Question

match each correlation coefficient to the appropriate scatter plot. the line in each scatter plot is the least squares regression line.
$r=-1$
$r = 0.4$

Explanation:

Step1: Understand Correlation Coefficients

A correlation coefficient \( r \) close to \( \pm1 \) indicates a strong linear relationship, and close to 0 indicates a weak relationship. \( r = -1 \) is a perfect negative linear relationship, \( r = 0.4 \) is a moderate positive linear relationship.

Step2: Analyze Scatter Plots

• First scatter plot: Points are close to a line with negative slope (since as \( x \) increases, \( y \) decreases), so it matches \( r = -1 \) (strong negative correlation).
• Second scatter plot: Points are more spread out around a line with positive slope, so it matches \( r = 0.4 \) (moderate positive correlation).

Answer:

• \( r = -1 \) matches the first scatter plot (with negative - sloped regression line, points close to the line).
• \( r = 0.4 \) matches the second scatter plot (with positive - sloped regression line, points more spread out).