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Question 6.97

2. You are going to use the Correlation and Regression applet to make different scatterplots with 10 points that have a correlation close to 0.7. Many patterns can have the same correlation. Always plot your data before you trust a correlation.

  1. 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. Make a lower-left to upper-right pattern of 10 points with a correlation of about . (You can drag points up or down to adjust after you have 10 points.) Make a rough sketch of your scatterplot.
  3. Make another scatterplot with nine 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 0.7. Make a rough sketch of your scatterplot.
  4. Make yet another scatterplot with 10 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 smooth curve with a correlation close to 0.7. Make a rough sketch of this scatterplot as well.
  5. Based on your answers to parts (b) through (d), what can you conclude about the pattern of dots in a scatterplot if ?