# How to find variance (in %) explained within the output coefficients?

I'm not very good with technical details or equations in stats as I'm quite new to running these in R. So I hope that you won't mind me asking these perhaps simple questions and also I would appreciate if someone could attempt to reply in layman terms.

What part of the model output can I use, which denotes the % of variance explained in the model? Is it $R^2$? i.e. if I have $R^2$ or $r$ (for regression and correlation tests respectively) = 0.65, does this mean that my model explains 65% of the variance? How can I do this with mixed models (e.g. lmer())? I've tried to find ways to calculate $R^2$ for lmer() but found much discussion on the topic, without a clearcut way, other than 'not necessary as not too reliable'. Hence, I will simply report the results of the model without the $R^2$ but rather with the likelihood ratio test results.

Does this lack of $R^2$ for lmer then mean that there's no way for me to say how much variance is explained by my model? Or is this something that the random effect coefficients represent and if not then how can you interpret them or what kind of statement would you write regarding your random effects coefficients?

Does this lack of $R^2$ for lmer then mean that there's no way for me to say how much variance is explained by my model?
Even if you had valid $R^2$, it wouldn't tell you much about how much variance was explained by your model. The whole idea of variance explained is often criticized. In general, $R^2$ can be misleading. Moreover, the idea of $R^2$ measuring explained variance applies only to linear regression with one predictor (or here), nonetheless, as described by Achen (1990) it still can be misleading at doing that.
That being said, there are several approaches to calculating $R^2$-like statistic for linear mixed models (see also here), so you can calculate it, but you have to remember that it does not tell you about "variance explained" and that it is not a perfect measure.