How can I interpret my findings when X shows contribution to the regression model (X predicts a unique variance in Y), however, X is not correlated with Y?
I agree with both David Eugene Booth and Daniel Wright , that a restatement of your question would help us feel more confident in giving suggestions about your query.
That said, I'll go out on a limb and suggest that you're asking whether a predictor, X, can show significant contribution to a regression model that includes one or more other predictors even though it (X) has a zero or negligible bivariate correlation with Y. The answer is, yes. A suppressor variable can manifest this behavior. See this link for more information: https://home.ubalt.edu/tmitch/645/articles/Thompson%20&%20Levine%20Ex%20supressor%20vars.pdf
Do you mean X predicts, AFTER CONDITIONING ON OTHER VARIABLES, Y to some level (hopefully not just p < .05), but the the bivariate association does not reach this level?
If so, the answer is these are different things. But, as David says, you should probably ask a new question that provides appropriate information.
I agree with both David Eugene Booth and Daniel Wright , that a restatement of your question would help us feel more confident in giving suggestions about your query.
That said, I'll go out on a limb and suggest that you're asking whether a predictor, X, can show significant contribution to a regression model that includes one or more other predictors even though it (X) has a zero or negligible bivariate correlation with Y. The answer is, yes. A suppressor variable can manifest this behavior. See this link for more information: https://home.ubalt.edu/tmitch/645/articles/Thompson%20&%20Levine%20Ex%20supressor%20vars.pdf