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2、0?8?Lfl?8?.?1?8V?8A?83?L8?!;.58?A:d3(J?Jn?8?.?aqu;.?SNJL!?&E?(SAS/STATu?8?PLSL0?8?Lfl?8?.?1?8V?8A?8pCY1,YpmgCX1,Xm?K?8?k3gC8J?1T1(T1X1,Xm?5|U/J?gC8?C&E);3C8J?1U1,T1U1?,?CY1,YpT1?8.XJ8?KKUY1?J?U?egC8J?rT1,T2,Tr?8LY1,YpT1,T2,Tr?8,?2LY1,Yp?gC?8=?8.?8V?8A?8pCY1,YpmgCX1,Xm?K?8?k3gC8J?1T1(T1X1,Xm?5|U/J?gC

3、8?C&E);3C8J?1U1,T1U1?,?CY1,YpT1?8.XJ8?KKUY1?J?U?egC8J?rT1,T2,Tr?8LY1,YpT1,T2,Tr?8,?2LY1,Yp?gC?8=?8.?8V?8A?8pCY1,YpmgCX1,Xm?K?8?k3gC8J?1T1(T1X1,Xm?5|U/J?gC8?C&E);3C8J?1U1,T1U1?,?CY1,YpT1?8.XJ8?KKUY1?J?U?egC8J?rT1,T2,Tr?8LY1,YpT1,T2,Tr?8,?2LY1,Yp?gC?8=?8.?8V?8A?8pCY1,YpmgCX1,Xm?K?8?k3gC8J?1T1(T1X1,Xm?

4、5|U/J?gC8?C&E);3C8J?1U1,T1U1?,?CY1,YpT1?8.XJ8?KKUY1?J?U?egC8J?rT1,T2,Tr?8LY1,YpT1,T2,Tr?8,?2LY1,Yp?gC?8=?8.?8V?8A?8pCY1,YpmgCX1,Xm?K?8?k3gC8J?1T1(T1X1,Xm?5|U/J?gC8?C&E);3C8J?1U1,T1U1?,?CY1,YpT1?8.XJ8?KKUY1?J?U?egC8J?rT1,T2,Tr?8LY1,YpT1,T2,Tr?8,?2LY1,Yp?gC?8=?8.?8V?8A?8pCY1,YpmgCX1,Xm?K?8?k3gC8J?1T1(

5、T1X1,Xm?5|U/J?gC8?C&E);3C8J?1U1,T1U1?,?CY1,YpT1?8.XJ8?KKUY1?J?U?egC8J?rT1,T2,Tr?8LY1,YpT1,T2,Tr?8,?2LY1,Yp?gC?8=?8.?8V?8A?B,bpCY1,YpmgCX1,XmIOzC.C|gC|?ngIOz*?OPY0=y11y1py21y2p.yn1ynp,X0=x11x1mx21x2m.xn1xnm.y30?8?N?8V?8A?B,bpCY1,YpmgCX1,XmIOzC.C|gC|?ngIOz*?OPY0=y11y1py21y2p.yn1ynp,X0=x11x1mx21x2m.xn1

8、1x12x1mx21x22x2m.xn1xn2xnmw11w12.w1m=t11t21.tn1,?8V?8A?8?N(B)T1U1?d|C8?IOz*?X0Y0,O1?OPt1u1:t1=X0w1=x11x12x1mx21x22x2m.xn1xn2xnmw11w12.w1m=t11t21.tn1,?8V?8A?8?Nu1=Y0v1=y11y12y1py21y22y2p.yn1yn2xynpv11v12.v1p=u11u21.un1,1T1U1?Cov(T1,U1)1?t1u1?S5O?(A)(B)z?4K(=wT1XT0Y0v1 wT1w1=kw1k2=1,vT1v1=kv1k2=1.?8V?

9、8A?8?Nu1=Y0v1=y11y12y1py21y22y2p.yn1yn2xynpv11v12.v1p=u11u21.un1,1T1U1?Cov(T1,U1)1?t1u1?S5O?(A)(B)z?4K(=wT1XT0Y0v1 wT1w1=kw1k2=1,vT1v1=kv1k2=1.?8V?8A?8?N|.KFfKz w1v11=wT1XT0Y0v1K?)LLOm?M=XT0Y0YT0X0?A?A?M?A?21A?A?)w1?v1dw1O?v1=11YT0X0w1.3SAS/STAT?PLSLw1=(w11,w1m)T?.?A?-(Model Effect Weights);v1=(v11,

10、v1p)TC?-(Dependent VariableWeights).?8V?8A?8?N|.KFfKz w1v11=wT1XT0Y0v1K?)LLOm?M=XT0Y0YT0X0?A?A?M?A?21A?A?)w1?v1dw1O?v1=11YT0X0w1.3SAS/STAT?PLSLw1=(w11,w1m)T?.?A?-(Model Effect Weights);v1=(v11,v1p)TC?-(Dependent VariableWeights).?8V?8A?8?N(2)Y1,YpT1?89X1,XmT1?8b8?.(X0=t1T1+E1,Y0=t1T1+F1,t1n?,T1=(11,

11、1m),T1=(11,1p)OC?kgC?8?.?E1F1Onmnp?.8X1,1?O(T1=(tT1t1)1tT1X0,T1=(tT1t1)1tT1Y0,1=XT0t1|t1|2,1=YT0t1|t1|2.3PLSL1=(11,1m)T?.?A1(Model Effect Loadings).?8V?8A?8?N(2)Y1,YpT1?89X1,XmT1?8b8?.(X0=t1T1+E1,Y0=t1T1+F1,t1n?,T1=(11,1m),T1=(11,1p)OC?kgC?8?.?E1F1Onmnp?.8X1,1?O(T1=(tT1t1)1tT1X0,T1=(tT1t1)1tT1Y0,1=X

12、T0t1|t1|2,1=YT0t1|t1|2.3PLSL1=(11,1m)T?.?A1(Model Effect Loadings).?8V?8A?8?N(3)?E1F1“OX0Y0,?2-EPX0=t1T1,Y0=t1T1,K?E1=X0X0,F1=Y0Y0.XJ?F1?Cq0K1?8vI?K?E1F1“OX0Y0-E=?w2=(w21,w2m)T,v2=(v21,v2p)T,O1?T2U2?-?8V?8A?8?N(3)?E1F1“OX0Y0,?2-EPX0=t1T1,Y0=t1T1,K?E1=X0X0,F1=Y0Y0.XJ?F1?Cq0K1?8vI?K?E1F1“OX0Y0-E=?w2=(

13、w21,w2m)T,v2=(v21,v2p)T,O1?T2U2?-?8V?8A?8?N?t2=E1w2,u2=F1v21?2=ET1t2kt2k2,2=FT1t2kt2k2OX,Y?1?1k(X0=t1T1+t2T2+E2,Y0=t1T1+t2T2+F2.?8V?8A?8?N?t2=E1w2,u2=F1v21?2=ET1t2kt2k2,2=FT1t2kt2k2OX,Y?1?1k(X0=t1T1+t2T2+E2,Y0=t1T1+t2T2+F2.?8V?8A?8?N(4)?nm?X0?r min(n1,m),K3rt1,tr,?(X0=t1T1+trTr+Er,Y0=t1T1+trTr+Fr.?X

14、i(i=1,m),Yj(j=1,p)LIOzC,rTk=wk1X1+wkmXm(k=1,r)“Yj=1jT1+rjTr(j=1,2,p),=?pIOzC?8:Yj=aj1X1+ajmXm(j=1,p).,?2?C?8Yj=aj0+aj1X1+ajmXm(j=1,p).?8V?8A?8?N(4)?nm?X0?r min(n1,m),K3rt1,tr,?(X0=t1T1+trTr+Er,Y0=t1T1+trTr+Fr.?Xi(i=1,m),Yj(j=1,p)LIOzC,rTk=wk1X1+wkmXm(k=1,r)“Yj=1jT1+rjTr(j=1,2,p),=?pIOzC?8:Yj=aj1X1+a

15、jmXm(j=1,p).,?2?C?8Yj=aj0+aj1X1+ajmXm(j=1,p).?8V?8A?8?N(4)?nm?X0?r min(n1,m),K3rt1,tr,?(X0=t1T1+trTr+Er,Y0=t1T1+trTr+Fr.?Xi(i=1,m),Yj(j=1,p)LIOzC,rTk=wk1X1+wkmXm(k=1,r)“Yj=1jT1+rjTr(j=1,2,p),=?pIOzC?8:Yj=aj1X1+ajmXm(j=1,p).,?2?C?8Yj=aj0+aj1X1+ajmXm(j=1,p).?8V?8A?8?N(5)(?l.e,?8I3?rt1,tr58,?”?,cl(l r)

16、,=?U?8?.?eA:?y1?y?y?y?8V?8A?8?N(5)(?l.e,?8I3?rt1,tr58,?”?,cl(l r),=?U?8?.?eA:?y1?y?y?y?8V?8A?8?N(5)(?l.e,?8I3?rt1,tr58,?”?,cl(l r),=?U?8?.?eA:?y1?y?y?y?8V?8A?8?N(5)(?l.e,?8I3?rt1,tr58,?”?,cl(l r),=?U?8?.?eA:?y1?y?y?y?8V?8A?8?N(5)(?l.e,?8I3?rt1,tr58,?”?,cl(l r),=?U?8?.?eA:?y1?y?y?y?8V?8AA12.1xEW20c?n

17、)nIweight(N-)!waist(?)!pulse(),nIchins(m)!situps(?)!jumps(ap)?8dn)nIOnI?8?.?O(J?1.Ln)nInI?X1N-X2?X3Y1mY2?Y3ap119136505162602189375221106031933858121011014162356212105375189354613155586182365641014272113856810138?8V?8AALn)nInI?X1N-X2?X3Y1mY2?Y3ap8167346061254091763174152004010154335617251250111693450

18、171203812166335213210115131543464142151051424746501505015193364667031162023762122101201717637544602518157325211230801915633541522573201383368211043?8V?8A)SAS/STATPLSL?1?8IOz1O?8)?t1,tl,u1,ul,9?8pC?(J(J11.111.3.SASStitle xEW?8;data d1121;input x1-x3 y1-y3;label x1=N-x2=?x3=y1=m y2=?y3=ap;cards;191 36

19、 50 5 162 60 189 37 52 2 110 60 193 38 58 12 101101 162 35 62 12 105 37 189 35 46 13 155 58 182 36 564 101 42 211 38?8V?8A)SAS/STATPLSL?1?8IOz1O?8)?t1,tl,u1,ul,9?8pC?(J(J11.111.3.SASStitle xEW?8;data d1121;input x1-x3 y1-y3;label x1=N-x2=?x3=y1=m y2=?y3=ap;cards;191 36 50 5 162 60 189 37 52 2 110 60

20、 193 38 58 12 101101 162 35 62 12 105 37 189 35 46 13 155 58 182 36 564 101 42 211 38?8V?8A56 8 101 38 167 34 60 6 125 40 176 31 74 15 200 40 15433 56 17 251 250 169 34 50 17 120 38 166 33 52 13 210115 154 34 64 14 215 105 247 46 50 1 50 50 193 36 46 670 31 202 37 62 12 210 120 176 37 54 4 60 25 157

21、 32 5211 230 80 156 33 54 15 225 73 138 33 68 2 110 43;proc pls data=d1121 details cv=one nfac=2;model y1-y3=x1-x3/solution;output out=outpls yscore=u xscore=tpredicted=yp1-yp3;run;proc print data=outpls;var y1-y3 yp1-yp3 t1 u1;run;?8V?8A12.1xEW?8The PLS ProcedurePercent Variation Accounted forby Pa

22、rtial Least Squares FactorsNumber ofExtractedModel EffectsDependent VariablesFactorsCurrentTotalCurrentTotal169.478169.478120.944720.9447222.669492.14752.949123.893837.8525100.00003.771827.6656l12.1wdgC|?1kTk(k=1,2,3)X=(X1,X2,X3)T(?.?A)C?zO69.4781%,22.6694%7.8525%.?Tk(k=1,2,3)C|Y=(Y1,Y2,Y3)TC?zO20.9

23、447%,2.9491%3.7718%.ddT2,T3Y?)Uf?.ddI?T1v?.?8V?8A12.2xEW?8Model Effect WeightsNumber ofInnerExtractedRegressionFactorsx1x2x3Coefficients1-0.598464-0.7825500.2423480.54905120.584054-0.707666-0.8427930.36068130.657469-0.2870580.6966580.693060Dependent Variable WeightsNumber ofExtractedFactorsy1y2y310.

24、6133070.7469720.25668520.7485170.6470490.14508630.6886030.657104-0.306659?8V?8A12.2?.?A?-wk(k=1,2,3)C?-vk(k=1,2,3)Xk=1?T1U1T1=wT1=0.5985X10.7826X2+0.2423X3,U1=vT1=0.6133Y1+0.7470Y2+0.2567Y3.12.3Model Effect LoadingsNumber ofExtractedFactorsx1x2x31-0.656377-0.6663400.3537802-0.015877-0.284692-0.95848

25、830.657469-0.2870580.69665812.3?.?A?Kk(k=1,2,3).X1=(0.656377,0.666340,0.353780)T)nIX1,X2X3uT1?8X.?8V?8A12.4?y(?1Cross Validation for the Number of Extracted FactorsNumber ofRootExtractedMeanFactorsPRESS01.05263210.99682921.046888Minimum root mean PRESS0.9968Minimizing number of factors13PLSL?y?1?y(?

26、(=?f)?.O(J?f,?,?0.9968.?8V?8A12.5f1?8?OParameter Estimates for Centered and Scaled Datay1y2y3Intercept0.00000000000.00000000000.0000000000 x1-.2015249745-.2454453490-.0843434721x2-.2635136754-.3209438740-.1102873645x30.08160764630.09939322540.0341549342Parameter Estimatesy1y2y3Intercept29.2001686430.2510765150.4807263x1-0.0431468-0.6219668-0.1751653x2-0.4350463-6.2712454-1.7661788x30.05983060.86246500.2428971?8V?8A12.5f1?8?Od11.5?CY2?IOz89?C?8OY2=0.2454X10.3209X2+0.0994X3,Y2=430.25110.6220X16.2712X2+0.8625X3.8X2(N-)X3()?K?S.

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