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# varselect - Variable Selection Methods Principle of...

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VariableSelectionMethods PrincipleofParsimony(Occam’srazor): Choosefewervariableswith sufficientexplanatorypower.Thisisadesirablemodelingstrategy. Thegoalisthustoidentifythesmallestsubsetofcovariatesthatprovides goodfit.Onewayofachievingthisistoretainthesignificantpredictorsin thefittedmultipleregression.Thismaynotworkwellifsomevariablesare stronglycorrelatedamongthemselvesoriftherearetoomanyvariables (e.g.,exceedingthesamplesize). Twootherpossiblestrategiesare BestsubsetregressionusingMallows’ C p statistic. Stepwiseregression. 38 BestSubsetRegression Foramodelwith p regressioncoefficients,(i.e., p - 1covariatesplusthe intercept β 0 ),defineits C p valueas C p = RSS s 2 - ( N - 2 p ) , where RSS = residualsumofsquaresforthegivenmodel, s 2 = meansquare error= RSS (forthecompletemodel) df(forthecompletemodel) , N = numberofobservations. Ifthemodelistrue,then E ( C p ) p .Thusoneshouldchoose p bypicking modelswhose C p valuesarelowandcloseto p .Forthesame p , choosea modelwiththesmallestC p value (i.e.,thesmallestRSSvalue).

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