Use the applet entitled Correlation by the Eye to explore the relationship between the pattern of data in a scatterplot and the corresponding correlation coefficient.
a. Run the applet several times. Each time, guess the value of the correlation coefficient. Then click Show r to see the actual correlation coefficient. How close is your value to the actual value of r? Click New data to reset the applet.
b. Click the trash can to clear the graph. Use the mouse to place five points on the scatterplot that are approximately in a straight line. Then guess the value of the correlation coefficient. Click Show r to see the actual correlation coefficient. How close were you this time?
c. Continue to clear the graph and plot sets of five points with different patterns among the points. Guess the value of r. How close do you come to the actual value of r each time?
d. On the basis of your experiences with the applet, explain why we need to use more reliable methods of finding the correlation coefficient than just "eyeing" it.