAnalysis).第六章回歸分析第六章回歸分析第六章回歸分析如果穩(wěn)定點(diǎn)不是理想點(diǎn)就要進(jìn)一步作嶺嵴分析,請(qǐng)看示意圖和例子演示第六章回歸分析RSREG的SAS過程二次型回歸響應(yīng)面分析SAS簡單程序如下:datarubber;inputyx1x2@@;cards;數(shù)(略);procsort;byx1x2;/*對(duì)自變量x1x2進(jìn)行sort由小到大排序*/procrsreg;modelf=td/lackfit;/*選項(xiàng)lackfit要求對(duì)回歸模型執(zhí)行不適合度檢定(lack-of-fittest),預(yù)先應(yīng)先對(duì)自變量進(jìn)行sort由小到大排序*/run;第六章回歸分析PROCRSREG<options>;

（options:data=SASdataset,指明回歸所用數(shù)據(jù)集Out=SASdataset,指明回歸分析所得輸出的數(shù)據(jù)集）MODELresponses=independents</options>;

指定模型，

響應(yīng)變量=自變量/選項(xiàng)（options:lackfif,要求回歸模型運(yùn)行不適合檢定.若選用此項(xiàng),則須先將數(shù)據(jù)集內(nèi)的自變量由小到大排序。Nooptimal,停止尋求二項(xiàng)式反應(yīng)面分析所需的臨界值Covar=n,指定前n個(gè)變量為共變量，所以它們只以一次式類型進(jìn)入回歸模型里。L95，輸出95%置信區(qū)間的下界。U95，輸出95%置信區(qū)間的上界。）二次型回歸RIDGE<options>;脊嶺分析（options:CENTER=uncoded-factor-values給出脊嶺分析的初始值。MAX，輸出脊嶺分析的最大響應(yīng)值。MIN，輸出脊嶺分析的最小響應(yīng)值。RADIUS=coded-radii，脊嶺分析的距離。例如，radius=mtonbyj）WEIGHTvariable;（給指定的變量加以權(quán)重。）IDvariables;指定名稱變量。BYvariables;指定要獨(dú)立分析的變量，此選項(xiàng)須要數(shù)據(jù)集以由小到大排序。二次型回歸程序：dataa;inputnx1-x2y@@;cards;1-1-176.52-1177.631-178.041179.550080.360080.070079.780079.891.414078.410-1.414075.61101.41478.5120-1.41477.0;proc

rsregdata=a;modely=x1x2;ridgemax;idn;run;二次型回歸結(jié)果1：TheRSREGProcedureCodingCoefficientsfortheIndependentVariablesFactorSubtractedoffDividedbyx101.414000x201.414000ResponseSurfaceforVariabley響應(yīng)變量的均值ResponseMean78.408333RootMSE0.372059R-Square0.9671變異系數(shù)CoefficientofVariation0.4745二次型回歸TypeISumRegressionDFofSquaresR-SquareFValuePr>F線性項(xiàng)Linear29.5571510.378534.520.0005方項(xiàng)Quadratic214.8214490.587053.530.0001交叉項(xiàng)Crossproduct10.0400000.00160.290.6102TotalModel524.4186000.967135.280.0002SumofResidualDFSquaresMeanSquareTotalError60.8305660.138428（總均方誤差參數(shù)估計(jì)與檢驗(yàn)二次型回歸EigenvectorsEigenvaluesx1x2-1.9239350.1298960.991528-2.7001280.991528-0.129896Stationarypointisamaximum.TheRSREGProcedure嶺嵴分析EstimatedRidgeofMaximumResponseforVariabley編碼半徑CodedEstimatedStandardUncodedFactorValuesRadiusResponseErrorx1x20.079.9499210.186029000.180.0808990.1851200.1150410.0822160.280.1654920.1826510.2214990.1758230.380.2048610.1794250.3188260.2798140.480.2001070.1768740.4070400.3927110.580.1522150.1770920.4866480.5128580.680.0620270.1826420.5584660.6386690.779.9302410.1960010.6234430.7687800.879.7574260.2188260.6825270.9020920.979.5440340.2516370.7365881.0377621.079.2904300.2940900.7863901.175154典型分析二次型回歸例2

1971年John組織作一試驗(yàn)要求達(dá)某一種難聞的化學(xué)氣味最小，設(shè)表示Odor一種難聞的化學(xué)氣味，T設(shè)表示溫度（Temperature）,R設(shè)表示氣體比（Gas-LiquidRatio）,H設(shè)表示容器高度（PackingHeight）,數(shù)據(jù)如下：編號(hào)溫度T氣體比R容器高度H化學(xué)氣味Odor1400.346621200.34393400.744341200.74495400.525861200.52177400.56-581200.56-409800.326510800.72711800.364312800.76-2213800.54-3114800.54-3515800.54-26SAS程序：title'ResponseSurfacewithaSimpleOptimum';datasmell;

inputOdorTRH@@;

label

T="Temperature"

R="Gas-LiquidRatio"

H="PackingHeight";

datalines;

6640.3439120.344340.7449120.74

5840.5217120.52-540.56-40120.56

6580.32780.724380.36-2280.76

-3180.54-3580.54-2680.54

procrsregdata=smell;

modelOdor=TRH/lackfit;

run;二次型回歸結(jié)果輸出TheRSREGProcedure

CodingCoefficientsfortheIndependentVariables

FactorSubtractedoffDividedby

T80.00000040.000000R0.5000000.200000H4.0000002.000000

ResponseSurfaceforVariableOdor

ResponseMean15.200000RootMSE22.478508R-Square0.8820CoefficientofVariation147.8849

二次型回歸TypeISumRegressionDFofSquaresR-SquareFValuePr>F

Linear37143.250.33374.710.0641Quadratic3114450.53467.550.0264Crossproduct3293.500.01370.190.8965TotalModel9188820.88204.150.0657

Sumof

ResidualDFSquaresMeanSquareFValuePr>F

LackofFit32485.750000828.58333340.750.0240PureError240.66666720.333333TotalError52526.416667505.283333

二次型回歸TheRSREGProcedureParameterEstimateStandardfromCodedParameterDFEstimateErrortValuePr>|t|Data

Intercept1568.958333134.6098164.230.0083-30.666667T1-4.1020831.489024-2.750.0401-12.125000R1-1345.833333335.220685-4.010.0102-17.000000H1-22.16666729.780489-0.740.4902-21.375000T*T10.0200520.0073112.740.040732.083333R*T11.0312501.4049070.730.49598.250000R*R11195.833333292.4546654.090.009547.833333H*T10.0187500.1404910.130.89901.500000H*R1-4.37500028.098135-0.160.8824-1.750000H*H11.5208332.9245470.520.62526.083333二次型回歸TheRSREGProcedure（響應(yīng)曲面點(diǎn)典型分析）CanonicalAnalysisofResponseSurfaceBasedonCodedData

CriticalValue（穩(wěn)定點(diǎn)）Factor（編碼）Coded（非編碼）UncodedLabel（注釋）T0.12191384.876502TemperatureR0.1995750.539915Gas-LiquidRatioH1.7705257.541050PackingHeight

（穩(wěn)定點(diǎn)最小預(yù)測(cè)值）Predictedvalueatstationarypoint:-52.024631

二次型回歸EigenvectorsEigenvaluesTRH（特征值）（特征向量）48.8588070.2380910.971116-0.01569031.1034610.970696-0.2373840.0373996.037732-0.0325940.0241350.999177

特征值全大于0，故曲面有最小值Stationarypointisaminimum.二次型回歸可以作二個(gè)因素的響應(yīng)面圖(固定其它因素),E62的響應(yīng)面圖如下(作圖程序參見SAS操作入門):第六章回歸分析一．正交、旋轉(zhuǎn)回歸設(shè)計(jì)步驟（一）．確定試驗(yàn)的因素及各因素的試驗(yàn)水平的上下限A、B、C．…..（二）對(duì)試驗(yàn)水平的上下限編碼因素試驗(yàn)的下限————》-1因素試驗(yàn)的上限————》1，例設(shè)因素A分為A1,A2兩水平[A1,A2];中點(diǎn):Z=(A1+A2)/2半間隔:H=(A2-A1)/2編碼值:Xi=(Ai-Z)/H編碼值在[-1,1]上.A1=225,A2=375Z=(225+375)/2=300H=(375-225)/2=75X2=(375-300)/75=1X1=(225-300)/75=-1X0=(300-300)/75=0對(duì)1.682=(At-300)/75可求得At=426（三）設(shè)計(jì)試驗(yàn)1.一般p個(gè)變量的組合設(shè)計(jì)由下列N個(gè)點(diǎn)：，，

——2水平（+1和-1）的全因子試驗(yàn)的試驗(yàn)點(diǎn)個(gè)數(shù)-----分布在p個(gè)坐標(biāo)軸上的星號(hào)點(diǎn)，它們與中心點(diǎn)的距離稱為星號(hào)臂——在各變量都取零水平的中心點(diǎn)的重復(fù)試驗(yàn)次數(shù)。它可以只做一次，也可以重復(fù)二次或多次。值表二次回歸正交2345(實(shí)施)11.001.4762.002.3921.1601.6502.1982.5831.3171.8312.3902.7741.4752.0002.5802.9551.6062.1642.7703.1461.7422.3252.9503.3171.8732.4813.1403.4982.0002.6333.3103.6692.1232.7823.4903.83102.2432.9283.664.003.二次回歸旋轉(zhuǎn)設(shè)計(jì)正交通用方案正交N通用N正交通用1241.4141613852381.68223209634162.000363112745322.37859117155(）162.0003632106dataExperiment;inputx1x2Yt1t2;datalines;8017076.5–1-18018077.0–1190170781-19018079.5118517579.9008517580.3008517580008517579.7008517579.80092.0717578.41.414077.9317575.6–1.414085182.0778.501.41485167.93770–1.414;procrsregdata=Experiment;modelY=x1x2;run;TheRSREGProcedureCodingCoefficientsfortheIndependentVariablesFactorSubtractedoffDividedbyx185.0000007.070000x2175.0000007.070000ResponseSurfaceforVariableYResponseMean78.476923RootMSE0.266290R-Square0.9827CoefficientofVariation0.3393

TypeISumRegressionDFofSquaresR-SquareFValuePr>FLinear210.0429550.349470.81<.0001Quadratic217.9537490.6246126.59<.0001Crossproduct10.2500000.00873.530.1025TotalModel528.2467030.982779.67<.0001SumofResidualDFSquaresMeanSquareTotalError70.4963730.070910

ParameterEstimateStandardfromCodedParameterDFEstimateErrortValuePr>|t|DataIntercept1-1430.688438152.851334-9.36<.000179.939955x117.8088651.1578236.740.00031.407001x2113.2717451.4846068.94<.00010.728497x1*x11-0.0550580.004039-13.63<.0001-2.752067x2*x110.0100000.0053261.880.10250.499849x2*x21-0.0400530.004039-9.92<.0001-2.002067SumofFactorDFSquaresMeanSquareFValuePr>Fx1321.3440087.114669100.33<.0001x239.3452513.11508443.93<.0001

TheRSREGProcedureCanonicalAnalysisofResponseSurfaceBasedonCodedDataCriticalValueFactorCodedUncodedx10.27526986.946152x20.216299176.529233Predictedvalueatstationarypoint:80.212393Eigenvectors