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Samenvatting Statistiek II: Hoofdstuk 8: Multivariate Regressie
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1Hoofdstuk 8: Meervoudige regressie...................................................................................................4
1. Meervoudige regressie uitgelegd adhv een voorbeeld .................................................................4
1.1. Onderzoeksvraag en probleemstelling ..................................................................................4
1.2. Data en operationalisering ...................................................................................................4
1.3. Voorbereidende bivariate analyse ........................................................................................5
1.3.1. Bivariate regressie van PERFORM op PTRUST .................................................................5
A) Scatterplot van PTRUST ifv PERFORM ..............................................................................5
B) Bivariate regressie van PERFORM op PTRUST ..................................................................5
1.3.2. Bivariate regressie van EDUYRS op PTRUST ....................................................................5
A) Scatterplot van PTRUST ifv EDUYRS .................................................................................5
B) Bivariate regressie van EDUYRS op PTRUST......................................................................5
1.4. Grafische voorstelling van meervoudige regressie ................................................................6
1.5. Het model van meervoudige regressie ..................................................................................6
1.5.1. Wat is meervoudige regressie? ......................................................................................6
1.5.2. Populatiemodel .............................................................................................................6
1.5.2. Steekproefmodel ...........................................................................................................6
1.5.3. Assumpties van het residu .............................................................................................7
1.6. Doelstellingen van meervoudige regressie ............................................................................7
1.6.1. Schatting van de regressieparameters ...........................................................................7
A) Inleiding ..........................................................................................................................7
B) De schatting adhv OLS .....................................................................................................7
C) Interpretatie regressieparameters/Ongestandaardiseerde regressiecoëfficiënten ...........8
D) Eigenschappen OLS-schatters ..........................................................................................9
E) Meervoudige regressie met gestandaardiseerde variabelen ............................................9
1.6.2. Sterkte van het verband............................................................................................... 10
A) Inleiding ........................................................................................................................ 10
B) De sterkte van het verband adhv meervoudige R ........................................................... 10
C) De sterkte van het verband adhv meervoudige R² ......................................................... 10
D) Adjusted R² ................................................................................................................... 11
1.6.3. Significantietesten ....................................................................................................... 11
A) Inleiding ........................................................................................................................ 11
B) Modelvergelijkingsprocedure en F-test .......................................................................... 11
C) T-test en betrouwbaarheidsinterval partiële regressiecoëfficiënten............................... 12
D) Modelvergelijking en F-test voor partiële regressiecoëfficiënten ................................... 14
E) T-test voor de regressieconstante .................................................................................. 15
, 2
2. Regressiediagnostiek ................................................................................................................. 16
2.1. Lineariteitsassumptie ......................................................................................................... 16
2.1.1. Wat?............................................................................................................................ 16
2.1.2. Schendingen van de lineairiteitsassumptie detecteren ................................................. 16
2.1.3. Andere functies dan lineaire functies ........................................................................... 16
A) Polynomiale functies ..................................................................................................... 16
B) Kubieke functies ............................................................................................................ 16
2.1.4. Test lineairiteitsassumptie ........................................................................................... 17
A) Inleiding ........................................................................................................................ 17
B) Test lineairiteitsassumptie PERFORM ............................................................................ 17
C) Test lineariteitsassumptie EDUYRS................................................................................. 17
2.2. Additiviteitsassumptie ........................................................................................................ 18
2.2.1. Wat?............................................................................................................................ 18
2.2.2. Test additiviteitsassumptie .......................................................................................... 18
2.3 Multicollineariteit ................................................................................................................ 19
2.3.1. Wat?............................................................................................................................ 19
2.3.2. Symptomen ................................................................................................................. 19
2.3.3. Hoe detecteren? .......................................................................................................... 19
2.3.4. Hoe remediëren? ......................................................................................................... 19
2.4. Afwezigheid van autocorrelatie .......................................................................................... 19
2.5. Homoskedasticiteitsassumptie ........................................................................................... 20
2.5.1. Wat?............................................................................................................................ 20
2.5.2. Hoe detecteren? .......................................................................................................... 20
2.6. Normaliteitsassumptie residuen ......................................................................................... 20
2.6.1. Wat?............................................................................................................................ 20
2.6.2. Hoe detecteren? .......................................................................................................... 20
2.6.3. Niet-normaliteit remediëren ........................................................................................ 21
2.7. Outliers/Uitbijters .............................................................................................................. 21
2.7.1. Wat?............................................................................................................................ 21
2.7.2. Hoe detecteren? .......................................................................................................... 21
2.8. Hefboompunten/Leverage points ....................................................................................... 22
2.8.1. Wat?............................................................................................................................ 22
2.8.2. Hoe detecteren? .......................................................................................................... 22
3. Zoemgroepen............................................................................................................................ 23
3.1. Zoemgroep 8.1.: Ongestandaardiseerde regressievergelijking............................................ 23
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3.2. Zoemgroep 8.2.: Verwachte waarden en residuen .............................................................. 23
3.3. Zoemgroep 8.3.: Gestandaardiseerde regressiecoëfficiënten .............................................. 24
3.4. Zoemgroep 8.4.: Significantietesten in meervoudige regressie ............................................ 24
3.5.: Zoemgroep 8.5. Meervoudige regressie............................................................................. 25
3.6. Zoemgroep 8.6.: Schending lineairiteitsassumptie .............................................................. 26
3.7. Zoemgroep 8.7.: Multicollineariteit .................................................................................... 27
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