Question

match each correlation coefficient to the appropriate scatter plot. the line in each scatter plot is the least squares regression line. $r=-0.3$ $r=-0.8$

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 \(1\). When \(r<0\), the relationship is negative (as \(x\) increases, \(y\) decreases). The closer \(|r|\) is to \(1\), the stronger the linear relationship.

Step2: Analyze the first scatter - plot

In the first scatter - plot, the points are more spread out from the regression line. This indicates a weaker linear relationship. Since \(|r=-0.3| = 0.3\) and \(|r = - 0.8|=0.8\), and \(0.3<0.8\), the correlation coefficient \(r=-0.3\) corresponds to the first scatter - plot.

Step3: Analyze the second scatter - plot

In the second scatter - plot, the points are closer to the regression line. This indicates a stronger linear relationship. Since \(|r=-0.8|>|r = - 0.3|\), the correlation coefficient \(r=-0.8\) corresponds to the second scatter - plot.

Answer:

Left scatter - plot: \(r=-0.3\); Right scatter - plot: \(r=-0.8\)