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L  *>> (_17  2( 4 <DL223  Ԁ2( 4 <DL2  *DD (_16   ," <DL,23  Ԁ," <DL,   *55 (_15  ) <DL)23  Ԁ) <DL)  *22 (_14 ` &<<DL&23  Ԁ&<<DL& ` *// (_13  #DL#23  Ԁ#DL#  *,, (_12   DL 23  Ԁ DL  *)) (_11 h DDL23  ԀDDL h *&& (_10  L23  ԀL  (## &_9   L23  Ԁ L  (>> &_8  2( 4 <DL223  2( 4 <DL2  (DD &_7   ," <DL,23  ," <DL,   (55 &_6  ) <DL)23  ) <DL)  (22 &_5 ` &<<DL&23  &<<DL& ` (// &_4  #DL#23  #DL#  (,, &_3   DL 23   DL  ()) &_2 h DDL23  DDL h (&& &_1  L23  L  &## $_   L23   L  \  `&Times New RomanX@5 2@ntFold3|xU<:Default Para(9 Z(Times New Roman !USUS.,  8Xdd8_XXXX @~ ~ ABSTRACTSUNDERGRADUATEMATHCONFERENCE X @SATURDAY,APRIL21,2012 D %%P%.XXSTUDENTTALKS:1:002:40,3:154:35  &%XXJohnCollins-UniversityofTennessee   Title:PricingVariableAnnuities  8 Abstract:Variableannuitiesareaverypopularretirementoptionduetothemanyguaranteesandprotectionstheyoffer. h   Fromtheinsurancecompanyspointofview,theyhavetochargeacomplicatedsetoffeestopreventbankruptcy. @   Insurancecompanieswantasimplifiedfeestructurethatwillattractcustomersandpossiblycostless.Beforewecanlook   atthefeestructure,wefirststrivetounderstandhowthevariousguaranteesaffecttheexpectedlossforinsurers.Wealso   areinterestedinthe_annuitization_Ԁphasewheredeathratescomeintoplay.  p   AliceCurtis-BelmontUniversity x   Title:ColossalCorn ( Abstract:TypeIIDiabeteswasoriginallyknownasadult-onsetdiabetes,butitwasrecentlyrenamedbecauseitbeganto  occurfrequentlyinchildrenaswell.Manyreasonsfortheincreaseindeathsduetodiabetescouldbeexplainedby  affluence,technology,poverty,changesinlifestyle,marketing,andchangesindiet.Butitisimportanttogettotheroute X ofallthesereasonsandrealizethatitissimplythis;whenfoodischeapandbountiful,humanswilleatmore.The 0 averageAmericansdailycalorieintakehasincreasedsubstantiallysince1977,approximatelybymorethantenpercent. ` Sowheredidalltheseextracaloriescomefrom?Theonlyplacepossible;thefarm.Today,cornaccountsformostofthe 8 extracalorieswearegrowing,andmostoftheextracaloriesweareeating.Corncanbeprocessedintohundredsof  differentgoods,suchasemulsifiers,chickennuggets,andthatdeliciousBigMacyouhadfordinneryesterday.Hasour  increasingproductionofcornledtotheincreasingnumbersofdifferenthealthdiseases?Thisstudyshowscorrelation h betweenthegrowingnumberofdeathsduetoTypeIIDiabetesandourheightenedproductionofcorn.Severalregression @ modelssuchasamultiplelinear,quadratic,andinteractionmodel,willbeanalyzed.Thedecreasingpricesoffast-food p mayseemlikeanadvantagetoaconstantlyincreasingpopulation,buttheover-useofcornhasalsoledtheconsumerto H payahighpriceforthesecheapcalories;heartdisease,obesity,andTypeIIDiabetes.    ,&%%&_Ashleigh_ԀJonesUniversityof_Montevallo_ x   Title:_Multivariate_Ԁstatisticsandmathematicalmodeling  ("  Abstract: The_WEC_ԀAnalysisGroup,LLC,conductedresearchondataprovidedbytheUniversityofFloridaWaterand X # SoilResearchInstitute,courtesyofenvironmentalengineerWilliamWhite,todetermineiftheindependentvariablesof 4!$ vegetationcommunitytype,soilorder,_ecoregion_,geology,andflowregimeaffectthedependentvariablesofheadwater  "% type,flowregime,andlengthsignificantly.Mathematicalmodelingcanbeusedtointerpretanddemonstratetheresults " & oftheresearch.Ourpurposeistoexplorehowregression,specifically,canbeusedtomodelthisdatamathematically. #d!' Wewillalsoexplorethetheoryof_multivariate_Ԁstatisticsaswellasitsapplicationandusefulnesstothisresearchproject. $<"( WewilloutlinetheresultsoftheTheoremofGeneralLinearRegression. l%#) TheGroupalsodeterminedthatlongitude,latitude,andelevationcannotbetreatedasfixed,butthatthesefactorsshould '$+ betreatedas_covariates_Ԁintheanalysisofdata.LookingattheEarthasatopologicalspaceandtreatingitasa_Hausdorff_Ԁ '%, space,wewillconstructanalgorithmtomodelthelongitudinalandlatitudinalinformationasdistinctspheres.Wecan (t&- thenapplyaregressionanalysistothisdatatodetermineiflocationontheEarthaffectsanyofthevariablessignificantly. )L'. #&%%,&Q #  ,,)1 XAngelaR._Gaetano_Ԁ&_Alina_ԀM._Lepkowski_Ԁ-BelmontUniversity X  Title:ExploringArtisticandCreativeInterestsofStudents  Abstract:Asuspicionhasbeenrecognizedthataninterest-levelinscienceoftheaveragecollegestudentcanbe  predictedbymeasuringhisorherinterestsinavarietyofleisureactivitiesandhobbies.Ourhypothesisclaimsthata ` connectionbetweenartandscienceexists,andthatthereisarelationshipbetweenSTEM(Science,Technology, 8 Engineering,andMathematics)disciplinesandartisticdisciplines.Ourmethodinvolvesfittingaregressionmodelto h differentcategoriesofinterests,andpredictingthescienceinterestofanarbitrarystudent.Specifically,theindependent @ variablesareCategory(Nature,Language,PerformingArts,VisualArts,andScience)andGroup(Humanities,Science).   Thedependentvariablesareaverageranksofinterestsderivedfromafactoranalysisandaregressionmodel.Alldatais    collectedusingaself-conductedquestionnaireofBelmontstudents.  p   Heather_Hardeman_Ԁ-Universityof_Montevallo_ x   Title:ClusteringLeukemiaPatients (  Abstract:ClusterAnalyticshelpstoanalyzethemassiveamountsofdatawhichhaveaccruedinthistechnologicalage.   Specifically,itemploystheideaofclustering,orgrouping,likeobjectswithsimilartraitswithinthedata.Thebenefitof   clusteringisthatclusteringmethodsdonotdependonanypriorknowledgeofthedata.Hence,throughclusteranalysis, X interpretinglargedatasetsbecomes,inmostcases,mucheasier.Howeveroneofthemajorchallengesinclusteranalytics 0 isdeterminingtheexactnumberofclusters,k,withinthedata.Formethodssuchask-meansandnonnegativematrix ` factorization,choosingtheappropriatekisimportant.OthermethodssuchasSingularValueDecompositionandReverse 8 Simon-_Ando_Ԁarenotasdependentonbeginningwiththecorrectk.Ourtaskthissummerwastoexploremethodsof  derivingthenumberofclustersfromthedataset.Weusedresultsfromotherclusteringmethodstofindthecorrectk.  ThisresearchwillaidintheunderstandingofdatasetssuchastheBroadInstituteleukemiadatasetaswellastheIris h dataset. @  ,&%%&_Kayla_ԀVon_Hagel_ԀKennesawStateUniversity H  Title:AccessControlLogic  Abstract:Accesscontrolisconcernedwiththepoliciesandmechanismsthatpermitordenytheuseofaresourceor x capabilityinamilitaryoperation.Thereexistsnostandardizedmethodtoreasonaboutorrepresentaccesscontrol,so P mathematicianscanutilizeAccessControlLogictoreasonandprovethesoundnessofaccesscontroldesignsand ( specifications.TheInformationAssuranceInternshipof2011allowedinterstoexploretheelementsofAccessControl X  LogicandMissionAssuranceinordertodesign,developandverifycuttingedgesystemsfortheUnitedStatesAirForce. 0! TheapplicationofAccessControlLogicconsistsofrigorousproofspertainingtoconfidentiality,integrity,availability, " authenticationandattribution.EachsolutioncreatedbytheinternsgavetheAirForceResearchLaboratoryvaluable # insightonthestateofthemilitarywithin_cyber_Ԁoperationsandiscurrentlybeingusedaframeworkfornewsolutions.  `$ #&%%,&^# ,&%%&RyanCarrollRhodesCollege#&%%,&$#,&%%&  h" & Title:GeneralizingtheEuler_Satake_ԀCharacteristicofClosed3_Orbifolds_ $!( Abstract:TheEulercharacteristicofamanifold,aspacethatyoucanpictureasasphereortorus,isaninvariantwhich $") providesanabundanceofinformationaboutthespace'sshapeincertaindimensions.An_orbifold_Ԁisatopologicalspace %p#* containingsingularpointsinducedbygroupactionssuchasreflectionsorrotations.Thesingularpointsofan_orbifold_ &H$+ necessitatedanewinvariantbedefinedtotakethesesingularitiesintoconsideration;this upgradedinvariantisknown x' %, astheEuler_Satake_Ԁcharacteristicwhichconsidersthesingularitiesasfractionsofaspace.Morerecently,CarlaFarsiand P(%- Christopher_Seaton_Ԁhaveworkedtofurthergeneralizethese_invariants_,exploringamorerecentfamilyof_invariants_ ()&. knownas__ԄEuler_Satake_Ԁcharacteristics.InsteadofconsideringtheEuler_Satake_Ԁcharacteristicofthe_orbifold_Ԁitself,this *'/ approachappliestheEuler_Satake_Ԁcharacteristictothepiecesofan_orbifold_Ԁwhichresultfromstrategicallybreaking *(0 downthe_orbifold_Ԁviasomefinitelygeneratedgroup__#&%%,&,%#,&%%&._Duval_,_Schulte_,_Seaton_,andTaylorshowedthesignificanceof +X)1 these_invariants_Ԁinclassifying2_orbifolds_,andlater_Seaton_ԀandIshoweditsclassificationofsingularpointson_orientable_ ,0*2 3_orbifolds_.Nowthetaskistotransitiontheseresultsintothemorecomplicatedcaseofnon_orientable_Ԁ3_orbifolds_. `-+3 Intuitively,non_orientable_Ԁspacesarethosewhich,ifyouwerewalkingaroundontheirboundary,youwouldnotbeable 8.+4 todefinearelativeleftorright.Thistalkwillprovidethemachineryneededtoextendthese_invariants_Ԁtothenon /,5 _orientable_Ԁcase,explicitlystatetheformulasofthe__#&%%,&,#,&%%&ԄEuler_Satake_Ԁcharacteristicsofgeneralclosed3_orbifolds_Ԁfor X certain__#&%%,&Y1#,&%%&,anddiscusstheinformationcontainedincertaincollectionsofthese_invariants_. 0 #&%%,&\2# JordanPalmerUniversityof_Montevallo_   Title:_RSA_ԀEncryption 8 Abstract:Sincetheirdiscovery,primenumbershavebeenconsideredapartofpuremathematicswithnorealworld h applications.Theprimenumbersarerandomlydistributedthroughoutthenumberline,andanequationforfindingor @ predictingthelocationofprimenumbershasyettobediscovered.Forthesereasons,moderncryptologistshavemade   usageofprimenumbersinvariousways.Cryptographycanbedefinedastheconversionofdataintoascrambledcode    thatcanbedecipheredandsentacrossapublicorprivatenetwork.Incryptography,primenumbersareusedaskeysfor  p  theconversionofdatabecausetheyonlyhavetwofactors.Dr.CartierandIareusingjavabasedprogramstogenerate  H  primeandpseudoprimenumbers,inthehopesoflearningmoreaboutthem.WearealsousingMapletocode_RSA_ x  encryptionalgorithms_RSA_Ԁstandsfor_Rivest_,ShamirandAdlemanandisanalgorithmforpublickeycryptography.We P  arealsocreatingagraphicaluserinterfacethatwillmakethe_encryptionand_Ԁdecryptionprocessmoreusersfriendly. (  Since_RSA_Ԁencryptionreliesheavilyonprimenumbers,wearelookingatseveralprimeproducingalgorithmsaswellas   someofthenumbertheorybehindprimenumbers.    _Stefanie_Ԁ_Erdman_Ԁ-KennesawStateUniversity 0  Title:IntermediateValueTheoremanditsApplications 8 Abstract:EverybodyknowsthatTopologyandAnalysisaremutuallyenrichingfields.However,thereisoneparticularly  beautifultopologicalresult,whichisintroducedasearlyasinthebeginningCalculuscoursesbuthasmany  counterintuitiveimplications.InthistalkwewillprovetheIntermediateValueTheoreminitsgeneralformanddiscuss h itsapplications,particularlytothe_Brouwer_ԀFixedPointTheorem.AmongothercuriousapplicationsoftheIntermediate @ ValueTheoremtobediscussedisthefollowinginterestingfact:assumingthesurfaceofEarthisasphere,andsurface p temperatureisacontinuousfunctiondefinedonthesphere,atanygiventimethereisapointonEarththathasexactlythe H sametemperatureasthepointdirectlyoppositetoit.    RyanAndersonKennesawStateUniversity  x _Title:Computing_Ԁtheminimum-normleast-squaressolutionofAx=bwithGauss-Jordanelimination ( Abstract:GivenasystemoflinearequationsAx=b,thesolutionisx=A1bifAisanonsingularsquarematrix.The X  solutioncanbefoundusingGaussJordanelimination.ForgeneralmatrixA(eitheranonsquarematrixorsingular 0! squarematrix),oneseekstofindtheminimumnormleastsquaressolutionA'bofthelinearsystemAx=bwhereA'is " theMoorePenroseinverseofmatrixA.Inthetalk,wewilldiscussawaytofindA'busingGaussJordanelimination. # Thisismotivatedbyarecentpaperby_Xingping_ԀShengand_guoliang_ԀChenforcomputingA'withGaussJordan  `$ Elimination. !8%  _Garrett_ԀRose-TennesseeWesleyanCollege @# '  Title:Predator/Prey:herbivoresversusplankton $") Abstract:Analysisofaherbivore/planktonmodel-lookingatthechangedynamicsnearthepositiveequilibrium.Showing %p#* thecoexistenceofthetwospecies. &H$+  _Zachery_ԀLindsey-UniversityofTennessee P(%-  Title:Simulationof_SLE_ *'/ Abstract:WeintroduceSchramm-_Loewner_ԀEvolution,whichisamethodofassigningregionsoftheupperhalfplane, *(0 called"hulls",tofunctions.Ithasimportantapplicationstoprobability,andwediscusstheimplementationofan +X)1 algorithmfornumericallyfindingthehullsproducedbyagivendrivingfunction.Thisnewcodeseekstobettermodel ,0*2 self-intersectionandspacefillingpropertiesofhullsarisingfromBrownianmotionthanBLEAT,whichusesasimilar `-+3 algorithmtomodel_SLE_. 8.+4  #XX%&# /,5 POSTERS:2:403:15 X &%XXShannonBryce-KennesawStateUniversity 0  Title:AdaptiveInterpolationofHyperbolicFunctionsbyLinearSplinesinL2-error:LocalEstimate  Abstract:Splinesarepiecewisepolynomialfunctions.Duetotheirsimplicity,approximationbyvarioustypesofsplines ` isoneofthestandardproceduresinmanyapplications(computer-aidedgeometricdesign,imageprocessing,numerical 8 solutionsforpartialdifferentialequationsetc.).Inalltheseapplications,thereisastandarddistinctionbetweenuniform h (meshelementsdontvarymuch)andadaptive(meshadjuststothegivenfunction)methodsofconstructingameshto @  buildsplines.Intheuniformcase,thedomainofinterestisdecomposedintoapartitionwhereelementsdonotvary    much.However,clearlymoreaccurateadaptivemethodsarehighlynonlinearandnopolynomialtimealgorithmexiststo    provideanoptimal_approximant_Ԁforeachgivenfunction.  p  Therefore,thenextnaturalquestionwouldbetoconstructasymptoticallyoptimalsequencesofpartitions(thatare x  triangulationswhenweuselinearsplines)andinterpolatingsplinesonthem.Tothatendwefirstneedtofindatriangle P  thatislocally(forsomesmallregion)optimal.Inthistalkweshalldiscusshowtofindtheoptimalshapeofthemesh (  elementtriangleinthecaseofapproximatingthebivariatefunctionswithnegativecurvaturebyinterpolatinglinear   splines,andtheapproximationerroronit.   _Teagan_ԀBryce-KennesawStateUniversity 0  Title:L2#XX%&H#&%XX-errorofAdaptiveInterpolationofHyperbolicFunctionsbyLinearSplines:LocalEstimate 8 Abstract:OncewefoundthelocalL2#XX%&O#&%XX-errorofapproximatingthebi-variatefunctionswithnegativecurvatureby  interpolatinglinearsplines,wewillputittogethertoobtaintheglobalestimatefortheoptimalerror.Weshalldiscussa  sketchofanalgorithmtoconstructasymptoticallyoptimalsequencesoftriangulationsandwillpresentthe_asymptotics_Ԁof h theoptimalerror. @ #XX%&P#L  M  L  M  L  M    L  M   XXXX  &%X XChris_Carlile_ԀUniversityofTennessee H  #&%% &R# &%%&Title:WhyDoWeLikeMath?  Abstract:Mathematicsisasportofthemind,alanguageofabstractionthatsinceitsinceptionhasconstantlywidenedits x scopeasafieldofhumanstudy.Itsutilityisundeniable,butwhatpropertiesdomathematicsandtherealityitdescribes P holdthatgivemaththatutility?Andlookingbeyondutility,whatisthepointofdoingmathematicsfornootherreason (  thantodomathematics?Whilethemainquestionaddressedisnot whydon'tsomepeopledislikemathor howcanwe X! justifygettingpaidtodomath,wewillseethatappreciationandaptitudeformathematicsrequiresnotonlyknowledge, 0" linearthinkingandhardstudy,butalsodemandsanappreciationforholismandinterconnectedness.Mathematicshelps  # usuncoverdeeptruthsaboutformsandthenatureofthetruthitselfthatlenditabeautytobeadmired,differentbutthe  $ sameasthebeautywefindinartandmusicasareflectionoftruthbothinsideandoutsideofhumanexperience.# XX% &S# !`% #XXX X̱S#  &%XX Duke_DeLoache_Ԁ-Davidsoncollege h#!'  Title:OptimizingGeneSplitsitesforBacterialComputing %") (Duke_DeLoache_,LillianWilson,A.MalcolmCampbell,LaurieJ._Heyer_) %#* Abstract:WeworkedasapartofDavidsonCollegessyntheticbiologyteam,incollaborationwithundergraduate &p$+ researchersatMissouriWesternUniversity,tosolvethe_Hamiltonian_ԀPathProblemusingDNAandbacterialcomputing. 'H%, Buildingonresearchdonebythe2009_iGEM_Ԁteam,weexperimentedwithanewapproachcalledGoldenGateAssembly x( &- (_GGA_)tosplitgenes.Wedesignedpartswiththegoalofbuildingabacterialcomputercapableofsolvinga9-node P)&. problem.Themajoradvantageof_GGA_Ԁisthatoncepartsarebuilt,theproblemcanbesolvedveryquickly(withinone (*'/ day).Buildingparts,however,requiresvarioustimeconsumingdecisionsthatneedtobemadewithprecision.To +(0 acceleratethedesignprocessupforfutureresearchers,webuiltatoolthatfindsoptimalsplitlocationsforasetof +)1 user-definedgenes,takingintoaccountanumberofbiologicalconstraints.Ouronlinetoolusesabinaryintegerlinear ,X*2 programthatweformulatedandsolvedwithIBMs_CPLEX_Ԁoptimizer.ItcanbeaccessedatthefollowingURL: -0+3 http://gcat.davidson.edu/iGEM11/Optimizer/WiserOptimizer `.,4  8/,5  ,&%%&Josh_Lipsmeyer_ԀUniversityofArkansasatLittleRock X  Title:TheStrengthofthe_Henstock_Ԅ_Kurzweil_ԀIntegralinTermsoftheMeasureofSingularitySets  #&%%,&_#,&%%&Abstract:Thepurposeofthisstudyistoofferanewwayofestablishingthestrengthofthe_Henstock_Ԅ_Kurzweil_Ԁintegral  overRiemannand_Lebesgue_Ԁbydeterminingthemaximummeasureofthesingularitysetswhichseparatean_Henstock_Ԅ ` _Kurzweil_Ԁ_integrable_Ԁfunctionfrombeingeither_Lebesgue_ԀorRiemann_integrable_.Itiswellknownthat_that_Ԁif 8 f:[a;b]isRiemann_integrable_,thenitisalso_Lebesgue_Ԁ_integrable_.However,theconverseofthisstatementisnot h true.Itisalsoknownthattheiff:[a;b]#&%%,&fa#,&%%&Ԁis_Lebesgue_Ԁ_integrable_,thenitisalso_Henstock_Ԅ_Kurzweil_Ԁ_integrable_. @ Again,theconverseofthisstatementisalsonottrue.Inotherwords,letIbeaclosedintervalin#&%%,&e#,&%%&.Nowlet#&%%,&Pg#,&%%&(I)bethe   setofallfunctionsthatareRiemann_integrable_ԀonI,letL(I)bethesetofallfunctionsthatare_Lebesgue_Ԁ_integrable_ԀonI,    andletHK(I)bethesetofallfunctionsthatare_Henstock_Ԅ_Kurzweil_Ԁ_integrable_ԀonI.Then#&%%,&g#,&%%&(I)isapropersubsetofL(I)  p  andL(I)isapropersubsetofHK(I).Supposef:I#&%%,&i#,&%%&ԀisHK_integrable_.ApointxIiscalledregularinRiemannif  H  thereexistsanopenintervalQ(x)containingx,suchthatfisRiemann_integrable_ԀonIQ(x).Apointx#&%%,&j#,&%%&ԀIiscalled x  regularin_Lebesgue_ifthereexistsanopenintervalP(x)containingx,suchthatfis_Lebesgue_Ԁ_integrable_ԀonIP(x).We P  denotethesetofallregularinRiemannpointsbyU(f)andthesetofallregularin_Lebesgue_ԀpointsbyV(f).Let (  W(f)=I\U(f)andX(f)=I\V(f).WedefineW(f)andX(f)tobethesingularitysetsonIinRiemannand_Lebesgue_,   respectively.TheessentialdifferenceofaHK_integrable_Ԁfunctionanda_Lebesgue_ԀorRiemann_integrable_Ԁfunctions   comesdowntothemeasureofthesingularitysets.WeusethismeasuretoestablishthestrengthoftheHKintegral.#&%%,& l#,&%%& X #&%%,&fp# MeganN_McElmurray_Ԁ-BelmontUniversity `  Title:TheHighSchoolStudent:Whatwillshegrowuptodo?  Abstract:BasedonahighschoolstudentsSATscoresandGPA,thereisatheorythatitispossibletopredictastudents  initialcollegemajor.Researchhasbeenfoundtosupportthistheory.Basedonresearchfromthepaststudyin2008,the h UniversityofMassachusettscollecteddatathatconsistedofintendedmajor,MathSATscore,CriticalReadingSAT @ score,CombinedSATscore,GPA,andgender.Whileanalyzingthisdata,apredictioncanbemadeforstudentsof p certaincombinationsofSAT,GPA,andgenderfactorsforwhichmajoraspecificstudentwillmostlikelystudy.This H studyalsoallowsforcomparisonbetweengenders,potentialmajors,andtheratiobetweenstandardizedtestingandGPA   averages.Forexample,onegenderhashighertestscores,whiletheothergenderhasanoverallhigherGPA.Thesedata  valuescanalsodeterminewhichareasofconcentrationseemtohavestudentswithsimilarminds.Theresultsofthisdata x concludethatthereisageneralpatternamongstudentswithsimilarnumbers,andeveryfactorthatgoesintothemodel P fordeterminingapredictedmajorcangreatlyaffecttheoutcome. (  BradWeaver-BelmontUniversity 0!  Title:AregressionanalysisoftheAmericanfrown # Abstract:AccordingtoaNationalHealthandNutritionSurvey,theuseofantidepressantshasincreasedby400%inthe  `$ pasttwodecades.WhatismakingAmericanssosad?Weareallawareofthecommoncausesandeffectsofdepression, !8% butaresomeofthesecausesmoreinfluentialthanothers?Usingsurveyedinformationfrom46states,wehaveanalyzed h" & theinfluenceofvariousdepressionfactorsbyconstructingamultipleregressionmodel.Withthismodel,weareableto @# ' predictthenumberofdepressioncasesinanygivenstate.Someofourfactorsinclude,unemployment,population, $!( alcoholconsumption,regionalweather,andaveragestateincome. $") #XX%&X#