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Data Collectionhard
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In a two-phase sampling design, suppose we have a primary sample of size n′n'n′ and a subsample of size nnn. The regression estimator for the population mean Yˉ\bar{Y}Yˉ is yˉlr=yˉ+b(Xˉ′−xˉ)\bar{y}_{lr} = \bar{y} + b(\bar{X}' - \bar{x})yˉ​lr​=yˉ​+b(Xˉ′−xˉ). What is the approximate variance of this estimator, assuming nnn and n′n'n′ are large?