Let me illustrate the question with an example: Imagine you construct a model to predict tomorrow's rainfall over London using some variables. Let's suppose that 300 years of data are available (1718-2018). Of those aprox. 110.000 points, you use 70.000 to train you model and 40.000 as a test set. If 95 % of the residuals of the test set range between -5 +5 mm:
1.Would it be correct to say that the uncertainty of the predicted values for 2019 would be +-5 mm or whatever asymmetric interval we get?
2.Does the answer to question no 1 depend in any sense on the theoretical distribution of the residuals according to the structure and/or assumptions of the model? (remember that the sample is large and representative).