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 )
a
b

Explanation:

Step1: Understand the correlation coefficient concept

The correlation coefficient \(r\) measures the strength and direction of a linear relationship between two variables. The value of \(r\) ranges from \(- 1\) to \(1\). If \(r = 1\), there is a perfect positive linear relationship. If \(r=-1\), there is a perfect negative linear relationship. The closer \(|r|\) is to \(1\), the stronger the linear relationship.

Step2: Analyze scatter - plot A

In scatter - plot A, the points lie very close to a straight line with a positive slope. The relationship is almost perfect positive linear. So \(r = 0.9\) (since \(r = 1\) is a perfect fit and here it is almost perfect but not exactly).

Step3: Analyze scatter - plot B

In scatter - plot B, the points are more spread out around the line of best - fit compared to plot A. But there is still a positive linear relationship. The value of \(r = 0.65\) (a moderate positive correlation) is more appropriate than \(r = 0.9\) or \(r = 1\) because of the spread of points.

Answer:

A corresponds to \(r = 0.9\) and B corresponds to \(r = 0.65\)