Question 2.39

2.39 Match the correlation

The Correlation and Regression applet at the text website allows you to create a scatterplot by clicking and dragging with the mouse. The applet calculates and displays the correlation as you change the plot. You will use this applet to make scatterplots with 10 points that have correlation close to 0.7. The lesson is that 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?
  2. Make a lower-left to upper-right pattern of 10 points with correlation about r = 0.7. (You can drag points up or down to adjust r 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 right of the plot. Add one point far to the left 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 quite smooth curve with correlation close to 0.7. Make a rough sketch of this scatterplot also.