Use the applet entitled Regression by Eye to explore the relationship between the pattern of data in a scatterplot and the corresponding least squares model.
a. Run the applet several times. For each time, attempt to move the green line into a position that appears to minimize the vertical distances of the points from the line. Then click Show regression line to see the actual regression line. How close is your line to the actual line? 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 move the green line to approximate the regression line. Click Show regression line to see the actual regression line. How close were you this time?
c. Continue to clear the graph, and plot sets of five points with different patterns among the points. Use the green line to approximate the regression line. How close do you come to the actual regression line each time?
d. On the basis of your experiences with the applet, explain why we need to use more reliable methods of finding the regression line than just "eyeing" it.