# Intuitive Explanation of R-squared

Here is a nice definition of R-squared that I have found on the internet.

R-squared is a statistical measure of how close the data are to the fitted regression line. It is also known as the coefficient of determination, or the coefficient of multiple determination for multiple regression.

The definition of R-squared is fairly straight-forward; it is the percentage of the response variable variation that is explained by a linear model. Or:

R-squared = Explained variation / Total variation

R-squared is always between 0 and 100%:

0% indicates that the model explains none of the variability of the response data around its mean. 100% indicates that the model explains all the variability of the response data around its mean. In general, the higher the R-squared, the better the model fits your data. However, there are important conditions for this guideline that I’ll talk about both in this post and my next post.

Could someone please explain to me what does "variability of the response data around its mean" stand for, and also "it is the percentage of the response variable variation that is explained by linear model"? I am having trouble understanding these concepts.

• I am quite sure that "variability of the response data around its mean" tells us how bad the data is scattered from its mean. In statistics, this is called variance that we all know. Meanwhile, for your second question, I think we may come to a clearer definition by visiting this site: khanacademy.org/math/ap-statistics/bivariate-data-ap/…. Feb 26, 2021 at 8:35