To create a scatterplot and determine the type of association from the provided data, let’s first list the values of \( x \) and \( y \) as pairs:
- (25, 375)
- (30, 225)
- (80, 120)
- (150, 75)
- (250, 50)
- (350, 100)
- (425, 175)
- (450, 275)
- (500, 400)
Creating the Scatterplot
You can plot these points on a Cartesian coordinate system with the \( x \) values on the horizontal axis and the \( y \) values on the vertical axis.
- For \( x = 25, y = 375 \): plot the point (25, 375)
- For \( x = 30, y = 225 \): plot the point (30, 225)
- For \( x = 80, y = 120 \): plot the point (80, 120)
- For \( x = 150, y = 75 \): plot the point (150, 75)
- For \( x = 250, y = 50 \): plot the point (250, 50)
- For \( x = 350, y = 100 \): plot the point (350, 100)
- For \( x = 425, y = 175 \): plot the point (425, 175)
- For \( x = 450, y = 275 \): plot the point (450, 275)
- For \( x = 500, y = 400 \): plot the point (500, 400)
Analyzing the Association
Now, let's analyze the pattern of these points:
- As \( x \) increases from 25 to 250, \( y \) decreases from 375 to 50, indicating a negative association in that range.
- When \( x \) increases further from 250 to 500, \( y \) increases from 50 to 400, indicating a positive association in that range.
This suggests that the overall association is not straightforward. However, overall:
- The first part of the dataset shows a negative correlation.
- The second part of the dataset shows a positive correlation.
Thus, we conclude that there is no consistent association—or a non-linear association—between \( x \) and ( y .
Final Answer
The scatterplot indicates a non-linear association with both negative and positive trends in different ranges.