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: Understand the correlation coefficient \( r \)

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 each scatter - plot

• For \( r = 1 \):

A perfect positive linear relationship. In scatter - plot \( A \), the points lie exactly on an increasing straight line. So \( A\) matches \( r = 1 \).

• For \( r=-1 \):

A perfect negative linear relationship. There is no scatter - plot with a perfect negative linear relationship.

• For \( r=-0.95 \):

A strong negative linear relationship. In scatter - plot \( C \), the points are closely clustered around a decreasing straight line.

• For \( r=-0.74 \):

A moderate negative linear relationship. In scatter - plot \( F \), the points are somewhat spread but still show a negative trend.

• For \( r=-0.06 \):

A very weak negative linear relationship. In scatter - plot \( G \), the points are randomly scattered with a very slight negative tendency.

• For \( r = 0.48 \):

A moderate positive linear relationship. In scatter - plot \( E \), the points are spread but show an increasing trend.

• For \( r = 0.65 \):

A relatively strong positive linear relationship. In scatter - plot \( B \), the points are more closely grouped around an increasing line compared to \( E \).

• For \( r = 0.9 \):

A strong positive linear relationship. There is no scatter - plot with \( r = 0.9 \) in the common sense (if we assume the closest strong positive is not shown as a perfect one). But if we consider the given options:
If we assume the following matches based on the trend:
\( A:r = 1\), \( B:r = 0.65\), \( C:r=-0.95\), \( D:r=-0.06\), \( E:r = 0.48\), \( F:r=-0.74\)

Answer:

\( A:r = 1\), \( B:r = 0.65\), \( C:r=-0.95\), \( D:r=-0.06\), \( E:r = 0.48\), \( F:r=-0.74\)