Leverage Points
- Occur where an observation’s independent-variable values are extreme or where an independent variable is highly correlated with others.
- Such observations can strongly influence a regression model’s predictions and may indicate potential outliers.
- Identifying leverage points can help improve model accuracy and support better decision making.
Definition
Section titled “Definition”Leverage points in regression analysis refer to the points in the independent variable space where the changes in the response variable are the greatest.
Explanation
Section titled “Explanation”Leverage points are observations whose locations in the independent-variable space give them a disproportionate ability to change the fitted regression relationship. Because of their position, these points can have a large impact on the model’s predictions and can serve to highlight potential outliers in the data.
Examples
Section titled “Examples”Extreme independent-variable value
Section titled “Extreme independent-variable value”A point where the independent variable takes on an extreme value. For example, in a regression model that predicts house price from size and location, a house that is significantly larger or smaller than the others in the sample could be a leverage point because its size is an extreme value. That point could have a large impact on the model’s predictions and could potentially be an outlier.
High multicollinearity
Section titled “High multicollinearity”A point where the independent variable has a high level of multicollinearity with other variables in the model. Multicollinearity occurs when two or more independent variables are highly correlated; in this case, a change in one variable could have a large impact on the response variable and could potentially be a leverage point.
Use cases
Section titled “Use cases”- Identifying potential outliers in a dataset.
- Improving the accuracy of regression models by detecting observations that disproportionately influence model predictions.
- Supporting more informed decisions based on the regression results by accounting for influential observations.
Notes or pitfalls
Section titled “Notes or pitfalls”- Leverage points can have a large impact on a model’s predictions and may therefore distort inference if not identified and handled appropriately.
Related terms
Section titled “Related terms”- Regression analysis
- Independent variable
- Response variable
- Outlier
- Multicollinearity
- Model predictions