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Macro-comparative research is characterized by a methodological paradox: it routinely violates the assumptions that underlie its dominant method, that is, multiple regression analysis. Comparative researchers have substantive interest in their cases, but multiple regression analysis treats such cases as random samples of a given population, making them invisible throughout the analysis, and providing the researcher with generalizable inferences of variable effects. Researchers do not always recognize this mismatch between macro-comparative demands and multiple regression analysis, and sometimes end up engaging in strenuous disputes over particular variable effects. Case in point is the question of whether income inequality affects health, which has produced hundreds of articles over 25 years of research, and no clear answer yet. Here, we offer an innovative methodology that combines variable-oriented and case-oriented approaches, by turning OLS regression models “inside out.” Using singular value decomposition, we estimate case-specific contributions to regression coefficient estimates. We reanalyze published data on income inequality, poverty, and life expectancy across affluent countries. We show that different model specifications are all dependent on two countries with values on the outcome that are extreme in magnitude and inconsistent with theoretical expectations.