Question

match the correlation coefficients with the scatterplots shown below.
scatterplot|correlation coefficient
scatterplot a|r = 0.39
scatterplot b|r = - 0.69
scatterplot c|r = - 0.85
scatterplot d|r = 0.74
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, $y$ tends to increase), and a negative $r$ indicates a negative - linear relationship (as $x$ increases, $y$ tends to decrease). The closer $|r|$ is to 1, the stronger the linear relationship.

Step2: Analyze Scatterplot A

Scatterplot A shows a weak positive linear relationship. Points are somewhat scattered but generally trend upwards from left - to - right. So, it matches $r = 0.39$.

Step3: Analyze Scatterplot B

Scatterplot B shows a moderate negative linear relationship. Points generally trend downwards from left - to - right. So, it matches $r=-0.69$.

Step4: Analyze Scatterplot C

Scatterplot C shows a strong negative linear relationship. Points are closely clustered around a line with a negative slope. So, it matches $r = - 0.85$.

Step5: Analyze Scatterplot D

Scatterplot D shows a moderate positive linear relationship. Points generally trend upwards from left - to - right and are more closely clustered than in Scatterplot A. So, it matches $r = 0.74$.

Answer:

Scatterplot A: $r = 0.39$
Scatterplot B: $r=-0.69$
Scatterplot C: $r = - 0.85$
Scatterplot D: $r = 0.74$