Multipla korelacija in regresija. Multipla regresija, multipla korelacija, statistično zaključevanje o multiplem R
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1 Multipla koelacia in egesia Multipla egesia, multipla koelacia, statistično zaklučevane o multiplem
2 Multipla egesia osnovni model in ačunane paametov Z multiplo egesio napoveduemo vednost kiteia (odvisne spemenlivke) na osnovi dveh ali več pediktoev (neodvisnih spemenlivk). Iščemo lineano kombinacio pediktoev, katee vednosti bodo čim bliže vednostim kiteia (ta lineana kombinacia bo imela navišo možno koelacio s kiteiem). Uteži, s kateimi obtežimo pediktoe, imenuemo egesiski nagibi. V nestandadiziani obliki lahko ta model zapišemo kot: Yˆ i a + P b X i Y i napovedana vednost kiteia za osebo i b egesiska utež za pedikto a pesečišče z odinato Ka pomenio egesiski paameti? egesiski nagib nam pove, za koliko se poveča napovedana vednost kiteia, če se vednost pediktoa poveča za eno enoto, vednosti ostalih pediktoev pa se ne spemenio. Pesečišče z odinato nam pove, kolikšna bi bila napovedana vednost kiteia, če bi bili vsi pediktoi enaki nič.
3 Multipla egesia osnovni model in ačunane paametov (nestandadiziane spemenlivke) Izačun egesiskih nagibov in pesečišča z odinato: b C - c b vekto egesiskih nagibov C kovaiančna matika pediktoev c vekto kovaianc med pediktoi in kiteiem a Y b X Izačun opavimo v statističnih paketih (np. SPSS/PASW) ali s pomočo Excela: COVA: za izačun kovaianc VAP: za izačun vaianc MINVESE: za izačun obnene oz. invezne kovaiančne matike MMULT: za izačun podukta med kovaiančno matiko in vektoem kovaianc med pediktoi in kiteiem Pime v Excelu: Izačun paametov egesiske enačbe za napovedovane impulzivnosti (I) na osnovi ekstavetnosti (E) in lestvice iskana dažlaev (D). I,3 + 0,34*E + 0,3*D
4 Multipla egesia osnovni model in ačunane paametov (standadiziane spemenlivke) V standadiziani obliki pa lahko zapišemo: i P z ˆ( Y ) β z( X ) i Pesečišča z odinato ne potebuemo več, ke e povpeče vsake vsote standadizianih spemenlivk enako nič. egesiske uteži β imenuemo standadiziani nagibi ali beta koeficienti. pogosto ih ačunamo za oceno elativne pomembnosti posameznih pediktoev beta koeficient e visok, če pedikto visoko koelia s kiteiem in nizko z ostalimi pediktoi Izačun beta koeficientov: β - Ali koelaciska matika pediktoev vekto koelaci med pediktoi in kiteiem
5 Multipla egesia osnovni model in ačunane paametov (standadiziane spemenlivke) izačun beta koeficientov: standadiziamo nestandadiziane egesiske nagibe: β b s s Y Pime: Pešni pime z napovedovanem impulzivnosti na osnovi ekstavetnosti in iskana dažlaev. b E 0,34 s E 4,75 β E 0,34 * 4,75 / 3,9 0,4 b D 0,3 s D 4,6 β D 0,3 * 4,6 / 3,9 0,4 s I 3,9 Izačun beta koeficientov v pimeu dveh pediktoev: β X YX YZ XZ XZ Y kitei X, Z pediktoa
6 Multipla koelacia ocenuemo natančnost napovedovana (višina povezanosti med napovedanimi in deanskimi vednostmi kiteia) multipla koelacia koelacia med obteženo vsoto pediktoev in kiteiem Y. XZ YYˆ Izačun multiple koelacie ' oz. ' β oz. P Y β Za dva pediktoa: YX + YZ YX XZ YZ XZ Pime: Pešni pime z ekstavetnosto, iskanem dažlaev in impulzivnosto β E 0,4 EI 0,5 β D 0,4 DI 0,4 sqt(0,5*0,4 + 0,4*0,4) 0,56
7 Multipla koelacia neka pomembnih lastnosti/načel Multipla koelacia e paviloma viša, če so posamezne koelacie med kiteiem in pediktoi više. Multipla koelacia e paviloma viša, če so koelacie med pediktoi niže. Če so pediktoi med sebo nekoleiani sum( ) Multipla koelacia ne moe biti negativna (napovedane in deanske vednosti kiteia moao imeti isti pedznak). Multipla koelacia ne moe biti niža od naviše velavnosti dodaane pediktoev ne moe znižati multiple koelacie. Paametov multiple koelacie/egesie ne moemo izačunati, če kovaiančna matika ni obnliva (noben pedikto ne sme biti obtežena vsota dugih pediktoev).
8 Multipla koelacia stat. zaklučevane o multiplem Za azliko od Peasonovega vzočni multipli ni nepistanska ocena populaciske multiple koelacie. Vzočni e v povpeču viši od populaciskega. Z Wheyevim obazcem lahko določimo pibližno nepistansko oceno populaciske multiple koelacie (v SPSSu Adusted ): p P( ) N P p ocena pop. multiple koelacie P število pediktoev N število udeležencev Pime: Pešni pime z ekstavetnosto, iskanem dažlaev in impulzivnosto 0,56 p sqt(0,56 (*(-0,56 )/(73--))) P p 0,54 N 73
9 Multipla koelacia stat. zaklučevane o multiplem Peveane hipoteze, da e populaciski 0 Testiamo z F-testom, ki temeli na azmeu med standadiziano poasneno ( ) in nepoasneno ( ) vaianco: F ( N P ) df P df N P ( ) P Pedhodni pime: 0,56 F (0,56 *(73--)) / (*(-0,56 )) P F 6,00 N 73 F 0,05 (,70) 3,3 [FINV()] p,89 * 0-6 [FDIST()]
10 Multipla koelacia stat. zaklučevane o multiplem Če pediktoi niso natančno določeni vnape: Bi vklučitev enega ali več pediktoev povzočila stat. pomembno zvišane multiple koelacie? Bi izklučitev enega ali več pediktoev povzočila stat. pomembno znižane multiple koelacie? Ali e spememba stat. pomembna? F ( PD P )( N P D ) df D df N P D ( ) D PD Pedhodni pime: V model dodamo še en pedikto, in sice vestnost (V). P 0,56 F (0,6 0,56 )(73---) / ((-0,6 )*) PD 0,6 F 7,94 F 0,05 (,69) 3,98 p 0,006
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