ALRChap10 - Chapter 10 Variable Selection Multicollinearity...

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Chapter 10 Variable Selection Multicollinearity A set of terms, X 1 ,X 2 , . . .,X p are approximately collinear if, for constants c 0 , c 1 , . . ., c p , which is similar to a linear regression mean function with intercept c 0 /c j and slopes - c l /c j . Diagnostic method: Step1: Regress X j on the other X ’s Step2: Calculate R 2 , which we will call R 2 j If the largest R 2 j is near 1, we would diagnose approximate collinearity. VIF When p > 2, the variance of the j -th coefficient is
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/( 1 - R 2 j ) is called the j th variance inflation factor , or VIF j Variable Selection Principle of Parsimony (Occam’s razor): Choose fewer variables with sufficient explanatory power. This is a desirable modeling strategy. The goal of variable selection is thus to identify the smallest subset of covariates that provides good fit. One way of achieving this is to retain the significant predictors in the fitted multiple regression. This may not work well if some variables are strongly correlated among themselves or if there are too many variables (e.g., exceeding the sample size).
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ALRChap10 - Chapter 10 Variable Selection Multicollinearity...

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