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Koncept

Regresní analýza je matematický model. Když má závislá proměnná a nezávislá proměnná lineární vztah, jedná se o speciální lineární model.

Nejjednodušší případ je lineární regrese proměnné, která se skládá z nezávislé proměnné a závislé proměnné, která je zhruba lineárně související; model je Y=a+bX+ε(X je nezávislá proměnná, Y je příčinouProměnná, εje náhodná chyba).

Usuallyassumethatthemeanvalueoftherandomerroris0,andthevarianceisσ^2(σ^2﹥0,σ^2hasnothingtodowiththevalueofX).Ifitisfurtherassumedthattherandomerrorfollowsanormaldistribution,itiscalledanormallinearmodel.Generally,iftherearekindependentvariablesand1dependentvariable,thevalueofthedependentvariableisdividedintotwoparts:onepartisaffectedbytheindependentvariable,thatis,expressedasitsfunction,thefunctionformisknownandcontainsunknownparameters;theotherpartisdeterminedbyOtherunconsideredfactorsandrandomeffectsarerandomerrors.

Whenthefunctionisalinearfunctionwithunknownparameters,itiscalledalinearregressionanalysismodel;whenthefunctionisanonlinearfunctionwithunknownparameters,itiscalledanonlinearregressionanalysismodel.Whenthenumberofindependentvariablesisgreaterthan1,itiscalledmultipleregression,andwhenthenumberofdependentvariablesisgreaterthan1,itiscalledmultipleregression.

Obsah regresní analýzy

Hlavní obsah regresní analýzy je následující:

①Startingfromasetofdata,determinethequantitativerelationshipbetweencertainvariables;Thatis,amathematicalmodelisestablishedandunknownparametersareestimated.Usuallytheleastsquaremethodisused.

②Otestujte důvěryhodnost těchto vztahů.

③Intherelationshipbetweenmultipleindependentvariablesaffectingadependentvariable,judgewhethertheindependentvariablehasasignificantimpact,andselectthesignificantimpactintothemodel,andeliminateinsignificantvariables.Stepwiseregression,forwardregression,andbackwardregressionareusuallyused.

④Usetherequiredrelationshiptopredictorcontrolacertainprocess.

Theapplicationofregressionanalysisisveryextensive,andtheuseofstatisticalsoftwarepackagescanmakevariousalgorithmsmoreconvenient.

Typy regrese

Hlavní typy regrese jsou: lineární regrese, křivočará regrese, binární logistická regrese a vícenásobná logistická regrese.

Applicationofanalysis

Correlationanalysisstudiesthecorrelationbetweenphenomena,thedirectionandclosenessofcorrelation,andgenerallydoesnotdistinguishbetweenindependentvariablesordependentvariables.Regressionanalysisistoanalyzethespecificformsofcorrelationbetweenphenomena,determinethecausalrelationship,andusemathematicalmodelstoexpressthespecificrelationship.Forexample,fromthecorrelationanalysis,wecanknowthatthe"quality"and"usersatisfaction"variablesarecloselyrelated,butwhichvariablebetweenthesetwovariablesisaffectedbywhichvariable,andthedegreeofinfluence,requiresregressionanalysisMethodtodetermine.

Generallyspeaking,regressionanalysisistodeterminethecausalrelationshipbetweendependentvariablesandindependentvariables,establisharegressionmodel,andsolvethevariousparametersofthemodelbasedonthemeasureddata,andthenevaluatewhethertheregressionmodelisItcanfitthemeasureddatawell;ifitcanfitwell,furtherpredictionscanbemadebasedontheindependentvariables.

Forexample,ifyouwanttostudythecausalrelationshipbetweenqualityandusersatisfaction,inapracticalsense,productqualitywillaffectusersatisfaction,sosetusersatisfactionasthedependentvariableandrecorditasY;Qualityistheindependentvariable,denotedasX.AccordingtothescatterplotinFigure8-3,thefollowinglinearrelationshipcanbeestablished:

Y=A+BX+§

where:AandBareundeterminedparameters,andAisregressionTheinterceptofthestraightline;Bistheslopeoftheregressionline,whichrepresentstheaveragechangeofYwhenXchangesbyoneunit;§istherandomerrortermthatdependsonusersatisfaction.

LinearregressioncanbeeasilyimplementedintheSPSSsoftware.Theregressionequationisasfollows:

y=0,857+0,836xÚsečka regresní přímky na ose ysou 0,857a se sklonem 0,836,To znamená,pro každý jeden bod zlepšení kvality,spokojenost uživatelů se zvyšuje o 0,836bodůvprůměru;jinými slovy,příspěvekzlepšeníkaždých 36bodů

Theexampleshownaboveisasimplelinearregressionproblemofoneindependentvariable.Duringdataanalysis,thiscanalsobeextendedtomultipleregressionofmultipleindependentvariables.PleaserefertothespecificregressionprocessandmeaningRefertorelevantstatisticsbooks.Inaddition,intheSPSSresultoutput,R2,FtestvalueandTtestvaluecanalsobereported.R2isalsocalledthecoefficientofdeterminationoftheequation,whichindicatesthedegreeofinterpretationofthevariableXtoYintheequation.ThevalueofR2isbetween0and1.Thecloserto1,thestrongertheinterpretationabilityofXtoYintheequation.R2isusuallymultipliedby100%toexpressthepercentageofYchangeexplainedbytheregressionequation.TheFtestisoutputthroughtheanalysisofvariancetable,andthesignificancelevelisusedtotestwhetherthelinearrelationshipoftheregressionequationissignificant.Generallyspeaking,significancelevelsbelow0.05aremeaningful.WhentheFtestpasses,itmeansthatatleastoneoftheregressioncoefficientsintheequationissignificant,butnotallregressioncoefficientsaresignificant,soaTtestisneededtoverifythesignificanceoftheregressioncoefficients.Similarly,theTtestcanbedeterminedbythesignificanceleveloralook-uptable.Intheexampleshownabove,themeaningofeachparameterisshowninTable1-1.

Test lineární regresní rovnice v tabulce 1-1