AP Statistics Discussion Study Sheet: Exploring Correlation Coefficient: r Page 1 of 2 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)}. B+ r=.96 (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 r 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. 2. 3. 4. 5. Change the point A in the scatterplot to the point (1,12). Calculate the correlation coefficient and note how much it differs from .96. 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? Why do you think this is so? Move only one point and make the correlation coefficient become negative. Write about what you did and why it made the correlation go negative. point and make the correl plot that had only Suppose you had a scatterplot that had only two points. Assuming your two points do not define either a horizontal line (both y-values the same) or a vertical line (both x-values the same), what is the correlation coefficient? Why do you think this is true? What happens as you try different points (again, without defining a horizontal or vertical line)? 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? AP Statistics Discussion Study Sheet: Exploring Correlation Coefficient: r Page 2 6. The following scatterplot was constructed by reversing the x- and y-values in the original scatterplot. Without calculating the new correlation coefficient, what do you think r is? Why? + * 7. The following scatterplot was constructed by taking the negative of each x-value in the original scatterplot. Without calculating the new correlation coefficient, what do you think r is? Why? What would the correlation coefficient be if we took the negative of all the x-values and all the y-values?