Question

match the correlation coefficients with the scatterplots shown below.
scatterplot | correlation coefficient
scatterplot a | (r = 0.67)
scatterplot b | (r=-0.33)
scatterplot c | (r = - 0.79)
scatterplot d | (r = 0.88)
scatterplot a
scatterplot b
scatterplot c
scatterplot d

Explanation:

Step1: Understand correlation coefficient

The correlation coefficient $r$ measures the strength and direction of a linear relationship. A positive $r$ indicates a positive linear - relationship (as $x$ increases, $y$ increases), and a negative $r$ indicates a negative linear - relationship (as $x$ increases, $y$ decreases). The closer $|r|$ is to 1, the stronger the linear relationship.

Step2: Analyze Scatterplot A

Scatterplot A shows a positive linear relationship. The points seem to follow an upward - sloping trend, and the linear relationship is moderately strong. So, $r = 0.67$ matches Scatterplot A.

Step3: Analyze Scatterplot B

Scatterplot B shows a negative linear relationship. The points follow a downward - sloping trend, but the relationship is not very strong. So, $r=-0.33$ matches Scatterplot B.

Step4: Analyze Scatterplot C

Scatterplot C shows a strong negative linear relationship. The points closely follow a downward - sloping line. So, $r = - 0.79$ matches Scatterplot C.

Step5: Analyze Scatterplot D

Scatterplot D shows a strong positive linear relationship. The points closely follow an upward - sloping line. So, $r = 0.88$ matches Scatterplot D.

Answer:

Scatterplot A: $r = 0.67$
Scatterplot B: $r=-0.33$
Scatterplot C: $r=-0.79$
Scatterplot D: $r = 0.88$