Question

match each correlation coefficient to the appropriate scatter plot. the line in each scatter plot is the least squares regression line. $r = 0.1$ $r = 0.6$

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. When \( r = 1 \), there is a perfect positive linear relationship; when \( r=-1 \), there is a perfect negative linear relationship. When \( r = 0 \), there is no linear relationship. The closer \( |r| \) is to 1, the stronger the linear relationship.

Step2: Analyze the scatter - plots

For \( r = 0.6 \): A value of \( r=0.6 \) indicates a moderate positive linear relationship. The data points in one of the scatter - plots will be somewhat clustered around the least - squares regression line, showing a tendency to increase as \( x \) increases.
For \( r = 0.1 \): A value of \( r = 0.1 \) indicates a very weak positive linear relationship. The data points in the other scatter - plot will be much more spread out from the least - squares regression line, with little evidence of a strong linear trend.

Answer:

The scatter - plot with data points more clustered around the regression line (showing a more noticeable upward trend) has \( r = 0.6 \), and the scatter - plot with data points more spread out (showing a very weak upward trend) has \( r=0.1 \)