I'm studying linear regression and there is a concept I can't wrap my head around.
I've heard many times the expression "the independent variable explains $a$% of the variance of the dependent variable $y$. (where $a$ is a number)
The variance of the random variable $y$ is the distance of the observartions from the mean value of $y$. By adding our independent variable $x$ in the model, we want it to explain some of this variance.
I think that when we say the word explain, we don't actually mean that we explain something and it's a metaphorical way of using it but I'm not really sure what it means.
I've found another similar question here but the answer didn't help me understand it. I'd really appreciate some help!