Residual Analysis

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Residual Analysis Residual analysis can be performed on regular, standardized or deleted residuals Regular residuals are simply the actual value minus the fitted value Standardized are calculated as ( Deleted residuals are calculated by separately removing each from the analysis) , 1, 2,. .., i i E e d i n MS = = ˆ i i e y y = -

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Which one to use? For analysis of a designed expt, we want to use standardized (or studentized ) residuals This assures no undue influence of a particular outlier observation
Transforming the Response Residual analysis is an important step in ANOVA. The underlying NID(0, σ 2 ) assumption must be verified. But what happens when this residual analysis shows a problem? Answer: We must transform the response, and then rerun the complete analysis

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Transformations
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Unformatted text preview: • We should start with no transformation of the response, and then successively use a stronger transformation until the residuals reveal an acceptable situation • We know we have gone too far in transforming the data when the non-random pattern actually reverses itself (i.e., a bowtie pattern switches to become narrower at the ends than the middle) Transformation Sequence Type Formula Example Use None Square Root y’=sqrt (y) Counts Natural Log y’=ln(y+k) Growth data Base 10 Log y’=log10(y+k) Variance Reciprocal Sq Rt y’=1/sqrt(y) Inverse y’=1/y Rate data Power y’=(y+k) x Logit Bounded data ArcSin Sq Rt y’=arcsin(sqrt(y)) Binomial data _ ' ln( ) _ y lower lmt y upper lmt y-=-...
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