实用多元统计分析答案11

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1、278Chapter1111.1(a)Thelineardiscriminantfunctiongivenin(11-19)isA(_-)'8-1AIX=aXY=Xl-X2pooledwhereS~moo=(_:-:isothethelineardiscriminantfunctionis((:i-(:iH-:-:1z=¡-2~=-2Xi(b)Al(AA)l(AIAI)'8m=-Yl+Y2=-aXl+aX2=-22Assignx~to'11ifYo=(27)xo~rñ=-8andassignXoto'12otherwise.Since(-2O)xo=-4is

2、greaterthanrñ=-8,assignx~topopulation'11-27911.2(a)'11=Riding-mowerowners;1T2=NonownersHerearesomesummarystatisticsforthedatainExample11.1:Z¡-(I:,,:::1'Z2-1::::15,-(~::::::-I:::::1'82=(200.705-2.5891-2;5894.4648pooled-,8-1pooled=-7.2044.273.00637.24475_(.276.675-7.204i(.00378AJ0637

3、1Thelinearclassification'functionforthedatainExample11.1using(11-19)is.006371rJ'x=L.100.785:.20.26717.633.00637.24475((109.475i-(87.400i)i(,00378where11ri=2"(Yl+Y2)=2"(â'xi+â'X2)=24.719280(b)Assignanobservationxto'11if0.100x¡+0.785xi~24.72Otherwise,assignxto'12Herearetheobservation

4、sandtheirclassifications:OwnersNonownersObservationa'xoClassificationObservationa/xoClassification123.44nonowner125.886owner224.738owner224.608nonowner326.436owner322.982nonowner425.478owner423.334nonowner530.2261owner525.216owner629.082owner621.736nonowner727.616owner721.500nonown

5、er828.864owner824.044nonowner925.600owner920.614nonowner1028.628owner1021.058nonowner1125.370owner1119.090nonowner1226.800owner1220.918nonownerFromthis,wecanconstructtheconfusionmatrix:PredictedMembership'11'12TotalActual11112membership:~j21012(c)Theapparenterrorrateis1~~i2=0.125(d

6、)Theassumptionsarethattheobservationsfrom7íiand7í2arefrommulti-variatenormaldistributions;withequalcovariancematrices,Li=L2=.L.11.3l,Nened.t-o'ShuwthattheregiunsRiandR2thatminimizetheECMaredefid281bythevaluesxforwhichthefollowinginequalitieshold:Ri:fi(x);:(C(lj2))(P2)h(x)-c(211)PiR

7、2:fiex)~(cC112))(P2)h(x)c(211)PiSubstitutingtheexpressionsforP(211)andp(ij2)into(11-5)givesECM=c(211)Pirfi(~)dx+c(li2)p2rh(x)dxJR2JRiAndsincen=RiUR2,1=rh(x)dx+rh(x)dx'JRiJR2andthus,ECM=c(211)Pi(1-k.ifi(x)dx)+c(112)p2~ih(x)rixSincebothoftheintegralsaboveareoverthesame.region,wehaveE

8、CM=r(c(112)p2h(x)dx-c(21l)