(An activity written by Felice Shore to accompany John Marden’s java applet on www.stat.uiuc.edu/~stat100/java/GCApplet/ )
This activity should be done after an introduction to correlation in an Introduction to Statistics course. It should take no longer than 20-30 minutes.
Objectives:
· Gain an intuitive sense of how strong a linear relationship is, as measured by the correlation coefficient, r.
· Use your understanding of the range of possible r-values to match scatter plots to r-values (e.g. Apply the meaning of positive versus negative values of r, as well as small and large magnitudes of r, to match scatter plots to r-values)
· Take notice of subtle differences in scatter plots matched to similar r-values.
Directions:
1. Go to the site http://www.stat.uiuc.edu/~stat100/java/GCApplet/ You will see “Guessing Correlations.”
2. Maximize the screen.
3. When you choose “New Plots,” four scatter plots labeled A, B, C, and D will appear. Below the plots there are four r-values with four empty boxes, labeled A, B, C, and D. Your job is to match the plots with the r-values by clicking on the appropriate box next to each r-value. Be sure that you only have one plot matched to each r-value, and that before you check answers, you have the choices you want. [Note that if you choose B to go with the first r-value and then try to choose B again, the program will automatically erase the “old” r, and keep only the B chosen for the current r-value you picked. However, the program will let you choose two plots for the same r-value (which can’t be correct.)]
4. Click “Answers” to check. Note the correct boxes will become highlighted. Check to see that the highlighted boxes contain your chosen answers. Also, notice that the correct r-values are written above each graph for easier comparison.
5. Click “New plots” to start over. Note that a running score is kept at the bottom of the screen, so if you play 5 times (20 plots), it will tell you how many out of the 20 you have gotten correct.
IF YOU DON”T HAVE THE FOGGIEST IDEA HOW TO VENTURE A GUESS…
Recall that there are two main issues involved: direction of the relationship and the strength of the relationship
Direction of the relationship:
Remember that r is a value between –1 and 1. A negative r-value indicates a negative relationship between the variables. (As one variable goes up, the other variable goes down.) A positive r-value indicates a positive relationship between the variables. (As one variable goes up, so does the other.)
1. If a scatter plot shows points heading downward, you would expect the r-value to be ___________.
2. If a scatter plot shows points heading upward, you would expect the r-value to be ___________.
Strength of the relationship:
Remember that a perfect linear relationship is one in which one variable changes by the same amount for every unit change in the other variable (Ex. Every time x increases by one unit, y changes by exactly 4 units.) This results in a straight line on a graph, and corresponds to an r-value of either +1 or –1, depending on the direction of the relationship. The less “exact”, or linear this relationship is, the more the points will look like a “blob” (rather than a line), and the lower the magnitude of the r-value. That is, the weaker the relationship, the closer the r-value will get to 0, either from the positive or negative side, and the more the scatter will look like a blob.
3. If a scatter plot looks like points that line up perfectly heading downward, the r-value will be _____.
4. If a scatter plot looks like points that head upward, but don’t line up perfectly, the r-value will be about _____.
5. If a scatter plot looks like points that are so scattered, you can’t tell if there is an upward or downward trend, the r-value might be roughly ____.
Go play Guessing Correlations at least 6 times (24 plots). Then answer:
1. Did you get better at the game the more you played? Why? What kind of strategies did you use to match?
2. Were any particular plots exceptionally difficult to match? Explain.
3. Do you think you could differentiate between: (For each one: If yes, what would you look for to make a decision? If no, explain what the problem might be.)