A Model-Based Look at Linear Regression with Survey Data
This article explores the ramifications of performing a linear regression on data obtained from a complex sample survey. The incorporation of sampling weights into estimated regression coefficients helps protect against the potential existence of missing regressors. In addition, the linearization variance estimator, computed by certain software regression packages designed specifically for use with survey data (e.g., SURREGR, SUPER CARP, and PC CARP), is robust against the likelihood of correlated errors and the possibility of heteroscedasticity
Kott, P. (1991). A Model-Based Look at Linear Regression with Survey Data. American Statistician, 45(2), 107-112.