The Correlation and Regression Applet allows you to animate the given figure. Click to create a group of 10 points in the lower-left corner of the scatterplot with a strong straight-line pattern (correlation approximately 0.9). Click the "Show least-squares line" box to display the regression line. Subject 16 Move the outlier 0.8 0.8 down .. 0.6 0.6 0.4 0.4 Removing Subject 16 moves the regression line only a little Brain activity 0.2 Brain activity 0.0 0.2 .. and the least-squares -0.4 -0.2 0.0 line chases it down. 4 -0.2 20 40 60 80 100 20 40 60 80 100 Empathy score Empathy score (a) (b) (a) Add one point at the upper right that is far from the other 10 points but exactly on the regression line. Why does this outlier have no effect on the line even though it changes the correlation? O The new point on the existing line does not change the standard deviations of x and y, meaning that the slope of the regression line cannot change. O The new point does not change the correlation, and this, in turn, means that the regression line does not change either. O The new point on the existing line exactly matches the prediction; thus, it has no residual. Since the regression line results in the least sum of residual squares, adding a point with zero residual does not change the line. Placing a new point on the existing line does not change the averages x and y. Thus, the parameters of the regression line remain the same. (b) Now use the mouse to drag this last point straight down. You see that one end of the least-squares line chases this single point, while the other end remains near the middle of the original group of 10 points. What makes the last point so influential? Select the correct statements. The outlier is far from the group in both the x and y directions, and, therefore, has a strong influence on the standard deviations of both variables x and y. The change in the standard deviations strongly influences the parameters of the regression line. The line always passes through (x, y), and the group of 10 points dominates the average. Thus, the line has to pass through the group in the lower left corner, i.e., the group acts as a pivot point for the line. The correlation is dominated by the group of points in the lower left corner, while the additional point strongly affects the averages x and y. This causes large changes in the regression line parameters. The outlier is far from the group in both the x and y directions, and, therefore, has a strong influence on the means x and y. The change in the means has a strong influence on the line. The outlier is far from the group in both the x and y directions, and, therefore, has a strong influence on the correlation, which, in turn, affects the slope of the line