[PDF] exercice fonction cout de production
[PDF] corrélation multiple définition
[PDF] corrélation multiple spss
[PDF] coefficient de détermination multiple excel
[PDF] definition fonction de cout total
[PDF] corrélation entre plusieurs variables excel
[PDF] corrélation multiple excel
[PDF] fonction de cout marginal
[PDF] régression multiple excel
[PDF] cours microeconomie
[PDF] microéconomie cours 1ere année pdf
[PDF] introduction ? la microéconomie varian pdf
[PDF] introduction ? la microéconomie varian pdf gratuit
[PDF] les multiples de 7
[PDF] les multiples de 8
Chapter5
Multiplecorrelationand multipleregression
Theprevi ouschapterconsideredhowt odeterminetherelat ionshipbetweentwovariables andhowt opredicton efromt heother.Thegeneralsolution wastoc onsiderthe ratioof thecovarian cebetweentwovariablestoth evarianceofthepredictorv ariable(regression) orth eratioofthe covariancetoth es quarerootoft heproductthevariances(correlation). Thissolutionma ybegeneralizedtothe problemofho wtopre dictasinglevariablefromthe weightedlinearsumofmult iplevariables(multipleregression)ort ome asureth estrengthof thisrelationsh ip(multiplecorrelatio n).Aspar toft heproblemof find ingthewe ights,the conceptsofpartialcovarianceandpartialcorrelationwillbeintro duced. Todoallofthiswill requirefindingthevarianc eofacompositescore,and thecovarian ceofthiscompositewit h anotherscore,which mightitselfbeac omposite. Muchofpsychome tri ctheoryismerelyanextension,anelaborati on,orageneralization ofth eseconcepts.Almost alltestsarecompositesofitems orsubtests.An unders tanding howtodecom posetes tvarianceintoitscomponen tparts,andconv ersely,anunderstandi ng howtoanaly zetest sascompositesofitem s,allowsustoanaly zet hemeaningoftests.But testsarenotmerely composit esofit ems.Testsrelatetooth ertests.Adeepappreciationof thebasicPe arsoncorrelationc oe ffi cientfacilitatesan understandingofitsgeneralization to multipleandpartialcorrelation ,tofact oranalysis,andtoque stionsofvalidity.
5.1Thevar ianceofco mposites
Ifx 1 andx 2 arevect orsofNobservationscente re darou ndtheirmean(thatis,deviation scores)theirvariances areV x1 =∑x 2 i1 /(N-1)and V x2 =∑x 2 i2 /(N-1),or,in matrix terms V x1 =x 1 x 1 /(N-1)and V x2 =x 2 x 2 /(N-1).Thev arianceofth ecompositemadeupofthe sum ofth ecorrespon dingscores,x+yisjus t V (x1+x2) ∑(x i +y i 2 N-1 ∑x 2 i +∑y 2 i +2∑x i y i N-1 (x+y) (x+y) N-1 .(5.1) Generalizing5.1tothec aseofnxs,th ecomposite matr ixof theseisju st N X n withdimension s ofNr ows andncolumns.Th ematri xofv ariancesandcovariancesofth eindividu alitemsof thiscompositei swrittenasSasit isasamp leesti mate ofthepopulationvari ance-covariance matrix,Σ.It isperh apshelp fultoviewSinterm sofitselements,n ofwh icharevari ances 127
1285Multiple correlation andmultipleregression
andn 2 -n=n?(n-1)are covarian ces: S= v x1 c x1x2
···c
x1xn c x1x2 v x2 c x2xn c x1xn c x2xn
···v
xn ThediagonalofS=diag(S)is justt hevectorofindi vidualvari ances.ThetraceofSis thesumoft hediagonalsand wil lbeuseda greatdealwhenconsid ering howtoestimate reliability.Itisconvenienttorepre sentth esumofal loftheelementsinthematrix,S,ast he varianceofthecompositem atr ix. V X X X N-1 1 (X X)1 N-1
5.2Multiple regression
Theproblem oftheoptimallinearpre dic tionofˆyinterm sofxmaybegener alizedt othe problemoflinearlypred ic tingˆyinterm sofacompositevariabl eXwhereXismadeu pof individualvariablesx 1 ,x 2 ,...,x n .Ju stasb y .x=cov xy /var x istheop timalslopef orpredicting y,soi tisposs ibleto findase tofweights(βweightsinthes tandardized case,bweightsin theunstan dardizedcase)foreachoftheindividualx i s.
Considerfirsttheproblemof twopredictor s,x
1 andx 2 ,we wantto findthefind weights , b i ,th atwhenmul tipliedbyx 1 andxquotesdbs_dbs2.pdfusesText_2
CHAPTER 13 INTRODUCTION TO MULTIPLE CORRELATION MULTIPLE