Variance vs Covariance
Variance thiab covariance yog ob qho kev ntsuas siv hauv kev txheeb cais. Variance yog ib qho kev ntsuas ntawm qhov tawg ntawm cov ntaub ntawv, thiab covariance qhia qhov kev hloov pauv ntawm ob qhov sib txawv sib txawv ua ke. Variance yog ib lub tswv yim intuitive, tab sis covariance yog txhais ua lej nyob rau hauv tsis yog intuitive thaum xub thawj.
Ntau txog Variance
Variance yog ib qho kev ntsuas ntawm kev tawg ntawm cov ntaub ntawv los ntawm tus nqi nruab nrab ntawm kev faib khoom. Nws qhia deb npaum li cas cov ntaub ntawv cov ntsiab lus nyob ntawm lub ntsiab lus ntawm kev faib khoom. Nws yog ib qho ntawm cov ntsiab lus piav qhia txog qhov tshwm sim ntawm kev faib tawm thiab ib qho ntawm lub sijhawm ntawm kev faib khoom. Tsis tas li ntawd, qhov sib txawv yog qhov ntsuas ntawm cov pejxeem, thiab qhov sib txawv ntawm cov qauv ntawm cov pejxeem ua tus kwv yees rau qhov sib txawv ntawm cov pejxeem. Los ntawm ib qho kev xav, nws txhais tau tias yog square ntawm tus qauv sib txawv.
Hauv lus dawb, nws tuaj yeem piav qhia raws li qhov nruab nrab ntawm cov squares ntawm qhov kev ncua deb ntawm txhua qhov chaw cov ntaub ntawv thiab qhov nruab nrab ntawm qhov kev faib tawm. Cov qauv hauv qab no yog siv los xam qhov sib txawv.
Var(X)=E[(X-µ)2] rau cov pejxeem, thiab
Var(X)=E[(X-‾x)2] for a sample
Nws tuaj yeem yooj yim ntxiv kom muab Var(X)=E[X2]-(E[X])2.
Variance muaj qee qhov kev kos npe, thiab feem ntau siv hauv kev txheeb cais los ua kom yooj yim siv. Variance tsis yog qhov tsis zoo vim nws yog qhov square ntawm qhov deb. Txawm li cas los xij, qhov sib txawv ntawm qhov sib txawv tsis raug kaw thiab nyob ntawm qhov kev faib tawm tshwj xeeb. Qhov sib txawv ntawm qhov sib txawv tsis tu ncua yog xoom, thiab qhov sib txawv tsis hloov raws li qhov chaw parameter.
Ntau txog Covariance
Nyob rau hauv cov kev tshawb xav statistical, covariance yog ib qho kev ntsuas ntawm ntau npaum li cas ob random variables hloov ua ke. Hauv lwm lo lus, kev sib txawv yog ib qho kev ntsuas ntawm lub zog ntawm kev sib raug zoo ntawm ob qho kev sib txawv. Tsis tas li ntawd, nws tuaj yeem suav tias yog qhov dav dav ntawm lub tswv yim ntawm qhov sib txawv ntawm ob qhov sib txawv.
Covariance ntawm ob qhov sib txawv ntawm qhov sib txawv X thiab Y, uas tau sib koom ua ke nrog lub sijhawm kawg thib ob, hu ua σXY=E[(X-E[X])(Y-E[Y])]. Los ntawm qhov no, qhov sib txawv tuaj yeem pom tau tias yog qhov tshwj xeeb ntawm kev sib txawv, qhov twg ob qhov sib txawv yog tib yam. Cov(X,X)=Var(X)
Los ntawm normalizing qhov sib txawv, cov kab sib txuas sib txuas lossis Pearson qhov sib txheeb coefficient tuaj yeem tau txais, uas txhais tau tias yog ρ=E[(X-E[X])(Y-E[Y])]/(σ X σY)=(Cov(X, Y))/(σX σY )
Graphically, kev sib txawv ntawm ib khub ntawm cov ntaub ntawv cov ntsiab lus tuaj yeem pom raws li thaj tsam ntawm daim duab plaub nrog cov ntaub ntawv cov ntsiab lus ntawm qhov sib txawv vertices. Nws tuaj yeem txhais tau tias yog qhov ntsuas qhov loj ntawm kev sib cais ntawm ob lub ntsiab lus. Xav txog cov duab plaub rau tag nrho cov pejxeem, qhov sib tshooj ntawm cov duab plaub sib thooj rau tag nrho cov ntaub ntawv cov ntsiab lus tuaj yeem suav tias yog lub zog ntawm kev sib cais; variance ntawm ob variables. Covariance yog nyob rau hauv ob qhov ntev, vim muaj ob qhov sib txawv, tab sis ua kom yooj yim rau ib qho kev sib txawv ua rau qhov sib txawv ntawm ib qho raws li kev sib cais hauv ib qhov ntev.
Qhov txawv ntawm Variance thiab Covariance yog dab tsi?
• Variance yog qhov ntsuas ntawm kev sib kis / kev sib cais hauv cov pej xeem thaum qhov sib txawv yog suav tias yog qhov ntsuas ntawm qhov sib txawv ntawm ob qhov sib txawv los yog lub zog ntawm kev sib raug zoo.
• Variance tuaj yeem suav tias yog qhov tshwj xeeb ntawm kev sib txawv.
• Variance thiab covariance yog nyob ntawm qhov loj ntawm cov ntaub ntawv muaj nuj nqis, thiab tsis tuaj yeem muab piv; Yog li ntawd, lawv yog normalized. Covariance yog normalized rau hauv correlation coefficient (sib faib los ntawm cov khoom ntawm tus qauv sib txawv ntawm ob random variables) thiab variance yog normalized rau hauv tus qauv sib txawv (los ntawm kev noj cov square hauv paus)
