Question

match each correlation coefficient to the appropriate scatter plot. the line in each scatter plot is the least squares regression line.
$r = 0.4$
$r = 0.9$

Explanation:

Step1: Recall correlation coefficient meaning

The correlation coefficient \( r \) measures the strength and direction of a linear relationship between two variables. A value closer to \( 1 \) (or \( -1 \)) indicates a stronger linear relationship, while a value closer to \( 0 \) indicates a weaker linear relationship.

Step2: Analyze the scatter plots

• For \( r = 0.9 \): This is a strong positive correlation, so the points should be closer to the regression line. Looking at the two plots, the first plot (left) has points that are more tightly clustered around the regression line, indicating a stronger linear relationship.
• For \( r = 0.4 \): This is a weak positive correlation, so the points should be more spread out from the regression line. The second plot (right) has points that are more scattered around the regression line, indicating a weaker linear relationship.

Answer:

• \( r = 0.9 \) matches the left scatter plot (points closer to the regression line).
• \( r = 0.4 \) matches the right scatter plot (points more spread out from the regression line).