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Is it remotely legitimate to use the standard errors of the coefficients from linear regression in a Monte Carlo simulation to bootstrap 2.5%/97.5% confidence intervals on the predictions? If so (or if not), is there any literature relevant to this approach?

I'm generating nested models using logistic regression and comparing them by AIC. One issue that arises is that not all samples have all independent variables coded. For sake of discussion, let's assume no imputation of missing independent vars: those samples just get dropped when generating...