# Significant first-step coefficient becomes insignificant in second step of hierarchical multiple regression

I've tried to find the answer to this on this website but haven't been able to, so apologies if this has already been resolved. I am carrying out a hierarchical multiple regression. In the first step, the model is significant, and the predictors $X_1$, $X_2$ and $X_3$ have significant coefficients. When I add $X_4$ in the second step, the model is significant and the $R^2$ change is significant. The coefficient for $X_4$ is also significant. However, the previously significant coefficient of $X_1$ becomes insignificant. Why would this be happening?

There do not appear to be any problems with multicollinearity. I don't know if the following is relevant, but $X_1$ and $X_4$ are moderately positively correlated and are equally correlated with the dependent variable. $X_2$ and $X_3$ are dummy variables of a categorical variable with 3 levels. All other variables are continuous. Thanks!

Multicollinearity doesn't have to be terribly high for this to happen. It sounds like $X_1$ is correlated with $X_4$, and so when $X_4$ is not included in the model, $X_1$ takes credit for the variability in $Y$ that $X_4$ is responsible for. When $X_4$ is included, the model recognizes that $X_4$ and not $X_1$ is responsible for the effect and switches to attributing the effect to $X_4$.

• I think this is discussed elsewhere, but I can't find it right now. I may add a link or more information later. – gung - Reinstate Monica Feb 26 '14 at 20:50
• Thanks for your reply! So would I be correct in interpreting this result as X4 being a better predictor of the dependent variable than X1? Again, I don't know if this information is relevant but the relationship between the dummy variables and the dependent variable is negative. I have just noticed that the part correlation of each of these dummy variables is larger than their zero-order correlation. Is this normal? What does that mean? – Claire Feb 26 '14 at 21:01
• The partial & semi-partial (part) correlation is described here. The best way to try to understand what's going on is to make some plots. Have you tried a scatterplot matrix with your continuous variables (ie, Y, X1 & X4)? – gung - Reinstate Monica Feb 26 '14 at 21:25

Could you be more precise about the meaning of your variables? What do they stand for? If your F test of the regression is significant and if X1 and X4 are simultaneously different from zero, there could be an imperfect multicollinearity problem (You could check it with a VIF), but if it is not too high, there isn't a real problem for the regression itself.

• X1 is benevolent sexism, X2 is hostile sexism, X3 and X4 are dummy variables representing group membership (which scenario they read). The dependent variable is victim blame. All of the VIFs are less than 5. So would I be correct in interpreting the results as scenario and hostile sexism being significant predictors of victim blame while benevolent sexism is not a significant predictor? – Claire Feb 26 '14 at 21:06
• @Claire, this is inconsistent w/ the description in your question. There you say that X2 & X3 are dummies, and X1 & X4 are continuous. Which is it? – gung - Reinstate Monica Feb 26 '14 at 21:20
• I agree with @gung. Moreover, did you do the tests that I have suggested to you? What are the results? – user40899 Feb 26 '14 at 21:24
• What kind of SE did you used? – user40899 Feb 26 '14 at 21:30
• @gung, my mistake. The original description is correct. X2 and X3 are dummies, X1 and X4 are continuous – Claire Feb 26 '14 at 22:22