Question

identify the correlation coefficient ( r ) that is most likely to correspond with the scatterplot below.
show your work here
( \bigcirc r=-0.96 )( \bigcirc r=-0.55 )
( \bigcirc r=0.07 )( \bigcirc r=0.57 )
( \bigcirc r=0.9 )

Explanation:

Step1: Analyze the scatter - plot pattern

A correlation coefficient \(r = 0\) indicates no linear relationship. Values close to \(1\) or \(- 1\) indicate a strong linear relationship. Values between \(0\) and \(1\) (or \(0\) and \(-1\)) indicate a weak to moderate linear relationship.
Looking at the scatter - plot, the points are very spread out and do not form a clear upward or downward linear trend.

Step2: Evaluate each option

• For \(r=-0.96\) and \(r = 0.9\), these values imply a strong negative or positive linear relationship respectively. But the scatter - plot does not show a strong linear pattern.
• For \(r=-0.55\) and \(r = 0.57\), these values imply a moderate negative or positive linear relationship. But the scatter - plot is too scattered for a moderate linear relationship.
• For \(r = 0.07\), this value is close to \(0\), which is consistent with the fact that there is no clear linear relationship in the scatter - plot.

Answer:

\(r = 0.07\)