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use the table to create a scatterplot. determine the type of association.

values of x and y for creating scatter plots and identifying associations

x 25 30 80 150 250 350 425 450 500
y 375 225 120 75 50 100 175 275 400

1 answer

To create a scatterplot based on the provided values of \(x\) and \(y\), you would typically plot the points on a graph where the horizontal axis (x-axis) represents the values of \(x\) and the vertical axis (y-axis) represents the values of \(y\).

Data Points:

Here are the values you provided:

  • Points: (25, 375), (30, 225), (80, 120), (150, 75), (250, 50), (350, 100), (425, 175), (450, 275), (500, 400)

Steps to Create a Scatterplot:

  1. Draw the Axes: Create a graph with a horizontal axis (x-axis) and a vertical axis (y-axis).
  2. Label the Axes: Label the x-axis with values from 0 to 500 (suitable scale depending on your graph size) and the y-axis with values from 0 to 400.
  3. Plot the Points: For each pair of values \((x, y)\), find the corresponding position on the graph and place a dot.

Data Plotting:

The plotted points would look like this:

  • Point (25, 375)
  • Point (30, 225)
  • Point (80, 120)
  • Point (150, 75)
  • Point (250, 50)
  • Point (350, 100)
  • Point (425, 175)
  • Point (450, 275)
  • Point (500, 400)

Determining the Type of Association:

To determine the type of association (relationship) between the variables:

  • Positive Association: As x increases, y also increases.
  • Negative Association: As x increases, y decreases.
  • No Association: There is no clear trend in y as x changes.

By observing the values in the given dataset, you can note the following:

  • As \(x\) increases from 25 to 250, \(y\) generally decreases.
  • After 250, as \(x\) continues to increase (350, 425, 450, 500), the values of \(y\) rise again.

Based on this, overall:

  • There is an initial negative association from \(x = 25\) to \(x = 250\).
  • Then, from \(x = 250\) to \(x = 500\), there is a positive association.

Conclusion:

The overall relationship is neither purely negative nor purely positive. It appears to have a complex behavior with a negative trend followed by a positive trend. Therefore, you could describe the overall association as having a non-linear relationship.

If you are plotting this using software or graphing tools, the distinct changes would be clearer visually.