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Material Type: Exam; Class: Applied Regression Analysis; Subject: Statistics; University: University of Georgia; Term: Spring 2008;

Typology: Exams

Pre 2010

1 / 6

Download Applied Regression Analysis - Midterm Exam 2 with Solutions | STAT 4230 and more Exams Statistics in PDF only on Docsity! i t SPRING 2008, STAT 416230 SECOND MIDTERM i-, ;-\ .I |.f ,f o*n 1 rvn STUDENT lD NUMBER: Oto rz1 j8,tr {This is your 81-0-number). INSTRUCTIONS For all students: There are four Problems with a combined 1-2 parts. Write your .nrt"r, in the space provided. tf you need more space, you can use the back of a page, but clearly indicate where the continuation of your answer can be found. For all questions, show your work.'For example, don't just answer a question by'yes' or 'no' or by writing a number without any explanation. For STAT 4230 students: You must ellswer Problem 4. lt has a maximum'score of 10 points' Answer any 10 parts from the first three problems. Each has a maximum score of 9 points. (You may attempt all 1L of these parts, in which case you will receive credit for your 10 highest scores only.) For ST.AT 6230 students: Answer all 12 parts. Each part of the first three problems has a maximum score of 8 points, while Problem 4 (which consists of only one part) has a maximum score of 12 points. Good luck! Fxr* [l.rl vrs'v[< l" pROBLEM 1. A transforfiation of the dependent variable can help with a number of possible issues that we have discussed. For each of the following issues decide whether a transformation of the dependent variable tan be helpful. Your answer should be "Yes" or "No" followed.by a r.- brief explanation for your choice. , _.. K.. i To dealwith multicollinearitY. \}U. rnu\\\ica\\''atsr"t1 i5 w\'t^ -[.q'.5{r.-i., lt yvaricult p\tt n4 flre*iron a( V\F uc.\,,es \o f*err"'.,zrt u.w.&\ pe\er5 l{ wu{r afata '(t ro\kdreAr b-t $. oc+.rrc{ ca{'e\ct'cv\ b. To dealwith heterogeneitY. ,l {eS- lL*n"gcaei\ occptt ,J^<n *^-. gari-^rr- 64 {i^c lt; *c< r'\c* e'tec-\I en.''.r- vFeq^t se Cannot 6ggvc( tr,,e L lv-+ ..,--, -r^ta*.r. $.o-e'iit, a- +t4^*c{e4t\o^ oE \u< -&e(<*A*"t v4r'.alok C.^va hcfg'$ {\-{- ,r'€<,\A'a'\ \rs. (rc&\ete} rrct-e (\ot Shori Jd{trt"te'^ :et<"J' Q+..^r Ccvil l2e d?, tolCl), f;,"*.. $$er \\^e |ran$<rer'.6, tl^. vnaAo\ YrctAs \a te- Ce-e.ro*i^6! G5 it 6n1 ^.{ LrJa.tr, grcLtc*5 .rr'.t\' ncrn^el.tl oec'ct et lro€ S'r wvu{ n9 \o*.rer b{ +'.jwi{.c-^+ c. To deal with lack of normalitY tlat ',[ erkrc*t (ain\s, no {or gag'.^ w'''JA\t of lr"tx'" f* r\6tmd\\\r \oor!' a\ rs"r- nofmol fsobarril(+1 (\0" \9 €ct .\ \t^.t.." ..5 d- 9\r4\1Lt \F-(. ?&d':11 tt^'*1^ (o'o)'\{ tt^t grob(eb "t tLst {'< <nEgoi^ts &rt €.f-tr{-rs'(rr*-,., s$e*<:r) tu,a^ c 1.*5d.-^t'.cn v-bi8 \a c&- tt \L..- f,ro\otc- \: {n* tt\'<f? '.j o "J.l'sx th.c *ilAte, {+t^ a {rang€a**t'.a^ -!oJl ^c^, t.e\g- 1ikct1 a^ l*tatq-^t tlar''oi"te(s) L.-s L.r,. tel+ .-\ "N w..Jc-t novXe\ NO. f;a.^1fo.*",-1 {\-c 1-vor'reg1a \i-'.\\ r\a'\ +t-L F- vc<'olatr - Ct-e^1'.-t -t*t tca\t J; _ \Lt i-vol"s l"clp'la /tli<.c t*\( u$l'l ihis gl&\.-, '.t '.1 \2e:* Svc,.fl La tc'vro.reA' tt \r^.ts v'gnr\ Inet(' +orF vs. :(e$''Sq U4a a\eo ? arrlo,t 1.". r<.rirnrda.t 'rd{or *a"t'cn alas.1 {V.e r1-vq/iab\x' ;l.th \t-{<r o-1"( 41 Ao rrct^i-q +6 hFq't<-I 5retqi^Q -(.t \octsg <* t{"<- E S \ac-rrr;ef- d. To deal with high leverage points. bvc.roT Fr w/Tun I q^swers pROBLEM 3. The manager of 'a retail appliance store wants to model the proportion of appliance owners who decide to purchase a service contract for a specific major appliance. The manager believes that this proportion decreases with the age of the appliance and wants to fit the model E(y) = Fo + Fr x, where y is the proportion of owners who buy the contract and x is tfie age of the applialnce. Fiftybwners of new appliances were contacted, as well as fifty owners each of 1-,2-,3- and 4-year 6ld machines. This was repeated one year later. The ten data points obtained in this way are plotted below. Prop 1.O o.9 o.8 o.7 o.6 o.5 o.4 o.3 o.2 2 age a. What common model assumption do you think might be violated with these data for ihe modelthat the manager intends to fit? Why? t{ .aff.g6rs 4\*t equ$t !ar'\c!nc{9 *..1 l're v'c\oteJ' {a eoints o'\ \kt" enA, ot'r both s''A6, &Qee4f {. !.-- s..c!t\ Urx-.ri6,1c-r< ..X'-tc lL< galv.t: In \t- tln".}Jlt (1' Z) op 'btr t(t:.^J Ovl. b. As a first step, would you recommend a transformation for the variable proportion, forthe variable age, for both, or for neither? Explain your answer, including which transformation(s) you would use, if any. t\ wc,r[ be best \o {ro^of..* {ue' Fogt'.m e€'r1 +r-4 <'.; (.fi). -G..; {,--5f,-1.,,n is $ooc\ t . Ao.LJ,t bu-"a da,{a- ( lorl.sr t..o} .rE t\- n^r\A\c) *l t. Eofr,rv'.c,. / gercen.+.4 &tr. L"r^'.a^ lht. rs)- With \L.s -"{.",rq{o.*.tr"1 11.,( s'bk- } ..rac1.*\ apta"\i ry T *J r t-.t Ctd^rj Web\w!.S mo^{ q!'t./- ,9o cl,cc! at\ ai:ue1t'.cn3 Atr -si*1 '*' 5 Problem 4. Provide a brief discussion that explains what a normal probability plot of the residuals is. Include what it is that we plot, what it is that we look for in the plot, what type of things might concern us in this plot, and what we might do if we do find reason for concern in the plot. ft flc'rvw"\ P'rohilart\\ \t9. $"r- nofma\g gcort< RB ."ro-,rd \ooG (r?c \oper {l^c^ 'lh'< ct\' ic,-eg gv\ Cec") \\is'- t a-. redrA-a\s qr\<: iLt-o Ce{tA-*ts (o^ +L4 1-o.xi:) q,t-r*lo,r| nonrwt( $:'s*sib-f''at o^ bb€ rr'-al!rs' -Tl-<- -iw- avuF vntst lae -()-t'{ll ^ a*- ".o t.e c+fl an L ttat\'1 o^) o(7b' foetrr i\. CX. 6.rdu\t* t'*a.'l tt{ !t*..n \o,\" er\tt*t tts"I*\s .^rLt\ e-xt"tv^< reS'$sclS b( zi(l- \.'{ttr \I-. qrrtl. {L',r. f,.r:t \s \o con$'*+ 'd'+ tqtl*- i;* a co.p\r c€ v*.{9 1' 5o<r\ ' ,tiLr ' ^ .. _ 1*on (o,*..-o, tt ma1 r- t'rl**,".j::;;-; ; kr ^ {rar,'{ar"'at"o'. T '{'r*''"' C...4- tlc 1rc.$ {o 1el "'ror"'f ,' hu{ 'v'-\t L<- !"re'{l\^ ' \"1 ' flnUh-1"cb\t*'te61.livr{'\-{-t'.'"'}A\"dF'-0\o{'-Tl''s''a't$ \^,,, obo;cr5 e\"-'1Lt h'"s ["tt; t^. **: - "t-' of tt<- &1". * wqt no4 tso'Fl Or \\ !,rq1 (*ts \'\t<- s\n"S" f,cGgc,r, f" +r^\3 "t t!'41 a^ quu/'.Jv k'*s *^1 hb not '.-p"ria^f{r^.,. o'{< 4.a^ct-c-\cl' tt-t* brag [^arr- , ]r-t { f;. ,r-o<t ftkti t*+t .^t. Sdi[.*", rn\tv act\cu 01 1 tro'{aynatian a'.tt rncrt. \t( ?L\t cc-'rA tcc'g \'rae- ene 'ctt"<' {'t\o-\1'- 7 I@b'\v"{-t* L,er\.. "*-''\r - :::T;lr* e*[ec{c\. ,-.I,,;,-..ls ^{< 9ra\t! tlt':t skewnerr 0vflrt0I ?