Residualstandardfelet

Residualstandardfelet, also referred to in English as the residual standard error or residual standard deviation, is a statistical measure used primarily in linear regression analysis to quantify the variability of the observed data points around the fitted regression line. It represents an estimate of the standard deviation of the error term in a regression model, providing insight into how well the model explains the variability in the response variable.

The residual standard error is calculated by taking the square root of the residual sum of squares (RSS) divided by the model's degrees of freedom, which is the number of observations minus the number of estimated parameters. Mathematically, it is expressed as sqrt(Σ(yi – ȳi)² / (n–k)), where yi are the observed values, ȳi are the predicted values, n is the sample size, and k is the number of predictors plus the intercept. This formula normalizes the residual sum of squares, giving a scale that can be compared across models and studies.

In practice, residualstandardfelet is widely reported in statistical software outputs, such as R's summary(lm) function, where it appears alongside degrees of freedom and other diagnostic statistics. A smaller residualstandardfelet indicates a better fit, with residuals closely clustered around the regression line, whereas a larger value suggests greater dispersion and possibly model misspecification. Analysts use this metric to evaluate the adequacy of regression models, perform hypothesis testing, construct confidence intervals, and assess the precision of predicted values.