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 Strength

The correlation coefficient \( r \) measures how closely data points follow the regression line. \( |r| \) closer to 1 means a stronger linear relationship. So \( r = 0.9 \) (strong) and \( r = 0.4 \) (weak).

Step2: Analyze Top Scatter Plot

The top scatter plot has points closely clustered around the regression line, indicating a strong linear relationship. Thus, it matches \( r = 0.9 \).

Step3: Analyze Bottom Scatter Plot

The bottom scatter plot has points more spread out from the regression line, indicating a weaker linear relationship. Thus, it matches \( r = 0.4 \).

Answer:

Top scatter plot: \( r = 0.9 \)
Bottom scatter plot: \( r = 0.4 \)