By Ravindra Khattree
Real-world difficulties and knowledge units are the spine of this ebook, which gives a different method of the subject, integrating statistical tools, info research, and purposes. Now commonly revised, the e-book comprises new information regarding combined results types, purposes of the combined process, regression diagnostics with the corresponding IML process code, and covariance constructions. The authors' method of the knowledge will relief professors, researchers, and scholars in a number of disciplines and industries. wide SAS code and the corresponding high-resolution output accompany pattern difficulties, and transparent motives of SAS methods are integrated. Emphasis is on right interpretation of the output to attract significant conclusions. that includes either the theoretical and the sensible, subject matters lined comprise multivariate research of experimental info and repeated measures facts, graphical illustration of information together with biplots, and multivariate regression. additionally, a brief creation to the IML approach with distinctive connection with multivariate information comes in an appendix. SAS courses and output built-in with the textual content make it effortless to learn and stick to the examples.
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Additional info for Applied Multivariate Statistics With SAS Software
A plot consisting of such curves is called an Andrews plot. The Andrews function, f y (t), has certain useful properties. Specifically, (i) If the vector y¯ represents the mean of n multivariate observations, y1 , y2 , . , yn , then 1 f y¯ (t) = f¯y (t) = n n f yi (t). i=1 Thus, the function f y (t) preserves the mean and as a result, in the Andrews plots the average of the data will be represented by the average of the corresponding Andrews curves in the plot. (ii) Apart from a constant, the L 2 -distance between two curves f yi (t) and f yi (t), defined π as, −π ( f yi (t) − f yi (t))2 dt is preserved as the squared Euclidean distance between the multidimensional points yi = (yi1 , yi2 , .
6 200 MMMMMM MM MM M PPP M MPPP PPP M MPPOOOOOOOOPPMM MPOOQQQQQQOOPPMM P QN QOP PMOOQQNQNNANANJAAJNAJNJANANQNQQOOPMM MMM MMMMM PMOQNAAJJUJUUUUUUJJAUAUJNANQQOOPPMM MMM MM M N J M K K P U K K U A Q J M N O K K A M PMOQNJUKKLLLLLKKUJAUJNQOP M M MM JQJQQJJMM PMOQNAAJUUKKLLLL LLKLKLKAUJUNAJNQQOOPP MMMMMMM QJJQOQJOQJOJQO OOOQOJQJM P JQOO U A PONQNAUJKKLLRRRRSRSFRFVSRFVSRFRFRR LLKLKJKUNJAUNAQQOQOOPPP UPUPUUOQOJQJM QOPJQOJPQOJUPPUPUUPUPUPUAP O J V Q F J V P F Q S V S L O M R U O R V F U P P F S V Q A S B B E E P L N J AKKAPKAPKAUUOQJ W B E W Q P O F B E W POQNUJKLRRSFSFVEBVFEBHCWGWVEBHGCWGEHCWGCHGCHGCHGBHCWGEBCWSGEBWVSGEBVWSGERFGEWVRFRF LKKLJAUNJAUQQOQOQOOOPOQPOQQPOQPJJUUUKAKAKAKAKAAKK PKAKPAUOQMJ A SFBEWHG TTTTTHCBSVWEF LKJNAU QQQ JU A KPAUKOQMJ POMQNAUJKLKRRSFSFEBWVHGEBWVHGCTWHGVTCCTIDTIDTIDDIIDIDIDIDTIDTHDIDCTIHCTIHDBDCTISGBDCWVGESDBRWVGESFWVRGEFWVRGEFFLKLKJANLKUNJAUJAUJUJUJUJUJUJJUUUKAKAKAKAK LLLLL LVNBLVNBLBLBB PAUKAOUQJ HITHCTIDBICBSDWRVGEWRGEFFLKNLKALNKAKKAKAKAKAAKKA LLLLLNVNVNRVNBRVNBRVNB LFEBCID RRVRNVRNLVRBLBPKOMQ HTHICTSDIBCSDIBVDWVRGEWVRGEFWGEFFFNLNLNLNLLNLNLNNLLNNVVNVNRNVRBVRBWRBWRBWSWSWSSW PONQMAUJRLKFRSFEHGBEBSWHGCVTVCWHGTDTIDID SWCSWHCSWHCSWHCNSCVRSNVRLBBAPUKOJ HTHCTSIBCSDIBDSIVRDVRWGEDGWVREVREWGFVGEWFVGWWVFWVFWVFWFVRFWVVRWVBWRWRBBWRWBSWICSSICSICCTHICTIHCTIHHCTI NQOUFRLKJSHBGEWVTCIDI HTITITITIWTHWHCSNHCRVSLRBAUQM PMRFAUSHGEBWTCVID HTHTCBCTSIBCSIBIDSBIDSBRDIREDIRGEDIRGEIDRGEIDBRGEIDBGEBSIDFIGEBSDFSIGEDCSIGFEDCSIGFEDCTTIGFEDCHTHGFEDTHGFEDTHGFEDGFEDGFEDGFEDGFED GFEDFEDGEGFDEGFDIEDFTIEWTIWNHCTIVSLHWTNCRVSLHCPBRKBAPOUKQJ N L K D E W HHTHTCCTTCSBTCSBCSBCSBCSTCSTCCTCTTHTHH I S J T G C OEARFHBWTVID GGFDEDGFEIWTNIVSLHCTRSHBAOMUJQ Q P HHHHTHTHTHHHHH NFRMGEUSLKHGBWTJCVID GFDEGFDEDWNIVCWTLIRVSPHCKBRAO O S F C M H A GFGFEDNEWTLISPHVTCUKBRHQJB Q D L I B E P R T G W K U N FV GFDNEGFDWLIESAWVTICUSROMKHQJB FEORGSHMWTLBJIDC NGFDPLEFDWTICAVRHTSOKB FGERPNGETSHQHWTBSLIDCIDCAUKVJV NGEPLGFDUICWVMEQHTSRJIHB GEFRNHTSCWQOIDBUMKA NLGFDAPCWUOKFEVGDTSRQIWJECBTH FGEEFGRHWTSRNIHDBWIDBPQOCLLVUKAVJ NMLAGFVUOKDSRIWQGFECDBTRIHSEHB F T PC S D I PNLAJVKWGFCDTIESRGFHB FGEFGETRIDHSNCWBQLVKJM PNMUOLAQVKUJWDCTIFEWSRGDCTIHGFEBWSRDHFETIGBFE FFFGEFGEGETIHDTIHDWSRBTRIHDWSBCWBNCLPQOVKUAUAJ NPOLVQKVCDWSRCTIHGWSRDBGFETIHDBFTIHGEFTIHGEFGEFGEGEIGETIHDTIHDTIHWSRDBWSRBCNVPLVOKM MNAPUOLJQLKVCWSRCWSRDBCDBSRWTIHDSRWBTIHDWSRBTHDSRWBWSRBWSRBCCCNLVQOKUAJ N C C PM MPAUOJNAQLKUNJVQLKVV CCC VNNVLVLQPOKQUAUJ O V VLKAJM MPAPOJUNALNQKULQNKLVLVLVLVNLVLNNLQPKQPKUOOUAJ MPOJPAUJOPAQNKUOQNKUNQKNQKQKQKUPQKUOPUOAAJJM M PJAOJPAUOAPJUOAPUPOAOAJAJJ M M JJ M M M M MM MM M MMM 100 0 -100 -200 -4 -3 TREE C G K O S W C G K O S W C G K O S W -2 1 5 9 13 17 21 25 -1 D H L P T D H L P T D H L P T 0 2 6 10 14 18 22 26 1 A E I M Q U A E I M Q U A E I M Q U 2 3 7 11 15 19 23 27 B F J N R V 3 B F J N R V B F J N R V 4 4 8 12 16 20 24 28 An examination of the Andrews plot indicates that the fifteenth tree (M) again stands out from the rest.
7 is interpreted as the overall score (weighted average), corrected for the mean, of an observation vector corresponding to a tree. This is so since the coefficients of the linear combination of the variables that are used to form the value corresponding to Dimension 1 are all positive and are approximately of the same magnitude (see the first coordinates of the four variables). Hence the trees whose corresponding values fall at the right in the positive direction have an overall larger score. For example, the fifteenth tree (T15) seems to have the largest weighted average after correcting for the mean.
Applied Multivariate Statistics With SAS Software by Ravindra Khattree