solu5 - 7.3 7.4 100 12.000 15 12.000 3.000] 35 5.657 9...

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Unformatted text preview: 7.3 7.4 100 12.000 15 12.000 3.000] 35 5.657 9 5.557 3.333 A A I 123 3.200 A. A 3 8.200 -5.200 y = 25 = fi 351 = 23.400 ; E = y-y = 25 " 23.400 = 1.500 ~ ~ 199 13 25? A' u h 9 I3 257 --5 257 142 9 457 13 9.407 3.533 Residual sum of squares: E'E = 301.467 Fitted equatian: y = -.55? +1.257 z.I Follow hint and note that 5* = Y"r - i?” ‘ VHUEY'V-UZZBN and {n-r-UU2 = if"? is distributed as xii“? n '1 a . A -1. _ _)f(.E z-)o = 2‘2) 2 y - f E z.y ._ J a) V:1 50 «EN ["* “" i=1 JJ 3+1 .1211 - '[ “lament Uzv 5° ' ‘ '4. ——- 'la, Una e h) v” is 002001131 “m 3 d 9 J n n ) -1 -1 .--1 a (‘1 3h)” E 2 A = I z V y ._ 3 Eu {5 v 5) __ ., H J J.1 1: so ' . h . .1 2 V'.[ is diagonal with 3-1:— diagona'l e1ement ! J c) T! - - 1 H1 _ n n E = {z‘v 1:) 1E v g - (j21iyJ/ZJ))J0 Nu .. .. 7.6 G) d} a} First note that A‘ = diagLL;1,...,1.-1 ,0,... 0] is a r1+1 genera‘lized inverse of (1 since ' 1 0 I .- 11“ +1 8 — 1 .- M = 1 50 M h = bl _ = A D U r1+1 Cl 0 "0 Since Z'Z = 1:313:53; = PAP' t" +1 _I (Z'Z)' = i 1; e1e1'. = PA‘P' i=1 " " with PP' = P'F‘ = I , we check that the defining relation holds p {z'z)(z'z)'{z‘2) mmpn'wnp' W PM; AP' = we = 2': b) By the hint, if IE is the projection, E = Z'iz - lg) or z‘zfi = Z‘y. In c), we show that IE is the projection of z . Consider 3i = Agifz 13. for i = 1,2,....r7+1. Then r1+1 1 F:*‘ I MN) 2' = u i M 21-52;)? = Z] Sifli 1:} 1": The {Si} are r1+l mutuaiiy perpendicuiar unit iength vectors that span the space of all linear combinations of the coiumns of Z. The projection of y is then {see Result 2A.2 and n.- Definition 2A.]2] 1+1 r1+1 r1 1£1(3iz)3i = 1.; 3431'!) "' ( .5 See Hint. T15 Hem-.2 -"- —3 A .-1r Efli'HIIIEHI'LJ]:EH}‘HIJIfln=[1 4f. = 3:1 . - 2% 1.5 1 2 5.11 5 -3 41.5 4.11 '— .z u :1 -1 3.5 —1.5 1-5.:J I g n = -. fl = 4 —'I - 3J3 u E - B I T 2 2 2.1 1.5 -.1 5 1 a 1.2 3.11 _—.2 D “rt-5'} + E'E r 55 —15 '- 55.1 -13.5 1.5 51 5 - + .15 21 [—13.5 22.5 -1.5 1.5 I] +5 {(1.10 3} “Sing KEEN“; LT. the 9515 mnfidence interva'l fur the ma.“ rennse is 511'“ by [1, .5] '3.u t 3.13 L? [1.35. 3.?5}. H Using RHIJ'J: LEI. the 95: affliction. frllth’fl fnr' the actual ‘1' 1: given by -. J! U l D. -.5J 3.n : 3.13 1 + [1,.5] 1;?)Dr } u ,1 ,5 3 -.9 [-25, 5.351.: . cJ using [343} a '95: predictinn ei'lipse fer the actua'l 3": 1'5 g'i van by 1.5 1.5 y —z_55 [yD1-2.55, yu2-..r5] [ ] [ “F ] L5' 5.5 3.32— J3 s :1 + .225} (}§%}§%) (:9: - 59.325 {$.12 {IJ best Haem- medium- In I 4:. + ru- H- ._. I -'| 1192? - 4 I: mEan square ermr = cr — u' “ [ 1| H ‘2’, + '9 3 : 'I 1" .1341 'i 1 I 'I J and flatly-mine Invariance In? [If ] given ::2 tn 1:! I 1 9 3 'I B E |: :|-|: :|[‘|II"1 [11.1]8 I: ]. Therefure 3 2 'I 2 1 ' 7.1:! L1 5 iail‘l':The Targa pnsititre cerr-e'iat-Ian between a manager't experience and achieved rate pf return an partfa'lie indicates an apparent advantage For lanaeen with experience.l"':iThe negatitre terrain- tiun between attitude tnmrd Hat and achieved rate at return indicates an at‘plr'ent advantage Far eensewatit-e managers. It} Frau E'i—EBJ r- -r r 3"“: “a 2112 = -31 "'1 - r' 1"'| - 1* $22 2.}:E Rater-"n9 'j‘EflTS pf eapETiente“ Frnm eels-ideratian, ue man have a nasitive terreiatidn between "attitude tut-ard risk" and "achieved return". AFter adjusting for years ef experienct, there is an apparent advantage tp manager: eha take risks. {a} HIHITaa amputer Uutput gives: i - 11.5mm + 2:53:21 1 15.322; residual ten:- of squares -= 2U4995fi12 with 1.? degrees at“ Thu: freedm. a I 34H. Haw far example, the estimated standard dead a- H.596] s“ = HIDE. the estimated standard deviat'iul'lfi of E1 and E2. tipn pf ED 15 Similar :a'ltulatinna give [hi hn ana'lytis at the residua‘ls indicate there are m: apparent mdeI inadequacies . Ire]- The 951 predict‘lua inter-mi '15 [$51.25; 555.235} _ ‘ —1 {.1} Damn; (Mn, F= “zuéggfirz 45-2 =.a25 Since JRa inLDEJ = 4.45 we cannot reject Hafiz - n. It appears as if 22 is not needed in the made] PWVidEd I] 1: included in the made]. 7.16 Fredi :tnrs ...
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solu5 - 7.3 7.4 100 12.000 15 12.000 3.000] 35 5.657 9...

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