Salman,

The most important figure-of-merit to judge the quality of your PLS model is the RMSEP. If you used an independent sample set to test the RMSEP of your model, and the RMSEP is satisfying in your opinion, I wouldn't worry too much. Maybe there are some outliers in your test set that result in a low R-square value?

Hi Salman,

I think that you may verify your R square because if you have a low rmse of prediction, the R square must be high.

Good luck

Hi Salman. what were the parameters? what do you define as low RMSEP? It would be great if you could supply some more info.

Did you check if there was no confusion with the parameters such as R^2 of calibration and RMSEP of validation? Did you assess the RMSEP value in comparison with the values of the dataset?

Thanks to all. I believe what @H. J. Ramaker is saying is the most appropriate answer. I got a similar answer from Professor Rasmus Bro.

R2 in prediction is indeed not important and NO, there is no "if RMSEP is low, then R2 should be high" in PLS prediction.

The point is that the new fields have lower variability compared to the big dataset that was used for model building using CV. RPIQ for prediction is high, so there is no problem with that. R2 in prediction is only indicating how good we fit the predicted vs. measured results. Since we have a lower variability range and the error might be in different "directions", that fit might not end up a very bad fit, which is not problematic at all.

RMSEP, removes the "direction" of error by squaring the values, and therefore the important figure to consider.

RMSE values are also dataset dependent Which means, if the dataset is between 0-100, RMSE can be even 10 or 20.

but R^2 value is not and it is always between 0-1