Question

2 matching correlation coefficients

1. take turns with your partner to match a scatter plot with a correlation coefficient.
2. for each match you find, explain to your partner how you know its a match.
3. for each match your partner finds, listen carefully to their explanation. if you disagree,

discuss your thinking and work to reach an agreement.
① ( r = 1 ) ② ( r = - 0.95 ) ③ ( r = - 0.74 ) ④ ( r = - 0.06 ) ⑤ ( r = 0.48 ) ⑥ ( r = 0.65 ) ⑦ ( r = 0.9 ) ⑧ ( r = 1 )

Explanation:

Step1: Analyze scatter - plot A

In scatter - plot A, the points are very closely clustered around a straight line with a negative slope. The closer the points are to the line, the closer the correlation coefficient \(r\) is to \(- 1\) or \(1\). Since it has a negative slope, and the points are extremely close to the line, \(r=-0.95\) (a strong negative correlation).

Step2: Analyze scatter - plot B

In scatter - plot B, the points are somewhat scattered around a line with a negative slope. The correlation coefficient \(r=-0.48\) (a moderate negative correlation) as the points are not as tightly clustered as in a stronger correlation case.

Answer:

A. \(r = - 0.95\); B. \(r=-0.48\)