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Sumukha has given the winning answer to this question. Short and crisp. Well done! Answer from Anish is also a must read.

In advanced regression techniques, we use R-sq (Pred) to assess the predictive performance of a model, this needs to be assessed separately even though we have R-sq and R-sq (Adj) calculated as part of the model which focuses on measuring the goodness of fit of any new factors to the model but don't assess the predictability of any new factor to the model. In order to make the model more predictable higher R-sq (Pred) is required against the R-sq and R-sq (Adj) and also fitment of any new factor or data to the model can be tested. This also helps in avoiding the multicollinearity in the model. Eg. Consider examples of predicting the prices of flats based on different factors like area of the flats, locality, bedrooms and amenities. You create a model based on historical data where R-sq and R-sq (Adj) values are calculated as 0.82 and 0.81 respectively, which indicates there are 81-82% variability in historical data. R-sq (Pred) is 0.75 predicting 75% of variability in new data. The predicted value will be lower as the data is new as compared to historical data aligned for other measures. These predicted values are more focused on future sales and decision making.

R squared = Measures the proportion of variance in the dependent variable(y) that is explained by the independent variables (x). It ranges from o to 1 and higher R-Squared value indicates that model is a good fit. The regression model is created based on training dataset. R Squared prediction = used to assess the predictive performance of a regression model. This is usually done using the test datasets (unseen data) to know how well the model could predict in the real world. Example: R- squared is a good indicator of how well the model fits based on the training data whereas R-square prediction will actually show how well the model fits the unseen data in the real world. This prediction is usually done with test data. One good example is the loan default prediction model created by a bank where they want to predict if the customer will default on loan based on various parameters(X factors such as age, gender nationality, loan amount, occupation, purpose of loan etc). The regression model is created based on the historical data using training data set. R-squared value = 0.93. This indicates that the model fits well.The regression model was then used on training dataset to predict how well the model fit for unseen data. R-squared prediction value =0.87 which also indicates that the model is a good fit for unseen data.