Using correlation to eliminate predictors? 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?
 A: Correlating the dependent variable with each of the potential regressors will not generally reveal all the useful information. It might very well be that a linear combination of a subset of regressors will be highly correlated with the dependent variable while each of the regressors in the subset will be only weakly correlated with the dependent variable. In other words, a regression with multiple regressors cannot be substituted with multiple pairwise regressions.
To answer your question, it is generally not wise to put only the IVs that are correlated with the DV into the regression.
For variable inclusion/exclusion strategies, you may check the posts under the feature-selection tag.
A: Generally, the answer is no, because the presence or absence of a third variable in the model may change the relationships between the independent and dependent variables. There are known phenomena like mediation and confounding, for instance. There are also sampling biases, which may mess up the correlations, hide relationships etc.
Having said this, the bi-variate correlations are informative. You should take them into account. It's just you shouldn't base your variable selection solely on bi-variate correlations.
