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I recently graduated graduate school and am looking for a proof on R squared. Specifically when to not use it. I really remember a professor impressing upon me multiple times not to report R squared due to the fact it is unreliable. I did a proof on the matter, I just do not remember it. I've looked all over the internet, and can not seem to remember the solution.

Of course do not use R square when the data is non-linear. And do not add variables in order to increase R square.

Here are some links to back me up:

http://jackman.stanford.edu/classes/ssmart/2011/rsquared.pdf Specifically section 3.1 #6

http://blog.minitab.com/blog/adventures-in-statistics/why-is-there-no-r-squared-for-nonlinear-regression Do not use R sq for non-linear regression

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marked as duplicate by whuber Jul 29 '15 at 1:13

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migrated from stackoverflow.com Jul 28 '15 at 23:03

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    $\begingroup$ It is difficult to tell what you are asking, because you have not made any assertion that is subject to "proof" in the usual sense of the word. I suspect the thread at stats.stackexchange.com/questions/13314 might address your concerns. If it does not, then please edit this question to show how it differs from the material discussed there. $\endgroup$ – whuber Jul 29 '15 at 1:13
  • $\begingroup$ I completely agree with @whuber. What exactly are you attempting to prove here? $\endgroup$ – StatsStudent Jul 29 '15 at 2:03
  • $\begingroup$ There is a proof shown in my regression theory class and I forgot it, and the book is very far away right now. I can post it after I come into possession of the book in about 2 weeks... $\endgroup$ – Sarah E Jul 29 '15 at 15:16
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I don't know if you should never use it, but like all metrics it simplifies things and thus has its limitations.

One caveat is that you should always use adjusted R-squared, not R-squared, as the latter will increase every time you add a new explanatory variable. This behavior may have been what you remember as a "proof" that you should never use it. Adjusted R-squared tries to compensate for this.

The courses that I have had teach that you should look at the adjusted R-squared, and then look at how the residuals are distributed with respect to the explanatory and explained variables, QQ-plots, etc. This will give you a sense not only for how well your model is doing, but if you are maybe missing some important explanatory variables, or if you your predictions are failing in particular areas of your parameter space. Essentially you are testing some hypothesis about your model, your data, and the residuals and there are different ways you can approach this, for example "eyeballing it" (like I describe above), or using sophisticated tests of normality.

Modeling is as much an art as a science, so any statement with "always" or "never" in it is bound to be wrong.

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  • $\begingroup$ I just remember in my MS for Statistics courses we never used R squared. And there was a proof at the beginning of my regression course that we did to show that it was a poor statistic to use. I just really wish I had the proof. Its several hundred miles away on a book shelf... :( $\endgroup$ – Sarah E Jul 28 '15 at 23:32
  • $\begingroup$ So what are your alternatives? $\endgroup$ – Mike Wise Jul 28 '15 at 23:51
  • $\begingroup$ Email my professor and ask for the proof? haha. I feel that only maximizing a r squared value when creating a model is inappropriate. That multiple measures such as a Q-Q plot, cooks Distance, individual variable significance, correlations between variables, and others need to be utilized when creating a model. Also the way in which a model will be used need to be considered. And that blindly following an R squared value is wrong. And I also feel that the proof will show empirical evidence that r squared is faulty. Rather than all of these 'opinions' I posses. $\endgroup$ – Sarah E Jul 29 '15 at 15:15
  • $\begingroup$ That is pretty straightforward and non-controversial advice. Why do you need a proof of it? $\endgroup$ – Mike Wise Jul 29 '15 at 15:28

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