Residual
The difference between an observed value and the value predicted by a statistical model.
What is Residual?
In regression analysis, a residual represents the error of the model for a specific data point. It is the vertical distance from the observed data point to the regression line or surface. Examining the distribution and patterns of these residuals is critical for diagnosing whether a model's assumptions are met.
Why Residual Matters
Residuals indicate how well the model fits the data. Analyzing them helps researchers identify outliers, detect non-linearity, and check assumptions like homoscedasticity and normality of errors.
Example
After fitting a model predicting student test scores, the researcher notices the residuals for high-performing students are systematically large and positive, indicating the linear model is failing to capture the upper end of the distribution.
Common Mistakes
- Focusing only on the R-squared value and completely ignoring residual analysis.
- Confusing residuals (sample errors) with the theoretical error term of the true population model.