Outlier
Outlier is a data point that sits far from the bulk of observations. In regression, a single extreme value can pull the fitted line toward it and distort all estimated coefficients.
Also known asoutliers
See it move
The infographic is a scatter plot with a fitted regression line, plotting Y against X, with one far-flung data point visibly distant from the main cluster. That single extreme observation pulls the OLS line away from the bulk of the data, distorting both the slope and the intercept and thereby misrepresenting the relationship for every other observation in the sample.
The formula
Variables
- Standardized residual for observation i
- Raw residual (observed value minus fitted value) for observation i
- Standard error of the regression (root mean squared error)
A standardized residual beyond ±2 flags the observation as a potential outlier that warrants investigation.
Check yourself
In a simple linear regression, one observation has a standardised residual of −3.4. Why is this a particular concern when the model is estimated by OLS?