Question

match the correlation coefficients with the scatterplots shown below.
scatterplot | correlation coefficient
scatterplot a | $r = 0.87$
scatterplot b | $r = 0.63$
scatterplot c | $r=-0.75$
scatterplot d | $r = - 0.41$
scatterplot a
scatterplot b

Explanation:

Step1: Understand correlation coefficient concept

The correlation coefficient $r$ measures the strength and direction of a linear relationship. Values close to 1 or - 1 indicate a strong linear relationship, values close to 0 indicate a weak linear relationship. Positive $r$ means positive - linear relationship (as $x$ increases, $y$ increases on average), negative $r$ means negative - linear relationship (as $x$ increases, $y$ decreases on average).

Step2: Analyze Scatterplot A

Scatterplot A shows a positive linear relationship. The points seem to follow an upward - sloping trend, and the points are relatively close to a straight - line pattern. Since $r = 0.87$ is a strong positive correlation, it matches Scatterplot A.

Step3: Analyze Scatterplot B

Scatterplot B also shows a positive linear relationship, but the points are more spread out compared to Scatterplot A. A correlation coefficient of $r = 0.63$ indicates a moderate positive correlation, which matches Scatterplot B.

Step4: Analyze Scatterplot C

Scatterplot C shows a negative linear relationship. The points follow a downward - sloping trend. A correlation coefficient of $r=-0.75$ indicates a strong negative correlation, which matches Scatterplot C.

Step5: Analyze Scatterplot D

Scatterplot D shows a negative linear relationship, but the points are more dispersed. A correlation coefficient of $r = - 0.41$ indicates a moderate negative correlation, which matches Scatterplot D.

Answer:

Scatterplot A: $r = 0.87$
Scatterplot B: $r = 0.63$
Scatterplot C: $r=-0.75$
Scatterplot D: $r = - 0.41$