To do these exercises, go to www.macmillanhighered.com/fapp10e.

Question 6.99

4. This time you will use the Correlation and Regression applet to examine the residual errors. Click Clear to remove any work done for Exercises 1–3. Click on the scatterplot to create a group of 15 to 20 points from the lower left to the upper right with a clear, positive straight-line pattern (with a correlation in the moderate range, say between 0.65 and 0.75). Click the “Show least-squares line” and “Show residuals” buttons.

  1. How can you tell from this graph which of the residuals are positive and which are negative? Do the residuals appear roughly balanced between positive and negative values?
  2. Pick a point that has an -value somewhere in the middle of -values of the other data points. If this point lies below the line, drag it vertically down. If this point lies above the line, drag it up. As you drag the point vertically, what happens to the size of its residual? What happens to the slope (or the tilt) of the least- squares line? Then switch the direction in which you drag the point and note the effect on the slope of the line.
  3. Return the point you were dragging in part (b) to approximately its original position. Next, click on a point that has the largest -value. Try dragging this point vertically both in the upward and downward direction. What effect does this have on the slope of the least-squares line?
  4. Which type of outlier, one with an -value that lies near the middle of the -values of the other data points or one with an -value that lies near the maximum (or minimum) of the -values of the other data points, will have a greater influence on the slope of the least-squares line?