Activity: Effect of moving a point The Explore Linear Regression web app accessible at the book’s website lets you add and delete points on a scatterplot. The regression line is automatically calculated for the points you provide.

a. Select the option “Draw Own” and add 5 points to the empty scatterplot that have an approximate linear relationship between x and y but a slope near 0.

b. Add a sixth observation that is influential. What did you have to do to get the slope to change noticeably from 0?

c. Now consider the effect of sample size on the existence of influential points. Start by creating 50 points with a similar pattern as in part

a. You can create this from scratch, point by point, or simply select “Random Scatter” from the drop down menu for the initial relationship and select 50 for the number of points. Is it now harder to add a single point that makes the slope change noticeably from 0? Why?

d. Try this activity, now exploring the effect of adding or deleting points on the correlation coefficient r.
(Check the box to display r.) Repeat parts a–c in terms of the correlation instead of the slope.