# How to find the fraction of variation in an independent variable that explains the dependent variable?

How can I find the fraction of the variation in a regressor, that explains the dependent variable.

For example, income determines crime rates. How do I find how the variation in income affects crime?

How do I got about finding that? What calculation should I use? I'll be using Stata.

• Unless your regressors are orthogonal, that fraction is not well defined. Mar 16 '16 at 13:20
• Are you looking for the fraction of the variance in the dependent variable explained by the independent variables? That is just the $R^2$, which is reported directly in the output of a linear regression model (regress in Stata) Mar 16 '16 at 14:11
• Hi, thanks. No, I'm looking for the fraction for one of the independent variables, and not all of the independent variables. Mar 16 '16 at 14:14
• As @Maarten Buis mentioned, you could use the R^2 value for a one-variable model (simple regression) to get the portion of the variance in crime rates that is explained by income. However, one (big) caveat in this approach is that you are not controlling for other factors (ceteris paribus). Mar 16 '16 at 15:42
• Maybe you are looking for a partial correlation coefficient squared? But us guessing at what you might want to know is not a very efficient way of getting an answer. Can you give a reference which discusses or uses the exact statistic you are looking for? Mar 17 '16 at 8:02