Prepare for the Discussion by graphing the scatterplot shown below on your graphing calculator. Convince yourself that the correlation coefficient is r = .96. The points shown on the scatterplot are {(-4,-3),(-3.5,-2),(-3,-.5),(-2.5,-1),(-2,-.5),(-1.5,-1),(-1,-.5), (-.5,.5),(.5,.5),A(1,2),(1.5,1),(2,1.5),(2.5,3),(3,3.5),(3.5,3.5),B(4,5)}.

(Remember, to calculate a correlation coefficient, you must do a linear regression on your graphing calculator. If the data are entered in L1 and L2 on the TI-83/84, the proper syntax is LinReg(a+bx),L1,L2 r will be given on the home screen, assuming you have Diagnostics on. If you don't see when you do the regression, consult your manual or the online study guide). (If you use a TI-89, you won't need to worry about this.)

In the Discussion, you'll be considering what happens to the correlation coefficient as you move points around.

Discussion Topic Questions

1. Change the point A in the scatterplot to the point (1,12). Calculate the correlation

coefficient and note how much it differs from .96.

2. Change the point A back to (1,2) and change the point B to (4,15). Calculate the correlation coefficient and note how much it differs from .96. Did the correlation coefficient change more when the point you raised 10 units was in the middle of the scatterplot or at the edge of the scatterplot? What makes you think this is so?

3. Move only one point and make the correlation coefficient become negative. Write the steps and why it made the correlation go negative.

4.Suppose you had a scatterplot that had only two points. Assuming your two points are not defining either a horizontal line (both y-values the same) or a vertical line (both x-values the same), what is the correlation coefficient? Why is it true? What happens as you try different points (again, without defining a horizontal or vertical line)?

5.Enter the points (1,2) and (3,2)this defines a horizontal line. Try to calculate the correlation coefficient. What did your calculator tell you? What happened? Enter the points (1,2) and (1,3)this defines a vertical line. Try to calculate the correlation coefficient. What did your graphing calculator tell you? What happened?

6. The following scatterplot was constructed by reversing thex- andy-values in the original scatterplot. Without calculating the new correlation coefficient, what is r based on your work? Why?

7. The following scatterplot was constructed by taking the negative of eachx-value in the original scatterplot. Without calculating the new correlation coefficient, what is r (guess)? Why? What would the correlation coefficient be if we took the negative of all thex-values and all they-values?

AP Statistics Discussion Study Sheet: Exploring Correlation Coefficient: r

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