北大暑期课程《回归分析》(Linear-Regression-Analysis)讲义PKU5

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...