Questions with Solutions for Applied Regression Analysis - Exam | STAT 4230, Exams of Statistics

Download Questions with Solutions for Applied Regression Analysis - Exam | STAT 4230 and more Exams Statistics in PDF only on Docsity! SPRTNG 2008, srAT 416230 FrRsr wtroTrRu- wAtvrFrf STUDENT lD NU.MBER'T (This is your 810-number). INSTRUCTIONS jf or alt students: There are four Problems, each with 3 parts. Write.your answers in the space provided: lf you need more space, you can use the back of a page, but clelarly indicate where the continuation of yo"ur answer can be found. Eor all questions, show your work. Foi example, d.on't just answer a question by 'yes' or'no' or"by writing a'number without any explanation. For STAT 4230 students:lnswer any 10 parts. Each has a maxinium score of 1-0 points. (You may attempt more than 10 paris, in which case you will receive credit for your 10 highest scores only.) For STAT 6230 students: Answer all.12'parts. Each has a maximum. score of 8.33 points. 'n Good luck! Ll L 3 b t b I Ia b, c ro fo /toto lo ?q Trw( Nork ) ,f ' PROBLEM 1. A car dealer specializing iii Corvettes..offered a nu.mber of used models for sale at a reopening celebraiion. the saies price jrodnded to the nearest thousandS of dollars) and age (in' -e .years) are shown on page 3 for 15"models. Rlio shown, are a statter plot with the regr6!;sion t' . line irnd some SAS output from the iegression of price on age. ' s'+ ! -.- 1 a) Based on the plot and the SAS ouiput, comment-on the iiroddl. For example, isnit a useful ..J model? ts ii a gooil'model? Explairi yorr rnr*"is. ." ! * <'t.T,t r.Ac/gl. ig a 6!'mglq- \i1ea.. ,uyrrS,ot vnodel [zgqsLv.\t i*' hc'1 996" $c-s**' af i"ftctaf Coy\' " 1l' +.a\ \]Jtnc\hcr ft .o c, .repi-r r".oAe,,noO Htr.9r:O \rs Ha"'F.{'Q' Ak 6i'", o< lercf '(:1,.6i.cr,) ]i}p 0Vera( ilgdc\ ff-"Airr. fl q p/ ooor\,'a.d lk lf g"l-.... (t-s+c.t=' b.4l 9t'64,t) atc 5,lnificanr Fca':,^1 . -*\u reia.t H9, f*r1 , o.a ,a.j-r $o.. \r^c r..aJet. Tt d'no-nt oS u,"n.ot.,1io1 *xe"4,-.o. ac\4l(\oN3hie etgii\n3 ., ',5 *o-rn b1 ,t'urh'rcr^ i5 --18b2 (1g.bZl.J.irorirre,t,\,\e er[rta\^t6 L1 tt"a f+aAet). fnrr il af ilt, fx \' rt, li*.ct1 rA^qt cdd,*,. o\["tr - indlggnl44t savrt^h\{s '9\N r\vrcr(:\qe fhc +(Lvawe' -1;t c:ki'*o'* io' +*tt' " € go.^ee\(rl i5,9r: 1t"u$Lin.t,. ol r1 '*hcn 4-o,^rt,cr1 'rr(oAaz* 1'J\ a"a ?i=-t'\o($.!' av""l l€a' ivlr.case '\4 c€la,.rti.*.a p*ic.c.&4.r3eacs"91 Z f,9 \ho"ar-d 4i;1tao)' lt'e sa*"a..d alawic{rcn o{ tr'<* 'ncd.tr = roov..$4:6: G.t,t$. -" ' ' '4ny t'o,lnv{le{lb' q llv /.f '? b) Based on the fitted model, provide an gstimate for the change in.price for every increase iAil-'-) r * - , '-. ' ?Y&&\cd 'aQ. fo.,r rl'ya7 '*1'crcai?-r-)Y'.X I l"?Y-i+ \ncr€4'tts )\'Z"gcJrt'l1 . - - . \ a<at, 'i'tcrcasf \'1 y, +$'- O,|f€c+idl' p' i"< ivlc'+crirty54 aa9 {cr evtt r'frdc,\l^,s., dtrteqt-'s 41 lY,'vz , of 5 years in age? r' \ :, 5\ 0,?) q1 - ?-. 6 o\1a v I 1 +u*,s.-a &trc7.- {.r--1*t {{ i1ef,{ , Ui - lq.uzre9. lha,e6.-/ t ' - tt c) prddict the price of a.n 1-8:year-old model. Also, explain why this prediction.may not be very'reliable., t. * ".6 ' ." rj 'tr' \=51:o0rel -.Z.belrr(1g1 : .5qru lhfosanil dotl^.I.r :,'- *"rttu. i *h\i a9*i'*o'r6 ' i1 l\r*\ \\a{ )L*vr\-+ CtA) i9 not' lnctr'dcdlWt-. Faobtat*"' \!'t rt j tl/\\) d"5Tw \"r- fhs ,(a^7e "P 't',^r, doto ( r- rS qrirr\ Veco.-1e- of t\il, wc ^o \*q.' Krq., tS tr'<--J l fv..'Ae\ it ,s.{-, a'rA 1.ca,.*1-., o-tlide +. data' f igt (r*t\eA CFlrrafa\atio3! \t Vt.l J.no,rr6r4 and ri1Ki. lf urcr,id 'ha trac"t'\*r clct''\n dc{a' el\th xLtB yea'9 elot ' l-'lt It) ' ', I ?dr.tt utwuptinl lrr yedict ' !"*+^, Vai-<l 6 fuc '. { I "' . 't 5t.L\q\t- -r ." \')^. + t* !i' *,f t.'r'*f'*""r'' lv ' PROBLEM g. fh6.three par# of this problem are unrelated, i ";"'" "'": "' ; "' t Il 1".{ft*.{{i d) Conlsider the'interdction'inodel for two quahtita'tivb variables xr and xz. Describe in . words, possibly supported by graphs, what flexibility this'model provides over-the first- .J ' order model. r? , I. I b) lf.a data set Containr f'g irUt"ruations and we',fit a complete second-order model iir-two indbSen'dent quantitdtirie variables, how many.degiees of Jreedom'will be left for errb'i? a- fi,+ il hiec'use ;{t 1 (a^ o^t1 lr -,+ll.trt crrC o\ .L vo\"cs \ 'ta", ., I {; F'* fir{rl ft..rz:'t 93rr}?*€-,"i1 ?r*e 2- d{'.,,o, - : V\- ?ar;*i'\i{1 c) A r,esearcher wants io'stuiy whether, for young*two-pareht fdmilies, iotal years of . , , educatidn for the parents (x1) and-faniily.income'(x2)'are useful piediciors for whbther . 'the fa"milyhas small.ilitOr"n'(y=l)or not (y=Q). He proposesto usethe model E(y)= Fo + grxr + 9 8r, with aslsumptions about the error t"erms as discussed in class. Do fou think' that this is a g6od rhodel idr this problemi Why or iruhy not?- " , ' -" t '. \b. \. *d2r \. .r,.- ,$* vvldA., \,rA- wt} \n'c\an1t wL bu. '[o hcvr * 6fr;od''i*rt've \-var(a\k- 1-v61.,e&(c( ia'. ba. {rnq{.-t*t\ut Or q\-le{\it'htrrr{ t".* rl p6vrt;Qllit,ht" Qvarttrt a't\vt' lor. O or f $t+i1 . o. t'1.1 p'^\'cs t^o 6dnsc At !r u^- - - .T tYhqq) ? o\tq! s\ \t\r b/yF. *j - l- {* PROBiEM 4."To predict sdles prices for liouses in a certairi neighborhood, a multiple linear rbgression mo'del was built with sales price as ihe response variable (y) and property tax for the current'year (x1), the number of baths (x2)," lot size (x3), living space (x4) and the'number of garage stalls (x5) as the independent variables. The model ' y J Po+ F-rx1+ p.x2 + prx3 + pox4.+ pr x5 + e o was fitted to data based on.24 recent sales. Edited output frtm a SAS program for these data - and this model can be found on'page'7. r, a) A student who looked at the output ofr page 7. concluded that if.forward selection were _ used With an alpha of .L0, then the first variable to be includbd in the model.would be ' xL. Does the output that is shown'on page 7 contain enough information to reach this conclusion? Explain. t ' lb.T*-.t,r.'f.g{ed'"on.?oS""?'t6-{U4frs'Arl+"'wi+(tra\['f,+[u-?'fara"^<-+i'.9+ihaii'r'n 'A' \f;l\n'torw?rvd'*gflect'onoy*ri'c^c,{'ro\ni\t vrnadcl'<' }'ot'-'cn\Y, VB73'?nt'?rt*;d;J*"n'7" .,1^* -f fordb{l mr ;llurn,rrlr:.rsf'w4tr erTau{tca'r*,7'a"J],!lyp-""9!4^ 'ry4a". l-";'q'' 1.:6|{rr* * i '$. -$r riffitto \Avrrp- fi*'.r \trrwgHt slgn't$'cltrt '1"' S''514*i^'i;'Sprroodet' \n""ai'l{At$t'*l Wtde\ C'f i;t 3,*i\'i )t,.r i.,ai o, r n^ai tvlot"U2u {R"'"vrnaat-''ra"q ni$' eo,a(, vair"ablc t*'"- ,. |[g,;rrtla,]r...i., .,r.r,! +!! i\.. ;, -? y-,r*r i-r*n{ { f -!rt r.1{ . i-..).},. 'r .,}*r-^& k ' '}o' I' ""'.\, *, *ro,r 'h+rr ?..1r' b) After some further ihought, the student who was introduied to you in the previous part of this problem also concluded that if backward eli.mination were used with an alpha of .10, then the first variable to be removed would be x4. Does the output shown on page 7 contain enough information to reach this conclusion? Explain. -l-ti o.,.tp'n \r..^s -. o . r,i lo gr*t t\ir . or '*d-)-1 \'. b*cts*rotf e\'t*\*'*t'io^'enC^rtt^ ints(w.c.ttc v,^odc\w(Latttr'vo'iiatzltsatlAdtte€\\<-lctr+t5'1nif''ac'otiFp>at' hag \ua larlcrt ?--.01/11 )'16- so i* 51ne-\d b*. r+*c-<d' Tl*^ andil*"'r t '$'.t l 9l9'\d be' i'c*o''cel'4lr\t +o teL { arull^.f ' ?vwr* 'a'F-\tqt 9k^ld h \rr. loote a\ {hr ln 'f\5- cc.tg x.r ,! c) When using all-possible-regressions with the adjusted R-square Value for these ilata, the modelthat included only x1 (propbrty tax) and x2 (number-of bathsJ yielded the largest adjusted R-square. The real estate agent who 6ad "req0ested this studrl rbsponded that this seemed absurd to her. My L0-year old knows, she exclaimed.in exaspeiation, that _ living space (xa) is important to predict housing prices, and you tell me now that I should not use this variable at all! What would you tell her?'nl V rl 0 n WOUIO O l n '' -i\tl.rt \iuin t?o,t'""r \o. r$"p'to.o{t, rt ib hlq\t, cclovtta\rJ d''th F*Ft\\ taf' *i !\t'\\v .'.'-l 'I- I arrd rrr^hr a$ b^ik $"ple.\ \ 1i",t', 1f{e nn"fq t'v!r,s l,stht r "h''1W ?rolett-1t4vl -[ir,.Lc, O^d t+ ^ A!c, 1 ,nifaut, It^. I ttlt .,1u6 yart6Yca do 6 ner'r,ble . Source DF Model 5 Error" " 18 coPrected Totel 23 Root ilSE Dependent , Coeff Var I , . Parameter Variable DF Esiimate fntercept 1. 9.49785 x1 1 2.15009 x2 " 1 7.1493i x3 -1 o,416b8 x4 I -0.77429 x5 1 1.18877 3.26988 2.90 0.72575 2.96 3.87804 .1 .84 0.44132. 0.94 3.78160 -0.20 1.15918 1,03 F Value Pr > F 16.27 <.0001 o.0094 -----1 \0.0083 I\---_-- 0.-0818.- 0.3576* PROC REG OUTPUT Sum of Squares '- t 678...84652 1s0.19973 829.04625 ' lilean Square 135.76930 8.34443 ilean \l 2 .88867. R-Square "'0.8188 34,612so edj. n-bq 0.768s 8.34575 '1 Parameter Estimates Standard : Error t Value Pr > ltl 0.3187 "7,