note4 - STAT5044: Regression and Anova Inyoung Kim Outline...

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Unformatted text preview: STAT5044: Regression and Anova Inyoung Kim Outline 1 Testing 2 Confidence interval 3 ANOVA table Testing procedure Decide what question we want to test: Null hypothesis and alternative hypothesis Test statistic Decision rule Make conclusion. Hypothesis H : 1 = 10 vs H A 1 : 1 > 10 H : 1 = 10 vs H A 1 : 1 < 10 H : 1 = 10 vs H A 3 : 1 6 = 10 What do we need for testing this hypothesis? Test statistics Test statistic? 1- 10 q Var ( 1 ) = 1- 10 p 2 / S xx = ( 1- 10 ) / p 2 / S xx p 2 / 2 = t n- 2 under which hypothesis? Test statistic Test statistic? 1- 10 q Var ( 1 ) = 1- 10 p 2 / S xx = ( 1- 10 ) / p 2 / S xx p 2 / 2 = t n- 2 under which hypothesis? null hypothesis. Why does the distribution of test statistic follow t n- 2 under H ? Test statistic Numerator: Under H , 1- 10 2 / Sxx N ( , 1 ) Denominator Let 2 = n i = 1 ( y i- y i ) 2 ( n- 2 ) r 2 2 s 2 n- 2 ( n- 2 ) 2 2 = SSE / ( n- 2 ) 2 2 n- 2 ( n- 2 ) NOTE: SSE 2 = y t ( I- H ) y 2 = y t Ay , where A = 1 2 ( I- H ) AV = ( I- H ) 1 2 2 = I- H : idempotent, Rank ( A ) = Rank ( I- H ) = n- 2 Test statistic and are independent: ( X t X )- 1 X t Y = By and y t ( I- H ) y = y t Ay are independent....
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note4 - STAT5044: Regression and Anova Inyoung Kim Outline...

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