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THEFIRSTLESSONOFTHESCHOOLYEARStatisticalThoughtEnglishEditionCourseware目CONTENTSIntroductionDescriptivestatisticsFundamentalsofProbabilityTheoryRegressionanalysis錄目CONTENTSStatisticalDecisionTheoryTimeseriesanalysisIntroductiontoStatisticalSoftware錄01IntroductionStatisticalthinkingisthekeytosolvecomplexproblems:Ithelpsusanalyzedata,identifypatterns,anddrawconclusionsfromevidencebaseddata,whichisessentialinmakinginformeddecisionsandimprovingdecisionmakingaccuracyStatisticalthinkingenhancingcriticalthinkingskills:Itresourcesustoquestionassessments,challengeconventionalwisdom,andthinkindependently,morethanjustacceptinformationatfacevalueStatisticalthinkingisapplicableacrossvariousfields:Itisnotlimitedtothefieldofstatistics,butcanbeappliedinfieldssuchasbusiness,medicine,science,andengineeringtosolvepracticalproblemsandimprovedecisionmakingeffectivenessTheimportanceofstatisticalthinkingTheapplicationfieldsofstatisticsBusinessandeconomics:Statisticsarewidelyusedinbusinessandeconomicresearch,analysis,anddecisionmakingprocessesTheyhelptounderstandconsumerbehavior,markettrends,andfinancialindicators,andareessentialinareassuchasmarketing,finance,andoperationsmanagementMedicineandhealthcare:StatisticsplayaclinicalroleinmedicalresearchandhealthcaredeliveryTheyareusedtoanalyzepatientdata,evaluatetheeffectivenessofdrugsandtreatmentmethods,andidentifypatternsindiseaseoutbreaksorchronicconditionsScienceandengineering:StatisticsareessentialinscientificresearchandengineeringdesignTheyareusedtoanalyzeexperimentaldata,validatescientifichypotheses,andimprovethereliabilityandprecisionofengineeringprojects01DescriptivestatisticsDatasourceDatacanbecollectedfromvarioussources,suchassurveys,experiences,observations,anddatabasesSamplingSamplingmethodsshouldbedesignedtoensurerepresentativeandunbiaseddataDataorganizationDatashouldbeorganizedinastructuredandsystematicmanualforanalysisDatacollectionandorganizationUsedtocomparecategoricaldata,showingthefrequencyorpromotionofeachcategoryBarchartUsedtoshowthepromotionofawhole,comparingdifferentpartsPiechartUsedtoshowtrendsorrelationshipsovertimeLinechartUsedtoshowtherelationshipbetweentwocontinuousvariablesScatterplot01030204ChartdisplayofdataABCDDigitalfeaturesofdataMeasuresofcentraltensionShowthecentraltensionofthedata,suchasmean,media,andmodeCategoricaldataDatathatcanonlytakeoncertificatevaluesorcategories,suchasgenderorcountryMeasuresofdistributionShowthespreadofthedata,suchasvarianceandstandarddeviationContinuousdataDatathatcantakeonanyvaluewithinarange,suchasheightorweight01FundamentalsofProbabilityTheoryThebasicconceptofprobabilityThebasicconceptofprobabilitydefinesthelifestyleofaneventhappeningSummaryProbabilityisameasureofthelikelihoodofaneventoccurring,expressedasanumberbetween0and1Aprobabilityof0meanstheeventcannothappen,whileaprobabilityof1meanstheeventwillhappenProbabilitytheoryisthefoundationforstatisticalinferenceanddecisionmakingDetailsRandomvariablesarequantitiesthatcantakedifferentvalues,andtheirdistributionsdescribethelifestyleofeachvalueSummaryRandomvariablescanbediscrete,takingafixedsetofvalues,orcontinuous,takinganyvaluewithinarangeDistributionsdescribethelikelihoodofeachvalue,suchasthebinarydistributionfordistinctvariablesorthenormaldistributionforcontinuousvariablesDetailsRandomvariablesandtheirdistributionsSummaryParameterestimationistheprocessofinferringunknownparametersofadistribution,whilehypothesistestingisusedtoevaluatewhereagivenhypothesisistrueorfalse要點一要點二DetailsParameterestimationtechniquesincludemaximumlikelihoodestimationandBayesianestimationHypothesistestingusesstatisticalteststodeterminewhichgivenhypothesisissupportedbythedataornotCommonlyusedhypothesistestsincludethet-test,chisquaretest,andANOVAtestParameterestimationandhypothesistesting01RegressionanalysisDefinitionUnivariatelinearregressionanalysisisastatisticalmethodusedtostudythelinearrelationshipbetweenadependentvariableandanindependentvariable.ApplicationscenarioWhenavariablemaybeinfluencedbyameasurableandfixedvariable,andthisrelationshipcanbeapproximatedbyastraightline,univariatelinearregressionanalysiscanbeused.Univariantlinearregressionstep1.Determinetheindependentanddependentvariables.Univariantlinearregression2.Collectdata.3.Drawascatterplottoobservetherelationshipbetweentheindependentanddependentvariables.UnivariantlinearregressionUnivariantlinearregression4.Establishandtestregressionequations.5.Explaintheresultsandpredictfuturevalues.VSMultiplelinearregressionanalysisisastatisticalmethodusedtostudythelinearrelationshipbetweenadependentvariableandmultipleindependentvariables.ApplicationscenarioWhenavariablemaybeinfluencedbymultiplemeasurableandfixedvariables,andthisrelationshipcanbeapproximatedbyastraightline,multiplelinearregressionanalysiscanbeused.DefinitionMultiplelinearregressionVSstep1.Determinetheindependentanddependentvariables.Multiplelinearregression2.Collectdata.3.Drawascatterplotmatrixandobservetherelationshipbetweeneachindependentvariableandthedependentvariable.Multiplelinearregression4.Establishandtestregressionequations.5.Explaintheresultsandpredictfuturevalues.MultiplelinearregressionDefinitionNonlinearregressionanalysisisastatisticalmethodusedtostudynonlinearrelationships.ApplicationscenarioWhentherelationshipbetweentheindependentanddependentvariablesisnotlinearandcannotberepresentedbyastraightline,nonlinearregressionanalysiscanbeused.Nonlinearregressionanalysisstep1.Determinetheindependentanddependentvariables.Nonlinearregressionanalysis2.Collectdata.3.Drawascatterplottoobservetherelationshipbetweentheindependentanddependentvariables.Nonlinearregressionanalysis4.Chooseasuitablenonlinearmodelforfitting.5.Verifythefittingeffectofthemodelandmakepredictions.Nonlinearregressionanalysis01StatisticalDecisionTheoryUtilityFunction:TheBayesiandecisionmakeralsohasautilityfunctionthatassignsnumericalvaluestodifferentoutcomesTheBayesianaimstomaximizetheexpectedutilityofhisdecisionsBayesian:TheBayesianapproachtodecisionmakingassessmentsthatthedecisionmakerhasadegreeofuncertaintyaboutthestateofnatureTheBayesianupdateshisbeliefinthelightofnewinformationandmakesoptimaldecisionsbasedontheupdatedbeliefSubjectiveProbability:InBayesian,probabilitiesaresubjectivebeliefsaboutthestateofnatureTheBayesianupdateshisbeliefinusingBayes'theoryandmakesoptimaldecisionsbasedontheupdatedbeliefBayesiandecisiontheoryInriskdecisionanalysis,thedecisionmakercalculatestheexpectedvalueofeachdecisionoption,whichistheweightedaverageofthepossibleoutcomesThedecisionmakerselectstheoptionwiththehighestexpectedvalueSensitivityanalysisisusedtoidentifythemostsensitivefactorsthataffecttheexpectedvalueofadecisionoptionThedecisionmakercanthenfocusonimprovingthosefactorstoincreasetheexpectedvalueDecisiontreesareusedtorepresentdecisionoptionsandtheirpossibleoutcomesThedecisionmakercalculatestheexpectedvalueofeachbranchofthetreeandselectsthebestoptionExpectedValueSensitivityAnalysisDecisionTreesRiskdecisionanalysisUncertaintiesUncertaintiesrefertothelakeofknowledgeaboutthestateofnatureorthepossibleoutcomesofadecisionoptionThedecisionmakermustmakedecisionsbasedonincompleteinformationorlimitedknowledgeRiskRiskreferstothelikelihoodofnegativeoutcomesorlossesThedecisionmakermustevaluatetheriskassociatedwithdifferentdecisionoptionsandtakeappropriatemeasurestominimizetheriskStochasticDominanceStochasticdominanceisamethodforcomparingdecisionoptionsbasedontheirexpectedvaluesandrisksAdecisionoptionissaidtostochasticdominateanotheroptionifithashigherexpectedvalueandlowerriskUncertaintyandriskdecisionmaking01TimeseriesanalysisDeterminewhetherthetimeseriesisstationaryIntimeseriesanalysis,thefirststepistodeterminewhetherthetimeseriesisstationary.Stationarityreferstothefactthatthestatisticalcharacteristicsofatimeseriesdonotchangeovertime.Thecommonlyusedmethodsfortestingstationarityincludegraphtest,unitroottest,andKPStest.TestingthestationoftimeseriesPredictionmethodsfortimeseriesPredictingfuturevaluesoftimeseriesPredictingthefuturevaluesoftimeseriesisoneoftheimportantapplicationsoftimeseriesanalysis.Commonpredictionmethodsincludeexponentialsmoothing,ARIMAmodels,neuralnetworks,supportvectormachines,etc.Thesemethodsarebasedonhistoricaldataandpredictfuturetrendsandfluctuationsbyestablishingmathematicalmodels.VSDecomposetimeseriesintotrend,seasonal,andrandomfluctuationcomponentsTimeseriesdecompositionanalysisisamethodofdecomposingacomplextimeseriesintoseveralsimplecomponents.Thesecomponentsincludetrends,seasonality,andrandomfluctuations.Throughdecomposition,itispossibletobetterunderstandthestructureandcharacteristicsoftimeseries,andadoptcorrespondinganalysisandpredictionmethodsfordifferentcomponents.Compositionanalysisoftimeseries01IntroductiontoStatisticalSoftwareSpreadsheetandChartingCapabilitiesExcelisawidelyusedspreadsheetprogramthatprovidesuserswiththeabilitytocreateandanalyzedatausingvariousstatisticalfunctionsandcharttypesStatisticalAddinsExcelhasavarietyofstatisticaladdinsavailablethatcanenhanceitscapabilities,improvingmoreadvancedstatisticalanalysistoolsDataAnalysisToolsExcelincludesasuiteofdataanalysistools,suchastheAnalysisToolpack,whichallowsuserstoperformvariablestatisticaloperations,includingdescriptivestatistics,hypothesistesti