4 Problems with Solutions in Midterm Exam - Applied Regression Analysis | STAT 4230, Exams of Statistics

Download 4 Problems with Solutions in Midterm Exam - Applied Regression Analysis | STAT 4230 and more Exams Statistics in PDF only on Docsity! SPR|NG 2008, STAT 416230 SECOND MIDTERM knYNAME: STUOEruT ID NUMBER: (This is your 810-number) INSTRUCTIONS For allstudents: There are four Problems with a conibined 12 parts. Write your answers in the space provided. lf 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 que'stion by 'yes' or 'no' or by writing a number without any explanation. For STAT 4230 students: You must answer Problem 4. lt has a maximum score of 1O points' Answer any 10 parts from the first three problems. Each has a maximum score of 9 points. (You may attempt all L1 of these parts, in which case you will receive credit for your 10 highest scores only.) For STAT 6230 students: Answer alt 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 L2 points. Good luckl PROBLEM 1. A transformation 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 can be helpful. Your answer should be "Yes" or "No" followed by a brief explanation for your choice. a. Todealwithmulticollinearity. r I l, - ,t N/p. IrautLicot)ioreariAY i: bor>rd Fn rulh+^i{t?th'fr| ' 'r" 'l? tta ulo' | 't';^ 2'[ur ; i+ ha"r r\rfn'rbt{u;ertr {h? X^l/Rfi4usteJ t ^lr 'tt^) tv'" J r^l ,\h +hr dept n e'ieot vqria bf< ' b \7:T' *lJ:'"ffiT"u;*,,1' o 1{* E; I iz 3, !"' ::h::'* }'vlt' N hi rh hm "/ ra w forw\hA>n 'r of J+ h+ d tPendBoi t {qr ia bfq. c. To deal with lack of normalitY. \frs A c/ass 4t'-' tl r-t {h,r PoD./Pli - hR eq"d) ; +trresr /a riq 6[p . -[ra n r fv rlna"l n/n Art cocr fo/ r P'l'fib& r {ru nffiPa*qAr^nf.r Cth* Box- Gr *r, irunrpr,nah'A'rf r[ {4* t{*2endenf d. To dea.lwith high leverage points. t{o " lsvernJt Cqs tvlQ ftJq R P[ bV {6r t\q dtpndr 'i3 eh +0u r- /eri o6["s A of '=t6t U*[^"n, F c/qv-iqt/l 6e I no f h*$ -'lql^teS a( qll , tl ( -vqlvar ),/ +rr(\tPn( r^q[>m t(ay+*4e PROBLEM 3. The manager of a retail appliance store wants to model the proportion of appliance owners who decide to purchase a service contrbct for a specific major appliance. The mahager believes that this proportion decreases with the age of the appliance and wants to fit the model E(y) = Fo + 9r x, where y is the proportion of owners who buy the contract and x is rhe age of the appliance. Fifty owners of hew appliances were contacted, as weii as fifty owners each of 1,-,2-,3- and 4-year old machines. This was repeated one year later. The ten data points obtained in this way are plotted below. 012 a. What common model assumption do you tt',inffint be violated with these data for the H;T:'"r'r-il:i";l'*ili l?;'l$ si^ti\ M "!:' aUF /r, ?** 1'*^,t,iif- 'JP i* rqg? t'rpror fr,"trl ",T ir 0 "trr '{" /^v) t'4? q tilr l+l"r + V? o q [ /ariq 4 {P-[ Ys sqslP t f b. As a first step, would you recommend a transformation for the variable proportion, for the variable age, for both, or for neither? Explain your answer, including which transformation(s) you would use, if anY. {06 rs 1ou ' t nv' o F " /nfuuJ r^,lirf ohoru q 6o u.l ^ 7a4[+rq -frttidwnls /s FtrtDttt'RP{\ ^ . ,,. r *' r^^ ';' H[, : ffi ,' t r\ "'#'^,Ph, tr;" ("f# il ; - ;4rd' r\^ wraorrft'r'^ | +hn[ N /tcMurp-'tvleul Ib.. +^'t ril.'tql'-o't iJ-04 YoP,f,"nJ^jhEf^hrt ,\ ; yerpoifi?b C'qJ R is n{['\. noTJ?U.,I errc s'^"cF) . -m fh:^'ilWk"Ar" .r,tn f. I w*lw tg. 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. Drl't Jrr +1, \p+rs +r dip,ffih- Alrypot'arrscr/ur nSwfil inpfr'tde AV )nurr-s, ,t *JM, lbt*U\ vlis wrsyltn fll : b 0rplur e-p/ rp.li#kq If al\DF A prvnq I AtnW -la;/.r m\d /iqhf ttils ovf ltrs ( tnry rvs,#wl ) .IhtruhrsS {6t renFr of !q- y["&,dvv -tt a nnl.m'hJ lhriwbfq h' *hp ^6rrc1 ir^p,etfa,rf tq r;v )It + "tf e **d*/ ;f +^D b ba .{6e 'r*E[en - Rdp{rerti\? nq nz{ltr '€ l\nt' .17eA? S fu h $o foLlerr'1 trltp"Y*R"r fi rcrvrtql \ C&r- Gr rnefhov) f +te[ .!re^^s ,b h- 'fie NLfr,r) {aPs 4ttzrwt..iv ,\F. IaqI hD(ntu T hn C*1v s /'