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 = 0.5

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 \(0<|r|<1\), there is a non - perfect linear relationship.

Step2: Analyze the first scatter - plot

In the first scatter - plot, the points are scattered randomly around a horizontal line (the regression line). A horizontal regression line implies that as \(x\) changes, \(y\) does not have a linear trend. So, \(r = 0\) should be matched with the first scatter - plot.

Step3: Analyze the second scatter - plot

In the second scatter - plot, the points show a positive trend (as \(x\) increases, \(y\) has a tendency to increase) but the points are not all on a straight line. Since \(r = 0.5\) indicates a positive, non - perfect linear relationship, \(r = 0.5\) should be matched with the second scatter - plot.

Answer:

\(r = 0\) matches the first scatter - plot and \(r=0.5\) matches the second scatter - plot.