In my current project I'm working with a previously developed linear model and asking how many training observations do I need to reproduce the model. The original model was developed with ~1000 observations, and I want to see how many I actually need to reproduce the original model parameters. To address this, I plan to sample the training data (keeping the response distribution representative of the training set) and develop new models for numerous repetitions - perhaps 100-1000 repeats. Each time the model is trained, I will use the same set of covariates used in the original model, and I would like to see how the coefficient estimate and standard error compare to the original, but, I'm unclear on how to combine the coefficients and standard errors from 1000 different models. The value for the coefficient could simply be the average or all trials, but how do I combine the standard errors for those same trials?