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August 3rd, 2018, 12:20 PM  #1 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 639 Thanks: 85  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[8] 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  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,160 Thanks: 878 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
Dan  
August 3rd, 2018, 01:58 PM  #3  
Senior Member Joined: Sep 2016 From: USA Posts: 609 Thanks: 378 Math Focus: Dynamical systems, analytic function theory, numerics  Quote:
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.  

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