Absolute value of a residual

Definition

The absolute value of a residual is the non-negative difference between an observed value and the corresponding predicted value from a regression model. It measures the magnitude of prediction errors without considering their direction.

5 Must Know Facts For Your Next Test

1. Residuals are computed as $observed - predicted$ values in a regression model.
2. Absolute values of residuals ignore whether the error is positive or negative, focusing only on its size.
3. Smaller absolute residuals indicate better model fit to the data points.
4. The sum of absolute values of residuals can be used to assess overall predictive accuracy.
5. Outliers often have large absolute residuals, indicating poor model fit for those data points.

Review Questions

• What does the absolute value of a residual represent in a regression model?
• How can you interpret smaller versus larger absolute residuals?
• Why might outliers have large absolute residuals?

Related terms

Residual:

The difference between an observed value and its predicted value from a regression model.

Mean Absolute Error (MAE): A measure of predictive accuracy that averages the absolute values of residuals.

$R^2$ (Coefficient of Determination): $R^2$ quantifies how well the regression model explains the variability in the response variable.