Use the image to answer the question.

An illustration of a scatterplot shows x on x-axis from 65 to 75 in increments of 1 and y on the y-axis from 200 to 240 in increments of 2.5. Eleven points are plotted. The approximate plotted points are as follows: left parenthesis 65 comma 205 right parenthesis, left parenthesis 67 comma 216 right parenthesis, left parenthesis 68 comma 210 right parenthesis, left parenthesis 68 comma 218 right parenthesis, left parenthesis 69 comma 224 right parenthesis, left parenthesis 70 comma 220 right parenthesis, left parenthesis 70 comma 224 right parenthesis, left parenthesis 71 comma 230 right parenthesis, left parenthesis 72 comma 235 right parenthesis, left parenthesis 74 comma 200 right parenthesis, and left parenthesis 74 comma 240 right parenthesis.

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

(1 point)
Responses

Yes, because the data points are not close to the trend line.
Yes, because the data points are not close to the trend line.

No, because the data points are not close to the trend line.
No, because the data points are not close to the trend line.

No, because the data points are close to the trend line.
No, because the data points are close to the trend line.

Yes, because the data points are close to the trend line.
Yes, because the data points are close to the trend line.
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1 answer

To determine whether there is a relationship between the two sets of data, we need to analyze how closely the points are grouped and if they show any discernible trend.

Typically, if data points are close to a trend line (often a line of best fit), it suggests a correlation between the variables represented on the x-axis and y-axis. Conversely, if the points are widely scattered and do not resemble a specific trend, this indicates a weak or no relationship.

From your description of the scatterplot data points, it appears that there are various y-values corresponding to the x-values, with some points clustering more closely together while others are more dispersed.

Given this ambiguity in how they relate, I cannot definitively state the existence of a strong relationship without visual confirmation of the plot itself. However, if the points are generally following an upward pattern and showing some level of closeness, it would suggest a positive relationship.

Considering your answer choices, the most accurate response seems to be:

Yes, because the data points are close to the trend line.

This choice implies that, despite some outliers (like the point at (74, 200)), there are enough points following a trend to suggest a relationship.