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 correlation coefficient

The correlation coefficient \(r\) measures the strength and direction of a linear relationship. \(r = 0\) means no linear relationship. \(r=- 0.5\) means a moderate negative linear relationship.

Step2: Analyze first scatter - plot

In the first scatter - plot, the points are scattered randomly around the regression line (which is horizontal in a sense of no clear linear trend). So, it has \(r = 0\).

Step3: Analyze second scatter - plot

In the second scatter - plot, as \(x\) increases, \(y\) has a tendency to decrease (negative direction) and the points are somewhat clustered around the regression line (moderate strength). So, it has \(r=-0.5\).

Answer:

The first scatter - plot (with random - like point distribution around the line) has \(r = 0\), and the second scatter - plot (with a negative trend) has \(r=-0.5\).