Test if one predictor's lack of a relationship with the DV is because of a negative relationship with another predictor correlated with the DV I recently collected some survey data where people made a series of judgments about others' actions and their willingness to make some choice about that action.
Looking at the zero-order correlations, I see that some of the judgments are significantly correlated with the choices of the participant, whereas some others are not.
I am concerned that actual relationships may be hiding between the uncorrelated judgments and choices. Let me give a generalized example.
Imagine Predictor A and B are correlated with DV X, but Predictor C is not correlated with DV X. I was thinking that there could actually be a relationship between C and X, but that C may be negatively correlated with A or B resulting in a zero-order correlation between X and C coming out as a wash (and therefore not looking significant).
I imagine I should be able to test for this using regression, but I am not quite sure on the exact procedure. Would simply putting all A, B, and C predicting X in a regression showing that C remains insignificant be sufficient so show that it is not due to this inverse correlation?
Thank you very much for your suggestions.
 A: This is very close (or exact!) to partial correlation. It is a measure of the correlation between the independent and the dependent given all other variables are accounted for.
See the wikipedia page for details 
here.
A: I think you're idea of a regression predicting X with A, B, and C, is a good place to start.  Make sure to distinguish between a statistically insignificant effect and a precisely estimated effect of zero (or close to zero).
Also, consider the possibility of non-linear relationships.  Throw squared or even cubed terms into the regression equation. 
A: If A is correlated with B or C, plugging them together into a linear regression will create colinearity and the results will be spurious (mean nothing).
There might be a more complex relationship between C and X than just a linear increasing one (for example, an inverse U shape relationship might look like zero correlation in the matrix).
One good way to test this (before regressions) is first to graph X vs A,B and C.
Then you might see a relationship which is not trivial (such as a squared one etc.).
In addition, there might be interaction between A,B and C, that is, for example, people make a choice only when their judgment is of some kind. Suppose this is the relationship between B and C. To run this in a regression, multiply the values of B and C and add them as a new variable (call it D) to the regression.
