By means of Cross-Validation performing - If results for training data set is more better, than for validation data set. 

By means of Cross-Validation performing - If results for training data set is more better, than for validation data set. 

In general, the over-fitting problem in prediction can be checked by validation. If the developed model is giving good  prediction for training data sets and biased prediction in case of validation, then model can be considered as over-fitted. In specific, for regression, there are several parameters such PRESS, R^2 pred, AIC, etc. which will give an indication of over-fitting in the model. Increased polynomial functions in the model is also an indication that model may be over-fitted. 

This is an excellent question with many possible answers.  In addition to the helpful answers that have already been given, there is a bit more to add.

A review of methods for examining lack of fit and detection of overfitting of models is given in

https://www.researchgate.net/publication/227940560_PrognosticClinical_Prediction_Models_Multivariable_Prognostic_Models_Issues_in_Developing_Models_Evaluating_Assumptions_and_Adequacy_and_Measuring_and_Reducing_Errors

and

https://www.researchgate.net/publication/223093096_Fixed-effect_variable_selection_in_linear_mixed_models_using_R2_statistics

See, also:

https://arxiv.org/pdf/1611.06245.pdf

Article Prognostic/Clinical Prediction Models: Multivariable Prognos...

Article Fixed-effect variable selection in linear mixed models using...

it is interested question

All the best for 2017

this is an excellent question! I would maybe specify a bit: let us have a parametric model with several parameters. How do we conclude that the model is overfitted and how do we recognize which variable contributes the most to this 'overfitting'?

I am curious how PRESS, AIC, R squared etc can be used to understand overfitting?

PRESS and Predicted R2 are calculated by omitting each data point from the dependent variable set and then trying to predict it from the regression model. These two parameters will assess the predictive ability of the model. If in case the model is over-fitted with too many variables and/or few data points, the predictive ability of such model will be low and hence the PRESS and Predicted R2 will be low. Further, the AIC parameter helps in building up parsimonious models with few variables and hence gives an indication when model is over-fitted with number of variables to simply to attain higher R2.  

interested answers

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