Question

match each correlation coefficient to the appropriate scatter plot. the line in each scatter plot is the least squares regression line.
$r = 0.1$
$r = 0.7$
submit

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 \(r = 1\) indicates a perfect positive linear relationship, \(r=-1\) indicates a perfect negative linear relationship, and \(r = 0\) indicates no linear relationship. When \(0<|r|<1\), the closer \(|r|\) is to \(1\), the stronger the linear relationship.

Step2: Analyze the first scatter - plot

In the first scatter - plot, the data points are somewhat close to the least - squares regression line. This indicates a moderately strong positive linear relationship. Since \(r = 0.7\) is closer to \(1\) (compared to \(r = 0.1\)) among the two given values for a positive relationship, it should be matched with the first scatter - plot.

Step3: Analyze the second scatter - plot

In the second scatter - plot, the data points are very spread out from the line (in fact, the line is almost horizontal and the points show no clear linear trend). A value of \(r = 0.1\) (which is close to \(0\)) indicates a very weak linear relationship, so it should be matched with the second scatter - plot.

Answer:

The first scatter - plot (\(y\) vs \(x\) with a line having a positive slope and data points somewhat close to the line) has \(r = 0.7\). The second scatter - plot (\(y\) vs \(x\) with a line that is almost horizontal and data points very spread out) has \(r = 0.1\).