I am trying to determine the key drivers from a series of 30 Independent Variables (IVs) (attributes rated on 10 pt scale) on 3 Dependent Variables (DVs) (i.e. purchase intent). The 30 IVs are pretty highly correlated, but the Variance Inflation Factors (VIFs) are all under 10 (though most are over 5). I did a backward regression, but some of the beta coefficients had negative signs, which don't make sense logically. Is it better to just run separate simple regressions on each IV, or take out the IV's with particularly high VIFs and run a regression with all of the remaining in the model together? Any suggestions would be appreciated!
The question is 5 years old, but it's the first I saw it. Welcome to CV after all this time (if you are still here).
First, doing backwards regression (or forwards or stepwise) is a bad idea. This has been covered many times here.
Second, beta coefficients having negative signs when you are controlling for other variables is not the same as them having negative signs in simple regression (with only one IV in the model).
Finally, whether to run simple regressions or to do something else really depends on your goal. They answer different questions. Neither is "better".