Question

Which of the following scatterplots most strongly suggests a negative linear relationship between x and y?

1) The scatter plot consists of about 17 data points clustered in a certain pattern in quadrant one. It starts in the upper-left corner, goes downward and to the right, and ends in the lower-right corner.
2) The scatter plot consists of about 17 data points clustered in a certain pattern in quadrant one and quadrant two. It starts in the upper-left corner in quadrant two, goes downward and to the right crossing the y-axis, and then goes upward and to the right, and extends towards the upper-right corner in quadrant one.
3) The scatter plot consists of about 17 data points clustered in a certain pattern in quadrant one and quadrant two. It starts in quadrant two near the origin, goes steeply upward and to the right crossing the y-axis, and then goes down and to the right, and extends towards the lower-right corner in quadrant one.
4) The scatter plot consists of about 17 data points clustered in a certain pattern in quadrant two. It starts in the lower-left corner, goes upward and to the right, and stops in the upper-right corner next to the y-axis.
5) The scatter plot consists of only 7 data points clustered in a certain pattern in quadrant one. It falls on a horizontal line.

Answer 1

The scatterplot described in option 3 most strongly suggests a negative linear relationship between x and y.

Step-by-step explanation:

Option 3 describes a scatterplot that starts in quadrant two near the origin, goes steeply upward and to the right, crossing the y-axis, then goes down and to the right, extending towards the lower-right corner in quadrant one.

This pattern is indicative of a negative linear relationship because as x increases, y initially decreases sharply, then continues to decrease but at a less steep rate. The steep initial upward movement followed by a downward trend suggests a negative correlation between the variables.

The fact that the points are clustered in quadrants one and two also aligns with a negative relationship, as both x and y values are either positive or negative. In contrast, the other options either describe positive relationships, horizontal relationships, or patterns that are less indicative of a clear linear correlation. Option 3, with its distinct and consistent negative trend, stands out as the most convincing representation of a negative linear relationship between x and y.