# Distinguishing between what makes up R-squared

I am interested in the relationship between religiosity and religious distrust (would you dislike having as neighbours people of different religions).

One of my main goals is to make the role of each individual religion insignificant; according to my argument monotheism leads to distrust, regardless of the particular religion. However, religions explain about 53% of my variation in religious distrust according to the R-squared. I wanted to include variables that would 'take away' from this influence of religion in terms of explanatory variable. For example, economic inequality in most Muslim countries might be a reason for differences in distrust, or the number of times people pray, which is less in Protestant countries. So I added as independent variables: Economic inequality, urbanization, separation church/state, number of times people pray, and education. When I include these in a model without religion I get an R-squared of about 37%.

When I include all these independent variables + religion, religion becomes significant again, I think because religion incorporates much more explanation than either single one of my other independent variables. My R-squared in this model is, again, 53. My question is, is there any way to support the claim that although religion might matter, my independent variables 'take away' at least some of its explanatory value?

So:

• religion alone explain 53%;
• my independent variables explain 37% alone;
• together they explain 53% again

Could I say that of the 53% religion used to explain, 37% / 53% is now explained by my other independent variables? So in a sense, I took away about 2/3 of the explanatory value of religion by introducing other variables? Or is this not statistically valid, because they might for example explain different parts of the variation in my dependent variable?

• Oh, and yeah, I do like the relaimpo package myself too. What does it tell you for the model without religion? – Geraldine Mar 25 '16 at 16:08