Question

The Comelation and Regression Applet allows you to animate the given figure. Click to create a group of 10 points in the lower-left comer of the scatterplot with a strong straight-line pattem (correlation approximately 09) Clickthe "Show least-squaresline"box to display the regression line. Move the outlier down Subject 16 Removing Subject 16 moves the regression line only a little. and the least-squares line chases it down 60 100 20 40 60 80 100 Empathy score Empathy score 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 ofthe original group of 10points. What makes the last point so influential? Select the correct statements. Hint: What did you see happen to the regression line and correlation as you dragged that point? The outlier is far from the groupin both the x and y directions, and, therefore, has a strong influence on the meansx andy. The change in the means has a strong influence on the line. The conrelation is dominated by the group ofpoints in the lower left comer, while the additional point strongly affects the averagesx andy. 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 standard deviations of both variables x andy. The change in the standard deviations strongly influences the parameters of theregression line 「The line always passes through(xx), andthe group of 10 pants dominates the average. Thus, the line has to pass through the group in the lower left comer, i.e, the group acts as a pivot point for theline The outlier is far from the groupin both the x and y directions, and, therefore, has a strong influence on the correlation, which, in turn, affects the slope of the line

Answer 1

right choice is third.

The outlier is far from the group in both x and y directions, and, therefore, has as 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.

After fitting a regression line for a group of data, a point which lies far from the line (and thus has a large residual value) is known as an outlier. Such points may represent erroneous data, or may indicate a poor fit of regression line.