Question

match the linear correlation coefficient to the scatter diagram. the scales on the x - and y - axes are the same for each diagram.
(a) ( r=-0.992 )
(b) ( r = 1 )
(c) ( r = 0.049 )
(d) ( r = 0.523 )
click the icon to view the scatter diagrams.
(d) identify the scatter diagram corresponding to ( r = 0.523 ). choose the correct answer.

Explanation:

Step1: Understand the nature of \( r = 0.523 \)

The correlation coefficient \( r = 0.523 \) indicates a positive, moderate linear relationship.

Step2: Analyze scatter - diagram characteristics

• A scatter - diagram with \( r = 1 \) (perfect positive linear relationship) has all points on a straight - line with a positive slope.
• A scatter - diagram with \( r=-0.992 \) (strong negative linear relationship) has points very close to a straight - line with a negative slope.
• A scatter - diagram with \( r = 0.049 \) (weak linear relationship) has points that are almost randomly scattered.
• A scatter - diagram with \( r = 0.523 \) (positive, moderate linear relationship) has points that show an upward trend, but not as tightly clustered as for \( r = 1 \)

Answer:

The scatter - diagram with an upward trend (not a perfect straight - line) among the given options corresponds to \( r = 0.523 \)