# note6b - STAT5044: Regression and Anova Inyoung Kim Outline...

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STAT5044: Regression and Anova Inyoung Kim

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Outline 1 Box-Cox transformation 2 Prediction Interval using Transformated model
Choosing a transformation Log transformation: common for skewed data with heterogeneity and nonlinearity Square root transformation: use with count data Arcsin square root: use with proportions Power transformation: use with heterogeneity of variance and nonlinearity Box-cox transformation

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Box Cox transformation Idea: consider a class of transformation based power that includes the log Pick the power that maximized the likelihood L ( β 0 , β 1 , σ 2 , λ ) = 1 ( 2 πσ 2 ) n / 2 exp [ - 1 2 σ 2 ( Y λ i - β 0 - β i x i ) 2 ]
Transformation model Box-cox(1964) transformation model g ( y i ; x ) = β 0 + β 1 x i + ε i , ε i N ( 0 , σ 2 ) g ( y , λ ) = ( y λ - 1 λ λ 6 = 0 log ( y ) λ = 0 where λ is a ﬁxed parameter

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Only applies when y > 0 The goals of the transformation transformed y is linearly related to x After transformation, the error would be normal. After transformation, the errors would have the same variance
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## This note was uploaded on 01/02/2012 for the course STAT 5044` taught by Professor Staff during the Fall '11 term at Virginia Tech.

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note6b - STAT5044: Regression and Anova Inyoung Kim Outline...

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