2.57 Use the applet. You are going to use the Correlation and Regression applet to make different scatterplots with 12 points that have correlation close to 0.8. Many patterns can have the same correlation. Always plot your data before you trust a correlation.

1. (a) Stop after adding the first two points. What is the value of the correlation? Why does it have this value no matter where the two points are located?

2. (b) Make a lower-left to upper-right pattern of 12 points with correlation about r = 0.8. (You can drag points up or down to adjust r after you have 12 points.) Make a rough sketch of your scatterplot.

3. (c) Make another scatterplot, this time with 11 points in a vertical stack at the left of the plot. Add one point far to the right and move it until the correlation is close to 0.8. Make a rough sketch of your scatterplot.

4. (d) Make yet another scatterplot, this time with 12 points in a curved pattern that starts at the lower left, rises to the right, then falls again at the far right. Adjust the points up or down until you have a quite smooth curve with correlation close to 0.8. Make a rough sketch of this scatterplot also.