Question

match the correlation coefficients with the scatterplots shown below.
scatterplot correlation coefficient
scatterplot a ( r = - 0.72 )
scatterplot b ( r = 0.65 )
scatterplot c ( r = - 0.02 )
scatterplot d ( r = 0.84 )
scatterplot a
scatterplot b
scatterplot c
scatterplot d

Explanation:

Step1: Analyze the correlation coefficient sign

• Positive \(r\) values (\(r = 0.65\) and \(r=0.84\)) correspond to scatterplots where \(y\) increases as \(x\) increases. Negative \(r\) values (\(r=- 0.72\) and \(r =-0.02\)) correspond to scatterplots where \(y\) decreases as \(x\) increases.
• \(r=-0.02\) is close to \(0\), indicating a very weak linear relationship.

Step2: Analyze the strength of the correlation

• The closer \(|r|\) is to \(1\), the stronger the linear relationship. For \(|r| = 0.84>0.72>0.65>0.02\)
• Scatterplot D has a strong positive linear relationship (\(r = 0.84\)) as the points follow an upward - sloping trend closely.
• Scatterplot B has a moderate positive linear relationship (\(r = 0.65\)) as the upward - sloping trend is less tight than in Scatterplot D.
• Scatterplot A has a moderate negative linear relationship (\(r=-0.72\)) as the points follow a downward - sloping trend.
• Scatterplot C has almost no linear relationship (\(r=-0.02\)) as the points are randomly scattered.

Answer:

Scatterplot A: \(r=-0.72\); Scatterplot B: \(r = 0.65\); Scatterplot C: \(r=-0.02\); Scatterplot D: \(r = 0.84\)