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

Question 6.98

3. It isn’t easy to guess the position of the least-squares line by eye (at least not without some practice). Use the Correlation and Regression applet to compare a line that you draw with the least-squares line. 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 of around 0.7). Click the “Draw your own line” button. Then click on two points, one in the lower left and the other in the upper right. Move these two points so that your line is drawn through the middle of the cloud of points and appears to do a good job of summarizing the pattern in the scatterplot.

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  1. You drew a line by eye through the middle of the pattern. Read off the value for Relative SS (directly below the “Draw your own line” button). This is the ratio of the sum of squares of residuals for your line and the sum of squares of the residuals for the least-squares regression line.
  2. Move your line until the Relative . (This means that the value of Relative SS is approximately 1, or equals 1 when rounded to two decimal places.) Your line should now closely match that of the least-squares regression line. To check this out, click the “Show least-squares line” box.
  3. Repeat this exercise several times with different sets of points. Try to guess the “best” line without looking at the value of Relative SS. Does your ability to pick a line that closely matches the least-squares regression line improve with practice?