residualized

Residualized refers to a state or process where residuals have been accounted for or removed. In statistical and econometric contexts, residuals are the differences between the observed values of a dependent variable and the values predicted by a model. When data is residualized, these differences are analyzed or utilized in a subsequent step. This process is common in regression analysis, where the goal is often to explain the variation in a dependent variable. After fitting a model, the residuals represent the unexplained variance. Residualizing these values means isolating them for further examination, perhaps to check model assumptions or to use them as predictors in another analysis. For instance, in a two-stage least squares regression, the first stage involves regressing an endogenous variable on exogenous variables and instruments. The predicted values of the endogenous variable are then used to calculate residuals. These residuals, representing the part of the endogenous variable not explained by the exogenous variables and instruments, are then used in the second stage of the regression, effectively residualizing the endogenous variable. This technique helps address issues of endogeneity. The term can also appear in other fields where a component or effect is isolated after accounting for other factors.