I would like to predict discrete (mean) values from discrete (mean & std) values of the extracted features. My question is how you should perform feature selection when you are applying K-fold cross-validation in multiple linear regression? Let's say you have 30 features and you should end up with only 3 features. My solution was that I computed all the possible combinations of subsets and then for each subset of features I applied cross-validation and multiple linear regression (train and test the model). I got some results for some feature subsets but I am not sure if these are reliable.
Your methodology is correct. Just to clarify, you have a dataset that you split in 3: insample-train, insample-test, and outsample.
You train model parameters (betas for your multiple linear reg) on the insample-train (that's when you train on your k-fold). You train hyperparameters (which 3 feature you end up choosing) on the in-sample-test. You evaluate your final model on the outsample, and use that number as your best guess at go-forward predictive error.
If you open up the outsample more than once, you'd have to discount your final go-forward error.