I am addressing multiple regression problem which has 7 predictor variables, currently I am planning to use ANOVA fro reducing number of predictor variables. Which is the better method to use ANOVA or subset selection method(e.g. best subset selection, stepwise subset selection)? Can I use subset selection method after eliminating non significant predictors using ANOVA? Why ANOVA is not commonly used as subset selection method?
Actually, ANOVA is indeed commonly used in deciding what to include in linear models. There are reasons to avoid stepwise methods: the stepwise technique might seem to make sense from a purely statistical point of view, but this does not mean it is valid or makes sense in the context of the theoretical and empirical background to whatever you're examining. You must build your model based on what is already known in the discipline you're working within.