Use the image to answer the question.

An illustration of a scatterplot shows x on x-axis from 1 to 5 in increments of 0.5 and y on the y-axis from 9 to 14 in increments of 0.5. Ten points are plotted. The approximate plotted points are as follows: left parenthesis 1 comma 10 right parenthesis, left parenthesis 1 comma 14 right parenthesis, left parenthesis 2 comma 11 right parenthesis, left parenthesis 2 comma 13 right parenthesis, left parenthesis 3 comma 9 right parenthesis, left parenthesis 3 comma 12 right parenthesis, left parenthesis 4 comma 11 right parenthesis, left parenthesis 4 comma 14 right parenthesis, left parenthesis 4.5 comma 12 right parenthesis, and left parenthesis 5 comma 9 right parenthesis.

Is there a relationship between the two sets of data? How do you know?

(1 point)
Responses

No, you cannot draw a trend line.
No, you cannot draw a trend line.

Yes, you cannot draw a trend line.
Yes, you cannot draw a trend line.

No, you can draw a trend line.
No, you can draw a trend line.

Yes, you can draw a trend line.
Yes, you can draw a trend line.
Remaining Attempts : 3

1 answer

Based on the description of the scattered data points plotted in the scatterplot, it appears that there is some level of variation in \( y \) values as \( x \) increases. While two \( y \) values may appear at one point for certain \( x \) locations, which makes the relationship between \( x \) and \( y \) more complex, you can still observe patterns or clusters in the data.

To determine if there is a linear or clear trend, you would typically look for a consistent upward or downward slope in the plotted points. In this case, given that there are various \( y \) values for a single \( x \) coordinate (especially with certain \( x \) values having multiple \( y \) values), it may indicate that while there are some relationships, they may not be linear or categorizable easily with a single trend line.

Thus, the most appropriate response would be:

No, you cannot draw a trend line.

This acknowledges the scattered nature of the points without a consistent linear relationship.