What Does Performing Linear Regression on Sample Survey Data Mean?

Most economists understand linear regression as the estimation of the parameters of a linear model. There are two other ways of interpreting the results of linear regression, however, and most software packages designed specifically to handle data from complex sample surveys (for example, SURREGR and PC CARP) assume one of these interpretations. This article contrasts the conventional model-based theory of linear regression to the design-based theories underlying survey-sampling software. The article demonstrates how procedures from design-based regression theory can be justified and exploited in a linear model framework. Proposed is a test for comparing the results of ordinary least squares and weighted regression.