Open the applet (available in ThomsonNOW at www .thomsonedu.com/login) called CorrelationPoints. You should see a screen like the one shown below.

1. Using the mouse, you can click to add points to form a scatterplot. The value of the correlation coefficient for the data in the plot at any given time (once you have two or more points in the plot) will be displayed at the top of the screen. Try to add points to obtain a correlation coefficient that is close to −.8. Briefly describe the factors that influenced where you placed the points.

2. Reset the plot (by clicking on the Reset bar in the lower left corner of the screen) and add points trying to produce a data set with a correlation that is close to +.4. Briefly describe the factors that influenced where you placed the points. Now open the applet called RegDecomp. You should see a screen that looks like the one shown here:

The black points in the plot represent the data set, and the blue line represents a possible line that might be used to describe the relationship between the two variables shown. The pink lines in the graph represent the deviations of points from the line, and the pink bar on the left hand side of the display depicts the sum of squared errors for the line shown.

3. Using your mouse, you can move the line and see how the deviations from the line and the sum of squared errors change as the line changes. Try to move the line into a position that you think is close to the least-squares regression line. When you think you are close to the line that minimizes the sum of squared errors, you can click on the bar that says “Find Best Model” to see how close you were to the actual least-squares line.

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