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## MultivarateAnalysis

by: Theresia Dare

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6

# MultivarateAnalysis STAT924

Marketplace > Drexel University > Business > STAT924 > MultivarateAnalysis
Theresia Dare
Drexel
GPA 3.77

Staff

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COURSE
PROF.
Staff
TYPE
Class Notes
PAGES
6
WORDS
KARMA
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This 6 page Class Notes was uploaded by Theresia Dare on Wednesday September 23, 2015. The Class Notes belongs to STAT924 at Drexel University taught by Staff in Fall. Since its upload, it has received 25 views. For similar materials see /class/212425/stat924-drexel-university in Business at Drexel University.

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Date Created: 09/23/15
Stat 924 Final Groupwork Name Tianxu Chen Workgroup Members Jingjing Lu7Ping Shao Problem 1125 a Use the formula on page 611 790 21 i2Soledxo m i1 izys oiedxo l 52 When we used all the data on variables X1 and X2 7 73326732 1 Fisher7s linear function 21 i 52 S01ed 748267397 71477550 g 7482673911 7 1477550 Decision rule Allocate 0 to 7T1 if g 2 7 Allocate 0 to 7T2 if g lt 7 Using this rule7 we classi ed all the sample observations 2 We constructed the confusion matrix Confusion Matrix for all data Predicted 7r1 Predicted 7r Actual 7r1 19 2 Actual 7r 4 21 APER013 1Please see the attached R code 2Please see page 2 of R code In g 17 we plotted the data and dicriminant line in the zhxg coordinate system Fig1 All data classified FigZ Projection All observations classified o 0 o Populationi o 0 A Popuiauon2 d m o o 2 o op ammo m an 0 o o A A AA AA 2 o 0 P2 0 gen 0 N 0 o 0 3 P2 P1 39 39 3931 39I 8 39 o m e 39 ltr O Populationi 39 o Popuiauon2 o I I I I I I I I I I I I I 706 704 702 00 02 04 06 710 8 6 74 72 0 xiCFTD Classification enerproiecuon We also projected the observations in g2 The projection presented the statistical distances of the observations from the discriminant rule and the number of misclassi cations b First we calculated the Fisher7s linear discriminant function with observation 16 from backrupt rms dropped 7 73303918 3 Fisher7s linear function 21 7 32 Sg oled 759731017 71462552 730 75973101x1 71462552x2 Decision rule 2 Allocate 0 to 7T1 if g 2 t Allocate 0 to 7T2 if zjo lt t Using this rule7 we classi ed sample observations with No16 from bankrupt rms dropped4 3Please see the attached R code 4Please see R code We constructed the confusion matrix Confusion Matrix Predicted 7r1 Predicted 7r Actual 7r1 19 1 Actual 7r 4 21 APER011111 In g 37 we plotted the data and dicriminant line in the zhxg coordinate system Figa Data classified with Observation 16 dropped fig4 Projection data classified with observation 16 dropped n O 2 o open no I on g o A A AA AA mmmA A 9 N I 2 P2 P1 rAn ltr O i I I I I I I 712 710 8 6 74 72 0 2 xiCFTD Classification after proiecuon We also plotted projections of sample observations with No16 from bankrupt rms dropped Second7 we calculated the Fisher7s linear discriminant function with observation 13 from nonbackrupt rms dropped t 743598215 Fisher7s linear function 21 i 32 S01ed 43796017 71969439 5Please see the attached R code 111 730 74379601x1 7 1969439 Decision rule 3 Allocate 0 to 7T1 if g 2 t Allocate 0 to 7T2 if zjo lt t Using this rule7 we classi ed sample observations with No13 from nonbankrupt rms dropped We constructed the confusion matrix Confusion Matrix Predicted 7r1 Predicted 7r Actual 7r1 20 1 Actual 7r 3 21 APER0089 In g 57 we plotted the data and dicriminant line in the zhxg coordinate system Fig Data classified with observation 13 from P2 dropped CACL X3 06 04 02 00 02 04 MCFTD 6Please see R code FigG Projection data classi ed with Observation 13 from P2 dropped I o o lo 0 moaoo O A A AA AAM MA N I 2 P2 P1 Pm st 3 I I I 40 75 0 Classification after projection We also plotted projections of sample observations with No13 from nonbankrupt rms dropped Analysis of in uential observations As required by the problem we used X1 and X3 as vari ables to conduct discriminant analysis Supported by preceding calculations we are now able to analyze the in uence of observation No16 from bankruptcy rms and observation No13 from nonbankrupt rms on the outcome of discriminant analysis Fig7 All data classi ed with different rules Fig8 Data classi ed with different rules Q5 d m o d m quot 49 as 5 5 4 H o H 09 a 9 o 9 39 018 N N 22 16 quotliu 17 ans 02 fig 0792 x o 23 as v ao 1 no a e 3 o Populationi 39 o Populationi 396 o o o as PopulationZ PopulationZ I I I I I I I I I I I I I I 706 704 702 00 02 04 06 706 704 702 00 02 04 06 xiCFTD xiCFTD As suggested by g and g8 the above mentioned two in uential observations have in uenced results of discriminant analysis Take observation 19 from population2 in g8 for intance The rst dicriminant rule misclass ed it to population 1 but when we used the third discriminant rule where we dropped one in uential observation from population 2 we correctly classi ed it to population 2 Particularly from gure 8 we can see that Observation No 16 of population 1 black dot numbered 16 and Observation No 13 of population 2 white dot numbered 13 were both wrongly predicted and exceeded the discriminant line further into the wrong population than other observations in the same population respectively This may suggest that these two observations could be problematic7 To observe their in uence more closely we dropped observation No16 from bankruptcy rms and found that the discriminant line moved clockwise and APER changed from 646 to 545 On the other hand however when we dropped observation No13 from nonbnkrupt rms the discriminant line moved counterclockwise and APER changed from 646 to 445 That is in both cases where we dropped in uential observations we got better APER ratio suggesting that we might have more accurately classi ed the observations Neverthelesswe should have in mind that we did not take into account the dropped observations when we calculated APER Therefore7 the decreased number of observations actually contributed at least in some degree to the decreasing of APER ratio From above analysis7 we learned that we should pay attention to in uential observations In some cases7 even though the statistical distances of these observations may not be substan tially away from their respective scatters7 their existence may in uence results of discriminant analysis To further calibrate our result7 we also utilized the Fisher7s Sample Linear Discriminant anal ysis formula 11 62 Results from following gures suggested that the two formulas produced almost the same results This is7 despite the differences in terms of calculation7 these meth ods could arrive at same conclusions7 which may signi cantly enhance the robustness of our conclusions 1125a 1125b1 o o N 39 N u o o 0 I o o F o F o 5 o o o 39 g 0 2 39 g c e p2 o g o P2 0 1 on a oo o u o o o o Q o o quot F o v a n I o o o I a u o o N N o I I o o I I I I I I I I I I I I 3 2 1 0 1 2 4 3 2 1 0 1 2 haly1 haly1 1125b2 039 o o N o o 3 F o S m E o 3 L n o a P2 c 5 03 as o o c a Q T o I 39 o o o N I o I I I I I I 3 2 1 0 1 2 haly1 Vl

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