Question

which scatter plot does not show a positive linear association? (four scatter plots are shown with x and y axes from 1 to 10)

Explanation:

Step1: Recall positive linear association

A positive linear association in a scatter plot means that as \( x \) increases, \( y \) generally increases, and the points follow a roughly straight - line pattern with a positive slope.

Step2: Analyze each scatter plot

• Top - left plot: As \( x \) increases from 1 to 8, \( y \) values generally increase and follow a roughly linear pattern. So, it shows a positive linear association.
• Top - right plot: As \( x \) increases from 1 to 9, \( y \) values generally increase and follow a roughly linear pattern. So, it shows a positive linear association.
• Bottom - left plot: As \( x \) increases, \( y \) values generally increase (from \( x = 1\) with \( y\approx5\) to \( x = 9\) with \( y\approx9\)) and have a roughly linear trend. So, it shows a positive linear association.
• Bottom - right plot: The points do not show a clear pattern of \( y\) increasing as \( x\) increases. The \( y\) - values fluctuate without a consistent upward trend as \( x\) increases. So, this scatter plot does not show a positive linear association.

Answer:

The bottom - right scatter plot (the fourth scatter plot, with \( x\) from 1 to 10 and \( y\) values with no clear positive linear trend)