sampfinalsoln - 45am fw’uA STA 825 Final Exam —...

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Unformatted text preview: 45am fw’uA STA 825 Final Exam — Wednesday, March 18 SHOW ALL WORK Name: 1. A study was conducted to evaluate the effects of different washing treatments on the quality of beef after storage. There were three washing treatments: normal, ‘ chlorine, and lactic acid. On each of four consecutive days, three samples of beef were prepared and each sample was randomly assigned to one of the three treatments such that each treatment was observed on one sample per day. The experiment had to be conducted over several days because it was not possible to prepare and treat more than three samples per day. After treatment, all samples were stored for 10 days. After storage, each of the samples was evaluated on six criteria: beefy aroma, bloody/serumy aroma, metallic aroma, grassy / barnyard aroma, sour aroma, and spoiled aroma. a. Why is this a multivariate rather than a univariate data situation? ‘BQCaLSL 5rd 0/ mg» ’3 A (an) it“ 36‘s ALAS (ix/M2,. (Lit/fa my éLVVL ' 5 CWTch; /\S~€{\JN\/( n L . (heth " as {fig/arse chhaLéJ. at s ei/‘firfrsc J / J~y€v¢£~ - V l 1) ?/49L [1 Cl \ b. What is the design here? (Hint: we only talked about three designs, and its one of those three.) |R&A&3Mi?€ J (an / (D463 («Li (J; i r ‘ ' 9 ., iajmflfi; K :6,“ Ma,» 4 M i W c. Write down an appropriate MANOVA model for analyzing these data. In— Ix \ Fe 5/0.;AS e Vi; V d. In terms of the parameters of your model, write down the null hypothesis for testing that there is no difference among the three washing methods. e. After testing the null hypothesis from (d), we will typically want to ob— tain simultaneous confidence intervals for specific comparisons among the treatment means on particular response variables. Give one reason that the Bonferroni method may be preferred in some cases over the Roy method for obtaining simultaneous confidence intervals. Give one reason that the Roy method may be preferred in some cases over the Bonferroni method. fang/«Tam Alan/g5 Cwll flu (at ROB ,Aiefvah gallon.) Snécpivai 2. In the early 1900’s, several investigators were interested in predicting behavioral and social outcomes among people based on physical characteristics. Macdon— nell (1902) reports a correlation matrix for the following seven physical variables measured on 3000 British criminals: (1) head length, (2) head breadth, (3) face breadth, (4) left finger length, (5) left forearm length, (6) left foot length, and (7) height. Assume that all original variables were measured in centimeters. The attached SAS program and output (labelled “Final Exam Problem #2”) per— forms a principal components analysis based Macdonnell’s correlation matrix. An- swer the following questions: a. One of the goals of principal components analysis is to reduce the dimen- sion of the original data. How would you choose the number of principal components to retain for subsequent analyses? In this example, how many principal components would you retain? mam/J..- Maw/019% g 2) uUL/Q 44942 Woman kdpu Wyn“; 4v “:0qu 3} (Xe 7% #0,.1 egqu/uw '> O 9) 5u23¢¢74m [swcli’zmi /%fe,' 10/2944 alwer 3 $6.5 5‘0 )461’7L I / “Kasai at Ila/[99M 43¢ 2’6 “’4”ch (YT2\ b. Briefly interpret the first two principal components in this example. That is, what aspect of the original variables is captured by the first principal component? the second? ‘ (Heb V5:?—L CiaflfaflS% Agave! 512g, org/LAPL //,m«l) ¢ Ami} [walk c. Explain why it is not appropriate for this example to perform a principal components analysis on the covariance matrix rather than the correlation matrix. gécwébq Myrlcmce n ch'za é S A 4 ‘3 C“ 114+ Jed. %/(“/L% 154' V4? Wcl‘ W"?- eméy/A} 52-8: 711/“ fixe/ r).ng UAgAA (/MJZQJ MPH“ 4/0) day A 2 [2e w’// (firm/14A #6. W P (L. a“ a, 7%; ff '2 c. w, // mag 43; flew’)3 fit” all yfiir‘mflael d. Suppose that in addition to the seven variables described above, an eighth variable, computed as head length minus head breadth, had been included in the analysis to capture head shape. What would be the variance of the last principal component in such an analysis and Why? fl E’é‘bea’t/JG») bum/[J AL 0 éQ/Q’WSQ [QQC/ I; A qux 50”; 27/ 0 darn/4mg 4 3‘? ( 1W1 (Man “a a4 ed M\ 39 is a I72, ’4 av“ K4 1/6 I1“ I 3. Annual financial data are available on firms. Four financial variables including 1121 2 (cash flow) / (total debt), 1:2 2 (net income) / (total assets), :33 2 (current as— sets) / (current liabilities), and x4 2 (current assets) / (net sales), were collected for 21 firms that subsequently went bankrupt and 25 financially sound firms at about the same point in time. A discriminant analysis for these data is performed in the attached SAS program and output (labelled “Final Exam Problem #3”). The discriminant analysis is based only on $2 and $3. Answer the following questions. a. In the SAS program, a hypothesis test is performed using PROC GLM of the hypothesis that the mean vectors are the same in the two groups (fi- nancially sound and financially troubled firms). Why is this test performed prior to performing a discriminant analysis, and what does the result of the hypothesis test say about how the discriminant analysis will perform? .fle 1; far floateJ Jaws/ac h J\ S CriMfyLCM+ 04 0w) / Q’Ja Per 4%. I“ ‘1 s are, JfiCZ/uzr 0/ {105/ 0 MEI [Mug if, )6 M) ,w/ amng Mm [v1 :SZWg/Q/ flt/ éx/ogc/ a" 5;») Effigy [all 05,57 ()2 :r Q/i-J‘C, F INM . £4 L 7{a,1 Z— - n I I V . ‘ I éd—‘SC {flea/15 are Afi'ijm'fiuxq‘f J Cél - 4. r I \ 7L {3 Dc’k’n So L'JK slaw/J ex/eg/ 76% [Cami _ + 4 74 am QM» La); //. l < w Mg b. In this example, equal priors and costs of misclassification were assumed. Explain why it may be more appropriate to use different costs of misclassi- fication in this analysis? Why might it be more appropriate to use different prior probabilities? /7Z 0087!? t?! /lx’\\§p’&,35ol{24 7gb» I’M—:33, 51 OflPWACf/Dfik'ie 5am, w/ max M a 6mm“; Jam; 4w ‘ ’ t - ‘ v J (inn ‘rLeaL‘L if Me» Li W #04311 145% Jul LL "if‘ohfi, r V a for),qu )6»i’i44" l—S [Mbsz LL’QS ‘4) gs; Q/qscd'ca‘ ; ,/ M3 reign mam 42f «CM saw flies/J 75403 5 ’17))" ’49 “VD-d 464 4r» ». \ \ tr x ,«Wg. I Q (L a (V (V'Q n (LL/“LAC fire w‘a (D. 9' .5 ‘0 L2 9 - I3 .500\C/ rm J HQ“ 47/0 éa ‘31’g5An ‘ MHZ 741:4 ("141/ ~ 0493 r.“ C A ‘ K , u / r Just flu: em fife/.4 m ‘ c. Write down the linear discriminant rule for classifying firms as financially sound or financially troubled. 1 1,0575" I )010‘3x1 Ali ; ('bll'zgg + w x : W'Zé'fog SINCE” '- 7.0%? d. There are two estimated error rates in the output. What error rate would you use and why, if you were describing how you expected the linear dis— criminant rule from (d) to perform in practice (when actually classifying firms of unknown status as either financial sound or troubled)? WOU’J VSi C F5955" Va [Jew/74“ carter- c, is 1’3 5* éum a mama/5M a i (Jena/tuxkrcl . l/ 3" 3'2th Luz Aim/q «A M Joy/7‘ wqucL Mb CL‘SCNMNYVW’I/ rule L203- (‘Z nib/J CL 47‘ , 4. The following table lists measurements on 5 nutritional variables for 12 breakfast cereals. TABLE 12.9 BREAKFAST-CEREAL DATA x1 x2 x3 x4 x5 Vitamin A Protein Carbohydrates Fat Calories (‘76 daily Cereal (gm) (gm) (gm) (per 02) allowance)a 1. Life 6 19 l 110 0 2. Grape Nuts 3 23 0 100 25 3. Super Sugar Crisp 2 26 0 HO 25 4. Special K 6 21 0 “0 25 5‘ Rice Krispies 2 25 0 HQ 25 6. Raisin Bran 3 28 l 120 25 7. Product 19 2 24 0 110 100 8. Wheaties 3 23 l MO 25 9. Total 3 23 1 HO 100 10. Puffed Rice l 13 0 50 0 l 1. Sugar Corn Pops l 26 0 l IO 25 12. Sugar Smacks 2 25 O 110 25 ‘ 0 indicates less than 2%. A cluster analysis for these 12 cereal brands is performed in the attached SAS program and output (labelled “Final Exam Problem #4”). Answer the following questions. a. Identify the type of clustering algorithm that was used in the SAS program. (Don’t describe the algorithm, just tell me the type of algorithm it is — more than one adjective is necessary). A ‘47 lU/wefa(7(ve/ fla’zmc/HQ / 6/95 ,1 Us“ . ' 30“ t y (XVQIch/Q, [A [C . b. What is the cluster structure for 5 clusters given by the results of PROC CLUSTER in this example. That is, assuming there are 5 clusters, tell me which cereals belong together. l 1: C5 ‘gPCLfa‘ /< C'ngf : Chi/2‘ «Ql‘ (<2 Mia/9,05" Sjtb/ can?” Ciuiw 3 : gal-{IA gré/U [tau/)9; [ la; [64’ Ll : 2014+ (Cl) 73/1, [lulu f; 77412-4 RM c. Based on the pseudo—T2 statistics printed in the SAS output, what is the appropriate number of clusters for this example. a, b 612(;;~v’5 L LL; M m AM 5’ 47; w (It; A,“ ’“J'C‘J‘”?Y *8le £1612!) mural 4g} 7184+ R's/re lea’lfirela A, {far}. d. Attached to the output is a page of star plots for the 12 cereals. Explain Why just a dot appears for Puffed Rice. Bfiuwse '72 (Q cl ane )LCLS 4Q?- V fimlles‘fz Value all '7/ Varied/es, ...
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sampfinalsoln - 45am fw’uA STA 825 Final Exam —...

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