Question

ch each correlation coefficient to the appropriate scatter plot.
r = 0.4 r = 0.9 r = -0.5 r = -1

Explanation:

Step1: Understand the correlation coefficient

The correlation coefficient \( r \) measures the strength and direction of a linear relationship between two variables. The value of \( r \) ranges from - 1 to 1. If \( r>0 \), it is a positive - linear relationship; if \( r < 0 \), it is a negative - linear relationship. The closer \( |r| \) is to 1, the stronger the linear relationship.

Step2: Analyze \( r = 0.9 \)

For \( r = 0.9 \), since \( r>0 \) and \( |r| \) is close to 1, we look for a scatter - plot with a strong positive - linear relationship. The first scatter - plot (top - left) has points that follow an upward trend and are relatively close to an imaginary straight line, so \( r = 0.9 \) corresponds to the first scatter - plot.

Step3: Analyze \( r = 0.4 \)

For \( r = 0.4 \), since \( r>0 \) but \( |r|=0.4 \) (not as close to 1 as 0.9), we look for a scatter - plot with a weaker positive - linear relationship. The second scatter - plot (top - right) has points that follow an upward trend but are more spread out than the first scatter - plot, so \( r = 0.4 \) corresponds to the second scatter - plot.

Step4: Analyze \( r=-1 \)

For \( r = - 1 \), since \( r<0 \) and \( |r| = 1 \), we look for a scatter - plot with a perfect negative - linear relationship. The third scatter - plot (bottom - left) has two clusters of points that follow a downward - linear trend (in a sense, if we consider the two - cluster pattern as a degenerate perfect negative - linear case in the context of the given options), so \( r=-1 \) corresponds to the third scatter - plot.

Step5: Analyze \( r=-0.5 \)

For \( r=-0.5 \), since \( r < 0 \) and \( |r|=0.5 \), we look for a scatter - plot with a moderate negative - linear relationship. The fourth scatter - plot (bottom - right) has points that follow a downward trend, so \( r=-0.5 \) corresponds to the fourth scatter - plot.

Answer:

\( r = 0.9 \) to the first scatter - plot (top - left), \( r = 0.4 \) to the second scatter - plot (top - right), \( r=-1 \) to the third scatter - plot (bottom - left), \( r=-0.5 \) to the fourth scatter - plot (bottom - right).