# Is $R^2$ useless? [duplicate]

I stumbled on a discussion regarding the usefulness of $R^2$ as a metric. Where $R^2$ is defined as:

$$\frac{\sum (\hat{y} - \bar{\hat{y}})^2 } {\sum(y - \bar{y})^2 }.$$

The criticism is backed by Carnegie Mellon's Cosma Shalizi and focused on these 4 points:

• $R^2$ does not measure goodness of fit.
• $R^2$ does not measure predictive error.
• $R^2$ does not allow you to compare models using transformed responses.
• $R^2$ does not measure how one variable explains another.

He even suggested that "I have never found a situation where it helped at all.".

The article I read can be found here.

What do you think. Have you encountered any situation where $R^2$ would be useful?

## marked as duplicate by COOLSerdash, Stephan Kolassa, Nick Cox, kjetil b halvorsen, Glen_b regression StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Sep 16 '18 at 6:48

• Well, that's Cosma Shalizi, who has his opinions. Yes, I do find $R^2$ useful on occasion, and have for many years. Like any statistical tool, you have to understand its strengths and weaknesses, understand how what you have been doing to build a model plays into them, understand how the objectives of your model-building exercise relate to them, and understand how the specifics of your problem relate to them. – jbowman Sep 16 '18 at 0:44
• To describe it as a distraction and a nuisance is consistent with my experience. It’s bad enough in the context where it belongs. Stray outside of linear regression, and be prepared to answer either the question “but what’s $R^2$?” or “but why is $R^2$ so low (less than 90%)?” – The Laconic Sep 16 '18 at 3:33