foutterm

Foutterm is a term used in Dutch mathematics and statistics to denote the error term in a mathematical model. It represents the portion of the observed outcome that cannot be explained by the model’s specified variables, and encompasses measurement error, random variation, and the effects of omitted or unmeasured factors. In a simple regression, y = β0 + β1 x + foutterm, the foutterm accounts for the discrepancy between the observed y and the predicted value.

Typically, models assume foutterm has an expected value of zero conditional on the predictors (E[foutterm | X] = 0), is uncorrelated with the explanatory variables, and has constant variance (homoscedasticity). These assumptions support unbiased and efficient estimation under methods like ordinary least squares (OLS). In time-series contexts, the error term is also assumed not to be autocorrelated; violations can affect inference.

The foutterm captures unobserved influences, including measurement error, model misspecification, and inherent randomness. If the foutterm is correlated with the regressors (endogeneity), standard estimators become biased and inconsistent, prompting methods such as instrumental variables or model re-specification.

After fitting a model, the observed residuals are estimates of the foutterm, but they may differ due to sampling variability and the particular estimation method. Analysts diagnose the nature of the foutterm with tests for heteroskedasticity, autocorrelation, and normality, and they address issues via robust standard errors, transformations, adding relevant variables, or alternative models.