C la ss 5: ANO V A (Ana l ysi s o f V arian c e) and F-t e s t s I . W h a t is A N O V A W hat i s A N OVA? AN O V A is t he s h o r t n a me f o r the Anal ysi s of V ar i ance. T he es senc e of A N O V A i s to d ec om p o s e t h e t ot a l varianc e o f t he d ep e nde n t varia b le i n to t wo a d di t i v e c o mpon ents, on e f or th e s tructur a l pa r t, a n d the other f o r the s to c h a stic par t, o f a r egr essi o n. T o da y w e ar e going t o e xami n e th e e a s i e st c a se. I I . ANOVA: An I n t r o ducti o n L e t th e m od el be.As sumin g x is a column v e c t o r (o f l e ng t h p) o f ind epe nde nt variabl e v a l u e s fo r the i th' observat i on, .T h en i s th e p redicte d va lue. s um o f sq ua r e s total: b e ca u se . T h i s is al wa y s true by OL S.= SS E + S SRImpo r ta n t: th e t o ta l vari a nce of the d ep e n d e nt var ia bl e is de comp osed in to two additive p ar ts: SSE, whic h is du e to er r ors, and SSR, w hic h i s du e t o re gression.G eo metric i n t e r pre t a t i on: [b la c kboa r d] 下载后可任意编辑De c o mp osit i on of Va r ia nceI f we trea t X as a r a n d om v a riable, we can d e compose t o ta l v ar ian ce t o t h e b e t w e e n-gr o u p po rti o n a n d th e wi th i n-gr o u p...