A note on centering in subsample selection for linear regression

Centring is a commonly used technique in linear regression analysis. With centred data on both the responses and covariates, ordinary least squares estimator of slope parameter can be calculated from model without intercept. If subsample selected full data, typically uncentred. In this case, it still appropriate to fit intercept? The answer yes, we show that obtained intercept unbiased has smaller variance covariance matrix Loewner order than with We further for noninformative weighted subsampling when used, using means relocate improves estimation efficiency.