Fejlsummen

Fejlsummen is a term used in statistics and measurement theory to denote the sum of the deviations between observed values and the predictions produced by a model. Given a data set with observations y_i and model predictions ŷ_i, the fejlsummen E is defined as E = Σ_i (y_i - ŷ_i). If the model includes an intercept term, ordinary least squares regression makes the sum of residuals zero, so E tends to be zero in that case; when no intercept is present, E may reveal systematic bias.

Because residuals have both signs, E alone does not capture the size of the errors. A nonzero but small fejlsummen can occur even with generally good fit, and a large E indicates bias in the predictions. Therefore, practitioners typically use alternatives or complements such as the sum of squared residuals (RSS = Σ_i (y_i - ŷ_i)^2), mean squared error, or mean absolute error (MAE), which quantify the magnitude of errors rather than their signed sum.

Applications include model diagnostics, quality control, and estimation where bias assessment is important. Fejlsummen is related to residual analysis; examining E alongside RSS and the pattern of residuals helps assess whether a model is well specified or if improvements are needed, such as adding predictors or transforming the response.