Two independent variables both correlate with the dependent variable, but none are significant in a regression analysis I recently encountered a problem in relation to my study of conflicts and performance. The two types of conflict in the study, task and relationship conflict, both correlated with performance $(-.39, P < .01)$ and $(-.37, P < .01)$. When I put these in a regression, the regression model came out significant, and it explained $22.1\%$ of the variance $(F\ (3, 82) = 7.76,\ P < .01)$. None of the two IVs were, however, significant coefficients! There were no other variables in the regression analysis. How could this be? 
 A: From your correlations it is predictable that a regression on task conflict alone would have $R^2$ about $15\%$ and relationship conflict alone about $13\%$. (To see this, just square the correlations.) 
So, using both predictors gives a gain of $7\%$ in one case and $9\%$ in the other case. Why not the full $15\%$ or $13\%$? The reason is that task and relationship conflict are correlated with each other, so adding one predictor does not add as much predictive information as you might think. 
In essence, the two predictors are fighting each other for a share of the "explanation". This need not be fatal, 
as the model is a team effort and it is often defensible to include non-significant predictors whenever a model is of (social or behavioural) scientific interest. But you might well 


*

*Consider scatter plots of all variables jointly in a scatter plot matrix in your favourite software. (If a scatter plot matrix is not easy in your favourite software, you deserve something better.) 

*Consider transforming either or both predictors if relationships appear nonlinear. 

*Consider adding an interaction term. 

*Discuss the relative merits of the single-predictor models and the two-predictor model. 
A: There could be several things going on.
You may have outliers in the two IVs. Which you need to remove using cookD or similar. Perform regression diagnostics. 
You have to increase The alpha level. Are the two IVs not significant at 95percent alpha level. Why not change alpha to 90?
Finally as part of diagnostics ensure residuals are normally distributed and there is no hetroskedasticity. 
When these steps performed I have seen IVs get significant. 
