Copyright ©2013, 2010, 2007, 2004 by W. H. Freeman and Company The Basic Practice of Statistics, 6 th Edition David S. Moore, William I. Notz, Michael A. Fligner Figure 5.1 Fat gain after 8 weeks of overeating, plotted against increase in nonexercise activity over the same period, for Example 5.1.

Copyright ©2013, 2010, 2007, 2004 by W. H. Freeman and Company The Basic Practice of Statistics, 6 th Edition David S. Moore, William I. Notz, Michael A. Fligner Figure 5.2 The least-squares idea. For each observation, find the vertical distance of each point on the scatterplot from a regression line. The least-squares regression line makes the sum of the squares of these distances as small as possible.

Copyright ©2013, 2010, 2007, 2004 by W. H. Freeman and Company The Basic Practice of Statistics, 6 th Edition David S. Moore, William I. Notz, Michael A. Fligner Figure 5.5 Scatterplot of activity in a region of the brain that responds to pain versus score on a test of empathy, for Example 5.5. Brain activity is measured as the subject watches her partner experience pain. The line is the least-squares regression line.

Copyright ©2013, 2010, 2007, 2004 by W. H. Freeman and Company The Basic Practice of Statistics, 6 th Edition David S. Moore, William I. Notz, Michael A. Fligner Figure 5.6 Residual plot for the data shown in Figure 5.5. The horizontal line at zero residual corresponds to the regression line in Figure 5.5.

Copyright ©2013, 2010, 2007, 2004 by W. H. Freeman and Company The Basic Practice of Statistics, 6 th Edition David S. Moore, William I. Notz, Michael A. Fligner Figure 5.7 Subject 16 is an outlier in the x direction. The outlier is not influential for least-squares regression, because removing it moves the regression line only a little.

Copyright ©2013, 2010, 2007, 2004 by W. H. Freeman and Company The Basic Practice of Statistics, 6 th Edition David S. Moore, William I. Notz, Michael A. Fligner Figure 5.8 An outlier in the x direction pulls the least-squares line to itself because there are no other observations with similar values of x to hold the line in place. When the outlier moves down, the regression line chases it down. The original regression line is solid, and the final position of the regression line is dashed.