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Samenvatting Econometrie en Multivariate Statistiek
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Samenvatting van EMS in 3de bachelor Handelsingenieur (in de beleidsinformatica) aan UA, gegeven door P. Goos. Zowel slides als boek.
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Samenvatting Econometrie enMultivariate Statistiek
1
,Inhoudsopgave
Introductie regressieemodellen/analyse.............................................................................................4
Verband zoeken tussen 2 of meer variabelen multvariate statstek.................................................4
Model: y = f(x1,x2,…) + ....................................................................................................................4
Lineaire regressiemodellen................................................................................................................5
Enkelvoudiege lieneaiere regressiee (kleiene herhalieng).............................................................................5
Traditonele model.............................................................................................................................5
Kleinste kwadratenmethode (least squares estmates)......................................................................6
Eigenschappen van kleinste kwadratenschaters...............................................................................7
Gauss-Markov Stelling.......................................................................................................................8
2 schaten.......................................................................................................................................9
Statsche interferente tussen ß0 en ß1................................................................................................9
Betrouwbaarheidsintervallen 1-...................................................................................................10
Hypothesetoetsen om helling en intercept te toetsen......................................................................10
Kwaliteit van het regressiemodel.....................................................................................................10
Signifcante van het model testen...................................................................................................11
Voorspellingen.................................................................................................................................11
Regressiediagnostek.......................................................................................................................12
Meervoudiege lieneaiere regressiee.......................................................................................................13
Het model........................................................................................................................................13
Schaten van meervoudige lineaire regressiemodel.........................................................................13
Eigenschappen van de kleinste kwadratenschater.........................................................................14
Schaten van (grote gelikkheid met schaten bik enkelvoudige regressie).........................................15
Statsche interferente (helemaal analoog)......................................................................................16
Kwaliteit van het regressiemodel (uitbreiding)................................................................................18
Informate criteria............................................................................................................................19
Signifcante van het model testen...................................................................................................19
Voorspellingen.................................................................................................................................20
Multcollineariteit............................................................................................................................20
Kwalietatieve verklarende varieabelen...............................................................................................25
Kwalitateve verklarende variabele met 2 niveaus...........................................................................26
Effects-type coding...........................................................................................................................26
Kwalitateve verklarende variabele met meer dan 2 niveaus...........................................................26
Toetsen van signifcante..................................................................................................................27
Opsplitsen van data.........................................................................................................................28
Heteroscedasticieteiet.........................................................................................................................28
Al gezien...........................................................................................................................................28
Nu....................................................................................................................................................28
Autocorrelatie.................................................................................................................................32
Tot nog toe.......................................................................................................................................32
Nu....................................................................................................................................................32
Wegwerken......................................................................................................................................33
Veralgemeende lieneaiere regressieemodellen.....................................................................................38
Waarom veralgemeende lineaire modellen.....................................................................................38
Wat zikn veralgemeende lineaire modellen......................................................................................38
Logisteke regressie (voorbeeld van ttanic).....................................................................................38
Schaten van het model (logistek regressiemodel)..........................................................................39
Enkelvoudiege varieantieeanalyse.......................................................................................................41
2
, Inleidend voorbeeld..........................................................................................................................41
Specifeke ANOVA-schrikfwikze.........................................................................................................41
Schaten van ANOVA-model............................................................................................................41
Contrasten.......................................................................................................................................43
Probleem bik betrouwbaarheid bik toetsen met meerdere contrasten.............................................43
Toetsen van assumptes...................................................................................................................44
Stochastsche factorinstellingen.......................................................................................................45
Schaters voor..................................................................................................................................45
Tweevoudiege varieantieeAnalyse.......................................................................................................46
Schaters..........................................................................................................................................46
Signifcante effecten........................................................................................................................47
Toetsen van contrasten....................................................................................................................48
Ongelikk aantal waarnemingen........................................................................................................48
Meervoudiege varieantieeanalyse (Nog een uietbreiedieng).....................................................................50
Voorbeeld.........................................................................................................................................50
Model...............................................................................................................................................50
Covarieantieeanalyse.........................................................................................................................50
Nut covariante-analyse...................................................................................................................50
Ancova Model (covariaat GPI-score)................................................................................................51
Inleiedieng tot multivarieaatanalyse.....................................................................................................52
Notate’s..........................................................................................................................................52
Euclidische afstand..........................................................................................................................53
Kansvector en bikbehorende verdelingsfuncte.................................................................................55
Multvariaat normale verdeling.......................................................................................................55
Prienciepale Componenten Analyse (PCA)..........................................................................................56
Zoeken naar principale componenten..............................................................................................56
Bewikzen...........................................................................................................................................57
Eigenschappen van de principale componenten..............................................................................58
Opmerkingen...................................................................................................................................58
Bepalen van het aantal zinvolle principale componenten................................................................59
Principale componentenscores........................................................................................................59
Voorbeeld.........................................................................................................................................59
Berekening principale componentenscores (voorbeeld)...................................................................60
Factoranalyse..................................................................................................................................60
Doel..................................................................................................................................................60
Uitgangspunt...................................................................................................................................61
Orthogonaal factormodel................................................................................................................61
De principale componentenmethode...............................................................................................62
Orthogonaal factormodel met p factoren........................................................................................62
Orthogonaal factormodel met m<p factoren...................................................................................63
Maximum likelihood methode (tweede, iterateve methode om L en te schaten)..........................64
3
, Regressieanalyse
Introductie regressiemodellen/analyse
Verband zoeken tussen 2 of meer variabelen multivariate statistiek
Gedrag van variabele beschrijven
Variatie verklaren
Schatenn/bouwen van een model mmodel fingin
y
o Afankelijke variabele
o Maatstaf voor de kwaliteit of de groote van de variabele
x
o Onafankelijke variabele
o Inputvariabele
o Predictoren
o Verklarende
z
o Inputvariabele waar je geen controle over hebt
o Geen rekening mee houden in model
Notatie
o y i= geobserveerde waarde i
o ^y i= voorspelde waarde i
o ý i= gemiddelde waarde i
Model: y = f(x1,x2,…) +
Enkelvoudig: met 1 variabele
Meervoudig: met meerdere variabelen
Van deterministisch model naar statisch
o Fouterm bijvoegen
Meetouten
Variabele waar geen rekening mee wordt gehouden mz-variabelenin
o y = fmx1,x2,… ,xkin Y = fmx1,x2,…,xkin + U
Modelcomponenten
o Systematische component fmx1, x2, …in
Beschrijf systematisch gedrag van model
EmY| x1, x2, …,xkin =fmx1, x2, …,xkin
o Random component U
Vangt willekeurige fuctuaties op
EmUin = 0
4
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