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Unformatted text preview: Stat 704: Multicollinearity and Variance Inflation Factors Multicollinearity occurs when several of the predictors under consideration x 1 ,x 2 ,...,x k are highly correlated with other predictors. Problems arising when this happens include: 1. Adding/removing a predictor changes estimated regression coefficients substantially, and hence some conclusions based on the model change substantially as well. 2. Sampling distribution of individual b j ’s may have hugely inflated variance, reflected in huge C.I.’s for some β j . 3. The standard interpretation of a β j as the mean change in the response when x j is increased by one is no longer valid. If x 2 is highly correlated with x 3 , we can’t think of holding x 3 fixed while increasing x 2 . Multicollinearity does not pose a problem when the main use of the regression model is for prediction ; predicted values and prediction intervals will not tend to change drastically when predictors correlated with other predictors are added to the model, when prediction is within the scope of the observed predictors. Multicollinearity can be seen as a duplication of information and is often avoided simply by “weeding out” predictors in the usual fashion: use of the best-subsets C ( p ) statistic,...
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This note was uploaded on 12/14/2011 for the course STAT 704 taught by Professor Staff during the Fall '11 term at South Carolina.
- Fall '11