ALRLec6 - Chapter 3 ANOVA and F-test H0 = E(Y|X=x = 0 Ha = E(Y|X=x = 0 1x1 pxp Equivalently H0 = 1 = 2 = = p = 0 Ha = At least one out of 1 p is

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1 Chapter 3 ANOVA and F-test H 0 = E(Y|X=x) = β 0 H a = E(Y|X=x) = β 0 + β 1 x 1 + … + β p x p Equivalently H 0 = β 1 = β 2 = … = β p = 0 H a = At least one out of β 1 ,…, β p is not equal to zero F-Statistic F= ?? ??? / ? ±?? /( ²−?− 1) The coefficient of Determination ± 2 = ?? ??? ±?? = 1 ±?? ?³³ R 2 is also called multiple correlation coefficient Two important results on R 2 (1) ± 2 = ´µ?? 2 ( ³ , ³ ) (2) ± 2 = ¶°· ¸ ´µ?? 2 ( ³ , ¹¸ ) Hypotheses on one coefficient only H 0 = β 1 = 0 β 0 , β 2 ,…, β p arbitrary H a = β 1 ≠ 0 β 0 , β 2 ,…, β p arbitrary t-statistic º = » ¼ 1 0 ½?¾» ¼ 1 ¿ ~ ºÀ² − ? − 1 Á Equivalently 1. Fit the model to data ³ = » 0 + » 1 · 1 + + » ? · ? + ? Get RSS
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2 2. Fit the model without x 1 to data ? = ± 0 + ± 2 ? 2 + + ± ? ? ? + ? Get RSS -1 3. RSS -1 – RSS F-Statistic = ²³³ 1 −²³³ /1 ²³³ /( ´−?− 1) ~ µ (1, ´ − ? − 1) Sequential Analysis of Variance SS reg can be divided into sum of squares “explained” by each variable
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This note was uploaded on 12/12/2010 for the course STAT 425 taught by Professor Ma,p during the Fall '08 term at University of Illinois, Urbana Champaign.

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ALRLec6 - Chapter 3 ANOVA and F-test H0 = E(Y|X=x = 0 Ha = E(Y|X=x = 0 1x1 pxp Equivalently H0 = 1 = 2 = = p = 0 Ha = At least one out of 1 p is

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