Dear SriKanth

The R² represents how much variance of the data is explained by the model, the R2=0.90 means that 0.10 of the variance can not explain by the model, the logical case when R2=1 the model completely fit and explained all variance.

The calculation of R2 above the 1 represent abnormal case and has no logical meaning and may result from the small sample size.

Good Luck

thank you prof. Khalid Hassan for your reply. 

your explanation is quite helpful for me in understanding the intricacies of the R-squared value. 

ultimately, do we have to ignore the interpretation of the DV which has got R-squared  value of more than 1 or is there any alternative way for interpreting such type of abnormal results.  how to conclude on such results

Dear Srikanth,

It is certainly spurious and has no statistical meaning. Have you reviewed your calculations?

thank you Prof. Nicolau Dionísio Fares Gualda 

i will review my calculations. 

As above, since the sum of squared errors is positive, R-square should be less than one, so such a result as yours would be due to the algorithm, sample size, round-off, or some other such cause, if over one and not an outright error.  It must still then be close to one, indicating a near perfect fit based on the available data.  I don't think that would generally hold up on subsequent data collections unless this is a deterministic process such as measurement of a physical law, and even then you would likely be impacted by measurement error beyond what is covered by rounding. 

If your number is much greater than one, then the calculation must be incorrect.  This would apply to other readers with this problem, as well. 

Perhaps you should estimate the variance of the prediction errors.  Their square roots are often informative.  You may then be more informed as to the adequacy of your sample size.  You may find software to do this.  If, for example, you used a regression covered by SAS PROC REG, then that square root could be found, labeled as "STDI."  There are other PROCs for other kinds of regression, I think.  Also, I expect that the R language likely has something on estimates of the variance of prediction errors written by someone.  -  Best to test any software you use to be sure it is doing what you think it is doing. 

If you have no intercept in your model main imply "strange" value of R².

Assuming that you have a constant term in your model, the only way to interpret an R² value of more than 1 is as an error in the calculations.

I think R^2 is overrated  as a measure of how well a curve firs data.  Have you tried plotting your regressed model and seeing how well the prediction curve fits the actual data? The "eye test" is usually more meaningful.

R2 is a good way to eliminate models that don't fit very well or show that reproducibility of the data is either good or bad.  It may also show that there are other important variables that are missing from your model that influence the results.

I also got r-squared more than 1. In my case, r-squared value is 1.1 for the training data, 1.15 for the testing data. I carefully checked all calculation procedure and verified it is correct.

The plot of prediction and actual is not straight line which is the case of r-squared is 1.

,,,9l999999ll OK ololo99

Probably your model is non linear. Check these posts:

http://statisticsbyjim.com/regression/r-squared-invalid-nonlinear-regression/

http://statisticsbyjim.com/regression/standard-error-regression-vs-r-squared/

According to what I have studied,

R2 = (sum(variation around the mean) - sum(variation around the model))/sum(variation around the mean)

Now, if you can realize that variation around the mean is always less than or equal to variation around the model, plus variation is always positive because they are the squared terms, then you can instantly realize that if your model is correct then R2 will always be between 0 and 1. If it is coming greater than 1, then that means that the data set shows less variation around the mean than the model, which sounds quiet akward!!