key_Exam2_DL - ‘ 1 1 0 ’ 76 1‘ ’ 0 I r it X 5 p DC...

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Unformatted text preview: ‘ 1 1 0 ’ 76 1‘ ’ 0 I \ r it? . X [ , 5) p / DC- +3. ’ ' .V .1; . 777? COIN/“+7644 mon hnwlifil’S 749:6 <éff7/7m7’5m 55/ £41777] \C’I’m'ultw (1/7284 [MI/51cm; of. +Inf’ Fifi/176‘an and fléffongé L/[M/[q/g/a +Y g+:_%~v ' i? fi-gffl%e ( i ‘3"? > “J :1 J 74611,. 74% I71oc‘l7‘lz’iecll X+ awi \f-‘r am 45' 'fpflé‘tv’f f £395 A; L 4“ «70.. f’_ a)? . ‘ '5? «129' 9’5 v my flat 5 ("/mw/lwd} z? 5/ Mé Aid}? (1 7L/Aé’m’ 75‘ Mo i'n 728/) '7Le‘ rm y’m A ‘/ a33' I ‘pgg’ R“ ika: I rkx’ ‘] 4k @35 / ’aéfi 0‘“ A -- A—254 r { 7" .rI/‘O/ 7/7“5/ <{9‘ ‘ r65 Y4 w 01/1? Y; T ’(\~fl.// ] 4y *Od/ /\,, A); O YZYL€ :[C? ] 0-94” 2 Set up the design matrix X and coefficient estimators 3 for each of the following. Assume I) i : 1...4 ' Y1 = 50 + 51X“ + 52X}an + 61' ‘l’ l0 ° 5093? = 30 + fllXil + fi2Xi2 + 6i 0 Yi = 51X“ + fiQXiQ + B3X¢21 + 61‘ ° = [50 + filXil + flQZOQXiQ + 51' 3) For this model Z [30 +/31Xi1 + B2Xi2 assume 2' = 3, set up and compute Compute the correlation between [3’1 and 32. Let _ A; ‘ F i A) Y: I X." X” ; Y= ’Y' «WM— T§= (>é'x) 'XY l Ll X12 Y1 ' >9; x5; t A' $55 SSE ‘ y’Y M Bx‘y / M315 ; T a; AP 2; ‘Huea‘ w,/(‘FH‘I§)): cram ’ Wk wrath I {(5 = 0. l‘ivwetwr (Trice 1:3 amt ~eree u nOWh‘ “)8 (5’~l”‘”0‘“li uompu‘l'e W oo-rfllcx‘txen. 3 These are ANOVA tables for some regressions of Y on four available covariates X1, X2, X3 and n = 100 observations. Model 1: Y 2 fig + 51X1+ fl2X2 + 33X?) + fi4X4 Model 2: Y 2 [3’0 + 3ng + [34X4 Source SS df MSfF SSR 25g .» 91 410 SSE :ic»?7 a26 SST 1mm 77 Fill in the missing values in the tables, including the F statistics. Now test if Model 2 is preferable to Model 1. Then test if Model 3 is preferable to Model 2 or Model 1. ,L/o ; fl, == [33 ‘= Z)“ i) F5: ' __ Mng X‘ )x3l X; ,Y4 ,) __ $42041, {Aged/'2 iSS/VY ,1 ..3 “ ~~ ~ ._ c - 5;; "M MSE (when) 1.43 H‘ a 514,153 > l:aq§(‘fl§> 'l‘ R€j€C+ Ho ‘7 Model / 75 Phe‘lfé/VZLA/f 4o f/o(/€j;2‘ 3) Ho T P4 55’ MLSEUerYS) 3" 3’4 Nam H; ‘> MOM/a rs pwfinb/o 7% MW 3. / w . . ‘- 47 m —Hu. (/6,Vy\(7/)6\+l(944 YMCCLJ“ <91“ Quesflém (j N6 Cam/[ULHEGJ ‘4 /~ g “ 0-9 . ‘. w X 5 V513, L9 ‘ 57W? X‘W (X—WIXy) 4 X4, 9 '0‘? “a; ~a§ ,&9 H : 0]” “0-95 "(1.25" ~ 0.25“ ( 5 09‘ (DJC 5. ’) 5’ w a 2 g” m 1 > a,“ :7 - I ,. g c: t flat 0’ E hm? 0-” 0.19 0.4;“ -025 Va) - 0) r I" r ‘ S 5 C .25 6226 . Link; (JfSVLcU’Ice Di : “6" . PMSE ( ,/,/m); [3 ' ‘T : [9 O [6.074 0007 ' 7/76 ENE/rages «MA: oéswmfiam- 50; +50! ( Y' Y ) - ix -/ 0% W» W We "1% M7?“ WWW 97%43. D71. {/02 7‘ how/w] 00 75 CU“, ‘ . . _ _ fl , C /< 0/157L ( (Jay #Mj [fi)X$)) (flixl) u /EL)?€§‘[ YES/1101 eff€ Ci. 5 True or False and Short Answer: Show work / reasonin [)0 Ina linear model with two covariates, if Corr(X1, X2) = 1 then SSR(X2) = SSR(X1). 2). The MSE is decreasing in number of covariates. 3)- Cook’s Distance for observation 2' equals (yi * 39¢)? ' hm k ‘ MSE (1 — hm.)2 4) o Cook’s distance is the same whether measured between the response variables or the regression coefficients. Extra Credit: Demonstrate that the variance of coefficient j increases with the associated partial coefficient of determination. 50 +5.1) Co,»rx,,.><i)-=z <=> 502454 mm ozék 351209): If 5. (Xi: ’7'): s E 00> -~ 58);?" gs‘H‘Xz) .1) ~ “3 @ MgE :: _ A5 Hug nuw‘lofl/ro’ir covcwia‘tes inc-was“) (WP) cleavage; Mal S’S'E [MCWCLSH as we} 77mg; we Cannd'l: m3 Hmt fie MSE 75 alums Aecrraf‘mr} "va Viulnbm' sf Covafiorltsg, u. f E.‘ IL~ 4 3) t 1 A“ r J” g, ‘ 1 g H t 63 D. - 72’} PM. ’ :4 gag—r") HM. L< g; (I, AV _. [1,1]” A —r A A A A T k M56 (/‘_/1H)L * I V 1 N; 69675 D ‘ (Y‘fi’fl (Y, n“) «3 [Pp/3(2)) x7)“ “[31 )) PME [’MSE ...
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This note was uploaded on 09/01/2011 for the course ISYE 6414 taught by Professor Staff during the Fall '08 term at Georgia Tech.

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key_Exam2_DL - ‘ 1 1 0 ’ 76 1‘ ’ 0 I r it X 5 p DC...

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