# Triangle correlation between independent variables

I am currently writing my thesis and I am about to conduct some t-tests and a regression analysis. Before using my data, I conducted a correlation test. Now I found the following: I have a couple of independent variables (one is the "real" IV, the others are control variables). Three of the control/independent variables correlate with each other in some kind of triangle:

x <-> y: 0.214***

x <-> z: 0.611***

y <-> z: 0.210***

Is this a problem for my analysis and if so, do you suggest me to remove the variables? (x and y do furthermore correlate with the dependent variable.)

## 1 Answer

That is exactly why you need regression analysis! The basic logic of regression analysis is that all independent variables "compete" for explaining the dependent variable. The better their claims, the stronger their coefficients/significances. Regression analysis also sorts out the correlation between independent variables for you. Thus keep all your variables in the model. (If you don't do so, you create the problem!)

• Thanks for your answer! But I assume the correlation between the control variables means that I have a problem with multicollinearity. Is that true? – user235306 Feb 4 at 9:10
• Multicollinearity is not a problem in the sense that it leads to wrong coefficients. The only thing what multicollinearity does is to increase your standard errors (and thus you p-values, too). In your case, I would be more worried that either $X$ or $Z$ is a confounder, because then in this case, your coefficients will be wrong. Furthermore, the correlation between $X$ and $Z$ isn't that bad to be worried about multicolineartiy. If you want to know more, I suggest you google the term variance inflation factor – Tom Pape Feb 4 at 9:31