I am running a series of hierarchical regressions with a lot of independent variables. All the IVs show a loose theoretical relationship to the DV. My supervisor has suggested excluding IVs from regression based on whether they correlate with the DV or not (if they don't, then they are out). It seems to be accepted enough to warrant studies using this technique to be published in high-end medical journals, but I can't find a reference directly supporting it.
I've also received some negative feedback regarding this process - namely, because some of the excluded IVs are correlated with the included IVs, it's been suggested that this will affect the potential coefficient for the ones left in the regression. And that including only those measures expected to be significant masks the likelihood that a few significant correlations will emerge by chance.
I have found reference suggesting that if the variables are not 'important' then excluding variables that correlate with other IVs is not a problem.
Can an IV's importance to a model be determined by whether they correlate with the DV or not?