So Many Variables, So Few Observations

Abstract:Increasingly in many fields (including marketing, business, and molecular biology), the number of variables collected in a factor analysis can dwarf the number of observations available for each variable. While you may start to deal with this problem by examining the bivariate relationship between the predictors and your independent variable, identifying those predictors that are highly intercorrelated is equally important. It is this scenario in which variable reduction techniques can be most useful. When the number of predictors is much greater than the number of observations, there are five statistical methods that can be used. These include two simple approaches based on least-squares regression: Stepwise forward regression and best subsets regression. The other methods are principle components analysis (PCA) with regression; ridge regression; and the least absolute shrinkage and selection operator (LASSO) method. The best method with the best fit will depend on the data set, the …

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