it would be very suspicious, especially if you are looking at rainfall.  Make sure that you're data is accurate and not someone's prediction but an actual measurement.  Do not remove any data because that will affect results and make sure you have enough data. Also make sure that you are calculating it correctly.  This is not likely a real result.

data is showing multicollinearity, if data is time series, it may happen and if cross sectional very serious problem. in cross sectional regression, R2 should not exceed  0.6

Thanks so much scholars

Test the data for multicollinearity. I'll also suggest you check the significance of the relationship.

Dear Amanambu

In practical circumstances, such description of the system is not possible. That is the merit and demerit of the analysis. 

You can test Multicollieniarity, Auto-collineraity (if time series) and even heterosdasticity. Moreover you must also check the independent variables.

It is advisiable to use Adj R2.

Kind Regards

Rajiv

Hello Amobichukwu -

The coefficient of determination is subject to misinterpretation, and if you are trying to use it for nonlinear regression, and get a near perfect fit, that sounds like an overfit.  That is, say you artifically drew a curve exactly through all of your points. You may have no legitimate reason for doing that, but now you have a perfect fit (in spite of  a nonzero lower limit on error you could have expected from "statistical learning"). 

To identify this problem, you should save some of your data, leaving it out when you select your model and estimate parameters.  Then you apply your model to the new data and see how closely you predict the y-values that you saved out for testing.  If the model worked well for the data used to determine the estimated parameters, but you do not obtain 'predictions'  close to the y-data you saved for testing, then you may have overfit your model.  (Too many parameters generally actually increases variance.)

Another possibility is that you may not be applying the coefficient of determination correctly.  Sorry if this is  already familiar to you, but in case it is not familiar, and/or other readers might want a good explanation for this regarding linear regression, here is a link that may be helpful:

https://onlinecourses.science.psu.edu/stat501/node/255

.....

Well, that is my guess here: overfitting.   

.....

It is probably not a good idea to look at the coefficient of determination for nonlinear regression, I think.   (Even for linear regression, it may not always be very helpful.) 

Cheers - Jim 

thank you all for your insight

Coefficient of determination (R^2)

• The coefficient of determination is a measure of the amount of variance in the dependent variable explained by the independent variable(s). A value of one (1) means perfect explanation and is not encountered in reality due to ever present error. A value of .91 means that 91% of the variance in the dependent variable is explained by the independent variables.

• The amount of variation explained by the regression model should be more than the variation explained by the average. Thus, R2 should be greater than zero.

• R2 is impacted by two facets of the data:

o the number of independent variables relative to the sample size. For this reason, analysts should use the adjusted coefficient of determination, which adjusts for inflation in R2 from overfitting the data.

o the number of independent variables included in the analysis. As you increase the number of independent variables in the model, you increase the R2 automatically because the sum of squared errors by regression begins to approach the sum of squared errors about the average.

Thanks for the explanation Profs Knaub and Alshibly