I am trying to develop a model between a 19 year record of climate data and a 19 year record of ice-off dates on rivers. The two variables are linearly correlated. The goal is to build a linear model so that we can use the climate data to predict the ice-off dates in future years when we don't have ice data but do have climate data.
What I have done thus far is bootstrapping: I randomly select 14 years as training data and the remaining 5 years as testing data. I build the linear model on the 14 year training dataset, then apply it to the remaining 5 years, and evaluate the model performance using the nash-sutcliffe coefficient (https://en.wikipedia.org/wiki/Nash–Sutcliffe_model_efficiency_coefficient#targetText=The%20Nash–Sutcliffe%20model%20efficiency,Qm%20is%20modeled%20discharge.). I then repeat that 1000 more times, randomly sampling the 14 years of training data each time.
Now that I have done this, I want to pick the best model of the bunch. Should I take the model with the median nash-sutcliff coefficient, or the one with the best nash-sutcliff coefficient? What is the best next step here that avoids overfitting?
I'm a statistics beginner, so your help is greatly appreciated!