Question

match each correlation coefficient to the appropriate scatter plot. the line in each scatter plot is the least squares regression line. $r = 1$ $r=-0.5$ submit work it out not feeling ready yet? these can help:

Explanation:

Step1: Understand the correlation coefficient

The correlation coefficient \(r\) measures the strength and direction of a linear relationship between two variables. When \(r = 1\), there is a perfect positive linear relationship. When \(r=- 0.5\), there is a moderate negative linear relationship.

Step2: Analyze the scatter - plots

• For the scatter - plot with a negative trend (points generally going from upper left to lower right), the correlation coefficient is negative. So, the scatter - plot with a negative trend (the left - hand scatter - plot) has \(r=-0.5\).
• For the scatter - plot with a positive trend (points closely following an upward - sloping line), since the points are very close to the regression line and the slope is positive, it has \(r = 1\).

Answer:

Left - hand scatter - plot: \(r=-0.5\); Right - hand scatter - plot: \(r = 1\)