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 August 3rd, 2018, 12:20 PM #1 Senior Member   Joined: Oct 2013 From: New York, USA Posts: 661 Thanks: 87 R Squared Not Ranging From 0 to 1 https://en.wikipedia.org/wiki/Coeffi...Interpretation says: "Values of R^2 outside the range 0 to 1 can occur when the model fits the data worse than a horizontal hyperplane. This would occur when the wrong model was chosen, or nonsensical constraints were applied by mistake. If equation 1 of Kvalseth is used (this is the equation used most often), R^2 can be less than zero. If equation 2 of Kvalseth is used, R^2 can be greater than one." How can R^2 be less than 0 if the data are real numbers? August 3rd, 2018, 01:03 PM   #2
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 Originally Posted by EvanJ https://en.wikipedia.org/wiki/Coeffi...Interpretation says: "Values of R^2 outside the range 0 to 1 can occur when the model fits the data worse than a horizontal hyperplane. This would occur when the wrong model was chosen, or nonsensical constraints were applied by mistake. If equation 1 of Kvalseth is used (this is the equation used most often), R^2 can be less than zero. If equation 2 of Kvalseth is used, R^2 can be greater than one." How can R^2 be less than 0 if the data are real numbers?
Sounds like the data sets I measured in my grad lab class. There's a reason why I'm a theorist. -Dan August 3rd, 2018, 01:58 PM   #3
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Quote:
 Originally Posted by EvanJ https://en.wikipedia.org/wiki/Coeffi...Interpretation says: "Values of R^2 outside the range 0 to 1 can occur when the model fits the data worse than a horizontal hyperplane. This would occur when the wrong model was chosen, or nonsensical constraints were applied by mistake. If equation 1 of Kvalseth is used (this is the equation used most often), R^2 can be less than zero. If equation 2 of Kvalseth is used, R^2 can be greater than one." How can R^2 be less than 0 if the data are real numbers?
The same article you linked has an explcit description of the formula for $R^2$. Note that it is not computed by just squaring something so negative numbers are possible. From inspection of the formula, you can get negative values if $SS_{res} > SS_{tot}$.

Intuitively, this happens if the regression model "often" takes values which do not lie between the mean and the observed values. This can be seen directly by applying the triangle inequality to the formulas specified in your article. Tags ranging, squared Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post jsmith613 Probability and Statistics 0 March 31st, 2016 12:07 PM iranch Advanced Statistics 1 December 13th, 2015 05:38 AM bignick79 Algebra 9 June 29th, 2010 12:59 PM Shocker Advanced Statistics 1 February 8th, 2010 04:47 AM RFurball Advanced Statistics 1 September 10th, 2007 05:02 AM

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