Exploring the Goodness of Fit in Linear Models - Outlier Data Point at End of Range: Outlier Tab

Scott A. Sinex

The Outlier worksheet (see Figure 7) starts with a perfect set of data for the y = x line (no scatter). What is the value of r2 for a perfect fit? Student now vary the scatter of the last datum point shown in red on the graph. How does it influence the regression line? There is a drastic influence on the line as a whole, especially to the value of the slope. This is the leverage effect, and it can be explored further using the downloadable JAVA simulation of Lohninger et al.  (undated) or the Putting Points applet at the University of Illinois at Urbana-Champaign Department of Statistics.

Figure 7. The Outlier worksheet
(Click on image for a larger view.)