Question

match each correlation coefficient to the appropriate scatter plot. the line in each scatter plot is the least squares regression line. $r = 0$ $r = 0.6$

Explanation:

Step1: Understand the correlation coefficient

The correlation coefficient \(r\) measures the strength and direction of a linear relationship between two variables. When \(r = 0\), there is no linear relationship. When \(r>0\), there is a positive linear relationship.

Step2: Analyze the first scatter - plot

In the first scatter - plot, the points are somewhat scattered around a line with a positive slope. The value \(r = 0.6\) indicates a moderate positive linear relationship, which matches the first scatter - plot as there is a tendency for \(y\) to increase as \(x\) increases.

Step3: Analyze the second scatter - plot

In the second scatter - plot, the points are randomly distributed around a horizontal line (the least - squares regression line has a slope close to \(0\)). This implies no linear relationship, so \(r = 0\) matches the second scatter - plot.

Answer:

\(r = 0.6\) matches the first scatter - plot and \(r = 0\) matches the second scatter - plot.