Outliers and Influential Observations for AP Statistics

Practice problems for these concepts can be found at:

• Two-Variable Data Analysis Multiple Choice Practice Problems for AP Statistics
• Two-Variable Data Analysis Free Response Practice Problems for AP Statistics
• Two-Variable Data Analysis Review Problems for AP Statistics
• Two-Variable Data Analysis Rapid Review for AP Statistics

Some observations have an impact on correlation and regression. We defined an outlier quite specifically when we were dealing with one-variable data (remember the 1.5 IQR rule?). There is no analogous definition when dealing with two-variable data, but it is the same basic idea: an outlier lies outside of the general pattern of the data. An outlier can certainly influence a correlation and, depending on where it is located, may also exert an influence on the slope of the regression line.

An influential observation is often an outlier in the x-direction. Its influence, if it doesn't line up with the rest of the data, is on the slope of the regression line. More generally, an influential observation is a datapoint that exerts a strong influence on a measure.

Example: Graphs I, II, and III are the same except for the point symbolized by the box in graphs II and III. Graph I below has no outliers or influential points. Graph II has an outlier that is an influential point that has an effect on the correlation. Graph III has an outlier that is an influential point that has an effect on the regression slope. Compare the correlation coefficients and regression lines for each graph. Note that the outlier in Graph II has some effect on the slope and a significant effect on the correlation coefficient. The influential point in Graph III has about the same effect on the correlation coefficient as the outlier in Graph II, but a major influence on the slope of the regression line.

Practice problems for these concepts can be found at:

• Two-Variable Data Analysis Multiple Choice Practice Problems for AP Statistics
• Two-Variable Data Analysis Free Response Practice Problems for AP Statistics
• Two-Variable Data Analysis Review Problems for AP Statistics
• Two-Variable Data Analysis Rapid Review for AP Statistics