Question

match each correlation coefficient to the appropriate scatter plot. the line in each scatter plot is the least squares regression line. r = 0.2 r = -0.4

Explanation:

Step1: Understand correlation coefficient

The correlation coefficient $r$ measures the strength and direction of a linear relationship. A positive $r$ means positive - linear relationship (as $x$ increases, $y$ tends to increase), and a negative $r$ means negative - linear relationship (as $x$ increases, $y$ tends to decrease). The closer $|r|$ is to 1, the stronger the linear relationship.

Step2: Analyze left - hand scatter plot

In the left - hand scatter plot, the least - squares regression line has a negative slope, indicating a negative linear relationship. So, the correlation coefficient for this plot is $r=-0.4$.

Step3: Analyze right - hand scatter plot

In the right - hand scatter plot, the least - squares regression line has a positive slope, indicating a positive linear relationship. So, the correlation coefficient for this plot is $r = 0.2$.

Answer:

Left - hand scatter plot: $r=-0.4$; Right - hand scatter plot: $r = 0.2$