Possibility of Negative R squared

Long time ago I had given an assignment to find the reasons of negative R squared, so I searched and all the statisticians responded my questions like I was trying to preach a new religion. But the wait is over…

Recently I found an interesting illustration of how R squared can be negative it is available at following link. According to this R squared is negative when the model is over restricted just like the image below where there is a restriction that intercept must be 1500 (don’t mind about the typo here intercept is written as 150 actually it is 1500).


Other reasons of the negative R squared is that you are running the regression other way around like if Y is a function of X but you ran regression of X is function of Y then there is a possibility that the result to show endogenous regression.

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