hi,

from what I understand you are doing a very close thing to multiple regression: condition on a certain level of a predictor variable, comparing "within group" and overal variabilities. I can imagine that certain properties of regression would be inherited in this analysis, for example:

Inclusion of significant predictor into the regression model may alter significance of other predictor.

In order to avoid obtaining just one observation after predictor-specific filtering (overfitting) and hence 0 deviation you may want to separate the data into GROUPS according to the levels of the predictor and compare means of the response across the groups. As you clearly see, this is just one-way ANOVA (read regression).

I am not really sure how you want to obtain the best estimate for all sets of predictors by your "one predictor level at a time approach", you will clearly run into multiple testing problems and will need to do Bonferroni adjustment of some sort.

anyway, just an opinion....