When both predictors are applied in the model with one outcome variable, they are both non-significant.
However, when I apply them on one to one basis, they both are significant.
Is it not weird? It is often in multiple regression that one is 'taking over' still being significant, while the other is not anymore...
Could anyone shed light?
Big, representative sample used.
Thank you
Does your predictors have a strong correlation? That might explain the issue. See https://stats.stackexchange.com/questions/86269/what-is-the-effect-of-having-correlated-predictors-in-a-multiple-regression-mode
This is typically what happens with multicollinearity. You should check the Persons' coefficient between the two IVs. In addition you can run the VIF test (in Stata the string is "estat VIF"). If you have value above 10 and an average VIF value far away from 1, this implies that the two IVs are highly correlated. If you face this situation, you cannot include both variables but you have to choose just one of them.
Hope this helps.
Andrea
Besides collinearity--which would also be my first guess--remember that "significant" involves an arbitrary boundary line. There is nothing fundamentally different that happens when a parameter estimate is "statistically significant" vs when it is not. If alpha = .05 is your condition for "significance," then p = .049 is "significant" but p = .051 is not. So what?
It also could be a matter of sample size. If n is small, then adding a predictor could inflate standard errors to the point that estimates are no longer "significant."
Witold,
Edward Rigdon's response is on point. I'd wager that a too-small sample is the culprit here. You can have strong collinearity in a pair of predictors and still show (at least) one to be a statistically non-zero contributor with sufficient sample size, assuming there is some relationship with the dependent variable.
Good luck with your work!
The joint confidence region for the two regression coefficients beta1 and beta2 is an ellipse (see attached sketch). The stronger the correlation between the two independent variables X1 and X2, the narrower the confidence ellipse and the stronger the slant of the ellipse. In the case illustrated in the attached file, the origin (0,0) is not inside the ellipse, i.e. the null hypothesis beta1=0, beta2=0 is rejected. However, the marginal confidence interval for beta1 includes 0, as does the marginal confidence interval for beta2. So Ho: betal=0 is not rejected and Ho: beta2=0 is not rejected. This is not "weird", it happens, the probability of this happening being larger if X1 and X2 are strongly correlated. If X1 and X2 are uncorrelated, then the ellipse will be orthogonal to the two axes, and in that case the joint hypothesis will be rejected if the marginal hyptheses are rejected.
Correction to my previous answer. The larger the sample size, the narrower the ellipse. The stronger the correlation between X1 and X2, the more slanted the ellipse will be. Thus, in addition to the true values of beta1 and beta2, the probability of the "weird" result depends on the sample size and the correlation between the independent variables. All it means is that, in order to predict Y, you need a regression equation which includes both X1 and X2.
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