# How to calculate the shared variance between multiple IVs in predicting DV?

I would like to know how to calculate the degree to which multiple IVs share variances with each other in predicting for the DV. For example, A, B, C, D and E predicts for Z. How do I calculate the degree of shared variance for A, B, C, D and E in predicting for Z?

• Welcome. Google for `Multiple regressin Venn's diagram'. You'll learn that, for example, if $R^2$ is the observed R-squared of multiple regression and $B$ is the squared part correlation between the DV and the pridictor B, and, likewise, $C$ is the squared part correlation between the DV and the pridictor C, then the the part of the variance of the DV that B and C share is $R^2-B-C$. Commented Sep 17, 2013 at 18:09
• stats.stackexchange.com/questions/64261/… Commented Oct 18, 2013 at 4:32
• You may want to search for commonality analysis Commented Apr 8, 2017 at 16:54

What you are looking for is the adjusted $R^2$. I won't go into detail about what it is, but you can read the wikipedia page if you would like to know more aboiut it:

One way to calculate the adjusted $R^2$ (which I like) is
$$\bar R^2 = {1-(1-R^{2}){n-1 \over n-p-1}}$$
Which I think is a nice way to write the formula because now was can see exactly how we are being penalized for having more parameters in the model. To make sure you understand the notation, $R^2$ is the usual coefficient of determination (which is not a particularly good measure to look at by itself when you have multiple independent variables), $n$ is the total amount of data (or samples) that you have, and $p$ is the number of parameters in your model (so in your case if your model included A,B,C,D,E, then $p=5$).
Now as you can see $$\frac{n-1}{n-p-1}>1$$ and that is why the adjusted $R^2$ is always penalized for having more parameters.