Question

match the correlation coefficients with the scatterplots shown below.
scatterplot correlation coefficient
scatterplot a ( r = 0.39 )
scatterplot b ( r = - 0.92 )
scatterplot c ( r = 0.85 )
scatterplot d ( r = - 0.71 )
scatterplot a
scatterplot b
scatterplot c
scatterplot d

Explanation:

Step1: Analyze the sign of \(r\)

• Positive \(r\) (\(r = 0.39\), \(r=0.85\)) means positive - linear - trend (as \(x\) increases, \(y\) increases). Scatterplot A and C have positive - trends.
• Negative \(r\) (\(r=-0.92\), \(r = - 0.71\)) means negative - linear - trend (as \(x\) increases, \(y\) decreases). Scatterplot B and D have negative - trends.

Step2: Analyze the magnitude of \(r\)

• The magnitude of \(r\) (\(\vert r\vert\)) measures the strength of the linear relationship.
• For positive \(r\):
• \(\vert0.85\vert>\vert0.39\vert\). Scatterplot C has a stronger positive - linear relationship than Scatterplot A. So \(r = 0.85\) corresponds to Scatterplot C and \(r=0.39\) corresponds to Scatterplot A.
• For negative \(r\):
• \(\vert - 0.92\vert>\vert-0.71\vert\). Scatterplot D has a stronger negative - linear relationship than Scatterplot B. So \(r=-0.92\) corresponds to Scatterplot D and \(r = - 0.71\) corresponds to Scatterplot B.

Answer:

Scatterplot A: \(r = 0.39\); Scatterplot B: \(r=-0.71\); Scatterplot C: \(r = 0.85\); Scatterplot D: \(r=-0.92\)