Hi, it is possible. R (correlation of coefficient) can be between -1 and 1. Thanks.

Hi.., R- values gives you indication how your variable correlate with each other ( your plot is linear or no as R-values approach 1 as the  correlate described as excellent linear correlation). Regression equation : you can use it to calculate values for a variable at any value you are using for second variable in regression equation

Giwa and Salim, Thanks for the interesting answers.

If you are referring to the coefficient of determination (R2) then my reaction is that this is really good news or really bad news.  The good news is that you have almost perfect prediction.  The bad news is that you have perfect prediction possibly due to a redundancy between the DV and IV.  I would also check to determine whether one of your observations is miscoded in a way that it is creating an undue influence on the outcome of the regression results.  Using least squares linear regression with anything less than interval level DVs may be problematic.  You should assure yourself that this is a coding that is approximately representative of an underlying normal distribution and that the variances conditioned on each level of the IVs is approximately equal (homoscedastic assumption.)   As a very simple diagnostic you might consider running your regression N times leaving out one observation at a time using N-1 observations.  Do the results of these regressions produce the same results or is one of them different in some substantial way?  If you have one split based on N-1 observations that is unusual, then check the quality of the data for the observation left out.

What you have reported is very unusual in the areas in which I work.  Perhaps this finding is quite reasonable (or even low) for your area of investigation.  Is there some way you can make an assessment of the reliabiity of the IV's.  Is it reasonable to assume that the DV is measured without error?  If you knew the reliability, you could calculate the expected attenuation of the IVs..  Would this explain why the prediction is not 1.0?  

You might also consider an alternative to least squares linear regression that can model contingency tables of considerable complexity.  For example, see Shelby Haberman, The analysis of frequency data.  There are other quite accessible texts on qualitative data analysis that might be helpful and an easier read than Haberman. 

Dear David,

I am totally pleased with your answer and the quality of the questions I must add to the observations and the regression which I am using with the examined Photovoltaic system.

I applied two different regression models, the exponential and 3rd order polynomial, I found that the 3rd order has much higher determination factor than the exponential regression type, that is because there are some hills and valleys in the data which I am considering.

Thank you once again for the valuable answer.

Kind Regards

How many data has used ? If you have two points, the R-Square will be 1, always. The model is significant? If Beta is not different from 0, there are no true relationship between predictors and response, since any variation in the predictors does not corresponds to variations in the response. There are no bias in data collection or preparation, creating an artificial relationship between response and predictors? The model represents a coherent effect? The assumptions of the analysis were checked? So, if all these points are ok, you have a almost perfect model to predict the effects based on the effects at the right of the equal sign.

It would be helpful here to know what the response variable (y) is and what the regressor variables (x1, x2, ..., xk) are. Multicollinearity can be a cause of such high R square values. A high R square value indicates a good fit. It is not necessarily a good model for prediction. As you see from the answers here, we have to guess what the regression is about. A no-intercept model can also create such R sqaure easily.

With R (or r) value of 0.95, the regression equation is highly significant. It can be used in similar cases.

What I am predicting is the output power of a Photovotlaic Module, While the regression variables is such as the voltage, current, power, sun irradiance and the PV module's temperature.

I used two regression types, 3rd order polynomial and exponential for the theoretical data of a PV modules, it turns to be that the 3rd order polynomial (R>0.99) has much higher R than the exponential value (R=0.95). However, when applying the equation for both regression, the exponential regression has almost the same prediction accuracy comparing to the 3rd order polynomial! For that instance, I could not find any answer on which method I should finally use to complete my work!

Make sure to measure any exisitng multicollinearity (such as using the Variance Inflation Factor for each X). Get also the PRESS statistic (it is an error sum of squares that is measuring the stability of the model when new data are used with the model for a true prediction). 

I'm not sure I understand the question, but if the issue is that a model with R^2 = .99 performs worse than one with R^2 = .95 on out of sample prediction, that is not surprising. It seems to be an example of overfitting and there is a large literature on why optimising fit in a sample won't optimise out of sample prediction with the same coefficients.

Intuitively I can perfectly predict performance in the 2015 Premier League with predictors such as goals scored, assists etc. of players. However, applying those parameters to 2016 won't give me perfect prediction.

Like Thom I would like more information. That said, a regression model with R = 0.95 suggests that all the main independent variables have been included. That is, there is not some missing factor that would have a large impact on the module performance.

From experience, I'll question any R2 values higher than 0.9 due to errors inherent in that cannot be avoided: human, instrument, environmental, etc, errors. I'll take such figures as curve over fitting of the data and I'll try other models to fit the curve..

Thank you Abayomu, I guess you are correct, There is no doubt that a statistical regrssion model with a confidence interval of 99%, can't be achievable in reality.

Cheers