I have eight independent variables and one dependent.  I have run a correlation matrix and 5 of them have a low correlation with the DV.  I have then run a stepwise multiple regression to see whether any/all of the IVs can predict the DV.  The regression showed that only two IV can predict the DV (can only account for about 20% of the variance though) and SPSS removed the rest from the model.  My supervisor reckons that I have not run the regression correctly, as due to the strength of the correlations, I should have found more predictors in the regression model. But the correlations were tiny, so my question is - if IVs and DV hardly correlate, can IVs still be good predictors of DV?