Residual
Residual is the difference between an observed data point and the value a fitted regression model predicts for it. It is the part of the outcome the model does not explain, and the basis for measuring fit.
Also known asresiduals
FrameworkOrdinary least squares (OLS)
See it move
A scatter-line chart plots advertising budget on the horizontal axis and sales in thousands of euros on the vertical axis, with the fitted regression line drawn through the data. At one highlighted observation, actual sales stand at €41,000 while the model predicted €38,000, producing a positive residual of +€3,000 and indicating that the model under-predicted sales at that point by €3,000.
The formula
Variables
- Residual for observation i
- Observed value of the outcome for observation i
- Fitted (predicted) value from the regression model
By construction, OLS residuals sum to zero across all observations.
Check yourself
A regression of annual store sales (€000) on retail floor space (sq m) predicts €520,000 for a 200 sq m store. The store's actual annual sales are €495,000. What is the residual for this observation?