Lösung zu Übungsblatt 4
Transcrição
Lösung zu Übungsblatt 4
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F{ tl rct<,.{^y 1."[ i"{ il r,,^-. rit\l "urc\ , clc^ss Cr\,csg H t4 { sir-l' "''lnt-cL,.t-,, I Ha u ptkom ponente lyse na na m it Kova ria nzmatrix: $cree F,l*t *f eiseffire*us$ a;ffier F*a fr* In, ,al 3 w ,E* ,6i .9 :lll iltiiiiililillilliliiiiii|ii s596cti Mean Ha u ptkom ponentena na -&- Eig,envalu:es lyse mit Korrelationsmatrix: Screq F$*t ,*f eigenvtr$u*s s,frer Fn& f{l ,IIl ,61 *E! .8fi ,{u .9 lll. 9596 Mean Cl -#- Eigefltral,u:es Cornponent loadlngs .8 Iil-r 1.; E ll} c fi-rSlriE[-tl &"'{ E ur\ frmlxhaie! Enagp+{ss b # ,; { \t +N {t qG rrr E F,. 6q (Jd a Fe o E9 ()d -$ -l -,5 0 f'l' +il g + Be e h€igideft 9o Fcl '0 5"i leelt. .. b€rgrlr€t{ E"r ti, t s -.5 it 3, tfr !* a 4* t €4 €t I !+ a re€trrl=tl t + :upFba{Ce l(3 *{ g ocv (t cL. Fsi frsbstsdffr :iGit*tltfid ,t) htrighdlt + heishtighi 5 (J, c,u (g *o "'r q ..5 0 Cornpone,nt I -5 $ + heighiietl neig.htriEht a -.2 0Cor*ponent .a .4I "6 t Ecv a ..t p {J; r ffprnpcnent tasgf.ll tsRgin + fa e'q 5; 5cr E. fo o eF 3B (o a -.2 0.e { $ Cor.nponent 2 1, (S .4 diago:r'El .5 1 r-, E!q $s*re v*ri,e,,bks {pcs} u $ .t r+ i o ItBls$.slff ."2 0 ? ".s ..4C*r*p,neat 4 S Ccrnponr,nt :fu ; qfr Ecr o !* -.s -.1 -.2 0 .2 Ctmpo:nent 4 ,5 (o ?t fi I 'a h€iehiidi ()Er Cornponerd 3 l€n8th ' *"r .o Io.- h€i€h.il&li + heig,hkighr , PslsDsg*a fr,upptwcx $ ga lrnSti t Cornper:r*nt SEifF-dise e 6 *w 6' ,$ .t 4 -- to go fg 0 Cs,rnp€oenl 3 U? i disrnrl '- Compo*ent u -.20.2,46.6 . C:orngorrcnt.Z b': E E po E*'r E-,e.i g, .8 Compenent ? 1 <i cCl F-*r F' aq (}d -.3 S .2 .4 .6 s Qqrnftpeflenl E Pc: *ur o' {t 9rn I to f'l qt g 6 a Eornpenent,:1 .!f tft g(} gF qd E ^S Bank. I og 1og: u:\Ubung4\Bank.log log type: text opened on: 18 lun 2011-, t4:00:21/ O n '., Jr .* * fr :k -.t * fr :t :t :'r Jr Js :t Jr Jr :t :k :k /r /z\ Js :t :? t'; Js :! Jr Jr Jr * :t x/ /* HAUPTKO 4 UBUNG :'r :t :t Jr * :t :t J.' * :t :l * * :! :t :t Jr Jr * :t Jr * rt :t :'r * :t :t Jr '* :! :! Jr '* rl Jr r; * * / 1r/ MPONENTENANALYSE tr/I ***rx:'c:.L:t*Jx:t***:t*z'i:t:tJlru!'k******J.r**// /***J,r***:'..:t**.,t***-:***-^L*:t**********':t*;k:'.',,t*****:1 t 1{6 & & & ri...iJ. * rL .i -L J. J. rr. .L J. .!. / if & ?. J. ii.t & .L 6 & ^ ^ ^ / /* 0. Preliminary x/ /l & J,.r. rL & J..r, rL & J..r..L r ^ ^^ t -.- & J-J..L /-i-6-d--z..i.r^.r.r / / * Daten ei nl esen use "U:\Ubung4\Bank.dta", clear Vc,r,*rg", J. & & .L .L & .L * Jr ;k ;t / * *x & ii7i?iZi7r7i?i7;7iAX7t7iz.6 lfi & /7i t -L & .r- rt *.r, .t + +.... -q xii L.r.'^".tii:i-;?;7;z;-,.--dzi6-^--d-a /'x 1-. Jr -+ * he'i 0,*l(c,^-\ _ ur^[ /. J' f J: J-r -L .L J..r. rL + J..i..tr 6 + J"r' ^ & - -.i ^ ^ / ^ ^ ^ ^ 1- Hauptkomponentenanal yse . mi pca 1 ength gtc^^,<lr.lrr:\caic. i'r r" & r' r' t ?i *ri *- :l -" * :tr. J.. "'^ ^ ^ '. / Hauptkomponentenanal yse /'" 1. * J< Vsr, rour<).c qC:c\.trlq t ic"r.^ J.,. i b*V. htj,,; r-,,,i\ .,\(, n^c{ ghtl eft hei ght t 'rouu rt anzmatri x rl gW frml owborder frmuppborder ltumber eri nci pa1 components/covari ance ruumber Trace -sEs- assume mul ti vari ate normal i sE of obs of comp. ' I 6 !. j''' 0 ' 000 L;*t!211 q'999 . ts8Ooz .2887648 0.000 |l.t11l9l1 .rsolroe .2300068 . . i:u9i.9iii1i9.99l1l9:1!:l9---::l99__ nu.,o o.3333 kg'D I?11-!:il:-lllH1l1 : I l'mi:lriia:ri 4.494725=LA', - --- 0.000 | .orsotsr Io.ig i :rg+olsz 0.000 | oaas0r6 zr ro. 3423 oos oasiiir i I L 200 = (Rho) 4- i compl = = = :t Hc i-nn-:-O- Goer)---*1:-tii: --=-+------\--.-/eisenvalues I - -^: -^ ^---- .2998663 1-0.013.0003q5 compl- | :etIotq6 :oeioiqq iq.pq .;.bt a;rbt i : 1414114 . o2irisg 10. s2 comp4 comp5 diagonar,@ Rho ty L]rrrn"t\vc"tcnlr^^n"9 _q_/te^x+ut!-^.^- ^ -. M*, n nn- J .085889 .LoLs627 ^rtr* r-1-12834 .7038607 ,i,i| (ffi,,H}iti[i 121-983 ili|iii fl,HflH l,iiiigii -.6402603 .l-670981- . . .832749L .2815493 -.5L7 5436 e,eee L=*:-ss-#4+ L::l:!!i!liii i sl:e111.!l?---:19,f -------s*-'It"*1-*Je-r+tl--5-k;:;-s"FT[;" ;t 4u-at.,? = 0 !i"lu^"s comoz f -.01070es .oirrier -g..Zl .*:'": .r.rsrr, i _Cmf _..?i22?r?i :3i3i313 0o-. E;',!t&s5 . ffi!#iif,iiiifii @P::iili:i ;iii, fi,flii "iili\iZ ',:e:itt; 5(1G- {:i*fL^:s u^f L.Ht4 9.."^ t,a-3tf cu.^ [ 2, HYt is! rclat'..l S-^l St)&, €.; *\ia:> / ^^t i ,r( .034834 litiblon 0.000 - .727s634 - . sel0166 r fi-s#> .04sz8ss L0.7e 0.000 .3ee7844 .s773004 i 6@ryt L iliagonat--+-----=:---- (f rmunoborder comp3 .3447 349 .21_8021_5 . 5 566841 . Comp4 (-f rmuppborde . 561_6896 . r 0 . 076 - .0340297 - .0302863 0.01-2 .47 6027 4 0.001_ .0860889 .2703s22 .4229622 0.A79 0.000 0.000 .6866664 .5482105 .6L34423 .349954L .84301_6 .760s61_9 ,7980942 . 32 528s 1206168 4 .66 0.000 0.000 .276s569 .6343586 0.001- .1-802733 .6503866 0.01-3 - . 3321-532 - .0400654 .4554578 .09L2776 4.99 .41_533 .11-99291" 3 .46 - .1_861-093 .0745L36 -2 . 50 - .4507004 .1780348 -2.s3 di agonal Comp5 r_460904 .086124 . s9L7 62 (' l ength heishtleft J heightright II frml owborder L.77 L.75 2 . 513 .24 3.81 6.87 .1838544 .L47 57 84 .L370982 .0673r_38 .32631_83 . 2 589621- 0_._011- - .7996422 - . 1017s85 ' - - - - l'fA;--:!:lt:gl.--:1!:1:g:----:'.-1,--@-).-_91!20-23.1-].070]-8 ^JtuaJ-.;I lltlD. z.-.8s41325 -.6s1_0153 - .7s25739 .051_81_66 -L4.52 0.000 .20386s6 .489737 . 3468013 .A729277 4.76 0.000 .408s881- .66071-1-8 . 5346499 .0643185 8. 31- 0.000 -.1_5L9478 - .0479873 - .0999675 .026521- -3 .77 0.000 -.20824L8 .0044384 - . l-0L901-7 .0s42 s61- -1-. 88 @T@) .0844s9s .04s91-64 1-. 84 @b -.0055349 ,L744539 Ei _ 1 ength f I hei ght-left I heishtrisht (frml owborde r frmuppborder di agonal I o&tT o'vtv\ '/ ' U"^- E ihlu'lli -'---. 1engthi-.0980959.063301-5.]..55@,/_.222L646'025g72g hei ghtl eft I .4329975 23.23 0.000 / I . 701-83817018381_ .831-l-861.831_l_861 ..7665L2L 7665LzL .A329975 {(. hei qhtri qht I - .6316969 .0459089 -L3.76 A.000 A.OA0 / /I - .72L6766 - .54L7L72 heightright frml owborde r I 1-.39 39 @-. 16D/ --.0091-931frmlowborder .0091-931- .0s36271 .0536271 .0222L7 .0L60259 1_. Q_.10Q/ frmuppborderi.q11qt91.9?7?+9+)[email protected]?q11 diasonal I .0456795 .0235441 1-.94 (Q.052) -.000466 .091-8251 LR LR test for test for i ndependence: chi 2 (15) = chi 2 (20) = sphericity: i1-n Expl ai ned vari ance by compone fts /411" Components I rigenvalue rroporti on- SE_Prop 0.667s 0.0266 0. 2082 0.021-6 0.0542 0.0064 0.0433 0.0051_ 0. 01_90 0 . 002 3 0.0079 0.001_0 .000305 .93s6206 .2434L34 .1946587 Compl 3 Comp2 Comp3 Comp4 Comp5 Comp6 .08521-21 . 03 5 51-48 prob Prob 51_1_.57 1-203.40 chi2 chi2 = = Bi as sE_cum 0.6675 0.0266 0 .87 57 0.01-08 0.9298 0 .97 3L 0.99211_.0000 .0497 82 - .00327L 0.0066 0.0027 0.00r-0 0.0000 .0a27 s3 - .0061_54 - .002016 - .001_094 :t 1-. 1-. 1- Erkl irungsgehal t de r vari abl en mat MEig=g(11 /* speichern der rigenvektoren (gamma)*/ mat MEV=€(rv) /* spe'i che rn de r Ei genwe rte (l ambda) */ sum 1 ength Variable length I 0bs I 200 Mean std. 21,4 ,896 Dev. .37 65542 seite 2 Min 213.8 0. 0000 0.0000 MAX 2l_6. 3 Bank. I og . scalar lvar=r(var) /* speichern der Varianz der Ldnge*/ . scal ar rho=MEi g [1, 1] * (rqrv [1, 1] . display rho =(25 -.201_36085 /lvar) n(L/2) /*eerechnung X Le,^^1t\,y4 . , . . . . )l. saved) / = 0,*4r,n L.L.2 Sc reepl ot . screeplot, scheme(s2mono) @@f . graph save scree, replace (file scree.gph von rho(xl, ,yL)" ^,^^ u^i{ 4rttc\'^:'--\ & !,,l.an r,i,ntc,, vutll * 1-. l-. 3 Test-Stati sti cs mat UMat=l(5,1-,0) mat pMat=J (5,1,0) local lnbar=MEV[1,6] local sumln=ln(urv[1,6]) forvalues k=2/6 { local 2. O*r-t,-r,^^ o\ k' ) ) o (exp ('1 npar ')+(L/ (' (.' :1) ) *MEV [1, 6- k'+1-] ) ) I nbar=l n ( ( (' k ' - t) / ('-suml Ug .^^^] n=' suinl n '+l n (tttEv [1, 6-' k'+1] ) I ochl 3. mat UMat[-k'-1,1]=(200-(2't6+11)l6)o('k'*'lnbar'-'sumln' ;} 4. 5. ptun X) -1) t' (' k'+2) I ocal v=(L/2) n ('.k' t-1, = ('v' k' uMat 1] I pMat 2tai -1, 1] mat [ ) , 6. =chi ['k \ 7. r Jw.1 ) . matlist uMat I r1 r2 r3 r4 r5 cl- 910. 8444 973.9544 996. 9272 1067. 311430.L77 luR. . matlist pMat I c1 r1 1-.6e-1-98 r4 r5 5.6e-21-9 3 .8e-291- r2 r3 2 .6e-208 7 .9e-209 I /.c1 -= P(uo.@X \ ) ';t x ^' wv X\/ 5 f,,^J.r&5;e"te [lI^la^., ( '. "* x L.2 Hauptkompongnlenanal yse . mi t Korrel ati onsmatri . pca lenqth heibhtleft heightright frmlowborder frmuppborder diagonal, VC e (normal ) (with pcnTcorrelation, sEs and tests are approximate) seite 3 erincipal Bank.l og- on components/cor rel ati t'tumber of obs = ot'o'o' +l:::" nho 200 = = 3 1' 0000 norma'lity !r,.rr*4p,Gr r,..i.\{, crc -"&'ol3o*r,..L,a'a\;< \JUP -f--------------------:l heu..^"\rc+ '----'---/'--z e>lzl / [95% conf' Intervall coef. std. ey'r. .r,,,\ I -- -- -- - - - - - - --:;:::-:;-::--T-----------/------7 sEs assume mu'ltivariate eigenvai:nrlil:3iffiii@il.?ig*P'iqi?itiiiiiiqi 1;9J791.? .86b0iZq :Qel9qlt ]9.1t 9.999 -\91*711 cil[; i .3640284 0.000 i-0.28 .0437462 :44016ti a;m'p4 i '.zosoi7l 0z t?29 i-0 4s 0 .000 .2L826LL .s3ss1-0s 31-90931 co*ps ::1r9 Compl 1 i . i :19::!?a __:!11?::1----19::9---9:999- :I1!9:9--- -:!!!!1??- 0.920 -,L435747 .L295988 0.000 .398531-2 . s3698510.000 .4270204 . s463366 0.000 .3243527 .4891-643 .367891- .A447397 8.22 0.000 .28a2a29 .4s5 579L -.006988 .0696884 -0.10 .+attsffi .035320s L3.24 . +aooTss .0304384 l-s .99 . +ooTsss .042044s I .67 ength hei ghtl eft hei ghtri ght frml owborder frmuppborde r di agonal --- comp2 'length hei ghtl eft hei ght ri ght frml owborder frmuppborde r d'iagonal comp3 1 ength he'ight'left hei ghtr-ight f rml owborder frmuppbo rde r di agona'l Comp4 1 ength he'ightl eft hei ghtri ght frml owborde r frmuppborde r di agonal Comp5 1 ength hei ghtl eft he'ightright frml owborde r frmuppborde r d'iagonal Comp6 1 ength hei ght'left hei ghtri ght frml owborde r . . s ::??1 : ! : --: 9 1 9 M'- --- -!2 :!1 - - -9: 9I I - - - -- : : : 3: 9I 9- - - : (TC;eb .$74zlz zL.zs o. ooo .0s7L723 s .98 o. ooo .0603703 4.l-8 o. ooo - .2662277 . 1-l-57599 -2.30 0.021.0914868 .L476963 -0.62 0. 536 --TTT6 ,742L4L4 .2299LA7 d3"firg'5''6b .Ll 2739402 )J1\ta- vaJJ .0576495 .\tJt 4t .75 " J 0.000 1-1- 0.912 L.L7 0 .24A 2 .L234737 .0794644 1.55 0.1-20 . s83s38 .0720062 8.10 0.000 .03s81-32 -21,.99 0.000 ffi798> .a774s7L L.47 0.L42 =Bffff - .5746L7 .Afi47L3 -1"0.75 0.000 . jgqgzq+ .0944952 4. l-8 0.000 .qiOztr: .091-6367 4.7a 0.000 - .q}latsz .0803006 - 5 .03 0.000 .0951-894 -1-.16 0.247 -.LL02266 . jgrgzgo .0730782 5 . 36 0.000 - .01-76821_ .1-604891- -0. . 1_03 3842 . 08801-5 ::1:9!3-: .8888493 .4 54021-9 .1_341-363 .37A7837 - .4931-1_3 -.3809662 .1_609494 - .039342 s .L979925 .386931L ,3322349 .2968706 .069L225 .27 58909 -.0322737 .27922L2 .4424A85 . 7246675 -.8s7764L -.7L7379L -.0379963 .26s7476 - -.6794188 - .46981-52 .2o97L7L . 5801-31-6 .25A67L6 .609881- . 561061-s - .2462889 -.2967944 .A7634L2 .248699 . 5351-602 .0587933 .0851-09 0.69 0.490 - .1080172 .2256038 0.000 -.8006273 -,47836510.000 .432801-8 .7953974 0.0s7 -.0065686 .4375L7 0.023 .0306665 .4090267 -.6394962 .0822LL3 -7.78 .61_40996 .092 s006 6. 64 .2L54742 .1-l-32892 1.90 .2198466 .0965222 2.28 ---::19I:: :I1:!1 -----a:!!---9:911 -:99:112----:919999: -0.58 0.562 -.1-361-s68 .0740442 .0385594 . 5569319 . s998s36 - .0984479 0.006 .73 .L279L2 -2 . 3491s08 .344693 . 58001-43 .4623537 .060032 7 .7A 0.000 -.031_0s63 .0536237 .2977457 .L322403 2.2s 0.024 seite 4 T frmuppborder diagonal I .4L89688 I .631-7998 Bank. I og 0 .000 7 .4s .05621-63 .0758806 0.000 8.33 .308787 .4830765 .5291_507 .7805231_ LRtestforindependence:chi2(].5)=5LL.57prob> prob 51-3 ' l-6 chi 2 (20) = sphe ri ci ty : aR test for e xp'l ai ned vari ance by components , wo^zr', t* c^\5 ,t itvor --::iry:::::-l-:le::Yil::- -l:2ry/-:!:li:e--::::11:1Y:---l!:!!i-------:li: 0.0201 0. 703e 0.01-ee .008s67 a;rbt i r .278082 o)Tm0. 8488 0.011-s - .011-928 a;r;i i . s090328 0. i-448 a.0L47 0.e737 0.0066 - ' 00s821a;';A i +qwogs 0.07s0 0.0081e68s 0.003s - .00s28 0.00s0 a.a448 a;rbi i .2GBG77L 0.031-s 0.003s 0.1-.0000 0.0000 - .0081-32 a;.b6 i : rasszgz :sil.iii'?iiii!ffii:[lEifi:iiiii:fiiil:fi6iiai . '. * 7.2,2 screeol ot . screeolot. scheme(s2mono) ci mean i"iarpretiris an asymptotic i.iitiifi'ii'"d;iil;ti; of a correlation matrix) iigenvalues . oraoh save scree2, rePlace (file' scree2.gph saved) - o t.Z.l vorhersaqe der lauptkomponenten . toiainqpiot, sih6me(s2mono) factors(6) combined . qraph save loadinq, rePlace (fi] e l oadi nq. gph saved) , scoreplot, scheme(s2mono) factors(6) combined . qraph save score, rePlace (file score.gph saved) . Ioo - cl ose og: u \Ubung4\eank. I og : text cloied'bn: 18 lun 20i-l- ' 14:06:28 'I l : oo tvoe seite 5 theory-based confidence interval of