Outliers, High-Leverage & Influential Points (College Board AP® Statistics)

Outliers in a regression model

What is an outlier in a regression model?

• An outlier in a regression model is a point that has an extreme -value relative to the least-squares regression line

  • It has a very large (positive or negative) residual

    • It does not follow the general linear trend shown by the rest of the data

High-leverage points

What is a high-leverage point?

• A high-leverage point is a data point that has an extreme -value relative to the other data points

• A high-leverage point may still follow the general linear trend shown by the data

Can a high-leverage point also be an outlier?

• A high-leverage point can also be an outlier if it has both:

  • an extreme -value relative to the other data points

  • an extreme -value (large residual) relative to the regression line

• Note that a high-leverage point that does follow the general linear trend is not considered an outlier

  • This is because, even though it has an extreme -value, it still lies close to the regression line

    • so does not have a large residual

Influential points

What is an influential point?

• An influential point in a regression model is a point that, if removed, changes the linear relationship significantly

  • Removing it could cause a significant change in:

    • the correlation coefficient

    • the slope of a regression line

    • the -intercept of a regression line

Can outliers and high-leverage points be influential points?

• An outlier that is also a high-leverage point is likely to be an influential point

  • it has an extreme -value relative to the other data points

  • it has an extreme -value (large residual) relative to the regression line

    • Including this point could significantly change the slope of the regression line, for example

• Outliers or high-leverage points alone may or may not be influential points

  • They all affect the linear relationship

    • but not necessarily significantly