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Trend Lines Quick Check

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Question
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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

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.

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

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

To determine if there is a relationship between the two sets of data in the scatterplot, we need to look at how closely the data points cluster around a potential trend line.

Based on the provided options:

  1. "No, because the data points are close to the trend line." - This is contradictory, as if data points are close to a trend line, it would suggest a relationship.

  2. "Yes, because the data points are close to the trend line." - This option makes sense; if the points are close to a trend line, it indicates a strong relationship between the x and y values.

  3. "No, because the data points are not close to the trend line." - This would suggest there is no relationship, which contradicts the earlier conclusion that data points must be close to show a relationship.

  4. "Yes, because the data points are not close to the trend line." - This is also contradictory because if the points are not close to the trend line, that implies no relationship.

Given these interpretations, the most logical answer is:

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

This response correctly identifies that if the data points cluster near a trend line, it indicates a relationship between the two sets of data.