Question

match each correlation coefficient to the appropriate scatter plot.
$r = 0.1$
$r = 0.6$

Explanation:

Step1: Understand the correlation coefficient

The correlation coefficient \(r\) measures the strength and direction of a linear relationship between two variables. The value of \(r\) ranges from \(- 1\) to \(1\). A value of \(r = 0\) indicates no linear relationship, \(r=1\) indicates a perfect positive linear relationship and \(r = - 1\) indicates a perfect negative linear relationship. When \(0

Step2: Analyze the scatter - plots

For \(r = 0.1\), since \(r\) is close to \(0\), the data points in the scatter - plot should be very scattered with almost no discernible linear pattern.
For \(r=0.6\), since \(r\) is moderately close to \(1\) (compared to \(0.1\)), the data points in the scatter - plot should show a more defined positive linear trend.

Answer:

\(r = 0.1\) matches the scatter - plot with more scattered points (the right - hand side scatter - plot in the given image), and \(r = 0.6\) matches the scatter - plot with a somewhat more defined positive trend (the left - hand side scatter - plot in the given image).