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.

1 answer

To determine if there is a relationship between the two sets of data based on the plotted points, we would typically look for a trend or pattern in the scatterplot.

From your description of the scatterplot and the points provided, we can analyze the distribution:

  • The majority of the points seem to cluster in the higher y-values as the x-values increase, particularly around \(x = 70\) and \(x = 71\).
  • There are some points that appear to be outliers or not following the same trend (e.g., the points at \(x=74\)).

However, if we generally observe that as \(x\) increases, \(y\) tends to increase as well with the majority of points positioned closely within a range, it suggests that there is a positive correlation or relationship between the two sets of data.

Therefore, based on this tendency of y-values increasing with x-values and the overall distribution of points, the correct response would be:

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