I have 1 dependent variable and 33 independent variables (continuous, categorical & dichotomous). Correlation analyses (2-tailed) show that the DV is only correlated to 7 of the IVs although most of the correlations are very weak, e.g. about 0.1 or less than 0.1.
Is it correct to put only IVs that are correlated with the DV into the regression model?
P.S. What's the use of the correlation matrix (1-tailed) produced with the regression analysis?