Question

4/70.
the following scatterplots have correlations ( r=-0.9, r = -0.6, r = 0.1 ), and ( r = 0.6 ).
which scatterplot has which correlation coefficient?

Explanation:

Step1: Analyze the sign of correlation

• Positive \( r \) values (\(r = 0.1\) and \(r = 0.6\)) correspond to scatterplots with an upward - trend (positive slope). Negative \( r \) values (\(r=-0.9\) and \(r = - 0.6\)) correspond to scatterplots with a downward - trend (negative slope).
• Scatterplots \(a\) and \(d\) have a downward - trend (negative correlation). Scatterplots \(b\) and \(c\) have an upward - trend (positive correlation).

Step2: Analyze the magnitude of correlation

• The magnitude of \(r\) (\(\vert r\vert\)) measures the strength of the linear relationship. A value of \(\vert r\vert\) close to \(1\) indicates a strong linear relationship, and a value of \(\vert r\vert\) close to \(0\) indicates a weak linear relationship.
• For negative correlations:
• Scatterplot \(d\) has a stronger linear relationship (points are closer to the line of best - fit) than scatterplot \(a\). So \(r=-0.9\) corresponds to scatterplot \(d\) and \(r = - 0.6\) corresponds to scatterplot \(a\).
• For positive correlations:
• Scatterplot \(c\) has a stronger linear relationship (points are closer to the line of best - fit) than scatterplot \(b\). So \(r = 0.6\) corresponds to scatterplot \(c\) and \(r=0.1\) corresponds to scatterplot \(b\).

Answer:

a. \(r=-0.6\), b. \(r = 0.1\), c. \(r=0.6\), d. \(r=-0.9\)