How large should my data set be before I can do a train-test split (cross validation)? Data set 
I am currently working on a data set that I would like to fit a regression on. It consists of 81 observations and 9 variables. The variables consisting of 1 response variable and 8 predictor variables.
Cross validation 
In general, the more data we have, the more it makes sense to do a train-validation-test split. This is of course useful to see how well the model that we fitted is doing on unseen cases. Cross-validation is commonly used to perform these splits.
Having a small data set like I have at the moment, having a validation set is probably not feasible. I am however thinking of doing a train-test split on my data.
Question 
How large should a data set be before it is feasible to do a train-test split?  (I realise that this could be subjective)
 A: You should always do a train/validation/test split (or better a train/test split with cross-validation on the training set for hyper-parameter tuning). I think your question arises from a common misconception of what splitting our data is for. A train/test/validation split is used only to estimate the generalization error of our algorithm and to choose between various algorithms.
People are often concerned with doing a train/validation/test split (or even just a train/test split) because they are concerned that this removes records from training and this will make their end model worse. The thing is, this isn't true since after we determine the error rate, we redetermine optimal hyper-parameters on all of the data (whether through a simple train/test split or cross-validation on all of the data) and after that we retrain the model on 100% of the data.
So in the end, your model is trained on all of the data and no data is "lost" just temporarily set aside. So to answer your question: Do you want to know how well your model is doing? If so, you need to split properly.
